POROUS SILICA GEL MONOLITHS:
STRUCTURAL EVOLUTION AND INTERACTIONS WITH WATER
By
STEPHEN WALLACE
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1991
ACKNOWLEDGEMENTS
It is impossible for me to thank all the people who have helped me
during this journey through graduate school, but I would especially like
to thank my advisor Dr. Larry L. Hench for his guidance, advice, encour
agement, patience and understanding, but especially for his patience and
support, without which this dissertation would not have seen the light
of day. His introduction to the strange and wonderful world of Gator
basketball was also a welcome gift!
I would like to thank Dr. David E. Clark, Dr. Eric A. Farber, Dr.
Robert W. Gould, Dr. Joseph H. Simmons and Dr. Jon K. West for their
help, advice and encouragement over the years. I would also like to
thank Dr. C. Jeffrey Brinker and Dr. George W. Scherer for their
helpful, thoughtprovoking discussions and their original contributions
to this field. I am grateful to Mr. Guy P. Latorre for his help and
technical advice. I would especially like to thank him for not allowing
me to become the longest serving member of Dr. Hench's technical staff!
It is with great sadness after his sudden recent death that I
recognize the role of Dr. Donald Ulrich in the completion of this work.
He and the Air Force Office of Scientific Research have been totally
supportive in both the funding and the scientific endeavors involved. I
am very grateful for the opportunities that their support provided.
I would finally like to acknowledge a chance encounter on Green
St., Urbana, without which none of this would have occurred, and the
financial assistance of the Elizabeth Tuckerman Scholarship Foundation,
which made graduate school a little easier.
ii
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS . . . . . . . . ... ...... ii
LIST OF TABLES . . . . . . . . .. . . . . . viii
LIST OF FIGURES . . . . . . . . .. . . . . . x
KEY TO SYMBOLS . . . . . . . . ... .... . xxiiii
ABSTRACT . . . . . . . . ... . . . . . xxxiiii
CHAPTER 1 INTRODUCTION . . . . . . . . ... . 1
PART 1 STRUCTURAL AND TEXTURAL EVOLUTION OF POROUS
SILICA GELS DURING SINTERING AND DURING WATER
ABSORPTION . . . . . . . . . . . 6
CHAPTERS
2 A CHRONOLOGICAL LITERATURE REVIEW OF THE STRUCTURE AND THE
VIBRATIONAL SPECTROSCOPY OF AMORPHOUS SILICA . . . . 6
2.1 The Structure of Amorphous Silica . . . . . 6
2.1.1 The Categories of the Types and
Structure Concepts of aSilica . . . . 6
2.1.2 Structural Models of aSilica . . . . 7
2.1.3 TEM Studies of aSilica Structure . . .. 18
2.1.4 Molecular Dynamic Simulations of
the Structure of aSilica ......... 19
2.1.5 Molecular Orbital (MO) Calculations of
the Structure of aSilica ......... 20
2.1.6 Bonding and Structure Relationships in
Silica Polymorphs . . . . . ... 22
2.2 The Theory of Raman and IR Scattering . . . ... 30
2.3 Modelling the Vibrational Behavior of aSilica . 44
2.4 Raman Spectroscopy of aSilica . . ... ..... 68
2.5 The Density, Spectroscopy and Structure of
Pressure Compacted aSilica . . . ... ..... 81
iii
2.6 Raman Spectroscopy of Neutron Irradiated aSilica . .
2.7 Theoretical Correction of Raman Spectra . . . .. 101
2.8 Curvefitting the Raman Spectra of Silica Gels . .. 109
2.9 Raman Spectroscopy of Silica Gels . . . . .. 121
2.10 FTIR Spectroscopy of Silica Gels . . . . .. 130
2.11 NMR spectroscopy of silica gels . . . . . .. 131
2.12 The Structural Density of Alkoxide
Derived Silica Gels . . . . . . . . .. 134
3 STRUCTURAL AND TEXTURAL ANALYSIS OF POROUS SILICA GELS DURING
SINTERING . . . . . . .. . . . . . 153
3.1 Experimental Procedure . . . . . . .. 153
3.1.1 The Production of the Silica Gel Monoliths . 153
3.1.2 Isothermal Nitrogen Adsorption . . . .. 155
3.1.3 Calculation of Structural Density from N2
Sorption at P/P0 = 0.999 . . . . .. 156
3.1.4 Water pycnometry . . . . . . .. 156
3.1.5 Helium Pycnometry . . . . . .. 158
3.1.6 Raman Spectroscopy . . . . . .. 159
3.1.7 Thermogravimetric Analysis (TGA) . . .. 161
3.1.8 Differential Scanning Calorimetry (DSC) . 161
3.1.9 29Si Magic Angle Spinning Nuclear Magnetic
Resonance (MAS NMR) . . . . . .. 161
3.2 Results . . . . . . . . . . . 161
3.2.1 Structural and Textural Property Measurements 161
3.2.2 The Calculation of Ds from Vp and Db
Using Vp = 1/Db +l/Ds . . .. . . . 164
3.2.3 Water Pycnometry . . . . . . .. 169
3.2.4 Helium Pycnometry . . . . . .. 175
3.2.5 Textural Properties of HF Catalyzed Silica
Gel Monoliths . . . . .. . . 186
3.2.6 Thermogravimetric Analysis . . . . .. 193
3.2.7 Raman Spectra of the Silica Gels . . .. 193
3.2.8 Curvefitted Raman Peak Positions . . .. 224
3.2.9 Curvefitted Raman Peak Areas . . . .. 235
3.3 Discussion . . . . .. . . . . . 253
3.3.1 Comparison of the Values of the Structural
Density Ds Calculated from Isothermal N2
Sorption and from H20 Pycnometry . . .. 253
3.3.2 The Dependence of the Magnitude of VP on the
Experimental Techniques Used to Measure V 254
3.3.3 Helium Pycnometry . . . . . . . 262
3.3.4 Comparison to Earlier Work . . . . .. 265
3.3.5 Reason for the similarity of Dsmax for type
OX, 2X and 5X gels . . . . . . . 265
100
3.3.6 The Raman Spectra of the Silica Gels . .. 274
3.3.7 Separation of the Condensation and Viscous
Sintering Processes . . . . . .. 279
3.3.8 Thermal Dependency of D2 concentration. . ... 281
3.3.9 Comparison of Dynasil and Dense Silica Gels 282
3.3.10 Relationship between the W3 and W4 Raman peak
positions and D . . . . . . 283
3.3.11 Molecular Orbital Explanation of the
Dependence of d(SiO) on 0 . . . . .. 283
3.3.12 Theoretical Relative Ds Calculation . . .. 286
3.3.13 29Si MASS NMR of gels . . . . . .. 296
3.3.14 Comparison of 0 Calculated from MASS NMR and
Raman Spectra . . . . . . . . 300
3.3.15 Explanation of the Increase of Ds to Dsmax at
T x . . . . . . . . . . 301
3.3.16 Possible Structural Mechanisms of Ds Increase
Below Tsmax . . . . . . . . . 315
3.3.17 MASS NMR versus Raman spectra between Tp =
200* and 400*C . . . . .. . . . 330
3.3.18 The Magnitude of Dsmx . . . . . .. 333
3.3.19 Dependence of Ds of Fused aSiO2 on [OH] . 334
3.4 Conclusions . . . . . . . . . . . 336
4 STRUCTURAL ANALYSIS OF POROUS SILICA GELS DURING THE
ABSORPTION OF WATER INTO THE GEL'S MICROPORES . . . .. 343
4.1 Introduction . . . . . . . . . . 343
4.2 Experimental Procedure . . .. . . . . 348
4.3 Results . . . . . . . .. . . . 350
4.4 Discussion . . . . . . . . . . 363
4.4.1 The Movement of H20 Molecules Through Pores 363
4.4.2 Water Vapor Absorption . . . . . .. 375
4.4.3 D2 Rehydrolysis Rate Analysis in type OX gels 377
4.4.4 The D2 Rehydrolysis Equilibrium Constant Kc
for type OX gels . . . . . . . 382
4.4.5 D2 Rehydrolysis Rate Analysis in type B2 gels
[33,175] . . . . . . . . . 386
4.4.6 The Tetrasiloxane D1 Peak .. . ...... 393
4.4.7 The D1 Rehydrolysis Equilibrium Constant Kc
for type OX gels . . . . . . . 394
4.4.8 SisOH Concentration During Rehydrolysis . . 399
4.4.9 SenThorpe Central Force Function Analysis Of
the Raman Spectra . .. . . . . 404
4.4.10 The effect of H20 absorption on the main 430
cm1 W1 Raman Peak . . . . . . .. 406
4.5 Conclusions . . . . .. . . . . . 407
4.6 A Summary of the Structure and Texture of Alkoxide Derived
Silica Gels During Sintering and Water Adsorption . 410
PART II
THE STRUCTURE OF WATER ABSORBED INTO THE
MICROPORES OF A MONOLITHIC SILICA GEL . . . ... 413
CHAPTERS
5 DIELECTRIC RELAXATION ANALYSIS OF WATER REMOVAL FROM A TYPE OX
SILICA GEL MONOLITH . . . . . . . . . . .
5.1 Introduction . . . . . . . . . . .
5.2 Theory . . . . . . . . . . . .
5.3 Experimental Technique . . . . . . . .
5.4 Results and Discussion . . . . . . . .
5.6 Conclusions . . . . . . . . . . .
6 DIELECTRIC RELAXATION ANALYSIS (DRS) OF WATER ABSORBED IN
MONOLITHIC POROUS SILICA GELS . . . . . . . .
6.1 Introduction . . . . . . . . . . .
6.2 Literature Review . . . . . . . . . .
6.2.1 Dielectric relaxation 1 (R) . . . . .
6.2.2 Dielectric Relaxation 2 (R2) . . . . .
6.2.3 Dielectric Relaxation 3 (R3) . . . . .
6.3 Objective . . . . . . . . . . . .
6.4 Method . . . . . . . . . . . .
6.5 Results . . . . . . . . . . . .
6.6 Discussion . . . . . . . . . . .
6.7 Conclusions .
7 STRUCTURAL ANALYSIS OF WATER ADSORBED IN THE PORES OF ALKOXIDE
DERIVED SILICA GEL MONOLITHS . . . . . . . .
7.1 Introduction . . . . . . . . .
7.2 Experimental Procedure . . . . . . . .
7.2.1 Dielectric Relaxation Spectroscopy (DRS)
7.2.2 Differential Scanning Calorimetry (DSC)
7.3 Results and Discussion . . . . . . . .
7.4 Conclusions . . . . . . . . . . .
413
413
414
421
423
432
433
433
434
434
435
436
436
438
438
446
. . . 453
455
455
457
457
458
460
474
8 NEARINFRARED SPECTROSCOPY OF WATER ADSORPTION IN A SILICA GEL
MONOLITH . . . . . . . . . . . . .
8.1 Introduction . . . . . . . . . . .
8.2 Experimental Procedure . . . . . . . .
8.3 Results . . . . . . . . . . . .
8.4 Discussion . . . . . . . . . . .
8.5 Conclusions . . . . . . . . . . .
9 DISCUSSION ON THE BEHAVIOR OF WATER ADSORBED INTO POROUS
SILICA GELS . . . . . . . . . . . . .
9.1 The Structure of H20 Absorbed into Microporous Silica
Gels . . . . . . . . . . . . .
9.2 H' NMR Analysis of Water Absorbed in Micropores . .
9.3 Structural Explanation of the Magnitude of Wc /Sa . .
9.4 Structural Explanation of the Magnitude of Wc2/S . .
9.5 Explanation of the Observed Changes in Slope of the
e'u(W) Plot . . . . . . . . . . .
9.6 The Dependence on W/Sa of the Mechanism of Proton
Conduction . . . . . . . . . . .
9.6.1 The Proton Conduction Mechanism for Wc1< W < Wc2
9.6.2 Proton Conduction Mechanism for Wc2< W < Wmax
9.7 Summary of the Proton Conduction Mechanisms in Adsorbed
Water . . . . . . . . . . . . .
9.8 Dissociation constant of adsorbed H20 versus bulk H20 .
9.9 Magnitude of Drift and Effective Velocity . . . .
9.10 Tunneling Theory . . . . . . . . . .
9.11 Conclusions and Future Work . . . . . . .
APPENDIX RAMAN SPECTRUM THERMAL REDUCTION FLOWCHART . . .
REFERENCES . . . . . . . . . . . . . .
BIOGRAPHICAL SKETCH . . . . . .
vii
475
475
476
476
481
481
482
482
486
487
488
490
491
496
498
499
500
501
502
503
506
507
522
LIST OF TABLES
Table Page
1. The estimated energy of the formation of planar silicate
rings of order n in aSiO2 calculated from Fig. 14. After
[67]. . . . . . . . . . ..... .... .80
2. Textural and structural properties of the type OX silica gel
discs used to calculate their structural density from their
bulk density and pore volume, Ds 1/((1/Db)Vp) (Fig. 30),
rH = 1.2 nm. . . . . . . . . . . . .. 168
3. Textural and structural properties of type OX silica
gelcylinders, rH 1.2 nm, which were used to measure
structural density using H20 pycnometry (Fig. 31).. ... 172
4. Textural properties of silica gel monoliths stabilized at
200*C as a function of HF concentration (Fig. 33). ... .176
5. Table 5. The data used to plot Fig. 34. (a). Structural
density of type OX, 2X and 5X silica gels powders measured
using helium pycnometry, plotted in Fig. 34(a).. . . . 181
Table 5 (b). Extrapolated data used to plot Fig. 34(b). . 182
6. Table 6. The textural properties of type OX, 2X and 5X
silica gels. (a). Textural properties of the type OX
cylindrical silica gels characterized by Raman Spectroscopy,
plotted in Figs. 35, 36 and 37.. . . . . . . .. 183
Table 6 (b). Textural properties of the type 2X cylindrical
silica gels characterized by Raman Spectroscopy. . . ... 184
Table 6 (c). Textural properties of the type 5X cylindrical
silica gels characterized by Raman Spectroscopy. . . ... 185
7. Position, height, width as FullWidthHalfMaximum (FWHM),
and area of the Gaussian peaks curvefitted to the Raman
spectrum of sample OXA stabilized at 400C (Fig. 42). .. 206
8. A comparison of the properties of densified metalalkoxide
derived silica gels and Dynasil. . . . . . . ... 282
9. Summary of a) Ds changes measured in type OX silica gels in
particular Tp ranges and the Db and [D2]/[Wt] change
viii
occurring in the same T ranges, and b) the Ds change caused
by a change in the [D2]/[Wt] of the same magnitude as
measured in the type OX gels in (i) Suprasil with different
Tf [100], and (ii) pressure compacted fused aSi02 [133]. 322
10. Properties of the cylindrical silica gel samples used for
H20 absorption studies. . . . . . . . . . 352
11. Some textural and structural values of type OX gels at
several stabilization temperatures Tp and water contents W. .411
12. Some structural and textural values of metalalkoxide
derived silica gels and of water absorbed into their pores. .464
13. NIR Transmission Peaks of H20 Molecules Hbonded to SisOH. 478
14. Activation energies measured for relaxation R1 in type OX
gels at W = W .ax .. .. . . . . . . . 499
LIST OF FIGURES
Figure Page
1. The bulk density Db of different Type I/II and Type III/IV
commercial aSiO2 as a function of fictive temperature Tf.
After [38]. Their bulk and structural densities are identical
because Vp = 0.0 cc/g . . . . . . ... . . .. 8
2. The relative orientation of two corner sharing silica
tetrahedra, Si044', showing the bridging oxygen bond angle, 0,
the siliconoxygen bond length, d(SiO), the OSiO bond
angle, 9, and the tetrahedral angles, 6 and A, which define
the angular orientation of the tetrahedra about their
bridging Si0 bonds. After [56]. . . . . . . ... 15
3. The Si0 bond length as a function of Sec(B) for the silica
polymorphs low tridymite, low quartz, and coesite. The
d(SiO) have a standard deviation < 0.005 A. The linear fit
line is the best fit linear regression analysis of all the
data points. After [74]. . . . . . . . .... . .26
4. A comparison of the experimental d(SiO) in coesite (upper
curves in (a) and (b)) with those calculated for the bridging
d(SiO) in a disilicate molecule, H6Si207 (lower curves in (a)
and (b)). d(SiO) varies nonlinearly with 0 and linearly with
fs = 1/(1 + A2), where A2 = Sec(0) is called the
hybridization index of the bridging 0 atom because its state
of hybridization is given by the symbol sp"'. After [76]. . 27
5. Potential energy surface for the disilicate molecule, H6Si207,
plotted as a function of d(SiO) and 0. The contours
represent increments in energy of 0.005 a.u. = 0.6257
kcal/mole relative to the minimum energy point (1091.76678
a.u.) denoted by the cross. Increasing contour numbers
represent increasing energy. The dashed line represents the
bond lengths and angles for the disiloxy groups in the silica
polymorphs coesite, tridymite, low cristobilite and aquartz.
After [76] . . . . . . . . . . . . . 28
6. The principles of Raman scattering. (a) The incident laser
beam, energy E, passes through the sample and the scattered
light is detected to the spectrometer. (b) The Raman spectrum
consists of a strong central peak at the wavelength of the
laser energy E due to the Rayleigh scattering, and the much
weaker Raman shifted lines at Eei, where ei = huI correspond
to the energies of vibrational transitions in the sample in
cm1, where E = 0 cm1. Stokes Ramanshifted frequencies (Ee)
are positive wavenumber values, and antiStokes Ramanshifted
frequencies are negative wavenumber. (c) The energy level
diagram for Rayleigh and Raman scattering. There are two
energy levels which are separated by an energy e = hv, where
v is the vibrational frequency. The incident laser photon,
energy E, excites the vibrational mode to a shortlived (1014
sec) electronic "virtual state", which decays with the
release of a photon. When the final vibrational state of the
molecule is higher than that of the initial state, the
released photon energy is Ee, and StokesRaman scattering
has occurred. When the final state is lower, the released
photon has energy E+e, and antiStokes scattering has
occurred. When the initial and final states are the same,
Rayleigh scattering has occurred and the incident and
released photons have the same energy E. After [81]. ... 34
7. The various types of crystal lattice vibrations. (a) The
wavelength of this lattice mode is long compared to the
crystal lattice constant, a, so the mode lies at the center
of the Brillouin zone (k = 0). (b) This mode has wavelength A
= 2a, and lies at the edge of the Brillouin zone (k = r/a).
The waves in (a) and (b) represent transverse lattice
vibrations for a monatomic chain of atoms. (c) This
illustrates a longitudinal lattice vibration for the same
monatomic chain. (d) For any crystal, there are three lattice
vibrations where all the atoms in a unit cell move in phase
in the same direction. These are the acoustic modes. (e) For
crystals with more than one atom in the primitive unit cell,
there are modes where atoms in the unit cell move in opposing
directions (illustrated for a diatomic chain). These motions
can generate a changing dipole moment and hence interact with
light. These are called optic modes. (f) A typical dispersion
curve in one direction in reciprocal space for a crystal, in
this case with n = 4 atoms in its unit cell. Only long
wavelength lattice vibrations (near k = 0) can be infrared or
Raman active due to the long wavelength of light compared
with crystal lattice spacings, which are marked with dots.
After [81] . . . . .. . . . . . . .. 36
8. Normal vibrations of a disilicate molecular unit in aSiO2.
The axes point along the direction in which the bridging 0
atom moves in the bond bending, stretching and rocking normal
modes. These normal modes correspond to peaks in the Raman
spectra of aSiO2. The bondbending axis is parallel to the
bisector of the SiOSi angle, and is assigned to the W3 peak
at 800 cm'1. The bond stretching axis is perpendicular to this
bisector, but still in the SiOSi plane, and is assigned to
the W4 peak at 1060 cm1 and 1200 cm"1. The bond rocking
direction is orthogonal to the other axes and is normal to
the SiOSi plane. After [85]. . . . . . . . .
9. Schematic of the normal modes of vibration in asilica. (a)
The outofphase (highfrequency) and inphase (low
. 46
frequency) vibrations of two coupled Si0 stretching motions,
where only Si0 stretching is considered. (b) The type of
motion suggested by various vibrational calculations for
silica polymorphs associated with the W3 Raman band at 800
cm'1. After [94]. . . . . . . . . . . .. 55
10. The dependence on the fictive temperature Tf of the Raman peak
frequencies of a sample of GE214 fused asilica. The changes
in the broad network peaks (Wi) in various directions are
consistent with reduction in 0 as Ds increases. The much
smaller shift in the positions of the D1 and D2 ring peaks are
consistent with their assignment to regular tetrasiloxane and
trisiloxane rings respectively in an otherwise more
disordered network. After [1123]. . . . .. . . . 66
11. The Raman spectrum of fused asilica at various temperatures.
The dots represent the low temperature spectrum calculated
from the room temperature spectrum after it had been
thermally corrected assuming first order processes, as
discussed in the text. After [115] . . . . . . . 70
12. The area of the D2 Raman peak, as a fraction of the total area
of the Raman spectra, versus Db. (a) For a sample of Suprasil
Wl at the indicated Tf. (b) the data from (a) extrapolated to
higher densities and compared to samples of asilica
densified via irradiation with neutrons to the indicated flux
densities. After [100] . . . . . . . . . .75
13. Planar Si0 rings of order n = 2, 3, 4 and 5, with SiOSi
angles 6 given for 0 = 109.50, the tetrahedral value [67]. . 76
14. The dependence of the energy of an =Si0Sis bridge on 0,
estimated using theoretical MO results. This enables
estimation of the energy of formation of various planar rings
having the angles 0n marked in the figure and listed in Table
1. The arrows show the tendencies for the puckering and
unpuckering of silicate rings. After [67]. . . . . ... 78
15. Comparison of the thermally reduced Raman spectra (a) of
fused asilica with the imaginary parts of the infrared
derived transverse (b) and longitudinal (c) dielectric
functions. Peaks in E2 = Im(c) and Im(e"1) mark transverse
and longitudinal optical vibrational modes, respectively.
After [88] . . . . . . . . . . . . 79
16. Probability distributions. (a) The probability distribution
of the tetrahedral bond angles, 0, in undensified (dashed
line) and 24%densified (solid line) samples of fused a
silica calculated from the distributions of the isotropic
hyperfine constants, Aiso. (b) The probability distribution of
defect d(SiO) obtained from the 0 distributions in (a) using
equation (16). After [140] . . . . . . . . 93
17. Variation in the vibrational peak positions and 0 of Si02 as a
function of compacted density. . . . . . . . ... 94
18. Contributions to the background in the Raman spectrum of
porous Vycor. The upper dashed spectra is the experimentally
determined raw Raman spectrum. The lower solid spectra is the
corrected spectrum with the Rayleigh elastic scattering and
the high frequency fluorescent background subtracted [85]. 111
19. The thermally reduced Raman spectra of a sample of asilica
with 5 wt% H20 dissolved in it, showing the Gaussian peaks
used to curvefit the spectra, and the residual difference
remaining when the curvefitted peaks are subtracted from the
Raman spectra. After [173]. . . . . . . . ... 119
20. The Raman spectra of silica gels at different stabilization
temperatures during densification compared to the spectrum of
fused asilica. The large background intensity at Tp = 2000C
is due to fluorescence, which is gone by Tp = 400C as the
organic burn out. Spectra I at Tp = 8000C is in a part of the
gel which is still porous, while spectra II is from a fully
dense part of the gel. After [24]. . . . . . .. 123
21. The relative bulk density, the relative structural density
(calculated from Vp and Db) and the first and second DSC
scans, DSC1 and DSC2 respectively, for silica gel A2, made
from TEOS with R = 5 and pH = 0.95. After [5,28,29]. . . 126
22. The temperature dependence of the structural density Ds of two
silica gel samples. Sample A was made with distilled water
with no catalyst added. Sample B was made with distilled
water containing 0.0085% NH4OH. After [9]. . . . . ... 135
23. The temperature dependence of the structural density of
monodispersed silica gel powders made by the base catalysis
of TEOS using excess NH40H [6]. After [179]. . . . ... 136
24. The temperature dependence of the shrinkage and structural
density of a 71% SiO2 18% B203 7% Al203 4% BaO
borosilicate gel, with R = 5 and pH = 6.8, heated at 2C/min.
After [5,12,29]. . . . . . . . . . . . 140
25. The temperature dependence of the weight loss, shrinkage and
surface area of silica gel sample A2, made from TEOS with R =
5 and pH = 0.95, heated at 2C/min in air. After [5,28,29]. .142
26. The temperature dependence of the bulk and structural density
of a silica aerogel made from TMOS using distilled water with
no catalyst, using methanol as a mutual solvent. After [17]. 148
27. The dependence on the bulk density of the structural density
of a silica aerogel made from TMOS using acidified water and
methanol, giving a pH 2. After [18]. . . . . ... 149
xiii
28. The temperature dependence of the structural density of
silica xerogels, made from TMOS using acidified water, R = 16
and pH = 1.0, with rH = 1.2 nm, 3.2 nm and 8.1 nm as
indicated. After [183] . . . . . ... . . . .151
29. The increase with time at 7500C of the bulk density Db of
sample #138, a type OX gel, after heating to 7500C in 62 hrs
in Florida air. The open squares (D) are the experimental
data points, while the solid line is a third order regression
with R2 = 0.990. . . . . . ... . . . . 163
30. The structural density Ds of type OX gels (rH = 1.2 nm)
calculated from V (measured using isothermal N2 sorption) and
Db, using Ds = 1/((l/Db)Vp), as a function of (a) the
sintering temperature and (b) the bulk density Db. The open
squares (D) are the data points, and the solid lines are 3rd
order regressions, giving R2= 0.6508 and R2 = 0.9117 respec
tively . . . .. . . . . . . . . . 166
31. The structural density Ds of type OX gels (rH = 1.2 nm)
measured using water pycnometry, as a function of (a) the
sintering temperature, and (b) the bulk density Db. The open
squares (0) are the data points, while the solid lines are
the third order regressions, giving R2 = 0.8716 and R2 =
0.8513 respectively. . . . ... . . . . . . 170
32. A comparison of the changes observed in Ds of silica gels. (a)
The dependence on Db of the Ds of type OX gels measured using
H20 pycnometry (0) and calculated from Ds = 1/((1/Db)V ) (0).
(b) The dependence on T of the Ds of type OX gels measured
using H20 pycnometry (D), Ds = 1/((1/Db)Vp) (0) and helium
pycnometry (X) . . . . . . . . . . . 173
33. The dependence on the HF concentration, [HF] (mole/liter H20),
of the textural properties of the silica gels investigated
here. (a) Db (g/cc) versus [HF]. (b) Vp (cc/g) versus [HF].
(c) Sa (m2/g) versus [HF]. (d) rH (nm) versus [HF]. . ... 177
34. The dependence of the structural density measured using
helium pycnometry on (a) T [C], and (b) Db [g/cc], for
sample OXA, rH 1.2 nm (DE, sample 2XA, rH H 4.5 nm (0) and
sample 5XA, rH ; 9.0 nm (x). The solid lines in (a) are best
fit 5th order linear regressions. . . . ... . .187
35. The dependency on the sintering temperature T of the bulk
density, Db, of the cylindrical samples characterized using
the Raman spectrometer. OX (0), OXA (+), 2X (0), 2XA (A), 5X
(x), 5XA (v) ....... .. . . . . . . . 189
36. The dependency on the sintering temperature T of the surface
area, S of the cylindrical samples characterized using the
Raman spectrometer. OX (D), OXA (+), 2X (0), 2XA (A), 5X (x),
5XA (v). . . . ... . . . . . . . . . 190
xiv
37. The dependency on the sintering temperature T of the average
pore radius, rH, of the cylindrical samples characterized
using the Raman spectrometer. OX (0), OXA (+), 2X (0), 2XA
(A), 5X (x), 5XA (v) . . . . . . . . . . 191
38. The thermogravimetric analysis (TGA) curves of powdered
samples of type OX, 2X and 5X gels heated in flowing dry
nitrogen as 10C/min. The weight loss observed below 180C is
due to the loss of H20 previously absorbed into their pores. .192
39. The raw, unreduced Raman spectrum of Dynasil. (a) 1001350
cm'1. (b) 36003800 cm'1. The peak assignments of aSiO2 are
shown. . . . . . . . . . . . . .. 197
40. The thermally reduced Raman spectrum of Dynasil. (a) 1001350
cm1. (b) 36003800 cm'1. The reduced Raman spectrum, the
curvefitted Gaussian peaks and their peak positions (PP), and
the fitted spectrum calculated from the addition of the
curvefitted peaks are shown. . . . . . ... . .199
41. The raw experimental Raman spectrum of silica gel sample OXA
stabilized at 400C for 400C. (a) 1001350 cm1. (b) 3600
3800 cm"1 . . . . . . . . . . . . 201
42. The thermally reduced Raman spectrum of silica gel sample OXA
stabilized at 400C for 24 hrs. (a) 1001350 cm". (b) 3600
3800 cm"1. The reduced Raman spectrum, the curvefitted Gaussi
an peaks and the fitted spectrum resulting from the addition
of these peaks are shown . . . . . ... . . . .203
43. The thermally reduced Raman spectra from Fig. 42(a) of sample
OXA stabilized at Tp 400C from a different angle. ... .207
44. The thermally reduced Raman spectrum from Fig. 42(a) of
silica gel sample OXA stabilized at 400C, along with the
residual intensity left after the curvefitted spectrum is
subtracted from the experimental spectrum, giving X2 =
127,685. . . . . . ... . . . . . . . 208
45. The evolution of the raw, unreduced Raman spectra of sample
OXA, rH = 1.2 nm, during densification via viscous sintering
as T increases from 400C to 900C. (a) 1001350 cm"1, (b)
35003800 cm1. . . . . . . . . . . .. 210
46. The evolution of the thermally reduced Raman spectra of
sample OXA, rH = 1.2 nm, during densification via viscous
sintering as T increases from 400C to 900C. (a) 1001350
cm1, (b) 35003800 cm. . . . . . . . . .. 212
47. The evolution of the thermally reduced Raman spectra of
sample 2XA, rH 4.5 nm, during densification via viscous
sintering as T increases from 400*C to 1000C. (a) 1001350
cm1, (b) 35003800 cm. . . . . . . . . .. 214
48. The evolution of the thermally reduced Raman spectra of
sample 5XA, rH Hs 9.0 nm, during densification via viscous
sintering as T increases from 400C to 1150C. (a) 1001350
cm1, (b) 35003800 cm1. . . . . . . . . . .
49. This shows that the concentration/unit area of internal pore
surface of the D2 trisiloxane rings, [D2]/[Wt]/Sa, exhibits the
same dependence on Tp for sample OX as for sample OXA within
the resolution of the curvefitting analysis in their
respective T ranges. . . . . . . . . . .
50. This shows that the concentration/unit volume of the D2
trisiloxane rings, [D2]/[Wt], exhibits the same dependence on
Tp for sample 2X and sample 2XA within the resolution of the
curvefitting analysis in their respective T ranges. . .
51. This shows that the ratio of the concentration/unit volume of
the D2 trisiloxane rings and the D1 tetrasiloxane rings,
[D2]/[D1], exhibits the same dependence on Tp for samples 5X
and 5XA within the resolution of the curvefitting analysis in
their respective T ranges. . . . . . . . . .
52. The dependence on the sintering temperature of the
siloxane ring curvefitted Raman peak position (PP)
samples OXA (E), 2XA (+) and 5XA (0). The D1 PP of
is shown for comparison. . . . . . .
DI tetra
for
Dynasil (A)
53. The dependence on the sintering temperature of the D2 trisil
oxane ring curvefitted Raman peak position (PP) for samples
OXA (0), 2XA (+) and 5XA (0). The D2 PP of Dynasil (A) is
shown for comparison . . . . . . . .. ..
54. The dependence on the sintering
curvefitted Raman peak position
(+) and 5XA (0). The Dynasil PP
55. The dependence on the sintering
curvefitted Raman peak position
(+) and 5XA (0). The Dynasil PP
56. The dependence on the sintering
curvefitted Raman peak position
(+) and 5XA (0). The Dynasil PP
57. The dependence on the sintering
curvefitted Raman peak position
(+) and 5XA (0). The Dynasil PP
58. The dependence on the sintering
curvefitted Raman peak position
(+) and 5XA (0). The Dynasil PP
temperature T of the W2 (?)
(PP) for samples OXA (E), 2XA
(A) is shown for comparison.
temperature T of the SiOH
(PP) for samples OXA (0), 2XA
(A) is shown for comparison.
temperature T of the W3 TO
(PP) for samples OXA (0), 2XA
(A) is shown for comparison.
temperature T of the W3 LO
(PP) for samples OXA (E), 2XA
(A) is shown for comparison.
temperature T of the W4 TO
(PP) for samples OXA (E), 2XA
(A) is shown for comparison.
216
221
222
223
225
226
59. The dependence on the sintering temperature T of the W4 LO
curvefitted Raman peak position (PP) for samples OXA (0), 2XA
(+) and 5XA (0). The Dynasil PP (A) is shown for comparison. 233
60. The dependence on the sintering temperature T of the SiOH
curvefitted Raman peak position (PP) for samples OXA (0), 2XA
(+) and 5XA (0). The Dynasil PP (A) is shown for comparison. 234
61. The dependence on the sintering temperature T of the area of
the W1 curvefitted Raman peak as a fraction of the total Raman
spectrum area for samples OXA (0), 2XA (+) and 5XA (0). The
Dynasil peak area (A) is shown for comparison. . . ... 236
62. The dependence on the sintering temperature T of the area of
the D1 tetrasiloxane ring curvefitted Raman peak as a fraction
of the total Raman spectrum area for samples OXA (0), 2XA (+)
and 5XA (0). The Dynasil peak area (A) is shown for
comparison. . . . . . . . . ... ..... 237
63. The dependence on the sintering temperature Tp of the concen
tration/unit area of the internal pore surface of the D1
tetrasiloxane ring, [Di]/[Wt]/Sa, for samples OXA (0), 2XA (+)
and 5XA (0). . . . . . . . . ... . . .. 238
64. The dependence on the sintering temperature of the area of
the D2 trisiloxane ring curvefitted Raman peak as a fraction
of the total Raman spectrum area. (a) For samples OXA (D),
2XA (+) and 5XA (0). The Dynasil peak area (A) is shown for
comparison. (b) For samples OX (0), OXA (+), 2X (0), 2XA (A),
5X (x) and 5XA (v). Within the resolution of the curvefitting
analysis the peak areas are the same for the two samples
examined for each type of gel within the T range of each
sample. . . . . . . . . ... ....... 239
65. The dependence on the bulk density Db (g/cc) of the area of
the D2 tetrasiloxane ring curvefitted Raman peak as a fraction
of the total Raman spectrum area for samples OXA (L), 2XA (+)
and 5XA (0). The Dynasil peak area (A) is shown for
comparison. . . . . . . . . ... ..... 241
66. The dependence on the sintering temperature Tp of the concen
tration/unit area of the internal pore surface of the D2
trisiloxane ring, [D2]/[Wt]/Sa, for samples OXA (D), 2XA (+)
and 5XA (0). . . . . . . . . ... . . .. 242
67. The dependence on the sintering temperature Tp of the area of
the 980 cm"1 SiOH curvefitted Raman peak as a fraction of the
total Raman spectrum area for samples OXA (D), 2XA (+) and
5XA (0). The Dynasil peak area (A) is shown for comparison. .245
68. The dependence on the sintering temperature of the concentra
tion/unit area of the internal pore surface of the 980 cm"1
surface silanols, [SiOH]/[Wt]/Sa, for samples OXA (D), 2XA
(+) and 5XA (0). . . . . . . . . ... . .. 246
xvii
69. The dependence on the sintering temperature Tp of the area of
the W3 (TO and LO) curvefitted Raman peak as a fraction of the
total Raman spectrum area for samples OXA (0), 2XA (+) and
5XA (0). The Dynasil peak area (a) is shown for comparison. .247
70. The dependence on the sintering temperature T of the area of
the W4 (TO and LO) curvefitted Raman peak as a fraction of the
total Raman spectrum area for samples OXA (0), 2XA (+) and
5XA (0). The Dynasil peak area (A) is shown for comparison. .248
71. The dependence on the sintering temperature Tp of the area of
the 3750 cm"1 SiOH curvefitted Raman peak as a fraction of
the total Raman spectrum area for samples OXA (D), 2XA (+)
and 5XA (0). The Dynasil peak area (A) is shown for
comparison. . . . . . . . . ... ..... 249
72. The dependence on the sintering temperature of the concentra
tion/unit area of the internal pore surface of the 3750 cm'1
surface silanols, [SiOH]/[Wt]/Sa, for samples OXA (D), 2XA
(+) and 5XA (0). . . . . . . . . ... . 250
73. The dependence on the sintering temperature TP of the ratio of
areas of the 3750 cm1 SiOH peak and the 980 cm" SiOH peak,
[SiOH]/[SiOH], for samples OXA (0), 2XA (+) and 5XA (0). .251
74. The dependence on the sintering temperature T (C) of the
structural density Ds [g/cc] ([) of a powdered type OX silica
gel, measured using He pycnometry, and the bulk density Db
[g/cc] of monolithic silica gels [169] sintered in humid
Florida air (+) and sintered in a dehydrating atmosphere of
flowing CC14 (0). . . . . . . . . ... . .. 264
75. The dependence on the sintering temperature Tp of the bridging
oxygen bond angle, 0 (), calculated from the W3 TO and the W4
LO Raman peak positions using equation (11), for samples OXA
(D), 2XA (+) and 5XA (0). . . . . . . . . ... 289
76. The dependence on the sintering temperature T of the Si0
bond length, d(SiO) (A), calculated from 0 in Fig. 75 using
equation (2), for samples OXA (D), 2XA (+) and 5XA (0). . 290
77. The dependence on the sintering temperature Tp of the calcu
lated relative structural density, which is calculated from 0
and d(SiO) as discussed in the text, for samples OXA (E),
2XA (+) and 5XA (0). . . . . . . . .. 293
78. The dependence on the sintering temperature T for samples
OXA (0), 2XA (+) and 5XA (0), of the calculated relative
structural density (from Fig.77) and the experimental
relative structural density, calculated from experimental Ds
data in Fig. 34 by assuming that at T = 4000C the
experimental Ds is equivalent to an experimental relative Ds
value of 1. . . . . . . . . ... ...... 294
xviii
79. The dependence on the sintering temperature T of the bridging
oxygen bond angle, 0 [*], calculated from the MASS NMR
spectra of a silica gel (0) [177], the MASS NMR spectra of an
A2 gel (A) [5], the peak positions of the IR spectra of a
type OX gel (X) [207], the W3 TO and W4 LO Raman peak
positions of sample OXA (+), and the MASS NMR of a type OX
gel (0). . . . . . . . . ... . . . .. 299
80. The dependence, on the sintering temperature T for type OX
gels, of the experimental relative structural densities
calculated from Fig. 32(b) and represented by the best fit
linear regressions (Ds = 1/((1/Db)V ) [D], water pycnometry
[+], He pycnometry [0]), the calculated relative structural
density (A) from Fig. 77, and the D2 trisiloxane Raman peak
area, [D2]/[Wt], as a percentage of the total Raman spectrum
area (X) calculated from Fig. 64. . . . . . . ... 311
81. The dependence on the sintering temperature T of the experi
mentally determined relative structural density measured
using He pycnometry (calculated from Fig. 34(a) assuming a
relative Ds 1.00 at T 400C), and the D2 trisiloxane
Raman peak area, [D2]/[ t], as a percentage of the total Raman
spectrum area (calculated from Fig. 64), for samples OXA, 2XA
and 5XA. . . . . . . . . ... . . . .. 312
82. The dependence on the sintering temperature T of the calcu
lated relative structural density (from Fig. 77), and the D2
trisiloxane Raman peak area, [D2]/[Wt], as a percentage of the
total Raman spectrum area and calculated from Fig. 64, for
samples OXA, 2XA and 5XA. . . . . . . . . ... 314
83. The dependence on their experimental structural density Ds
[g/cc] of the D2 trisiloxane Raman peak area, [D2]/[Wt], as a
percentage of the total area of their respective Raman
spectrum, for silica gel sample OXA (0), for fused asilica
with increasing fictive temperature [100], and for pressure
compacted fused asilica [133]. . . . . . . ... 320
84. The dependence on their experimental Ds of the calculated
relative Ds (calculated from the W3 TO and W4 LO Raman peak
positions) for silica gel samples OXA (o), 2XA (+) and 5XA
(0), for fused asilica with increasing fictive temperature
[100], and for pressure compacted fused asilica [133]. . 324
85. The extrapolated dependence on the hydroxyl concentration,
[OH] (Wt %), of the structural density of Amersil [210], a
Type II asilica, and of Suprasil [211], a Type IV asilica. 335
86. The rate of absorption of water vapor from a reservoir of
deionized water into the pores of type OX gel samples #124,
#141, #127, #136, with rH w 1.2 nm, and type 2X gel sample
#139, with rH 4.5 nm. . . . . . . . . ... 351
87. The evolution of the Raman spectrum (1001350 cm"1) of sample
#127, stabilized at T 6500C (Db s 1.28 g/cc, rH H 1.2 nm)
as the water content W increases from 0.0 g H20/g gel to W
Wmax = 0.329 g/g, and then as the gel is then redried by
reheating at Tp = 1900C. . . . . . . . . . 353
88. The dependence on time t (hrs) of the area of the D2 trisilox
ane curvefitted Raman peak, as a fraction of the total
spectrum area, for samples #124, #136, #127, #141 and #139,
and for a B2 gel [5] . . . . . . . . .. 355
89. The dependence on the water content W of the area of the D2
trisiloxane curvefitted Raman peak, as a fraction of the
total Raman spectrum area, for samples #124, #136, #127, #141
and #139 . . . . .. . . . . . . . .. 356
90. The dependence on time t (hrs) of the SiO force function, Ks
(N/m), calculated from the W3 TO and W4 LO Raman peaks using
equation (11), for samples #124, #136, #127, #141 and #139. .358
91. The dependence on the water content W (g/g) of the SiO force
function, Ks (N/m), calculated from the W3 TO and W4 LO Raman
peaks using equation (11), for samples #124, #136, #127, #141
and #139 . . . ... . . . . . . . . 359
92. The dependence on time t (hrs) of the bridging oxygen bond, 0
(), calculated from the W3 TO and W4 LO Raman peaks using
equation (12), for samples #124, #136, #127, #141 and #139. .360
93. The dependence on the water content, W (g/g), of the bridging
oxygen bond, 0 (*), calculated from the W3 TO and W4 LO Raman
peaks using equation (12), for samples #124, #136, #127, #141
and #139 . . ... . . . . . . . . . 361
94. The dependence on the water content, W (g/g), of the calcu
lated relative structural density, determined from 0 and
d(SiO), for samples #124, #136, #127, #141 and #139. .. 362
95. The natural log of the D2 trisiloxane curvefitted Raman peak
area, In [D2]/[Wt], plotted against the natural log of the
time of absorption, In t (mins), for samples #136, #127, #141
and #139 . . . .. . ... . . . . . . 380
96. The dependence on the water content, W (g/g), of the area, as
a fraction of the total Raman spectrum area, of the 605 cm1
D2 trisiloxane and the 980 cm1 SiOH curvefitted Raman peaks,
for samples # 136 (D and + respectively) and #127 (0 and A
respectively). . ... . . . . . . . . . 398
97. The dependence on log frequency, log f (Hz), of log conduc
tivity G (S/m), log susceptance B (S/m) and log loss tangent,
tan 8, of sample #10A for a water content W = 0.467 g/g. 416
xx
98. The dependence on log frequency, log f (Hz), of log dielec
tric constant, e', log dielectric loss factor, e", and log
loss tangent, tan 6, of sample #10A for a water content W 
0.467 g/g. . . . . . . . . ... .. . .417
99. The ColeCole plot [231], otherwise known as a complex plane
plot, of the imaginary part of the complex dielectric
constant, the loss factor e", plotted against the real part
of the complex dielectric constant, the dielectric constant
e", for sample #10A at W = 0.467 g/g. The angle of
suppression, a, of the semicircular plot of relaxation RI
below the xaxis is indicated (not to scale). Relaxation Rs
can be seen as the tail on the low frequency side of
relaxation R .. ........... . . . . . . 418
100. The evolution, in sample #10A, of the dielectric constant
spectra, log e'(log f), as the water content W increases from
0.032 g/g to 0.4782 g/g. . . . . . . . . ... 426
101. The evolution, in sample #10A, of the loss tangent spectra,
log tan 6 (log f), as the water content W increases from
0.032 g/g to 0.478 g/g . . . . . ... . . .427
102. The dependence of the log of the frequency of the maximum of
the peak in the loss tangent spectra, log f81, on the water
content W (g/g) in sample #10A at 25*C. . . . . .. 428
103. The dependence of the dielectric constant measured at 13 MHz,
e'13MHz' on the water content W (g/g) for sample #10A at 25*C. 429
104. The dependence of the log of the dielectric constant measured
at 1 KHz, 10 KHz, 100 KHz, 1 MHz, and 10 MHz on the water
content W (g/g) for sample #10A at 25*C. . . . . ... 430
105. The dependence of the shape of the dielectric loss tangent
spectra, log e"(log f), on the material used as measuring
electrodes. Curve A: silver paint, showing relaxation R1 and
the tail of relaxation Rs. Curve B: carbon paint showing just
relaxation R1. Curve C: vapor deposited aluminum showing just
relaxation R .. ............ . . . . .......... 439
106. The dependency of the log of the characteristic loss tangent
frequency, f.1 (Hz) of relaxation R1 on the log of the sample
thickness 1 (cm), i.e. of the electrode separation, using
silver paint electrodes for samples #25 (T = 180*), #71 (T =
800*C) and #34 (T = 1800C), with their pores full saturated
with water, i.e. = W . . . . . . . . . 440
107. The dependence of the log of the characteristic loss tangent
frequency of relaxation R1, f.1, on the log of the water
content W at T = 25*C, showing that above Wc = 0.275 g/g the
dependence of fl1 on W is no longer logarithmic. . . .. .443
108. The dependence of the characteristic loss tangent frequency
of relaxation R1, f81, on the water content W at T = 25*C,
showing that below Wc2 = 0.275 g/g the dependence of f,1 on W
is no longer linear. . . . . . . . . .. 444
109. The evolution of the susceptance spectra, log B [S/m] (log
f), as the length of the sample, and therefore the measuring
electrode separation, changes from 2.19 to 0.23 cm, for
sample #71, Tp = 180 C. . . . . . . . . . 451
110. A simple schematic representation of the two models discussed
in the text. (a) Flat pore geometry, i.e. statistical
thickness. (b) Cylindrical pore geometry. Not to scale. . 461
111. The dependence of the log of the characteristic loss tangent
frequency of relaxation R1, f,1 (Hz), on the log of the
statistical thickness, W/Sa (g water/1000 m2 = nm) for the
type OX gel samples B180 (which is actually sample #10A),
B650 and B800 at 250C, showing the slight increase in Wb/S =
Wc2/Sa as the stabilization Tp increases. . . . . ... 465
112. The DSC spectra of pure water, type OX gel sample A180 (rH k
1.2 nm) with its pores fully saturated with absorbed water,
and type 2X gel sample C45 (rH w 4.5 nm) with its pores fully
saturated with absorbed water. The dT/dt = 10=C/min in
flowing dry nitrogen . . . . . . . . . . 466
113. The relationship between the average cylindrical pore radius,
rH (nm), and the surface silanol concentration, [SisOH] (#
SisOH/nm2) for the silica gel samples investigated in Chapter
7 . . . . . . . . . . . . . 467
114. The dependence of the thickness of the bound adsorbed water
for the flat pore geometry model, W S Wc/Sa, and the
cylindrical pore geometry model, Rb, on the surface silanol
concentration, [SisOH] (# SisOH/nm2), from the DSC and DRS
analysis . . . . . . . . . . . .. 468
115. The dependence of the thickness of the bound adsorbed water
for the flat pore geometry model, W/S S Wc/Sa, and the
cylindrical pore geometry model, Rb, on the average
cylindrical pore radius, rH (nm), from the DSC and DRS
analysis . . . . . . . . . . . .. 469
116. The evolution of the near infrared (NIR) absorption spectra
of type OX gel sample #114 as water is absorbed into its
micropores and the water content W increases from 0.0 g/g to
0.121 g/g. . . . . . . . . .. . . 477
117. The change in the wavelength (pm) of the positions of the 2vu,
2v3 and 2v4 NIR peaks as W (g/g) increases in sample #114. . 479
xxii
118. A schematic 2dimensional representation of a structural
model which might explain the changes observed in the
conductivity of H20 adsorbed in the pores of a silica gel as
its statistical thickness, W/Sa, changes. This is a "snapshot"
of what is actually a dynamic system which is in constant
motion because of the short lifetime of Hbonds. The values
of the critical statistical thicknesses are indicated. =
permanent bonds,  = transitionary Hbonds. . . . ... 489
xxiii
KEY TO SYMBOLS
Symbol Meaning
R Approximately equal to
 Equivalent to
[ ] Concentration, e.g., [OH] = hydroxyl concentration
0c Abbreviation for "directly proportional to"
a Angle of suppression in ColeCole plots radss]
a = Ks Born nearestneighbor bondstretching central force function
[N/m]
ab Bond polarizability = am/coordination of atom
am Molecular polarizability
9 Born nearneighbor bondbending noncentral force [N/m]
ILV Liquidvapor surface tension or free energy [N/m,J/m2]
6 and A Dihedral angles [*]
AE Activation energy [Kcal/mole] = 'hKsa02
AHf Heat of formation [Kcal/mole]
AP Capillary stress [MPa]
APL Pressure gradient in a liquid
e' = KI Dielectric constant, E' = B/weo
e" = K2 Dielectric loss factor, e" = G/wEo
Ie"ft The magnitude of maximum of the dielectric loss factor of
dielectric relaxation Ri at fai, where i = 1, 2, 3 or S.
e'R = E'S Relaxed, or stationary, dielectric constant at low f < 1/7
e'u = e' Unrelaxed, or infinite, dielectric constant at high f > 1/rD
xxiv
E* = K* Complex dielectric constant e* (= K*)
co Permittivity of free space = 8.854 x 1012 F/m
1L Viscosity of a liquid [Pa.s]
6 Contact angle in the LaplaceYoung equation []
6 Intertetrahedral sSi0SiE bridging 0 bond angle [*], i.e.
the average bridging O bond angle representing the V(6)
associated with aSiO2, 6 =
Oc Critical bridging oxygen bond angle []
Oe Equilibrium bridging oxygen bond angle [] 144148
A2 Hybridization index
A Mean free path [m]
A Wavelength [m]
p Instantaneous dipole moment vector
0o Permanent molecular dipole moment
v Wavenumber [m'] = f/c
vt Laser wavenumber [m1] = 19436 cm1 a 514.5 nm
p Scattered phonon wavenumber [m''] = vtUR s 1933615436 cm1
VR Raman frequency wavenumber [m"1] a 1004000 cm1
p Volume fraction of solid phase = Db/Ds
On Standard deviation of n values
T Relaxation time [sec]
rT Relaxation time of tan 6 at Itan 61 [sec]
Tri Relaxation time of the maximum of the dielectric loss factor
of dielectric relaxation Ri at f.i, where i = 1, 2, 3 or S.
Ti = l/wei [sec]
TD Relaxation time at Debye peak [sec], Tr = l/wD
rn Nuclear Correlation Relaxation Time [sec]
SIntratetrahedral OSiO angle [*], s= <0Si0
w Radial frequency [rad/s] = 2rf = 1/r
xxV
WD
WL
WP
WR
A
asilica
a0
Aiso
AS
B(f)
c
Cb
Cn
CPMASS NMR
CRN
D
d(OH)
d(O..0)
d(Si..Si)
d(SiO)
Di
[D1]
[Di]/[Wt]
[D ]/[Wt]/S
[D ]0
Radial frequency at Debye peak [rad/sec] = 1/r
Laser light frequency [Hz] = 2rft = 2Icv1, where r = 3.142
Scattered phonon frequency [Hz] = 2rcvp
Raman shift frequency [Hz] E 2rcvR
Crosssectional area [m2]
Amorphous silica = aSiO2
Interatomic bond distance
Isotropic hyperfine constant
Asymmetric stretch vibrational mode
Susceptance B at frequency f [S/m]
Speed of light = 3 x 108 m/s
Raman coupling constant
Coordination number
Cross Polarized MASS NMR
Continuous Random Network
Permeability [m2]
OxygenHydrogen (OH) bond length [nm]
Oxygen to first 0 neighbor distance [nm]
Silicon to first Si neighbor distance [nm]
SiliconOxygen (SiO) bond length [nm]
A tetrasiloxane ring, whose oxygen breathing mode causes
the peak at 495 cm'1 in the Raman spectrum of asilica
Cyclic tetrasiloxane ring concentration
Fractional or internally normalized D1 concentration
D1 concentration/unit surface area of internal pores [#
rings D1/nm2]
[D1] at t = 0 mins
A trisiloxane ring, whose oxygen breathing mode causes the
peak at 605 cm1 in the Raman spectrum of amorphous silica
xxvi
[D2]
[D2]/[Wt]
[D2]/[Wt]/S,
[D2]0
[D2 t
Db
df
Df
DRS
ds
DS
DSC
Dsmax
dVp/drH
dW/dt
dW/dtc
f
f6i
fe,
Fb
Ff
f,
ft
fs
ft
Cyclic trisiloxane ring concentration
Fractional or internally normalized D2 concentration
D2 concentration/unit surface area of internal pores [# D2
rings/nm2]
[D2] at t = 0 hrs
[D2] at time t for t > 0 hrs
Bulk density, which includes the open porosity [g/cc]
Mass fractal dimension
Fictive density [g/cc], i.e. Ds at a particular Tf
Dielectric Relaxation Spectroscopy
Surface fractal dimension
Skeletal, structural or true density of material, which
does not include any open porosity [g/cc]
Differential Scanning Calorimetry
Maximum experimental structural density value [g/cc]
Pore volume distribution [cc/g/nm]
Drying rate [g/g/sec]
Critical drying rate, below which a gel does not crack
Frequency [Hz]
Frequency of the maximum of the tan 6 spectra, Itan Si, of
dielectric relaxation Ri, where i = 1, 2, 3 or S [Hz]
Frequency of the maximum of the E" spectra, e"il of
dielectric relaxation Ri, where i = 1, 2, 3 or S [Hz]
Fraction of bound H20 adsorbed onto the internal pore
surface
Fraction of free H20 adsorbed on top of the bound H20
Frequency of mode i [Hz]
Frequency of laser [Hz] = cvt
Fraction scharacter
Tortuosity factor in the CarmenKozeny equation
xxvii
Fused aSi02 Type I, II, III or IV nonporous amorphous silica
g(w) Band vibrational density of states (VDOS)
G(f) Conductivity G at frequency f [S/m]
G(ij) d(Si..Si) distribution
Gdc D.C. conductivity [S/m]
Gf81 Conductivity at f81 [S/m]
Gi Gruneisen parameter
GR = Gs Low frequency limit of G below 1/r
Gu = G= High frequency limit of G above 1/r
h Planck's constant = 6.626 x 1034 J.sec
I Current [Amps]
I(wl,wR) Experimental Raman intensity (background corrected)
IP(w) Stokes intensity, IP(w) = I(w)
Ired(W) Reduced Raman intensity
IS Impedance Spectroscopy
J Flux [volume/(area x time) = m/s]
J(w) Instrument transfer function
k Boltzman's constant = 1.3806 x 1023 J/K
k Reaction rate [Mole1min]
k Wavevector = 22/A [m1]
k' = k[H20]0 Reaction rate for a pseudofirstorder rate law [min"1]
K* E Complex dielectric constant = KI + iK2 = Re(K) + Im(K)
Ka = g The 0SiO bondbending noncentral force function [N/m =
1000 dyn/cm]
Kc Equilibrium constant = [products]/[reactants]
Kn Knudsen number = A/rH
KoH The OH bondstretching force function [N/m]
xxviii
Ks = a The SiO bondstretching central force function [N/m] =
W2 (l/Msi + 1/Mo)
Kg The SiOSi bondbending noncentralforcefunction [N/m]
KT Isothermal bulk modulus [N/m2]
L or 1 Sample length [m]
LO Longitudinal optical mode
m Gram formula weight [g]
M Molarity [moles/liter = mol dm1]
M Atomic mass
MASS NMR Magic Angle Sample Spinning NMR
MD Molecular Dynamics
MO Molecular Orbital
n Refractive index
n(wR) BoseEinstein thermal phonon population factor =
[(exp((h/2~)2rcvR)/kT)l]1 = 3.0063 for vR 104 cm1
NA Avagadro's number = 6.023 x 1023 atoms/mole
NBO/BO Ratio of nonbridging oxygen (i.e. SiOH) to bridging oxygen
(i.e. SiOSi) bonds
NMR Nuclear Magnetic Resonance
OH Hydroxyl group
OR Alkoxide group
Os Nonbridging oxygen surface atoms
p Depolarization ratio = I /I=
P/Po Relative vapor pressure
PP Peak positions
q, Vibrational displacement coordinates
Qn NMR terminology for a Si atom with n bridging 0 atoms
R2 Least squares correlation coefficient
r Radius of curvature [m]
xxix
r
R
R(f)
RI
Rb
RDF
Rf
Rg
rH
Rh
R,
r
S
Sa
SANS
SAXS
[SiOH]/[Wt]
[SiOH]/[Wt]/Sa
Si3
Si4
SiOH
Surface silicon atom
XXX
Bond directionality ratio = KG/Ks
Molar ratio of [H20]/[silica precursor]
Resistivity R at frequency f [Om]
The main dielectric relaxation due to the movement of
protons in water absorbed in the pores of a silica gel
Bound cylindrical thickness [nm]
Radial Distribution Function
Free cylindrical thickness [nm]
Guinier radius of gyration [m]
Average cylindrical pore radius = 2Vp/Sa [m]
Relative humidity [%]
Molar refraction
Average particle radius [nm]
The unit Siemens = n1
Surface area [m2/g] of a porous material calculated from
the N2 sorption isotherm using BET theory
Small Angle Neutron Scattering
Small Angle Xray Scattering
Fractional or internally normalized SiOH concentration,
i.e. the area of the SiOH peak as a percentage or
fraction of the total area of the spectra
SiOH concentration/unit surface area of the internal
pores [# OH groups/nm2]
Silicon atom in a D2 trisiloxane ring
Silicon atom in a D1 tetrasiloxane ring
The SiO stretching vibration of an SiOH group at 970 cm
The OH stretching vibration of an SiOH group at 3750 cm
SiOH
SisOH = SiOHs
SS
t
T
T(t)
ti/2
tan 6
Itan 6i
Tb
Tdb
TEM
TEOS
Tf
Tg
TGA
Tm
TMOS
TO
Tp
Tsmax
TV
type
type
type
V(0)
Vac
OX gel
5X gel
2X gel
Surface silanol group
Symmetric stretch vibrational mode
Time [sec, min, hr, day, yr, century, millennium, eon]
Temperature [*C]
Thermal history, time t at temperature T
Halflife [mins] = ln2/k for a firstorder reaction
Dielectric loss tangent = G/B = e"/e'
The magnitude of the maximum of the tan 6 peak at r6 of
dielectric relaxation R1, where i = 1, 2, 3 or S
Boiling point [*C]
Temperature at which densification begins by viscous sint
ering in silica gels
Transmission Electron Microscopy
Tetraethoxysilane or silicon tetraethoxide, Si(OC2H5)4
Fictive temperature [*C]
Glass transition temperature [*C]
Thermogravimetric Analysis
Fusion or melting point [C or K]
Tetramethoxysilane or silicon tetramethoxide, Si(OCH3)4
Transverse optical mode
Processing, stabilization or sintering temperature [C]
Temperature at which Dsmax occurs [*C]
Vaporization or boiling temperature [C or K]
Silica gel made with no HF, giving rH, 1.2 nm
Silica gel made with 0.075 moles HF/1 of H20, rH w 9.0 nm
Silica gel made with 0.03 moles HF/1 of H20, rH 4.5 nm
0 distribution
The a.c. peaktopeak voltage [Volts]
xxxi
v i
Vp
V
V,
VDOS
W
W/Sa
[Wt]
W1
W2
W3 TO, LO
W4 TO, LO
W5
WANS
WAXS
Wb/Sa Wc2/Sa
Wb W2
c2 b= W
Wc2/Sa b/Sa
Wf/Sa
Wf
Vibrational quantum number
Molar volume [cc/mole]
Pore volume [cc/g] = Db1 Ds1
Volume fraction of pores = (lp)
Vibrational density of states
Water content [g water/g silica gel]
Statistical thickness [g H20/1000 m2 m nm]
Total area under a reduced Raman spectrum except for the
970 cm1 SiOH, the 495 cm1 D1 and the 605 cm'1 D2 peaks
Main asilica Raman peak at 450 cm'"
Theoretical asilica Raman peak in 800950 cm1 region
Symmetric Si0 stretch (SS) peaks at 792, 828 cm'1 in the
Raman spectrum of asilica
Asymmetric SiO stretch (AS) peaks at 1066, 1196 cm1 in
the Raman spectrum of asilica
Raman peak of SiOH stretch vibration at 970 cm'
Raman peak of SiOH stretch vibration at 3750 cm'1
Wide angle neutron scattering
Wide angle Xray scattering
Bound statistical thickness [g H20/1000 m2 ] nm]
Bound water content [g H20/g Si02 gel]
The first critical water content [g H20/g SiO2 gel]
First critical statistical thickness 0.088 g H20/1000 m2
= nm
The second critical water content [g H20/g SiO2 gel]
Second critical statistical thickness 0.36 g H20/1000 m2
M nm
Free statistical thickness [g H20/1000 m2 r nm]
Free water content [g H20/g SiO2 gel]
xxxii
Wi Peak assignment of aSiO2 structural vibrations in Raman
spectroscopy, where i = 1, 2, 3, 4, or 6
W1x Maximum water content [g water/g silica gel]
X(f) Reactance X at frequency f [Om]
Y(f) Admittance Y at frequency f [S/m == nm'1], Y(f) = G (f) +
jBp(f), where p = parallel RC circuit
Z(f) Impedance Z at frequency f [fm], Z(f) Rs(f) jXs(f), s
= series RC circuit
xxxiii
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
POROUS SILICA GEL MONOLITHS:
STRUCTURAL EVOLUTION AND INTERACTIONS WITH WATER
By
Stephen Wallace
May 1991
Chairperson: Dr. Larry L. Hench
Major Department: Materials Science and Engineering
Monolithic silica gels are produced by the hydrolysis and
condensation of silicon tetramethoxide (TMOS) using acidified water. The
pH and concentration of this water determines the structure of silica
gels, which are fractal, porous materials possessing large surface areas
and small average pore radii. This research elucidates changes in the
structure of silica gels during viscous sintering, and structural
evolution of both the silica gels and water during adsorption into their
micropores.
The changes during densification were probed using Raman
spectroscopy, isothermal N2 sorption, pycnometry and thermogravimetric
analysis. As the temperature, Tp, increases, the structural density, Ds,
increases to a maximum value Dsmax. Dsmax is larger than the Ds of fused
amorphous silica, which is 2.2 g/cc. Most of the increase in Ds to Dsmax
is due to weight loss as Tp increases. Some of the weight loss occurs
during the formation of strained, high density, planar D2 trisiloxane
xxxiv
rings by the condensation of adjacent silanols on the pore surface. The
D2 concentration is partially responsible for the increase in Ds. As
densification is completed, Ds decreases from Dsmax to 2.2 g/cc.
Application of the centralforcefunction model for the vibrational
structure of amorphous silica to the gel's Raman spectra shows that the
average bridging oxygen bond angle, 0, is responsible for this decrease
in Ds. Both 0 and the associated skeletal volume are at a minimum at
Dsmx, and as Tp increases further, 6 increases as Ds decreases.
The structure of adsorbed water, and the porous silica
gels into which it is absorbed, are investigated using Raman
spectroscopy, dielectric relaxation spectroscopy and differential
scanning calorimetry (DSC). Surface D2 rings are rehydrolyzed on contact
with water during adsorption. For D2 rehydrolysis at 25C, the reaction
rate f 0.000173 (#D2 rings/nm2)"1 min"1 and the equilibrium constant r
0.25. The first monolayer of water adsorbed onto the pore surface does
not contribute to the melting peak in the DSC spectra. The proton
conduction mechanism and the relaxation properties of adsorbed water
depend on its statistical thickness.
xxxV
CHAPTER 1
INTRODUCTION
The sintering and resulting densification of alkoxide derived
silica gel monoliths is a complex process. The actual path taken during
processing to produce dry, stabilized or dense monoliths of silica gel
depends on many variables. These include a) precursor and solvent (if
any) used; b) molar water concentration, R, where R = number of moles of
water/number of moles of silica precursor, R = 4 is the stoichiometric
ratio for hydrolysis of silica precursors; c) pH, determined by the
catalyst used (The pH controls the relative rates of hydrolysis and
condensation, which in turn control the final gel structure); d) the
specific catalyst used; e) temperature Tp; f) drying method used, i.e.
whether the monolithic gel is dried via i) atmosphere or environmental
control of the relative humidity to produce xerogels, ii) slow evapora
tion at room temperature with no relative humidity control, or iii)
hypercritical drying, producing an aerogel; and g) sintering atmosphere.
For example, in this investigation, a typical monolithic xerogel,
sample type OX, is made from a nitric acid catalyzed tetramethoxysilane
(TMOS) sol with an R ratio of 16 and a HNO3 catalyst concentration = 25
cm3 concentrated HN03/1975 cm3 H20. TMOS is also known as silicon tetram
ethoxide or tetramethyl orthosilicate. After drying, this silica gel
will produce a xerogel with a pore volume, Vp, of about 0.45 cc/g and a
surface area, Sa, of about 750 m2/g. The internally interconnected
1
2
microporosity can be modelled as a single continuous cylinder with the
Vp and Sa of the gel [1,2]. This gives a value of the average cylin
drical pore radius, rh, = 20,000 x V/Sa = 20,000 x 0.45/750 = 1.2 nm.
The exact shape of the pores in silica gels is unknown, so a "modelless"
pore radius can be used, called the hydraulic pore radius and defined by
Brunauer et al. [3] as Vp/Sa. The hydraulic radius = rH/2 [2].
For the production of monolithic silica gels an acid catalyzed,
high R ratio sol is required. This produces a polymeric, crosslinked,
fractal structure with two levels of particle size and an incomplete
condensation polymerization reaction [4]. The primary particle size has
an average radius, rp, 2 nm, and the secondary particle size, composed
of the agglomerated primary particles, has an average particle radius rp
w 6.0 nm [4]. The structure of the final dry gel is dependent on the sol
structure and contains micropores and both internal and surface silanols
(SisOH).
The addition of HF as a catalyst drastically decreases the time to
gelation by increasing the kinetic rate of the condensation reaction.
The influence of HF is thought to be due to the basic behavior of F'
ions compared to the acidic H* groups, i.e. it acts as a Lewis base (or
Bronsted acid) [5]. The sol still has a low pH (pH e 1), so the overall
reaction is acidic as opposed to basic. This means that the rate
constant of the hydrolysis reaction is still large relative to the
condensation reaction, and hydrolysis still occurs rapidly. The F ion
acts as a strong base, catalyzing the condensation reaction. The net
effect is to reduce Sa and to increase Vp, but Sa is reduced by a larger
factor than Vp. This has the effect of increasing rH. The effect of HF
on particle size is not so clear, as the relationship between particle
3
size and pore radius involves both the coordination number, C packing
factor, P.F., the radius, rp, of the particles, and the width of the
particle size distribution. For a given rp, a decrease in the coordina
tion number, Cn, of the particles causes a larger average pore radius,
rH, with no change in particle size.
Silica gels catalyzed by a base have a more compact structure,
with a larger average particle size [5]. Compared to an acid catalyzed
sol, the hydrolysis rate constant of a base catalyzed gel is lower, and
the condensation rate constant is larger. A very high pH, for instance
caused by the addition of an excess of NH4OH to a silicon tetraethoxide
(TEOS) sol, causes the formation of monodispersed, submicron, colloidal
silica spheres, known as Stober spheres [6]. These form by the continu
ous agglomeration of condensed silica particles from a high pH silica
sol.
Several authors [719] have recently published data showing values
of the skeletal density, Ds, of metalalkoxidederived silica gels
during sintering which are greater than that of fused asilica. The
skeletal density, Ds, of fused asilica is 2.20 g/cc. Since the reported
values of the skeletal density, Ds (also called the true or structural
density), of the silica gel are larger than the density of asilica
their accuracy has been questioned. The absolute magnitude of the
structural density, Ds, for a given thermal history, depends on the
experimental technique used to measure D due to the fractal nature of
the gels [5,20]. This means that the size of the yardstick used, i.e the
molecular diameter in this case, governs the magnitude of D The
dependence of Ds on the thermal history of the gel is related to the
structure of the gel. For example, the reported dependence of the
4
structural density, Ds, on the sintering temperature Tp depends on the
pH of the starting sol. The texture and structure of asilica gel also
depend strongly on the pH.
In Part I of this investigation, the structural and textural
properties of monolithic silica gels will be characterized during
densification via viscous sintering and during the adsorption of water
into the micropores of stabilized gels. Raman Spectroscopy, Isothermal
Nitrogen Sorption, Helium and Water pycnometry, Differential Scanning
Calorimetry (DSC), Thermogravimetric Analysis (TGA) and Magic Angle
Sample Spinning 29Si Nuclear Magnetic Resonance (MASS 29Si NMR) will be
used. The experimentally determined temperature dependency of Ds of
monolithic gels will be explained in terms of these properties. The
Raman spectra of silica gels obtained during processing have been
investigated before [2137] and are qualitatively well understood. The
thermal dependency of Ds will be investigated by quantifying the changes
in the peak positions and areas of the Raman spectra of silica gels as a
function of temperature and other textural variables. These quantified
properties can then be related to the changes in D .
The initial hypothesis used to explain the experimentally observed
Ds behavior was that the changes in Ds were related to the changes in
the concentration of the 3membered silicate rings in the silica gel.
The oxygen breathing mode of these trisiloxane rings produces the 605
cm'1 D2 peak in the Raman spectra of amorphous silica [5]. The D2 peak
undergoes definite but subtle changes with an increase in the sintering
temperature of the gels during densification. The D2 peak is on the
shoulder of the large main Raman peak at 440 cm'1, so measuring its peak
position and intensity using French curves to draw in the appropriate
baseline is not very accurate. The peak position of the D2 peaks will be
shifted from its true value because the main peak distorts the D2 peak
shape. Consequently, to extract quantitative spectral data allowing this
hypothesis to be tested, Gaussian peaks were curvefitted to the baseline
corrected, thermally reduced experimental Raman curves using criteria
discussed in the literature review section on curvefitting.
A chronological critique of the literature concerning the struc
ture and vibrational spectroscopy of asilica is presented in Chapter 2.
The relevance of the literature to Part I is considered in the discus
sion in Chapter 4.
In Part II of this investigation, the structure of water absorbed
into the micropores of stabilized silica gels will be characterized and
the dependence of the conduction mechanism of protons in the adsorbed
water on the statistical thickness of the adsorbed water will be
discussed. Dielectric Relaxation Spectroscopy, Impedance Spectroscopy
and Differential Scanning Calorimetry (DSC) will be used.
PART I
STRUCTURAL AND TEXTURAL EVOLUTION OF POROUS SILICA GELS
DURING SINTERING AND DURING WATER ABSORPTION
CHAPTER 2
A CHRONOLOGICAL LITERATURE REVIEW OF THE STRUCTURE AND
THE VIBRATIONAL SPECTROSCOPY OF AMORPHOUS SILICA
2.1 The Structure of Amorphous Silica
2.1.1 The Categories of the Types and Structure Concepts of aSilica
Bruckner [38,39] wrote a broad review of the properties and
structure of silica. He defined the four categories or types of commer
cially available silica glasses:
a) Type I silica glasses are produced from natural quartz by electrical
fusion under vacuum or under an inert gas atmosphere. They contain
nearly no hydroxyl, OH, groups (<5 ppm) but relatively high metallic
impurities ([Al] = 30100 ppm and [Na] = 4 ppm). These include Infrasil,
IRVitreosil, G.E. 105, 201, 204.
b) Type II silica glasses are produced from quartz crystal powder by
flame fusion (the Verneuille process). They contain a much lower
metallic impurity level, but because of the H202 flame, [OH] = 150400
ppm. These include Herasil, Homosil, Optosil and G.E. 104.
7
c). Type III silica glasses are synthetic vitreous silica produced by
hydrolyzation of SiC14 when sprayed into an 02H2 flame. This gives a
very low metallic impurity level, but [OH] = 1000 ppm and [Cl] = 100
ppm. These include Dynasil, Suprasil, Spectrosil and Corning 7940.
d) Type IV silica glasses are synthetic silica produced from SiC14 in a
water free plasma flame, with [OH] = 0.4 ppm and [Cl] = 200 ppm. These
include Dynasil UV5000, Suprasil W, Spectrosil WF and Corning 7943.
All these different types of silica glasses have slight differenc
es in their properties and therefore characteristic differences in their
structure. Bruckner [38,39] pointed out that the anomalous behavior of
the volumeT curve, which shows minima at 15000C and 80C. This may be
used to decide whether or not the material in question is a glass.
2.1.2 Structural Models of aSilica
Figure 1 shows the bulk, or geometric, density, Db, of silica as a
function of the fictive temperature Tf [38]. The bulk density includes
all the porosity, both open and closed, existing in the sample. The
magnitude of the bulk density, Db, for a specific Tf depends on the type
of silica being measured. Types I and II, of natural origin, have larger
densities than Type III, of synthetic origin. Both types reach a maximum
at 1500*C of 2.2026 g/cc (Type I and II) and 2.2056 g/cc (Type III).
They tend towards a similar value of 2.2000 g/cc at a Tf of 900*C.
Bruckner [38,39] divided the structure concepts of oxide glasses
into 4 groups. Group 1 is based on the Continuous Random Network (CRN)
model due to Zachariasen [40], which was verified using Xrays [41] and
later modified [42]. It is now the generally accepted model for the
structure of silica. Group II is based on the crystallite hypothesis,
2.2060
\ U
SHe
2.2050 / / H
JR
o 2.2040 TYPE Iln aSilica
S// Infrasil (I) Fa. Heraeus
SHerasil (He) Fa. Heraeus
Vitreosil (JR) Fa. ThermalSyndicate
>_ Homosil (H) Fa. Heraeus
S2.2030 Ultrasil (U) Fa. Heraeus
Z
IL
SpH
J
m 2.2020 SpV
S
2.2010 TYPE ITTIV aSilica
Suprasil (S) Fa. Heraeus
Spectrosil (SpV) Fa. ThermalSyndicate
Spectrosil (SpH) Fa. ThermalSyndicate
2.2002
1000 1200 1400 1600 1800
FICTIVE TEMPERATURE TF [C]
Figure 1. The bulk density Db of different Type I/II and Type III/IV
commercial aSiO2 as a function of fictive temperature Tf. After [38].
Their bulk and structural densities are identical because V = 0.0 cc/g.
9
which was also examined by Xray analysis and modified, but has been
rejected as an unrealistic model for the structure of silica [43]. Group
III is based on the microheterogeneous structure concept first claimed
as "latent decomposition" in systems with an Sshaped liquidus curve. It
was brought to a thermodynamicalstatistical base of phase separation,
nucleation and decomposition. Group IV includes all those hypotheses
based on geometrical considerations [44], and pure statistical models of
certain partition functions.
Mozzi and Warren [41] performed the classic xray scattering
analysis of the structure of silica, obtaining pair function distribu
tion curves for silica (Fig. 4 in Mozzi and Warren [41]). This repre
sents a structure which is averaged over the whole sample interpreted in
terms of pair functions. Each silicon is tetrahedrally surrounded by 4
oxygen atoms, with an average Si0 distance d(SiO) = 1.62 A. Each
oxygen atom is bonded to 2 Si atoms. The 0 to first 0 neighbor distance
d(0...0) = 2.65 A. These distances have narrow size distributions. The
SiOSi bridging 0 bond angle, 0, shows a broad distribution, V(6),
extending all the way from 120* to 180*, with a maximum at 0 r 1440. The
related Si to first Si neighbor distance, d(Si...Si), also has a broad
distribution, G(ij), extending all the way from 2.78 to 3.24 A (Fig. 5
of Mozzi and Warren [41] shows these distributions). This wide variation
in 0 is an important distinction between amorphous and crystalline
silica. It is also an important criterion for any proposed model for the
structure of aSi02. Good agreement with the measured pair function
distribution curve was obtained by assuming a random orientation of the
dihedral angle, 6, about the Si0 bond directions, except where prevent
ed by the close approach of neighboring atoms. (The dihedral angle gives
10
the orientation of two neighboring tetrahedra relative to the SiOSi
plane.) This interpretation confirmed Zachariasen's CRN model [40].
Bock and Su [45] applied some of the results from the models of
crystalline silica to yield a semiquantitative description of aSiO2.
The truly characteristic part of the electromagnetic spectrum is the
farinfrared region, which can be probed by both IR and Raman spectros
copy [45]. Far IR absorption is a manifestation of the modes of vibra
tion of a disordered structure, which can be used to distinguish a
glassy material from a crystalline material. These modes cannot be
described by any model based on an ordered structure in the crystalline
form. The short range order in the glass was described by assuming that
the average structural unit was aquartz and used the valencebond force
field approximation, giving d(SiO) w 0.16 nm and 0 1500. They
obtained force constant values of Ks w 480 N/m (Si0 stretching), Ka
35 N/m (OSiO bending) and KBg 5 N/m (SiOSi bending). Although the
selection rules were not adhered to, 15 predicted frequencies were
within the ranges of the spectra of fused aSiO2 reported. The Raman
spectra Bock and Su obtained is very poor in comparison to more recent
literature. Bock and Su [45] commented that Wadia and Balloomal's model
[46] is physically unrealistic, but similar to their own, which means
that their own model is also unrealistic!
Gaskell [47] developed a model for the structure of amorphous
tetrahedral materials using ordered units with carefully prescribed
boundary conditions. It gave a reasonable comparison with the observed
radial distribution function (RDF) of an amorphous material. This shows
one of the many problems with trying to decide whether a model is a good
simulation of amorphous material. Even this model, which contains
11
definite local crystalline order, can simulate an RDF. The modern
accepted model of amorphous material is the continuous random network
(CRN) [40] model which contains no crystalline order. This point
illustrates Galeener and Wright's [43] observation that to be any good,
a model must give very good agreement with an RDF, as well as reproduce
other experimental evidence, e.g., Raman spectra, etc.
Gaskell and Tallant [48] reexamined Bell and Dean's ball and stick
inorganic polymer model [49,50,51] of the structure of aSiO2 which was
developed to investigate the vibrational spectroscopy of aSi02. They
applied an energy minimization technique with a Keating forcefield to
obtain equilibrium atomic coordinates from the original model and
concluded that the BellDean random structure is an acceptable descrip
tion of aSiO2. The relaxed structure gave approximately the correct
values for the density, enthalpy of crystallization and the Xray and
neutron scattering data. The main weakness of the model was the large
surface area to volume ratio intrinsic to the few atoms in the model.
This requires that larger relaxed models of perhaps several thousand
atoms be constructed with improved stereochemical characterization
before further progress can be made in the analysis of random network
models for glass. An improved forcefield function is also required, as
well as better information on the bondangle distributions. Gaskell
obtained values 0 = 144 149*, in good agreement with Mozzi and
Warren's [41] value of 144*, and a dihedral angle, 6, distribution
showing a non random distribution with peaks visible at 60*. This
implied the presence of puckered 4, 5 and 6 membered rings.
Phillips [52] has a different view of the structure of aSi02,
which has been strongly refuted by Galeener and Wright [43]. Phillips
12
does not believe the CRN model can be logically supported, similarly
rejecting the PoraiKoshits and Evstropyev [53] paracrystalline model of
glass structure. Instead he says that glass formation occurs in oxides
not for topological reasons, but for a specific chemical reason, namely
the ability of 0 atoms to form double bonds rather than single bonds at
little expense in enthalpy. Clusters with noncoalescing interfaces
covered with nonbridging surface oxygen atoms, O *, form. This suppress
es crystallization and allows the cluster interfaces to fit together
very snugly with little void volume while creating true surfaces in the
usual sense of crystalline boundaries. Phillips said that this, combined
with the fact that for aSiO2 the number of structural constraints
exceeds the number of degrees of freedom, means that aSiO2 must have a
granular structure. He gave a broad review [52] of the spectroscopic
properties of aSiO2 while trying to prove his hypothesis.
Phillips [52] calculated that 20% of the molecules in a cluster
are on the surface, a very large concentration for a defect. He shows
TEM micrographs of aSi02 fibers claiming to show clusters of about 6.0
nm diameter, similar to the cluster size calculated to be formed from
his model. This argument reverts to whether or not the researcher
believes that the TEM samples are representative of bulk aSiO2. Do the
TEM micrographs show clusters, or are they artifacts of sample prepara
tion or electron beam damage?
Galeener and Wright [43] pointed out that modern diffraction
experiments are able to provide accurate data with high real space
resolution. In practice this provides an extremely fine filter for the
various structural models proposed in the literature. The problem is
that most authors term "good agreement" with experiment as getting peaks
13
in the "right place" in either the reciprocal space interference
function or the real space correlation function. Only very poor models
fail to achieve this. Correct peak shapes and areas must also be
obtained, which requires including the effects of thermal vibration in
the model. A given model fitting experimental diffraction data is no
guarantee that no other models will also fit. Agreement with diffraction
data is a necessary but not sufficient criterion for any structural
model of amorphous solids [43].
Galeener and Wright [43] strongly refuted Phillips [54] model by
showing that it is incompatible with neutron diffraction and Raman
spectroscopic data. Phillips predicted the wrong number of peaks in the
important part of the neutron diffraction pattern, with the wrong shape
and the wrong width. Thus it does not meet Galeener and Wright's [43]
criterion and has to be rejected. Analysis of experimental neutron
scattering data shows that any crystalline structure has to have a
maximum correlation length of 1.0 nm or less if it to reproduce the
experimental amorphous scattering spectra. Phillips [54] claimed a
microcrystallite size of 6.0 nm. Also, since 90% of the 0 atoms in
Phillip's model were in the interior of the 9cristobalite microcryst
als, the Raman spectrum of aSiO2 should resemble 9cristobalite, which
is not the case. There is no known double bond of Si that is stable at
room temperature. This and other spectroscopic evidence disproves the
assignment of the 495 cm'1 peak to the wagging motion of Si=O bonds
specified by Phillips' model.
Evans et al. [55] examined several atomic models for aSiO2 with
radically different mediumrange structures. They compared the RDF and
the neutron and Xray structure factors computed from each model with
14
experimental data. Despite the differences in mediumrange structure,
all the models provided a reasonable fit to the experimental data but
could not reproduce all the details. They suggested this meant that RDF
are relatively insensitive to the medium range order and that all CRN
models contain too little strain. They also suggested that incorporation
of a granular structure would introduce the strain, putting him in the
paracrystalline model school of thought. The calculation of the vibra
tional density of states for each model and comparison to experimental
Raman spectra was also insensitive to medium range topology. They
concluded that knowledge of the structure of aSi02, a material first
studied extensively over 50 years ago, is essentially incomplete. The
local structure is defined beyond reasonable doubt [41], but the medium
range structure, e.g., the ring statistics, extent of randomness, etc.,
is still a matter of debate.
Galeener [56] looked at the structural models for aSiO2 for the
four ranges of order, namely short (SRO), intermediate (IRO, or
medium), long (LRO) and globalrange order (GRO). SRO involves specifi
cation of the bonding environment of each atomic species, essentially
the nearest neighbor (nn) environment, up to 0.3 nm. Each Si atom is
surrounded tetrahedrally by four 0 atoms at d(SiO) ; 0.161 nm, and each
0 atom bridges between 2 Si atoms. There is a small spread in d(SiO), a
small spread in the OSiO angles, 0, (spread w 0.75*), and a large
spread in 0. Bell and Dean's ball and stick model [4951] contained a
well specified SRO and poorly specified IRO due to the way it was built.
IRO involves specifications of relative atomic positions over
several nm distances, given the SRO. It may take the form of specifica
tion of the dihedral angles, 6 and A, (see Fig. 2) for two corner shar
0= Si
0=0
Figure 2. The relative orientation of two corner sharing silica tetrahe
dra, SiO44", showing the bridging oxygen bond angle, 0, the silicon
oxygen bond length, d(SiO), the OSiO bond angle, b, and the tetrahe
dral angles, 6 and A, which define the angular orientation of the
tetrahedra about their bridging SiO bonds. After [56].
16
ing tetrahedra, distributions of rings of completed bonds, network
connectivity, or some currently unformulated measure. The planar
cyclotrisiloxane D2 ring is an example, as is the assumption of random
dihedral angles used in the ZachariasenWarren model [40,41] for aSiO2.
SRO and IRO specify structure in a volume 1.0 nm in diameter.
Morphological LRO accounts for order in noncrystalline structures
on a long range scale, > 1.0 nm. These could be extended voids, chan
nels, spherulites, amorphous microphases, etc. Global range order
accounts for structural order which exists and/or is defined over
macroscopic distances, e.g., macroscopic isotropy, network connectivity,
chemical or structural homogeneity or heterogeneity.
Galeener [56] defines some aSiO2 models in the above defined
range of ordering: 1) the Zachariasen model [40]; 2) the Zachariasen
Warren (ZW) CRN model [40,41], same as the well known Zachariasen model
except that d(SiO) is distributed over a narrow range about 0.161 nm (0
is broadly and unimodally distributed from about 120 to 180*, with the
most probable value of 1440; the dihedral angle is randomly distributed,
having no preferred value); 3) the Lebedev PoraiKoshits [LPK] micro
crystalline model [57], which consists of microcrystallites of cristoba
lite, with connective Si0 bonds between crystallites, and is specified
as noncrystalline crystallitee size is undefined but leads to structural
heterogeneity; this model was rejected by Warren in 1937 [58]); 4) the
Phillips model [59,52,54], rejected by Galeener [43], as discussed
earlier. Galeener [56] points out for model 3) that for 1.5 nm crystal
lites, nearly half of the atoms will be on their surfaces, which should
show up as a peak in Raman spectra, but do not.
17
Galeener [60] pointed out that glasses contain sufficient disorder
that their structure must be defined statistically, as must gases.
Numerous properties of aSiO2 vary with preparation conditions, so
presumably does their structure in some statistically significant way.
Statistical structural models are very difficult to prove uniquely. Some
obvious shortcomings of the ZW models are as follows: in real life,
chemical order may occasionally be broken. Point defects are known to
exist in aSiO2. Structural parameters are not uncorrelated; d(SiO) and
0 are known from chemical theory to be correlated. Furthermore 6 must be
correlated with d(SiO), 0, 0 and other values of 6 in order for the
ring of bonds to close on themselves. Significant numbers of regular
rings (planar 3fold and puckered 4fold) are believed to exist in
aSi02, and this implies special nonrandom values of 6. These shortcom
ings do not invalidate the ZW model, but rather point out improvements
that could be made in its specific details.
Marians and Hobbs [61] looked at the structure of periodic SiO2
as a function of network topology, specifically at the ring structure.
They defined rings which are taken to be structurally significant as
those which are not decomposable into smaller rings. They defined a ring
to be indecomposable if there exists no path in the network which
connects any two of its vertices which is shorter than both of the paths
belonging to the ring which connect those two vertices. They applied
this model to the question of how many 3membered rings a network of
corner sharing tetrahedra could accommodate, such that the networks
should be strain free besides the 3membered rings themselves. They
found that large interconnected voids were formed which allowed the
network to form in a strain free manner with a low density. The struc
18
ture consisted of tetrahedra with a 3membered ring through each of two
nonintersecting edges. Topologically then Marians and Hobbs [61] stated
that it is possible to produce strain free structures only if porosity
is included. This describes the structure of silica gel, but statisti
cally a real silica gel would not possess 3membered rings in the
correct topological configuration to make them strain free. Some strain
would exist in the structure, possibly causing Ds values larger than
that of aSiO2.
2.1.3 TEM Studies of aSilica Structure
Gaskell and Mistry [62] produced high resolution TEM micrographs
of small aSiO2 particles about 15 nm in diameter. Micrographs of solu
tionprecipitated aSiO2 had a more regular, ordered appearance than
those of a flame hydrolyzed aSi02. They suggested that regions of local
order could be observed in the micrographs, which would support an
"amorphous cluster" model of the structure. The regions of local order
that they suggested exist are not obvious, and their interpretation
could be different from that suggested, i.e. the structure could
actually be more random than Gaskell and Mistry [62] suggests.
Bando and Ishizuka [63] also examined the structure of aSi02
using dark field TEM images. Bright spots observed in the darkfield
image were interpreted as originating from microcrystallites about 1.7
nm in diameter. Yet again, as for other TEM references, the conclusions
are open to interpretation, because of the difficulty in assigning the
bright spots observed to a particular structural origin. This is due to
the problems in obtaining TEM micrographs of amorphous material, so the
bright spots could just as easily be due to mass thickness contrast.
19
2.1.4 Molecular Dynamic Simulations of the Structure of aSilica
Molecular Dynamics (MD) simulations of structure allow detailed
analysis of the atomistic motion and the complex microstructure that
give rise to the average properties of aSi02. The main disadvantage of
MD is the reliance upon an effective interaction potential, which cannot
effectively model the real binding energy and atomic forces of a
material. Nevertheless, MD simulations of the structure of aSiO2 have
yielded reasonably accurate descriptions of the vitreous state. Molecu
lar Dynamics gives too high a defect concentration and too broad a range
of both bond angles, 0 and 0. This is due to the omission of any
directionally dependent terms in the effective potential, required to
reflect the partial covalency of the system.
Feuston and Garafolini [64] added a small 3body interaction term
to a modified ionic pair potential to simulate the directionally
dependent bonding in aSiO2. This improved the modeling of the short
range order around the Si atom, i.e the silica tetrahedra. The model's
RDF improved enough to give fairly good agreement with the Xray and
neutron scattering data on aSiO2. Ring size distribution measurements
of the 648 atom aSi02 model gave equal concentrations (31%) of 5 and
6 membered rings, but with concentrations of 3% and 15% for D1 and D2
rings, respectively, which are too high.
Ochoa et al. [65] investigated the failure mode of aSi02 by
applying a uniaxial strain throughout an MD cell. They used a 2body
BornMayerHuggins potential because a 3body potential provided no
improvement in the behavior they investigated. The fracture stress of
the MD aSi02 structure increased as the strain rate increased. At "low"
strain rates below the speed of sound structural rearrangement occurred
20
by rotation of silica tetrahedra to increase 0 in the direction of the
applied stress. The system rearranged itself so that atoms attained new
equilibrium positions through vibrational motions. At "high" strain
rates above the speed of sound this was not possible and atoms were
forced far from their equilibrium positions so that the aSiO2 failed by
extension of the SiO bonds while 0 did not have time to increase.
2.1.5 Molecular Orbital (MO) Calculations of the Structure of aSilica
O'Keeffe and Gibbs [66] used MO theory to model defects in aSiO2.
MO calculations on model molecules can accurately reproduce structural
configurations in solid oxides. They concluded that Phillips [54] model
of paracrystalline clusters with Si=O at the internal surfaces was not
correct because the Si=O bond energy is 380 kJ/mol less stable than two
SiO single bonds, so Si=O bonds can be ruled out as a major defect in
aSi02. The strain energy in 2membered siloxane rings eliminates this
configuration as a possibility, while larger rings are not specifically
excluded due to strain energy. The calculated frequencies and the ratio
of calculated frequencies strongly supported Galeener's assignment [67]
of the DI and D2 bands in the Raman spectrum of aSi02 to be 0 breathing
modes in 4 and 3 membered siloxane rings respectively.
Michalske and Bunker [68] examined the dependence on strain of
siloxane bonds to rehydroxylation, and therefore bondbreaking, by H20
molecules. Molecular Orbital calculations suggested that bond angle
deformation (i.e. strain) is most effective in increasing the chemical
activity of the SiOSi bond. Strain transforms an inert SiO bond into
a reactive site for adsorption, which consists of a Lewis acidic Si atom
and a Lewis basic 0 atom, while also weakening the SiO bond.
21
The strainfree bonding configuration corresponded [67] to the
minimum energy value where d(SiO) = 0.163 nm, the 0SiO tetrahedral
angle, 0, is 109.5*, and 0 = 144. Molecular Orbital calculations showed
that < 4 Kcal/mole is required to straighten 0 from 144* to 1800 or
decrease 0 from 144* down to 1300. Decreasing 0 from 144* to 1000
required over 30 kcal/mole, a significant fraction of the total Si0
bond energy of 100 kcal/mole. Increasing or decreasing d(SiO) by 0.01
nm required 330 kcal/mole. Changing b by 10* required %25 kcal/mole.
Strained surface defects in dehydroxylated aSiO2 exhibited en
hanced reactivity compared to unstrained defects in two respects [68].
First, the strained defects acted as strong acidbase sites which
adsorbed chemicals such as H20 more efficiently than did unstrained
siloxane bonds. Adsorption of electron donor molecules such as pyradine
demonstrated the Lewis acidity of the strained surface defects. Sec
ondly, the Si0 bond in the strained defects were more susceptible to
reactions with adsorbed chemicals, which resulted in bond rupture.
McMillan [69] did a series of abinitio MO calculations to obtain
nonempirical force fields for silicate molecules. He obtained values of
around Ks = 600 Nm"1 for Si0 stretching, K. = 4050 Nm"1 for 0SiO
bending, and Kg = 17 Nm1 for SiOSi bending force constants, similar
to those used in structural model calculations. McMillan's calculations
revealed some low frequency dynamic modes, including the coupled
torsional motions of adjacent SiO4 tetrahedra which might give rise to
the low frequency excitations observed in aSiO2. He speculated that
these excitations might explain the asymmetric shape of the main Raman
peak at 430 cm'1, which makes accurate and theoretically supportable
curvefitting of that peak so difficult.
22
2.1.6 Bonding and Structure Relationships in Silica Polymorphs
The variation in refractive index seen in the polymorphs of silica
are usually attributed to the associated changes in density. Revesz [70]
says that the molar refraction exhibits a systematic variation repre
senting differences in the Si0 bond which are related to the magnitude
of the r bonding between Si and 0. The Si0 bond is mainly covalent, so
calculation of ionic polarizabilities is not meaningful, and bond
polarizability, ab, can be used instead. This is determined by dividing
the molecular polarizability am by the coordination of silicon, where am
is calculated from the LorenzLorentz equation:
R = (n2l/n2+2)Vm rNAam4/3 (1)
where Rm = molar refraction, n = refractive index, Vm = the molar volume
and NA = Avagadro's number. An increase in ab is associated with a
decrease in bond length.
For the crystalline polymorphs of silica, as the density increases
from 2.27 to 2.87 g/cc the 1100 cm1 peak shifts from 1106 to 1077 cm1.
The bond strength also decreases, the average 0 decreases from 146.8 to
139*, the d(SiO) increases from 0.160 to 0.163 nm, n increases from
1.473 to 1.596, and ab decreases [70].
These changes are related to r bonding decreasing as the density
increases and the ionic component of the Si0 bond increases concomi
tantly [70]. The increase in density can be attributed to decreasing
drpr bonding between Si and 0. The r bonding arises from the overlap of
the originally empty Si 3d orbitals with the 0 2p orbital containing the
lone pair of electrons. i bonding increases as 0 increases [71],
23
resulting in increased bond strength, increased ab and an increase in
the Si0 vibration frequency, as well as in decreased bond length. The
ionic component of the bond also decreases.
Revesz [70] gave a value for the ratio of the relative increase in
%b to the relative decrease in bond length, 1, i.e. (Aa/ab)/(Al/l) =
9.3 for Si0. This correlation only applied for the crystalline
polymorphs of silica with densities above 2.33 g/cc, corresponding to
cristobalite. Below 2.33 g/cc, as density increases, ab and d(SiO)
decrease as the Si0 vibration frequency and the bond strength increase.
This is the reverse to the behavior above 2.33 g/cc, which Revesz [70]
said was due to increasing delocalization of r electrons. Delocalization
of r electrons in Si0 rings increases with ring size, but so does the
bond strain, presumably above the value of the equilibrium unstrained
ring. The t bonding and delocalization increase as density decreases.
The directionality ratio r = Ka/Ks decreases from 0.199 to 0.163
as the density increases and the bonds become less directional, i.e.
less covalent and more ionic. Multiple bonding of the drpr type for Si
is well established, especially in bonds to 0 [7073]. Overlap between
filled 0 pr and Si dr orbitals increases as 0 increases.
Hill and Gibbs [74] examined the interdependence between tetrahe
dral d(SiO) bond length, the nonbonded nearest neighbor d(Si...Si)
separations and the bridging oxygen bond angle, 0 or
regression analysis of crystalline silica data. They found that d(SiO)
correlates linearly with sec8 over the entire range of observed angles
(137180*). Shorter bonds involve wider angles, so that
d(SiO) = 0.068 secO + 1.526, R2 = 0.74
for d(SiO) = 0.1585 0.1623 nm.
The variance in d(SiO) is small compared to d(Si...Si), so the
Si...Si separation involved in a SiOSi linkage can be approximated by
the linear equation
log d(Si...Si) = log 2d(Si0) + 0.81 log sin(0/2). (3)
Log 2d(Si0) is the intercept = 0.503. It has been proposed [74] that
Si...Si controls the lower limit of 0 at a value = 0.300.31 nm. Values
as low as 0.29 nm fit into this empirical equation, suggesting [74] that
nonbonded interactions change continuously into bonded interactions
without showing a sharp break. A particular "hardsphere" nonbonded
radius for silicon may not be realized in solids.
The d(SiO) bond length also depends weakly on the d(Si...Si)
separation distance. As the Si atoms approach each other as 0 decreases,
d(SiO) increases slightly.
d(SiO) = 0.121 d(Si...Si) + 1.982 (4)
for d(Si...Si) = 0.3 0.32 nm.
Newton and Gibbs [75] used abinitio MO theory to calculate
energyoptimized d(SiO) and angles for molecular orthosilicic and
pyrosilicic acids. They conclude that the local bonding forces in solids
are not very different from those in molecules and clusters. An extended
basis calculation for H6SiO4 implied there were about 0.6 electrons in
the 3d orbitals on Si. The bond length and angle correlations were
ascribed to changes in the hybridization state of the bridging 0 and the
25
(dp) ibonding involving all 5 of the 3d atomic orbitals of Si and the
lonepair atomic orbitals of the 0. There was a buildup of charge
density between Si and 0. The atomic charges of +1.3 and 0.65 calculat
ed for Si and 0 in a silica moiety of the low quartz structure conformed
with the electroneutrality postulate and with experimental charges
obtained from monopole and diffraction data for low quartz.
Gibbs [76] reviewed the abinitio calculations of bonding in
silicates. He showed that the disiloxy (SiOSi) group is very similar
in silicates, aSi02 and the gas phase molecule disiloxane with d(SiO)
= 0.162 0.165 nm and 0 = 140 150*. d(SiO) shortened nonlinearly
when plotted against 0, but linearly when plotted against either the
hybridization index of the bridging 0 atom, A2 = l/cos
fraction scharacter, fs = (1+A2)1. It is called the hybridization index
because its state of hybridization is given by the symbol sp1. Figures
3 and 4 show this relationship for experimental and theoretical data.
Figure 5 shows a potential energy surface for the disilicic acid
molecule, H6Si207, with d(SiO) plotted against 0, on which is superim
posed the experimental bond length and angle data for the aSiO2 polym
orphs [76]. The data follow the general contour of the surface, but the
observed d(SiO) are about 0.002 nm longer on the average than that
defined by the valley in the energy surface. The difference may be
related to lattice vibrations at room temperature. The barrier to
linearity of the disiloxy molecule is defined to be the difference
between the total energy of this molecule evaluated for a straight
bridging angle and that evaluated at the minimum energy angle. This is
small, about 3kT at 300 K, so a relatively small amount of energy is
expended in deforming the disiloxy angle from its minimum energy value
1.4 1.3 1.2 1.1
Sec 0 [0]
Figure 3. The SiO bond length as a function of Sec(0) for the silica
polymorphs low tridymite, low quartz, and coesite. The d(SiO) have a
standard deviation < 0.005 A. The linear fit line is the best fit linear
regression analysis of all the data points. After [74].
1.62 
< 1.60 (i)
O
1
"o 1.58  
ii)
1.568
1.56 (a) 1 I (b)
1400 1600 1800 0.40 0.45 0.50
0 [1] fs
Figure 4. A comparison of the experimental d(SiO) in coesite (upper
curves in (a) and (b)) with those calculated for the bridging d(SiO) in
a disilicate molecule, H6Si207 (lower curves in (a) and (b)). d(SiO)
varies nonlinearly with 0 and linearly with fs = 1/(1 + A2), where A2 =
Sec(0) is called the hybridization index of the bridging 0 atom because
its state of hybridization is given by the symbol sp2'. After [76].
1.65 
'1.60 1
. \
1.55 6
1200 1400 1600 1800
e [0]
Figure 5. Potential energy surface for the disilicate molecule, H6Si207,
plotted as a function of d(SiO) and 0. The contours represent incre
ments in energy of 0.005 a.u. E 0.6257 kcal/mole relative to the minimum
energy point (1091.76678 a.u.) denoted by the cross. Increasing contour
numbers represent increasing energy. The dashed line represents the bond
lengths and angles for the disiloxy groups in the silica polymorphs
coesite, tridymite, low cristobilite and aquartz. After [76].
29
to 180*. If the bonding force in disilicic acid and the silica polymor
phs are similar, then the disiloxy angles in the latter may be readily
deformed from their equilibrium values. This causes the broad distribu
tion of 0 seen in polymorphs and aSi02 without destabilizing the final
structure.
Gibbs [76] calculated the 0 distributions for 3, 4, 5 and 6
membered rings in silicates and siloxanes. The expected increase in the
average 0 and the width of the 0 distribution with ring size is ob
served, showing reasonable agreement with experimental observations.
Janes and Oldfield [723] investigated the bond structure of the
SiO bond and favored the (dp)r bonding model, discussed by Revesz
[70], for the SiO bond in silicates. This involves the atomic dorbit
als of Si and the porbitals of 0 in Si04 tetrahedra, with the possibil
ity of an admixture of s and p character in the dorbitals as well as
significant overlap with the three Si dorbitals and/or the Si
a orbitals. Janes and Oldfield [73] examined the question, given the
existence of (dp) rbonding, to what extent is the effect significant;
i.e. does the correlation between d(SiO) and 0 originate from changes
in (dp) rbonding? Molecular Orbital calculations showed the possibili
ty of (dp) ibonding but implied only minor structural significance, so
the (dp) wbonding effect facilitated charge transfer, but it was
insensitive to variations in d(SiO) or 0.
Devine et al. [7780] concluded from Magic Angle Sample Spinning
Nuclear Magnetic Resonance (MASS NMR) data of compacted aSiO2, in
agreement with Revesz [70], that 0 variation causes charge transfer
effects in the bridging bonds. From the MAS NMR and photoemission
spectroscopy data Devine [79] derived the relationship
d(29Si chemical shift,ppm)/d(Si2p3/2 core shift) = 1316 ppm/eV. (5)
When combined with the NMR data on the dependency of the chemical shift
on 0, direct data on the spread in bond charge transfer can be obtained.
Therefore i bonding magnitude due to 0 variation can also be obtained.
2.2 The Theory of Raman and IR Scattering
Vibrational spectroscopy involves the use of light to probe the
vibrational behavior of molecular systems, using an absorption or a
light scattering experiment. Vibrational energies of molecules and
crystals lie in the approximate energy range 060 KJ/mol, or 05000
cm1. This is equivalent to a temperature (kT) of 06000 K, and is in
the IR region of the electromagnetic spectrum [81].
The simplest description of vibrations of molecules and crystals
is a classical mechanical model. Nuclei are represented by point masses,
and the interatomic interactions (bonding and repulsive interactions) by
springs. The atoms are allowed to undergo small vibrational displace
ments about their equilibrium positions and their equations of motion
are analyzed using Newtonian mechanics. If the springs are assumed ideal
so the restoring force is directly proportional to displacement (Hooke's
law), then the vibrational motion is harmonic, or sinusoidal in time.
The proportionality constant which relates the restoring force to
vibrational displacement is termed the force constant of the spring.
Solution of the equations of motion for the system allows a set of
vibrational frequencies fi to be identified. Each frequency corresponds
to a particular atomic displacement pattern, known as a normal mode of
vibration. In many vibrational studies the object is to deduce the form
31
of the normal modes associated with particular vibrational frequencies.
This allows vibrational spectroscopy to be used as a structural tool.
The classical model allows a description of the basic features of
vibrational motion. It does not give any insight into why vibrational
spectra are line spectra rather than continuous absorptions, nor into
the interaction of vibrations with light. For this, you must construct a
quantum mechanical model, where Schrodinger's wave equation is con
structed in terms of the vibrational displacement coordinates q.. An
appropriate potential energy function V(qi) is assumed. This gives a set
of partial differential equations from the vibrational wave equation.
Solution of these differential equations gives a set of vibration
al wave functions. Each function describes a vibrational normal mode and
a set of associated vibrational energies. These wave functions and
energies are quantized, so they can take only discrete values determined
by a vibrational quantum number vi, where i = 0, 1, 2, 3, etc. The
quantized energies are usually shown on an energy level diagram as the
vibrational energy levels for the system. In a vibrational spectroscopic
experiment, the system undergoes a transition between vibrational levels
with quantum numbers vi and vj. Light is absorbed or emitted with an
energy (AE = hv) corresponding to the separation between the levels.
In a Raman scattering experiment, visible light from an intrinsi
cally polarized monochromatic laser is passed through the sample. About
0.1% of the laser light is scattered by atoms. About 0.1% of the 0.1%
scattered light interacts with the sample in such a way as to induce a
vibrational mode. When this occurs, the energy of the scattered light is
reduced by an amount corresponding to the energy of the vibrational
transition. This type of inelastic scattering is known as Raman scatter
32
ing, while the elastic light scattering with no change in energy or
frequency is known as Rayleigh scattering. The energy of the scattered
light is analyzed using a spectrometer. Raman lines appear as weak peaks
shifted in energy from the Rayleigh line (Fig. 6). The positions of
these Raman peaks about the incident line correspond to the frequencies
of Raman active vibrations in the sample.
In Raman scattering, the light beam induces an instantaneous
dipole moment in the molecule by deforming its electronic wave function.
The atomic nuclei follow the deformed electron positions. If the nuclear
displacement pattern corresponds to that of a molecular vibration, the
mode is Raman active. The size of the induced dipole moment is related
to the ease with which the electron cloud may be deformed, described by
the molecular polarizability am. The Raman activity of a given mode is
related to the change in polarizability during the vibration. In general
the molecules containing easily polarizable atoms, such as I, S and Ti
have very strong Raman spectra. Similar molecules with less polarizable
atoms, such as Si, C and 0, have much weaker spectra. In contrast to IR
spectra, the most symmetric modes give the strongest Raman signals since
these are associated with the largest changes in polarizability.
The number of vibrational modes seen for a molecule is equal to
the number of classical degrees of vibrational freedom, 3N6. N is the
number of atoms in the molecule. For crystals, N is equal to Avagadro's
number, but most of the modes are not seen. This is due to the translat
ional symmetry of the atoms in the crystal. The vibration of each atom
about its equilibrium position is influenced by the vibrational motion
of its neighbors. Since the atoms are arranged in a periodic pattern,
the vibrational modes take the form of displacement waves travelling
Figure 6. The principles of Raman scattering. (a) The incident laser
beam, energy E, passes through the sample and the scattered light is
detected to the spectrometer. (b) The Raman spectrum consists of a
strong central peak at the wavelength of the laser energy E due to the
Rayleigh scattering, and the much weaker Raman shifted lines at Eei,
where ei = hvI correspond to the energies of vibrational transitions in
the sample in cm'1, where E = 0 cm'1. Stokes Ramanshifted frequencies
(Ee) are positive wavenumber values, and antiStokes Ramanshifted
frequencies are negative wavenumber. (c) The energy level diagram for
Rayleigh and Raman scattering. There are two energy levels which are
separated by an energy e = hv, where v is the vibrational frequency. The
incident laser photon, energy E, excites the vibrational mode to a
shortlived (1014 sec) electronic "virtual state", which decays with
the release of a photon. When the final vibrational state of the
molecule is higher than that of the initial state, the released photon
energy is Ee, and StokesRaman scattering has occurred. When the final
state is lower, the released photon has energy E+e, and antiStokes
scattering has occurred. When the initial and final states are the same,
Rayleigh scattering has occurred and the incident and released photons
have the same energy E. After [81].
C
L
(
L
1*
(a)
Incident Laser Energy E
Beam
(b)
S RAMAN SPECTRUM
u AntiStokes
E +e
Li
U
0
(c)
T
E
i
AntiStokes
Raman
Raleigh
Ee
SStokes
Virtual
State
n=l
Stokes n=
Raman
i I 
e 0 e
WAVENUMBER [cnT1]
I I \
/ I \
I I \
/ I \
I
Figure 7. The various types of crystal lattice vibrations. (a) The
wavelength of this lattice mode is long compared to the crystal lattice
constant, a, so the mode lies at the center of the Brillouin zone (k =
0). (b) This mode has wavelength A = 2a, and lies at the edge of the
Brillouin zone (k = 7/a). The waves in (a) and (b) represent transverse
lattice vibrations for a monatomic chain of atoms. (c) This illustrates
a longitudinal lattice vibration for the same monatomic chain. (d) For
any crystal, there are three lattice vibrations where all the atoms in a
unit cell move in phase in the same direction. These are the acoustic
modes. (e) For crystals with more than one atom in the primitive unit
cell, there are modes where atoms in the unit cell move in opposing
directions (illustrated for a diatomic chain). These motions can
generate a changing dipole moment and hence interact with light. These
are called optic modes. (f) A typical dispersion curve in one direction
in reciprocal space for a crystal, in this case with n = 4 atoms in its
unit cell. Only long wavelength lattice vibrations (near k = 0) can be
infrared or Raman active due to the long wavelength of light compared
with crystal lattice spacings, which are marked with dots. After [81].
(a) I
a
(b)
a =Lattice Spacing
0* 0 0 00 0 0
(d)
d = Unit Cell Dimension
(e) I ;
*oo k= 0
k = Wavevector
X= 2a k =
Transverse
Longitudial
Acoustic Mode
Optic Mode
kmax
Wavevector k =
a
37
through the crystal. These are known as lattice vibrations. The lattice
waves are described as longitudinal when the nuclear displacements are
parallel to the wave propagation direction. They are described as
transverse when the displacements are perpendicular to the propagation
direction (Fig. 7).
The nuclear displacements give rise to an oscillating dipole
moment, which interacts with light in a spectroscopic experiment. The
frequency of this oscillating dipole wave is defined by the oscillation
frequency of individual atoms about their equilibrium position. Its
wavelength is defined by that of the associated lattice vibrations. In
order for the lattice vibration to interact with light, the wavelength
of the lattice vibration must be comparable to that of light, for
example 514.5 nm. This is much larger than the dimensions of crystalline
unit cells. Therefore only very long wavelength lattice modes can
interact with light in an IR or Raman experiment. In these long wave
length lattice vibrations, the vibrations within adjacent unit cells are
essentially in phase. The number of vibrational modes which may be seen
in IR or Raman spectroscopy is equal to 3N3. N is the number of atoms
in the primitive unit cell. These 3N3 vibrations which can interact
with light are termed the "optic modes." Transverse and longitudinal
optic modes are termed TO and LO modes for short.
Crystal lattice vibrations are usually described by k, the wave
vector. The direction of k is the direction of propagation of the
lattice wave, and the size of k is 2r/A. A is the wavelength of the
lattice wave. The relationship between the frequency of a particular
normal mode and the wavelength of its propagation through the lattice is
known as a dispersion relation. This is usually represented graphically
38
as a dispersion curve v(k) (Fig. 7). Each normal mode is associated with
a branch of the dispersion diagram. In any particular crystallographic
direction in reciprocal space, there are 3N branches. Three of these are
the acoustic branches, which cause the propagation of sound waves
through the lattice. At infinite wavelength, that is at k = 0, the three
acoustic modes have zero frequency, and correspond to translations of
the entire crystal. The remaining 3N3 branches are known as the optic
branches. They can give rise to IR and Raman active vibrations for long
wavelength modes (k ; 0).
The shortest wavelength A for lattice vibrations is defined by the
lattice constant, a, with the adjacent unit cells vibrating exactly out
of phase. The A of the lattice wave is then 2a, corresponding to k =
r/a. The phase relations between vibrations in adjacent unit cells
define a region in reciprocal space between k = r/a and k = r/a. This
region is known as the first Brillouin zone. Long A lattice vibrations
with k = 0 are said to lie at the center of the first Brillouin zone.
Just like molecules, crystal lattice vibrations are more completely
described by the quantum mechanical model. The vibrational spectra of
crystals correspond to transitions between vibrational states. The basic
unit of vibrational excitation in a crystal is known as a phonon, by
analogy with the term photon for a quantized unit of light energy.
In a spectroscopic experiment, such as IR and Raman spectroscopy
for probing vibrational modes, we are concerned with transitions between
quantized states, from some initial state, n, to another state, m. The
energy associated with the transition is the difference between the
energies of the two states, AE = EM En. The intensity of the observed
line is related to the probability of the transition n * m, described by
39
the Einstein transition probabilities for absorption (Bn) and induced
emission (Bm). The Einstein coefficient for absorption describes the
case where a system is initially in state n and absorbs a quantum of
energy from an applied radiation field to undergo a transition to a
higher energy state m [82]. The transition probability is maximized when
the energy of the radiation corresponds to AEmn. The set of probabili
ties for transitions between sets of levels are known as the selection
rules for the spectroscopic transitions in the system.
For IR absorption, the oscillating electromagnetic field of the
incident light causes a timedependent perturbation of the system from
its initial state n. This perturbation is responsible for the transition
to the higher energy state m, so IR absorption can be considered as a
timeindependent perturbation followed by a timedependent perturbation.
In Raman scattering, the system is perturbed by the incident beam before
the transition takes place, so Raman scattering can be considered as two
consecutive timedependent perturbations to the system.
In an IR experiment the system absorbs a quantum of light with
energy in the infrared region of the spectrum. This causes the system to
change from a vibrational state with quantum number vn to one with
quantum number vm. For the timedependent perturbation theory, the
perturbation can be described as an interaction between the oscillating
electric field vector, E, of the light and the instantaneous dipole
moment vector, p, of the molecule. For a diatomic molecule, the dipole
moment is defined by p = Qra. Q is the charge difference between the
atom centers, and ra is the atomic separation. When ra = r, (the equi
librium bond distance), pC is the permanent molecular dipole moment.
40
During a vibration, the atoms undergo small displacements, Ar, in
relation to each other.
The size of the instantaneous dipole moment generated depends on
Ar and p. Vibrations are IR active if there is a dipole moment change
during the vibration and if n = m 1, i.e. if the vibrational quantum
number v changes by one unit. These two conditions are the selection
rules for IR of the harmonic oscillator. For an absorption line, if the
lower state is the vibrational ground state (v = 0), this is the
fundamental absorption line, from v = 0 to v = 1. The intensity of the
transition is a the size of the dipole moment change during the vibra
tion (dy/d(Ar)). These selection rules can be extended to polyatomic
molecules and condensed phases. In general for a vibration to be IR
active the vibrational motion must cause a change in the dipole moment,
i.e. dp/dqi 0 0, where qi = the vibrational normal coordinate. This can
occur even when the molecule has no permanent dipole moment.
For crystals, an additional selection rule is introduced by the
translational symmetry of the crystal. The vibrational normal modes are
cooperative lattice distortions. If the mode causes a dipole change
within the unit cell, an electric dipole wave forms within the crystal.
It has a well defined wavelength and wave vector in the direction of
propagation. This dipole wave can only interact with light when its
wavelength is comparable with that of infrared radiation. This occurs
when the wavelength of the electric dipole wave is very large or the
wave vector tends to zero.
In Raman spectroscopy a beam of light is passed through a sample
and the energy of the scattered light is analyzed. Both elastic (Ray
leigh) and inelastic (Raman) scattering is seen. Raman scattering occurs
41
via interaction with the vibrational wave function of the system. The
scattering mechanism can be described by the instantaneous dipole moment
Aid induced in the system by the incident light beam:
p = amE = amE0cos2rft (6)
where E is the oscillating electric field vector of the radiation with
frequency f and amplitude E0 and am is the molecular polarizability
which expresses the deformability of the electron density by the
radiation field. Since pin and E are not collinear, am is a second order
tensor. Since the polarizability will in general change during a
molecular vibration, it is commonly expanded in a Taylor series. The
action of the light beam in creating the instantaneous induced dipole
moment is the first timedependent perturbation on the system. In the
second step of the analysis the vibrational wave functions corresponding
to the initial and final states of the system are allowed to interact,
modulated by the induced dipole moment [82].
This treatment results in the selection rules for the vibrational
Raman effect. The Raman intensity for a transition between vibrational
states n and m is proportional to the square of the transition moment
M A vibration is Raman active then, i.e. Mm + 0, when the vibrational
quantum number changes by one unit between states n and m, and the term
dp/d(Ar) # 0. The first selection rule is relaxed for anharmonic
molecular vibrations, allowing overtone bands to appear in the Raman
spectrum, as for IR absorption. The second selection rule implies that
for a vibrational mode to be Raman active there must be a change in
molecular polarizability associated with the vibration [82].
42
The methods of symmetry and group theory provide techniques for
predicting the IR and Raman activities of all vibrational modes of even
complex molecules and crystals. Molecular symmetry is described for a
set of conventionally chosen symmetry elements, which express certain
spatial relations between different parts of the molecule. For any
molecular system, the set of symmetry operations showing the symmetry of
the molecule forms a mathematical group. This is a special type of set,
satisfying particular combination relations between the elements of the
set. Group theory is the mathematical framework within which quantita
tive descriptions of the symmetry possessed by a structure are con
structed. McMillan and Hess [82] discuss the theory of symmetry and
group theory as applied to molecular structure and spectroscopy.
Knowledge of the symmetry information from group theory then
allows prediction of which vibrations will be IR active and which will
be Raman active. For each symmetry operation found (associated with a
particular vibration), the Cartesian translations of the coordinate
origin caused by each are examined. If the origin shows any translatio
nal (as opposed to rotational) movement for a particular vibration
associated with a symmetry operation, that vibration will be IR active.
This is because for IR activity there must be a change in the dipole
moment, AM, during the vibration. Since the dipole moment is a vector,
this change can be expressed by the Cartesian coordinates Apx, AMy and
Apz. These belong to the same symmetry species as Cartesian translations
of the origin, so they can be examined to check for IR activity [82].
The condition for Raman activity of a vibrational mode is that
there must be a change in its polarizability am during the vibration.
This polarizability change can be expressed in terms of the second order
43
tensor elements ae, a, az, axy, axz and ayz. Since this tensor is a
linear function of the atomic displacement [83,p.154], the elements of
the tensor transform in the same way as the quadratic combinations of
the Cartesian translations x, y and z of the coordinate origin of the
atom for a particular vibration. Examination of these quadratic combina
tions for a particular molecule or crystal by group theory identifies
the symmetry species of Raman active vibrational modes, and therefore
the vibrational modes themselves [82].
The determination of the symmetry species for the vibrational
modes of a molecule or crystal allows immediate prediction of the number
and type of IR and Raman active vibrations of the molecule or crystal.
For a crystal structure only those vibrational modes for which all units
cells vibrate in phase can give rise to an infrared or Raman spectrum.
Therefore you need only consider the unit cell symmetry to determine the
number and species of IR and Raman active modes of a crystal [82].
For an amorphous material the selection rules no longer apply. The
theory of which modes will be IR or Raman active is not as well devel
oped. IR and Raman spectroscopies probe the same vibrational modes in
pure aSiO2. In IR spectroscopy, the electric field of the IR radiation
couples with the instantaneous dipole moment created by the relative
motions of atoms with opposite charges. Raman spectroscopy probes non
polar modes, which explains why Raman modes involve symmetric vibration
al modes, as these do not involve the dipole creation caused by asymmet
ric charge movement [84]. This supports the assignment of the symmetric
0 breathing mode of the 3 and 4 membered silicate rings to the D2 and D1
Raman peaks, respectively. The known theories of the vibrational spectra
of aSi02 are discussed in the next section.
44
2.3 Modelling the Vibrational Behavior of aSilica
Wadia and Balloomal [46] developed a model explaining the Raman
and IR spectra of aSiO2 in which the tetrahedral Si04 units were linked
to fixed walls, and claimed that the model's predictions gave a satis
factory but not very accurate interpretation of the observed spectra.
Bell and Dean [49] pointed out that traditionally there are two
main approaches to the problem of determining atomic vibrational
behavior in glasses. The first one used methods developed in the theory
of molecular spectroscopy, and the second was based on the techniques of
crystal lattice dynamics. The first approach rests upon the implicit
assumption that the vibrational behavior of a small unit of the glass
structure can adequately characterize the entire glass system. The small
unit contains only several molecules [49]. Such a method often gives
quite a reasonable account of the number and position of bands in the
vibrational spectra. However, it can give a description of the detailed
atomic motions only for those vibrational modes of the full glass system
which are intensely localized in regions similar to the units consid
ered. The second approach replaces the glass, not with a small molecular
unit, but with an infinite regular crystalline array. The vibrational
properties of this array are derived using conventional lattice dynamics
procedures. This method gives a fair account of the band positions.
Implicit in the approach is the assumption of an extended wavelike form
for the normal modes of vibration.
Bell and Dean [49] took a third approach to determining the
vibrational behavior of aSiO2. They used a physical ball and stick
model of a giant inorganic molecule complying with short range structur
al data obtained from Xray and neutron scattering experiments on
45
aSiO2. They calculated the normal mode frequencies and atomic ampli
tudes of vibration of the model using a central Si0 force constant Ks =
400 N m'1 (1 N m'1 = 1000 dynes/cm). The ratio of the noncentral OSiO
force constant Ka to the Ks was taken as 3/17 w 0.176. They obtained
frequency distribution histograms for aSiO2 which were similar to
experimental Raman spectra, possessing all the main structural peaks.
With the surface nonbridging bonds fixed, they obtained peaks at 400,
500 (shoulder), 750 and 1050 cm'1. This compared with their observed
experimental peaks at 500, 600, 800 and 1100 cm1.
Detailed analysis of selected normal modes by Bell and Dean [49]
showed that the 1050 cm1 band in the calculated spectrum was associated
with an asymmetric bond stretching vibration where bridging oxygen atoms
moved parallel to the Si...Si line joining their immediate Si neighbor
(Fig. 8). The modes in the 500 cm1 (shoulder) and 800 cm'1 regions were
associated with bond bending vibrations in which 0 atoms moved along the
bisectors of the SiOSi angles (Fig. 8). In the 400 cm1 peak the modes
were associated with the bondrocking motion of bridging oxygens
vibrating perpendicular to the SiOSi planes (Fig.8). Bell and Dean
[49] concluded that neither the purely molecular approach nor that based
on an undiscriminating use of crystal lattice dynamics was likely to be
fully successful in yielding information on vibrational modes throughout
the spectrum. Only a much more flexible scheme, such as that based on an
extended atomic model is capable of reproducing the full range of vibra
tional behavior. Galeener and Wright [43] agree with this method being
the best way to prove a theoretical model of the structure of glass.
Galeener has done a lot of work on the structure of aSiO2 and the
interpretation of its Raman and IR spectra. The Raman spectrum of fused
Oxygen
Silicon * :.
o 0
Bending = W3
Stretching = W4
Rocking
Figure 8. Normal vibrations of a disilicate molecular unit in aSiO2.
The axes point along the direction in which the bridging 0 atom moves in
the bond bending, stretching and outofplane rocking normal modes.
These normal modes correspond to peaks in the Raman spectra of aSiO2.
The bondbending axis is parallel to the bisector of the SiOSi angle,
and is assigned to the W3 peak at 800 cm'1. The bond stretching axis is
perpendicular to this bisector, but still in the SiOSi plane, and is
assigned to the W4 peak at 1060 cm'1 and 1200 cm'". The bond rocking
direction is orthogonal to the other axes and is normal to the SiOSi
plane, i.e. outofplane. After [85].
47
aSiO2 (also known as vitreous or melt derived silica) has long been
puzzling because it contains peaks which have not been explained by
vibrational calculations on the favored CRN structural model. Galeener
and Lucovsky [86] demonstrated that a complete explanation of the
vibrational spectra requires incorporation of another type of interac
tion between the tetrahedra. That is the longrange interaction provided
by the Coulomb fields associated with certain excitations of the system.
There are two types of macroscopic modes: transverse and longitu
dinal. In an isotropic medium such as glass, transverse modes are those
in which the average electric vector E is perpendicular to the direction
of periodicity of the wave (Fig. 7(b)). Their resonant frequencies are
determined by poles in K2 = Im(K), where K* K* + iK2 = Re(K) + Im(K) is
the complex dielectric constant of the medium. Longitudinal modes are a
complementary set whose average electric field is completely parallel to
the direction of periodicity (Fig. 7(c)). Longitudinal modes normally
resonate at zero values of K*. In the long wavelength limit [86,87] they
resonate at poles of the dielectric energyloss function Im(l/K*). The
converse statement then follows. Peaks in K2 reveal transverse modes,
while peaks in Im(l/K*) identify longitudinal modes [86,87]. The ob
served poles in Im(l/K*) occur at zeros of K* [86].
Galeener et al. [86,87] investigated the possibility of longitu
dinal response in aSiO2 by determining the poles in K2 and Im(l/K*)
and comparing their positions with those of the observed Raman spectra.
KramersKronig techniques were applied to IR reflectivity spectra to
obtain IR values of K* = K1 + iK2, and the latter were used to compute
Im(l/K*) = K2/(K12+K22). Galeener reported the existence of three TOLO
pairs at 455 and 495 cm1, 800 and 820 cm1, and 1065 and 1200 cm1. They
are called optical modes because they appear at sufficiently high
frequencies to obviate the possibility of their being acoustic. Galeen
er's initial interpretation [86] of the 495 cm1 peak was wrong [87], as
was [5] Walrafen's [88,89] assignment to mSi+ and mSiO0 defect centers.
Wong and Angell [90] reviewed the early literature of the paracry
stalline models for the vibrational spectroscopy of aSiO2. They pointed
out that the abnormal excess heat capacity of aSi02 is contributed by
the optical modes of very low frequencies.
The lack of translational symmetry in amorphous materials prevents
their vibrational excitations from being described by plane waves
propagating from unit cell to unit cell. The theoretical understanding
of the vibrational properties of random networks is much less complete
than it is for crystals [91]. The principal theoretical approaches
applied to amorphous materials have involved either numerical techniques
to determine the modes of random networks, or attempts to identify
molecular units that retain their integrity to some degree in the
amorphous solid that can be analyzed on their own. Numerical techniques
involve building a ballandstick model of the structure, and the
problem is reduced to diagonalizing a large matrix and finding the
associated density of eigenvalues. With care over the treatment of the
surface, reasonable density of states have been obtained for aSiO2
[4951]. This approach reproduced the broad density of states, implying
that aSi02 is best regarded as a giant covalently bonded molecule which
cannot be subdivided into molecular units in any obvious way. The
density of states would contain sharp peaks if the structure could be
decomposed into weakly interacting molecular units.
49
aSi02 consists of a random 3dimensional network of SiO44 tetra
hedra and these basic tetrahedra retain their integrity in the crystal
line polymorphs of silica. The molecular modes of SiO44 play an impor
tant role in determining the vibrational spectra of aSi02, as does the
magnitude of the bridging 0 bond, 0. 0 determines whether the material
possesses narrow molecular modes or broader solidstate bandlike modes
due to increased effective coupling of the individual tetrahedra. The
transition occurs as 6 increases from 90 to 1800 [91]. The normal
vibrational modes of AX4 tetrahedral molecules are well known [52]. They
consist of a nondegenerate scalar Al (symmetric breathing) mode, a
doubly degenerate E tensor mode, and two triply degenerate vector
bending and stretching f21,2 modes. All modes are Raman active, but only
the f21,2 vector modes are infrared active. The CRN model leads to the
separation of continuum modes in the glass and this establishes their
connection to the normal modes of AX4 free molecules [91].
Sen and Thorpe [91] developed a simple model to study the vibra
tional density of states of aSi02. They used just the nearestneighbor
central Bornforce, Ks, between Si atoms bonded to 0 atoms, which
allowed them to study the transition from molecular to solidstate
behavior as 6 changes. They showed that because 0 is larger than a
critical angle 0C, where 08 = cos"1(2Mo/3Msi) = 112.4* for aSi02, effec
tive coupling among the tetrahedra leads to solidstate modes, rather
than molecular modes. Therefore the vibrational characteristics of
aSi02 are determined more by 0 than by the Si04 tetrahedra. Inclusion
of a small noncentral force does not modify these results, because the
nearneighbor noncentral force constant K is small so the high fre
quency optic modes are well represented by this model. K. is the bond
50
bending noncentral force function acting at right angles to the central
bond stretching force function, Ks (also known as a). Ka must be includ
ed when examining low frequency modes.
Sen and Thorpe [91] developed equations for the dependency on the
atomic masses of silicon and oxygen, Msi and Mo, the central force
function Ks (N/m), and 0 (), of the spectral limits of the two highest
frequency modes in the vibrational density of states of aSiO2
W2 = (Ks/Mo) (1 + cosO) (7)
w22 = (K/Mo) (1 cosO) (8)
32 = (Ks/Mo) (1 + cos9) + 4/3 Ks/Msi (9)
42 = (Ks/M) (1 cos9) + 4/3 Ks/Msi (10)
where w1, w2, w3 and w4 are the angular frequencies (rad/sec) of the
spectral limits of the two highestfrequency bands in the vibrational
density of states (VDOS) of aSiO2. These limits therefore equate to
four states in the VDOS, which account for four of the nine expected per
formula unit SiO2. The remaining five states are acoustical states
driven to zero frequency because K. = 0 in this model [87,88,91].
Equations (7)(10) (as well as equations (11) and (12)) remain
true if w (rad/sec) is replaced by the wavenumber value (cm'1) of the
frequency, M by the atomic weight of the atom, and Ks by Ks/0.0593,
where Ks (dyn/sec) 1000 Ks (N/m) [92]. Dimensional analysis of equa
tions (7)(10) shows that radians is missing as a dimensional unit, so
the equations do not balance. This is because the assumptions that had
to be made to solve the three body problem used for Sen and Thorpe's
51
model [91] of the vibrational density of states involved removing 0
(units of radians) as an implicit variable [93].
Bell and Dean assign wl (mW1) to the bond rocking (R), outof
plane motion of the Si0Si bridging bonds, w3 (= W3) to the bond
bending (B), or symmetric stretch (SS), motion of the SiOSi bridging
bonds, and w (m W4) to the bond stretching (S), or antisymmetric
stretch (AS), motion of the SiOSi bridging bonds [94] (Fig. 8). In Sen
and Thorpe's model [91] the bond rocking (R) motion perpendicular to the
plane of the SiOSi plane does not occur because there is no restoring
force for this vibration, i.e. K. = 0, so no bond length change is
involved in the vibration.
Galeener [92] developed a method for analyzing the vibrational
spectra and structure of AX2 tetrahedral glasses, based on interpreting
the vibrationalband limits calculated for the centralforce network
model developed by Sen and Thorpe [91]. The model assumed a certain
geometry for neighboring bonded silica tetrahedra which was not periodic
in space but had identical OSiO angles 0 = cos1'(1/3) = 109.5* and
common SiOSi angles 0. The dihedral angle, 6, was allowed to have any
value. The bonds possessed the types of vibrations known to exist in the
aSi02 structure. These are the bending, stretching and rocking motions
of the 0 atom, using the nomenclature in Fig. 8 [51].
A statistical distribution of 0 is used to simulate disorder in
the model. From his analysis of this model, Galeener concluded that the
centers of the two high frequency bands seen in aSi02, W3 (810 cm') and
W4, (1060 and 1200 cm"1) are associated with w3 and w4, evaluated at the
most probable intertetrahedral angle. Galeener [92] therefore developed
expressions for the calculation of the Si0 bondstretching constant,
52
Ks, and the SiOSi angle, 0, from the experimentally determined values
"3 = W3() W3 and w4 = w4(0) = W4, and the masses of the vibrating
atoms
Ks = 0.5 (w32+W42)M (l+4M/3Ms,)1 (11)
cosO = (W32W42) (32+w42)1 (+4M0/3Msi). (12)
Substitution of the W3 and W4 peak positions of aSiO2 into
equations (7)(12) yielded quantities that were within 10% of those
given by the calculation based on Born forces and realistic disorder
developed by Bell et al. [49,50,95], even though these expressions
involve the assumption that K. = 0. Galeener [92] therefore concluded
that the SenThorpe theory was realistic and could be used to analyze
the structure of aSiO2.
The splitting of the highestfrequency mode W4 into a wellsepa
rated transverseoptical longitudinaloptical (TOLO) pair is not
accounted for by this theory. The position of the so called baremode,
whose frequency is split by Coulomb interactions into the TOLO pair,
cannot be predicted by any known theory. Galeener [92] showed that the
bare mode lies nearer the LO frequency than the TO frequency. He applied
equations (11) and (12) to the measured values of W3 LO and W4 LO and
obtained values of Ks = 569 N/m and 0 = 130*, compared to the Xray
diffraction value of 144* [41]. Galeener [92] obtained values of Ks z
444569 N/m and 0 126130.
The calculated wavenumber of the lowestfrequency limit wI is very
similar to the main 450 cm'1 W1 Raman peak. From this, Galeener [92]
inferred that the dominant W1 450 cm'1 Raman peak occurred at the
53
lowfrequency edge of the band whose parentage is the breathing mode of
the isolated molecule. Therefore, the Raman matrix element (or coupling
coefficient) must peak sharply at this position. This demonstrates a
case where the coupling coefficient in Shuker's theory [9697] is not
constant, but is a sharp function of frequency over the band involved,
and peaks near one edge [92].
Raman scattering is known to arise largely from symmetrical
changes in bond length (bond polarization) rather than bond angle [92]
(as opposed to IR scattering which arises from asymmetrical vibrations).
The Raman strength is therefore maximum for the inphase stretching
associated with bendingtype motion at W1. It is reduced for the outof
phase stretching associated with the stretchingtype motion which occurs
at the theoretical W2 band edge. This explains why the main 450 cm'1
peak is so intense and the theoretical peak W2 is not visible in experi
mental Raman spectra. Galeener was therefore able to attribute on a
theoretical basis the main Raman peaks to vibrations of the structural
units of aSiO2. These are: 450 cm1 w= Wi, 800 cm'1 = 3 = W3, 1060
and 1180 cm'1 = 1 4 = W4, while W2 was assigned to 990 cm1. He
derived an expression relating the fullwidthhalfmaximum (FWHM) of the
Raman peaks to the FWHM of 0, i.e AO. The Xray diffraction derived
value of AO is ; 35 [41]. Galeener [92] calculated a value from W4 of
AO w 34*, which is the same within the resolution of the calculation.
Since the w, mode is near the W1 peak, the mode of vibration of W.
can be described [88]. It involves inphase symmetric stretch (SS)
motion of all the 0 atoms in the glass while the Si atoms are at rest.
This assignment has been supported by the observation of isotopic shifts
for 160 for 180 substitution in aSiO2 that are consistent with no Si
54
motion in Wi [88]. Thus W, was assigned to very strong Raman activity by
a relatively small number of states having SS motion, and should,
therefore, not normally correspond to a peak in the VDOS.
Therefore, the dominant lowest frequency Raman peak W1 involves
the symmetric motion of the 0 atom along a line bisecting the SiOSi
angle, the bending (B) motion [92]. Galeener preferred to call this the
symmetricstretch (SS) motion [92] (Fig. 9(a)). (The W1 peak is IR inac
tive. The low frequency IR peak at 480 cm"1, which does not equate to
the 450 cm'1 W1 or the 495 cm'1 DI Raman peak, is primarily due to the
rocking motion (R) of ESiOSi= bridging oxygen bonds (Fig. 8), but
includes some Si motion.) The next lower frequency W3 peak is both IR
and Raman active, but is most intense in the Raman mode because it is
mainly a symmetric vibration. W3 involves SS motion of the 0 atom, but
there is some Si motion depending on the ratio of the masses of O/Si,
the average 0 value and the coordination of the cation Si (Fig. 9(b)).
The high frequency W4 peak is also both IR and Raman active,
though it is a much more intense IR mode because it is an asymmetric
vibration. W4 involves motion of the 0 atom along a line parallel to
Si...Si (the line between the bridged atoms), the S motion in Fig. 8.
Galeener [92] calls this the asymmetricstretch (AS) motion (Fig .9(a)).
Lucovsky [98] presented evidence for the existence of a Raman
active peak in the 900950 cm'1 region. He approached the peak assign
ment from the school of thought involving the intrinsic defect state.
This is used by the optical fibre and Electron Spin Resonance (ESR)
fields, following the ideas of Mott [99] on the chalcogenide amorphous
semiconductors. Lucovsky assigned this peak to nonbridging oxygen atoms
C 1, (which means a chalcogen with a covalent coordination of 1 and a
Si si
OutofPhase
High Frequency,
(a) Bending or
Asymmetric
Stretching (AS)
W4 LO
1190 cm1
Si Si
InPhase
Low Frequency,
Bending or
Symmetric
Stretching (SS)
W1
450 cm1
9 P
Si Si 0
/
/ \
O 0
Silicon "Cage" Motion,
Involving some SS of the O Atom
W3 TO
790 cm1
W3 LO
810 cm1
Figure 9. Schematic of the normal modes of vibration in asilica. (a)
The outofphase (highfrequency) and inphase (lowfrequency) vibra
tions of two coupled SiO stretching motions, where only SiO stretching
is considered. (b) The type of motion suggested by various vibrational
calculations for silica polymorphs associated with the W3 Raman band at
800 cm1. After [94].
W4TO
1060 cmT1
56
charge state of 1) though he did not actually show a Raman spectra
showing this peak. Lucovsky assigned the 605 cm1 peak to threecoordi
nated oxygen atoms (C3), describing the peak as an intrinsic defect in
terms of the valencealternationpair model. Galeener [67,100103] and
Brinker et al. [5] have since shown that this assignment is wrong.
Bell [50] showed that the fit between experimental ballandstick
model and theoretical Raman curves for aSiO2 improved after further
refinement of the CRN model. The theory predicted the 1200 cm"1 peak and
slightly exaggerated the size of the 800 cm"1 peak due to too small a
cluster size. It did not predict the correct behavior of the 600 and 495
cm1 peaks due to lack of some unspecified symmetry in the SiO2 network
and the absence of three membered rings respectively.
McMillan [94] comes from the geochemical school of thought,
examining the silicate melt phase, or magma, in igneous processes. He
extrapolates the Raman vibrational spectroscopy of the equivalent glass
phase to the equivalent melt composition. McMillan reviewed the litera
ture of Raman spectroscopy of aSiO2 glasses, and their interpretation
in terms of structural models. He pointed out that the first successful
Raman spectra of aSiO2 was obtained by Gross et al. [104] in 1929.
McMillan [94] summarized his knowledge of the aSi02 Raman peaks.
These were: a) Two weak, depolarized bands depolarizationn ratio p
0.75) near 1060 and 1200 cm1, b) A strong band at 430 cm"1 which is
highly polarized and also asymmetric, partly due to thermal effects and
partly due to weak bands near 270 and 380 cm'1 which correspond to
maxima in the depolarized spectrum, c) Two weak sharp polarizable peaks
near 500 and 600 cm"1 of controversial origin, attributed to broken
SiOSi bonds, or to small siloxane rings. McMillan [94] dismissed
57
Phillips [52] assignment involving doublebonded Si=O linkages as not
being supported by abinitio molecular calculations, d) An asymmetric
band near 800 cm'1 with probable components near 790 and 830 cm1.
McMillan [94] also gave the current literature peak assignments to
structural vibrations. The high frequency bands were assigned either to
asymmetric SiO stretching vibrations within the framework structure, or
to the TO and LO vibrational components, separated in frequency by the
electrostatic field in the glass. The 430 cm1 peak was assigned to the
symmetric motion of the bridging oxygen in the plane bisecting the
SiOSi linkages. The 800 cm'1 peak was assigned to the motion of Si
against its tetrahedral 0 cage, with little associated O motion.
The vibrational modes of aSiO2 are highly localized [94], despite
the macroscopic disorder of the structure, as shown by the well defined
and highly polarizable Raman peaks. This suggests vibrating units with
high symmetry within the glass structure. The vibrational assignments
above were based on the energies (= frequencies) and symmetries of the
observed vibrational transitions. McMillan [94] did not give a detailed
description of the nature and extent of each mode, which is only
possible from a dynamical analysis of the system. The molecular struc
ture of a system defines the relative positions of its constituent atoms
and the interactions between them. If one or more atoms are moved from
their equilibrium position, the interatomic forces restore the system to
its equilibrium configuration. The atomic displacements executed during
this process are described by the equations of motion of the system,
whose solution are its normal modes of vibration. The mathematical
formulation for the dynamics of discrete molecules are well established
58
and the force constants for the system describe the curvature of the
potential energy surface near the equilibrium geometry [94].
For aSiO2 the assumed force constants are a function of the
particular model used to describe both the interatomic interactions and
the vibrational motions. Solution of the equations of motion for the
system using appropriate force constants gives the energies of the
vibrational transitions, and their associated atomic transitions. Using
these methods, vibrational calculations have been carried out on aSiO2
by considering the amorphous network as a single large network and by
considering small representative units, as discussed earlier. The
validity of such vibrational calculations is critically dependent on the
force constant model used and its relevance to the true interatomic
potential surface. Realistic force constants may be evaluated if this
surface is known analytically, which is not the case for silica [94].
Several methods are available to construct sets of force constants
designed to model interatomic interactions in aSiO2. The calculated
vibrational spectra are compared with the experimental spectra as a
criterion for the applicability of that force constant set. However, an
observed spectrum may be reproduced using a variety of force fields. If
the chosen force field does not approximate the true potential surface
then the calculated atomic displacements may not resemble the motions
associated with the true vibrational modes, although the Raman and IR
spectra may have been calculated to within experimental error. From
these considerations, a rigorous correlation of the vibrational proper
ties of aSi02 with its structural properites awaits a better under
standing of its interatomic bonding [94]. The vibrational calculations
performed in the literature [45,46,49,53,91] are subject to these
59
limitations, and the structural assignments to vibrational peaks can not
be taken much further than the general assignments discussed above.
All of these models have included an SiO stretching force
constant, Ks, with values varying from 300 to 700 Nm"1. Gibbs et al.
[105] carried out an abinitio molecular orbital (MO) calculation for
the SiOH4 molecule, giving Ks = 665 Nm1. This is consistent with most of
the calculations which have reproduced the highfrequency region of the
vibrational spectrum, associated with the Si0 stretching motions.
Inclusion of the nearestneighbor 0...0 interaction, which changes
during SiO stretching, might lead to slightly lower values.
Most MO calculations have also considered the 0SiO and SiOSi
bending forces, Ka and Kg respectively. The estimated K, value has
ranged from 20 to 70 Nm1, expressed as (l/d(Si0)2)(dE/d(d(SiO)2)},
where d(SiO) is the Si0 bond length and E is the theoretically
determined energy [94]. Kg has been estimated at 220 Nm1. Gibbs et al.
[105] calculated a similar value of 100 Nm"1 for K and 818 Nm1 (as a
function of the 6) for Kg for H6Si207 [94].
Revesz [70] discussed the directionality ratio, r, of silica
polymorphs and asilica. The directionality ratio r is a dimensionless
ratio originally mentioned by Phillips [106,p.337], defined as the ratio
of the nextnearestneighbor bondbending noncentral (directed) force,
1, to the nearestneighbor central (undirected) bonding force, a, so r =
S/a. The ratio r measures the covalency of a bond. As r increases the
covalency of the bond increases and the ionicity decreases, so the
directionality, i.e. the resistance to bending, increases. The ratio r
governs the vibrational density of states of aSiO2.
60
Phillips [106] discussed r for binary crystals of formula ANB8N,
for which a = Ks is the bondstretching force function of the AB bond.
There should be both ABA and BAB bondbending noncentral force
functions in ANB8N, i.e. Ka and K but Phillips does not distinguish
between them. The ABA bondbending force function Kg determines the
resistance to rotation of A around B, while the BAB bondbending force
function K. determines the resistance to rotation of B around A. These
are identical only if the charge distribution and valency are identical
in A and B, which is unlikely except in pure elements. The ionic radii
also have to be identical to avoid different steric effects such as are
seen in asilica. For diamond, r = 0.7 (which would explain its high
elastic modulus), while r = 0.3 for Ge and Si. These all have just one
value of 8 [106]. Phillips gives values of r [106] for some ANB8"N crys
tals without discussing whether r involves Ka and Kg in each crystal, so
it is unclear from [106] whether r = Ka/Ks or r = KB/Ks in this case.
In aSiO2 the 0SiO bondbending force, Ka, is larger than the
SiOSi bondbending force, Kg, because the 0...0 steric repulsion is
larger than the Si...Si steric repulsion. This is because not only is 0
much larger than Si but Si is tetravalent while 0 is bivalent. The
OSiO bond angle 0 = 109.5* is very rigid, while the SiOSi bond
angle, 0, is much more flexible, so Ka > Kg. The Si0 bond is the most
rigid, so Ks > Ka. Bock and Su [45], McMillan [69,94], Barrio et al.
[107,108], Gibbs et al. [105] and Galeener [92] calculated bond force
function values of the correct order, Ks > K, > Kg. The ratio r can be
Ka/Ks and KB/Ks, and 0 depends on Ka/Ks while 0 depends on Kg/Ks. The
vibrational spectroscopy of silica is determined by Ka/Ks and KB/Ks.
61
Ks, the SiO bond stretching force constant, is the largest and
consequently the dominant force function, so it is used in all vibra
tional models [45,912,107,108]. Some models also include a bondbending
forcefunction called 9, but they do not explicitly define 6 as either
K. or KB so it is unclear which force function they are talking about.
The next largest influence on the vibrational spectra of silica after Ks
is the next largest force function, which is K so 6 must be K. in
these vibrational models. For instance Barrio and Galeener [107,108]
model the vibrational spectra of aSi02 using a Bethe lattice and quote
a value for 6 of 78 N/m. They define 9 as the noncentral force con
stant, so must be the 0SiO bondbending force function Ka in this
case.
Revesz [70] calculates r for the polymorphs of silica from earlier
references which give the values of the appropriate force functions.
Revesz said that r is KB/Ks, where Kg is the force constant of the
SiOSi bending vibrations [70]. He gave a value for aSiO2 of r =
0.182. For Ks = 600 N/m, this gives a value of Kg = 109 N/m, which is
much too large to be the SiOSi bending force function. On the other
hand this value is very similar to the expected value of the OSiO
bending force function Ka. According to Sen and Thorpe [91], Ka/Ks 5 0.2
for AX2 glasses, where Ka is the OSiO bending force constant. Sen and
Thorpe [91] disagree with Revesz [70] over the definition of the ratio
r, although they agree that r k 0.2 in aSiO2. Revesz gives a value for
acristobalite of r = 0.199 calculated from values given by Rey [109].
Examination of [109] shows that Rey gives values for the OSiO bending
force constant, not the SiOSi bending force constant, so Rey [109]
62
disagrees with Revesz. Revesz [70] is therefore wrong in his definition
of the ratio r, and the correct definition is r = Ka/Ks.
Amorphous silica may be considered as a network of Si04 tetrahedra
polymerized by cornersharing each oxygen between two Si04 units. Sen
and Thorpe [91] found that the vibrations derived from Si0 stretching
in asilica depend on 0 between the tetrahedra. As this angle is larger
than 112* in aSiO2 (1440, in fact [41]) the stretching modes of adja
cent tetrahedra become coupled. This causes the highfrequency bands
(1060 cm1 and 1200 cm"1) of modes where the coupled Si0 stretches are
out of phase, giving the resultant oxygen motion parallel to the Si...Si
line (Fig. 9(a)). A lowfrequency set of modes (the 450 cm'1 W, peak)
where adjacent Si0 stretching is in phase give the resultant oxygen
motion in the plane bisecting the SiOSi bond (Fig. 9(a)), which agrees
with Galeener et al. [42,55,88,92]. This model does not predict the 800
cm1 Raman peak, which must involve other considerations. Bell and Dean
[51] did reproduce this peak, involving predominantly Si motion (consis
tent with the isotopic substitution experiments of Galeener and Geiss
berger [110]), as a silicon cage motion shown in Fig. 9(b).
Barrio and Galeener [107,108] tried another approach to modeling
the vibrational behavior of aSiO2. They used the Bethe lattice [111]
(which had already been done successfully by Sen and Thorpe [91]), an
infinite simply connected network of points, as an approximate disor
dered structure which only uses central bondlength restoring forces.
Barrio included the noncentral (or intrinsic angle restoring) forces by
specifying the positions of bonded atoms over a random distribution of
the dihedral angles at the successive branches. This caused a random and
uncorrelated dihedral angle, 6, as expected in aSiO2. They obtained
63
expressions for the vibrational density of states and the polarized
portion of the Raman response. Values of 0 = 154*, Ks = 507 Nm"1 and K 
78 Nm'1 gave the best fit to the central frequencies of the broad peaks
at 420 and 820 cm'1 and the width of the 420 cm' peak.
Barrio and Galeener claimed an improvement in theoretical spectra
to "nearperfect" [107] agreement with the vibrational density of states
(VDOS) produced by the largecluster calculations of Bell and Dean. They
did this by (a) averaging over realistic distributions of 0, and (b)
adding a small component to the frequency to correct for the known
tendency of the Bethe lattice to produce narrow bands. Both group VDOS
calculations are less accurate at < 100 cm'1 because of deficiencies in
the Born Ka forces and at > 800 cm1 because of neglected Coulomb
forces. The 495 and 606 cm'1 peaks are not reproduced because they arise
from defects in the structure not modeled by the Bethe lattice.
The Born noncentral force Ka is a twobody force which can accu
rately simulate the more accurately simulate the more realistic Keating
threebody noncentral force, except at the lowest frequencies [107].
Phillips [54,59] examined the Raman defect peaks in detail to try
to fit them into his model of aSiO2. Isotopic substitution of 160 by 180
showed a complete isotopic shift (e.g., D1 moves from 495 to 465 cm'1)
which implies little or no Si participation in these vibrations. This
conclusion is reinforced by direct measurement of the effect of replace
ment of 28Si by 30Si on the D1 and D2 frequencies. Within the limits of
the experimental resolution [110] nothing happens. These experiments
imply a pure 0 isotope shift for these peaks and require that the
molecular structures responsible contain a high degree of symmetry.
Phillips [54,59] model of aSi02 structure consisted of clusters having
64
the internal topology of cristobalite, a cubic structure with density 5%
greater than aSiO2. The Si atoms are arranged on a diamond lattice,
with the dominant surface texture of these cristobalite paracrystallites
having a (100) plane. The basic surface molecule is (01/2)2Si=0s on
crystallites of about 6.0 nm diameter. He assigns the 495 cm'1 peak to a
vibrational mode of the Os* atoms normal to the (100) surface normal,
i.e. parallel to the (100) surface plane.
The narrower a Raman peak, the larger the distance over which
structural units causing the peak must possess periodicity, so narrow
Raman peaks imply some structural order over a significant distance. The
problem is discovering the size of the significant distance. Phillips
[54,59] claims that the 6.0 nm periodicity of his clusters is easily
large enough to explain the narrowness of the D1 peak (FWHM 30 cm1).
This is refuted by Galeener and Wright [43]. Phillips [54] attributed
the D2 peak to a ring mode associated with intercluster crosslinking.
Galeener [103,112] reviewed the Raman and ESR spectroscopic
evidence for the structure of aSiO2. He pointed out that the properties
of vitreous silica depend on the thermal history of the sample, often
expressed as the fictive temperature, Tf, and the [OH] concentration.
The primary SiOH Raman peaks appear at W6 = 3700 cm"1 = SiOH vibration,
and W5 = 970 cm1 s SiOH vibration. He showed that the equilibrium
defect concentrations, [D1] and [D2], are independent of [OH], and
proportional to Tf. On the other hand the relaxation time to, i.e the
time it takes the sample to reach the equilibrium defect concentrations
is inversely proportional to [OH] and T. The Arhennius activation energy
for D1 and D2 are 0.14 and 0.40 eV respectively for the tetrasiloxane
and trisiloxane rings causing each peak. These are calculated from the
65
log of the percent area of the total reduced spectrum under D1 and D2
peaks plotted against inverse Tf. Figure 10 shows the observed depen
dence of the peak frequencies on Tf for pure aSiO2, with W1 and W3
increasing as Tf increases from 900 to 1500*C, and W4 TO and LO decreas
ing. These shifts are in the directions to be expected if the average 0
decreased, by an amount estimated to be by about 2*, as the aSiO2
density increases. The defect peak positions change very little in
comparison due to the rigidity of these small strained ring structures
compared to the larger rings of the bulk structure.
Raman spectroscopy provides information about structural features
of glass which have concentrations greater than about 1% [112], i.e. its
detection limit is > 1%. Electron Spin Resonance (ESR) can probe
structural features associated with defects at much lower concentra
tions, if the defects are spin active. Pure aSiO2 shows no detectable
ESR signals, so ESR signals are seen only after the sample is subject to
various kinds of radiation, including Cu Ka Xrays. The most important
of these signals is the E' line whose origin is the spin of an electron
in the unbonded sp3 of a 3bonded Si atom. The number of preexisting E'
defects is inversely proportional to [OH], and are more resistant to
their formation the lower is the fictive annealing T. These defects do
not relate to the nonbridging oxygen defects discussed earlier concern
ing Raman defects.
McMillan [69] summarized the vibrational studies of aSi02. He
discussed a defect peak seen at 910 cm1 in wet and dry aSi02 samples
which does not scale with any other defect peaks. This band occurred in
the region commonly assigned to the symmetric SiO stretching vibration
of an =Si0', or sSi=O group.

STRUCTURAL DENSITY Ds [g/cc]
151
Figure 28. The temperature dependence of the structural density of
silica xerogels, made from TMOS using acidified water, R = 16 and pH =
1.0, with ^ = 1.2 ran, 3.2 nm and 8.1 nm as indicated. After [183]
32
ing, while the elastic light scattering with no change in energy or
frequency is known as Rayleigh scattering. The energy of the scattered
light is analyzed using a spectrometer. Raman lines appear as weak peaks
shifted in energy from the Rayleigh line (Fig. 6). The positions of
these Raman peaks about the incident line correspond to the frequencies
of Raman active vibrations in the sample.
In Raman scattering, the light beam induces an instantaneous
dipole moment in the molecule by deforming its electronic wave function.
The atomic nuclei follow the deformed electron positions. If the nuclear
displacement pattern corresponds to that of a molecular vibration, the
mode is Raman active. The size of the induced dipole moment is related
to the ease with which the electron cloud may be deformed, described by
the molecular polarizability am. The Raman activity of a given mode is
related to the change in polarizability during the vibration. In general
the molecules containing easily polarizable atoms, such as I, S and Ti
have very strong Raman spectra. Similar molecules with less polarizable
atoms, such as Si, C and 0, have much weaker spectra. In contrast to IR
spectra, the most symmetric modes give the strongest Raman signals since
these are associated with the largest changes in polarizability.
The number of vibrational modes seen for a molecule is equal to
the number of classical degrees of vibrational freedom, 3N6. N is the
number of atoms in the molecule. For crystals, N is equal to Avagadro's
number, but most of the modes are not seen. This is due to the translat
ional symmetry of the atoms in the crystal. The vibration of each atom
about its equilibrium position is influenced by the vibrational motion
of its neighbors. Since the atoms are arranged in a periodic pattern,
the vibrational modes take the form of displacement waves travelling
77
Galeener [67,102,103,113] proposed that the D1 and D2 peaks at 495
cm"1 and 605 cm'1 are due to puckered 4membered silicate rings and to
planar 3membered silicate rings, respectively. They are connected to
the rest of the structure by elongated Si0 bonds. Figure 13 shows the
structure of the rings involved. Puckering of these rings always reduces
9 below the planar value. Figure 14 shows the energy per bridging bond
as a function of 6, showing the energy for each ring and their relation
ship to the equilibrium minimum energy value. The OSiO angle is always
around 109.5, with a narrow distribution. Table 1 lists the energy of
formation of each ring calculated from Fig. 14, showing their stability.
The breathing motion of 0 atoms in planar rings cause the frequency,
sharpness, strong polarization and lack of companion lines of the Raman
defect peaks. D2 rings have a concentration of about 1% in aSi02.
Revesz and Walrafen [121,122] directly contradict Galeener
[67,101103]. They assign the D1 peak at 495 cm"1 to planar 3membered
rings and the D2 peak at 600 cm'1 to planar and puckered 4membered
rings. Galeener's assignment has been proven to be correct [5].
Galeener [88] reviewed the neutron, Raman, and IR vibrational
spectra of aSi02, summarizing his own work in this area. He pointed out
that the Raman and IR spectra provide insight into vibrational modes,
but they do not provide a direct measure of the vibrational density of
states, VDOS or g(w). This is because the coupling coefficient linking
the spectra with the VDOS are not easily obtained and are sometimes
strong functions of w. The HV Raman spectrum did mimic g(w). He obtained
inelastic neutron scattering spectra, which give a direct measure of
g(w) for w > 250 cm'1, as the coupling coefficients varied slowly with
frequency. The data for crystalline and aSi02 were very similar,
BULK DENSITY [g/cc]
163
TIME AT 750C IHRS]
Figure 29. The increase with time at 750C of the bulk density Dfa of
sample #138, a type OX gel, after heating to 750C in 62 hrs in Florida
air. The open squares () are the experimental data points, while the
solid line is a third order regression with R2 = 0.990.
407
goes a stage of strain as H20 is removed during drying. It is possible
then that the changes in the W1 peak observed during H20 absorption are
due to strain in the aSi02 structure and that the Raman spectra are
responding to these changes as the absorption of H20 returns the main
peak to its original low Tp shape.
4.5 Conclusions
The rehydrolysis of a dehydroxylated silica gel is a two step
process involving adsorption of H20 molecules onto the D2 trisiloxane
rings on the internal pore surface (physisorption) followed by rehydrox
ylation via a dissociative bondbreaking reaction (chemisorption). D2
rehydrolysis occurs after a H20 molecule has been physisorbed onto a
strained Si3 atom, which is a Lewis acid since it possesses an unoccu
pied d orbital that is available as an electron acceptor. The reaction
kinetics of the rehydrolysis of D2 rings is therefore determined by the
ratelimiting H20 physisorption (adsorption) step [5,p.651], because the
subsequent dissociative chemisorption step is very rapid in comparison.
When the physical dimension (i.e. the gel sample size) of a gel is
small enough or rH is large enough, the rate of absorption of water from
an Rh = 100% atmosphere is large and the H20 physisorption (adsorption)
step onto the D2 rings is the rate determining step in D2 rehydrolysis.
When the physical dimension of a gel is large enough or rH is small
enough, as in the type OX and 2X gels investigated here, the rate of
transport of water molecules (i.e. the water absorption step) through
the pores to the surface D2 rings is the rate determining step because
the surface D2 rehydrolysis occurs more quickly than the water vapor
absorption. The transport of water molecules through the pores of a gel
D2 PEAK AREA, In [D2]/[Wt]
380
In TIME, In t [mins]
+ #136 0 #127 A #141 X #139
Figure 95. The natural log of the D2 trisiloxane curvefitted Raman peak
area, In [D2]/[Wt] plotted against the natural log of the time of
absorption, In t (mins), for samples #136, #127, #141 and #139.
50
bending noncentral force function acting at right angles to the central
bond stretching force function, Kg (also known as a). Ka must be includ
ed when examining low frequency modes.
Sen and Thorpe [91] developed equations for the dependency on the
atomic masses of silicon and oxygen, M$j and Mq, the central force
function Kg (N/m) and (), of the spectral limits of the two highest
frequency modes in the vibrational density of states of aSi02
Wl2 = (V^) (1 + cos) (7)
w22 = (Kg/Mj,) (1 cos) (8)
w32 (Kg/^) (1 + cos) + 4/3 Kg/Msj (9)
w42 = (Kg/Mjj) (1 cos) + 4/3 Kg/Msi, (10)
where w1, a>2, w3 and w4 are the angular frequencies (rad/sec) of the
spectral limits of the two highestfrequency bands in the vibrational
density of states (VDOS) of aSi02. These limits therefore equate to
four states in the VDOS, which account for four of the nine expected per
formula unit Si02. The remaining five states are acoustical states
driven to zero frequency because Ka = 0 in this model [87,88,91],
Equations (7)(10) (as well as equations (11) and (12)) remain
true if w (rad/sec) is replaced by the wavenumber value (cm'1) of the
frequency, M by the atomic weight of the atom, and Kg by Kg/0.0593,
where Kg (dyn/sec) = 1000 Kg (N/m) [92] Dimensional analysis of equa
tions (7)(10) shows that radians is missing as a dimensional unit, so
the equations do not balance. This is because the assumptions that had
to be made to solve the three body problem used for Sen and Thorpe's
INTENSITY [COUNTS]
214
figure 47. The evolution of the thermally reduced Raman spectr
sample 2XA, rH w 4.5 nm, during densification via viscous sinti
Tp increases from 400C to 1000C. (a) 1001350 cm'1, (b) 3500
as
cm'1.
STRUCTURAL DENSITY, Ds [g/cc]
166
SINTERING TEMPERATURE, Tp PC]
Ds = 1/((1/Db)Vp) R2 = 0.6508
Figure 30. The structural density Dg of type OX gels (rH = 1.2 ran)
calculated from Vp (measured using isothermal N2 sorption) and Db, using
Dg l/((1/Db)Vp) as a function of (a) the sintering temperature and
(b) the bulk density Du. The open squares () are the data points, and
the solid lines are 3r order regressions, giving Rz = 0.6508 and Rz =
0.9117 respectively.
108. The dependence of the characteristic loss tangent frequency
of relaxation R1, on the water content W at T = 25C,
showing that below Wc2 = 0.275 g/g the dependence of f51 on W
is no longer linear 444
109. The evolution of the susceptance spectra, log B [S/m] (log
f), as the length of the sample, and therefore the measuring
electrode separation, changes from 2.19 to 0.23 cm, for
sample #71, Tp = 180C 451
110. A simple schematic representation of the two models discussed
in the text, (a) Flat pore geometry, i.e. statistical
thickness, (b) Cylindrical pore geometry. Not to scale. . 461
111. The dependence of the log of the characteristic loss tangent
frequency of relaxation R1, f^ (Hz), on the log of the
statistical thickness, W/Sg (g water/1000 m2 = nm) for the
type OX gel samples B180 (which is actually sample #10A),
B650 and B800 at 25C, showing the slight increase in Wfa/S s
W.,/S as the stabilization T increases 465
c' a p
112. The DSC spectra of pure water, type OX gel sample A180 (rH
1.2 nm) with its pores fully saturated with absorbed water,
and type 2X gel sample C45 (rH 4.5 nm) with its pores fully
saturated with absorbed water. The dT/dt = 10C/min in
flowing dry nitrogen 466
113. The relationship between the average cylindrical pore radius,
rH (nm), and the surface silanol concentration, [Sig0H] (#
SigOH/nm2) for the silica gel samples investigated in Chapter
7 467
114. The dependence of the thickness of the bound adsorbed water
for the flat pore geometry model, W^S = Wc2/Sg, and the
cylindrical pore geometry model, Rfa, on the surface silanol
concentration, [Sig0H] (# Sis0H/nm2 ), from the DSC and DRS
analysis 468
115. The dependence of the thickness of the bound adsorbed water
for the flat pore geometry model, W^S s Wc2/Sg, and the
cylindrical pore geometry model, Rb, on the average
cylindrical pore radius, rH (nm), from the DSC and DRS
analysis 469
116. The evolution of the near infrared (NIR) absorption spectra
of type OX gel sample #114 as water is absorbed into its
micropores and the water content W increases from 0.0 g/g to
0.121 g/g 477
117. The change in the wavelength (tm) of the positions of the 2u1,
2u3 and 2v^ NIR peaks as W (g/g) increases in sample #114. . 479
xxii
483
Wc2 0.275 g/g. Sample #10A has a Sg = 752 mz/g, so the critical water
content Wc2 is equivalent to a statistical thickness of Wc2/Sg 0.36 g
H20/1000 m2 (Figs. 107 and 108). Fig. 102 shows that as W increases the
high frequency, unrelaxed dielectric constant, of #10A measured at
13 MHz also undergoes a change in slope at Wc/Sg 0.36 g/1000 m2 In
addition, Fig.102 shows that e'^W) undergoes another small but measur
able change in slope at Wc1 0.066 g/g = Wc1/Sg 0.088 g/1000 m2 For 0
< W < Wc1, e'u 75.57W + 3.488, R2 = 0.9997, for Wc1 < W < Wc2, e'u 
65.40W + 4.094, R2 = 0.9997, and for Wc2 < W < Wmax, 80.03W +
0.0351, R2 = 0.9992. Two changes in the slope of ^(W) have also been
observed (at 1 MHz) by Kurosaki [271] and by Nair et al. [238,p.973] at
similar values of Wc1 and Wc2.
Below W = 0.065 g/g it was not possible to tell if the dependence
of f1 on W also changed at Wc1 0.066 g in sample #10A, because f^
decreased below 5 Hz, which is the lowest measurable frequency of the
impedance spectrometer.
In #10A, the e'^W) slope changes occurred at the critical H20
contents Wc1 0.066 g/g and Wc2 0.275 g/g. Similar changes in the
slope of the dependence on W of G measured at 5 HHz, G5Hz, and G at 13
MHz, G13MHz, were also found at Wc1/Sg 0.088 g/1000 m2 and at Wc2/Sg
0.36 g/1000 m2. The density of H20 is 1.0 g/cc, so these statistical
thicknesses are equivalent to layers of adsorbed water Wc1/Scg 0.088 nm
and Wc2/Sg 0.36 nm thick. As discussed in Chapter 6, the dc conduc
tivity Gdc [257259] and the nuclear correlation relaxation time rf
[261] of H20 adsorbed in silica gels also undergo changes in dependence
on W at critical statistical thicknesses Wc1/Sg 0.065 nm and Wc2/Sfl
0.36 nm. Thus, all these properties of H20 adsorbed onto the internal
99
showed that the insitu Raman spectra of compacted fused silica are very
different from the Raman spectra obtained after removal.
2.5.1 Raman Spectroscopy of aSiCU Under Tensile Stress
Walrafen et al. [144] examined the tensile stress dependence of
the Raman transmission spectra of a stressed aSi02 optical fibre up to
3.34 GPa. They used the same elastic scattering baseline template for
each spectra obtained, but performed no thermal reduction. The D1 peak
was baseline corrected using a French curve to follow the main peak
shoulder on which the smaller peak is situated. They concluded that the
D1 peak increased in intensity, which visually it does. They did not
show the main and D1 peak positions, or consider the effect of movement
of the main peak on D1 peak shape and intensity, so this conclusion is
questionable. The main peak, the D2 peak and the 800 cm"1 peak do not
change in intensity with applied tensile stress, but the main peak
increased in width. They explain their observations in terms of revers
ible Si0 bond elongation and aSi02 network distortion, with no chemi
cally active sites created by a large tensile stress.
Kobayashi et al. [145] examined the effect of tensile stress on
the Raman spectra of aSi02 fibers. They concluded, in direct contradic
tion to all other work, that the 6 angle and d(SiO) are not affected by
the applied stress. The observed changes in the main 450 cm'1 peak are
due to changes in the OSiO bond angles.
Tallent at al. [132] and Michalske et al. [146] examined the Raman
spectra of aSi02 fibers under tensile stress, and observed that the
443, 491, 604, 792, 832, 1055 and 1187 cm"1 peaks shifted to 426, 486,
600, 769, 811, 1016 and 1164 cm"1 respectively at 10.3 GPa. This con
321
Dg 2.092 g/cc. For fused aSi02 compacted using a compressive force
[133], the linear regression (R2 = 0.62) fitted to the measured
[D2]/[Wt] values (Fig. 83) shows that [D2]/[Wt] is roughly constant as Dg
increases. For fused aSi02 with different Tf, the linear regression (R2
= 0.96) fitted to the [D2]/[Wt] values in Fig. 12 is shown in Fig. 83.
[D2]/[Wt] increases very quickly as Dg increases in comparison to type
OX gels. Overall, for a specified increase in Dg, [D2]/[Wt] increases by
very different amounts in each system so different mechanisms must be
causing the increases in Ds, and increases in [D2]/[Wt] can not be
causing the increases in Dg.
Table 9 summarizes the Dg changes in type OX gels above and below
Tsmax an<* the associated changes in [D2]/[Wt] Table 9 shows the calcu
lated equivalent changes in Dg in pressure compacted fused aSi02 [133]
and fused aSi02 with different Tf [100] caused by the changes in the
magnitude of [D2]/[Wt] measured in type OX gels during sintering.
[D2]/[Wt] increases by 0.057 below Tgmax and decreases by 0.050 above
T _v in type OX gels. Below T ,v an increase in [D5]/[Wt] of 0.057 is
associated with an increase in Dg 0.21 g/cc (He pycnometry) in type OX
gels, which equates to an increase in = 2.2120 2.1975 = 0.0145 g/cc
in fused aSi02 with different Tf. In pressure compacted aSi02 the
increase in [D2]/[Wt] as Dg increases is so small that the increase in Dg
for an increase in [D2]/[Wt] of 0.057 can not be calculated. Above Tgmax
a decrease in [D2]/[Wt] of 0.050 is associated with a decrease of Dg =
0.070 g/cc (He pycnometry) in type OX gels, which equated to a decrease
in Dg 2.2120 2.1993 = 0.0127 g/cc in fused aSi02 with different Tf.
The mechanism causing [D2]/[Wt] to increase in fused aSi02 as Tf
increases is roughly an order of magnitude too small to directly cause
LOG LOSS TAN GENT PEAK FREQUENCY [Hz]
443
LOG WATER CONTENT, log W [g H20/g GEL]
Fig. 107. The dependence of the log of the characteristic loss tangent
frequency of relaxation R.,, ftf1, on the log of the water content W at T
= 25C, showing that above Wc2 0.275 g/g the dependence of f1 on W is
no longer logarithmic.
[D2]/[Wt], (** D2 RINGS/UNIT VOLUME)
356
WATER CONTENT, W [g WATER/g GEL]
#124 + #136 O #127 A #141 X #139
Figure 89. The dependence on the water content W of the area of the D2
trisiloxane curvefitted Raman peak, as a fraction of the total Raman
spectrum area, for samples #124, #136, #127, #141 and #139.
vi
Vibrational quantum number
Vn,
Molar volume [cc/mole]
VP
Pore volume [cc/g] Db'1 Dg'1
Vv
Volume fraction of pores = (1p)
VDOS
Vibrational density of states
W
Water content [g water/g silica gel]
w/sa
Statistical thickness [g H20/1000 m2 = nm]
twt]
Total area under a reduced Raman spectrum except for the
970 cm'1 SiOH, the 495 cm'1 D1 and the 605 cm'1 D2 peaks
W1
Main asilica Raman peak at 450 cm'1
w2
Theoretical asilica Raman peak in 800950 cm'1 region
w3 TO, LO
Symmetric Si0 stretch (SS) peaks at 792, 828 cm'1 in the
Raman spectrum of asilica
W4 TO, LO
Asymmetric Si0 stretch (AS) peaks at 1066, 1196 cm'1 in
the Raman spectrum of asilica
w5
Raman peak of SiOH stretch vibration at 970 cm"1
W6
Raman peak of SiOH stretch vibration at 3750 cm"1
WANS
Wide angle neutron scattering
WAXS
Wide angle Xray scattering
VSa Wc2/Sa
Bound statistical thickness [g H20/1000 m2 = nm]
Wb s Wc2
Bound water content [g H20/g Si02 gel]
Wc1
The first critical water content [g H20/g Si02 gel]
Wd/Sa
First critical statistical thickness 0.088 g H20/1000 m2
s nm
Wc2 s Wb
The second critical water content [g H20/g Si02 gel]
Wc2/Sa VSa
Second critical statistical thickness 0.36 g H20/1000 m2
= nm
VSa
Free statistical thickness [g H20/1000 m2 = nm]
Wf
Free water content [g H20/g Si02 gel]
xxx i i
POROUS SILICA GEL MONOLITHS:
STRUCTURAL EVOLUTION AND INTERACTIONS WITH WATER
By
STEPHEN WALLACE
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1991
ACKNOWLEDGEMENTS
It is impossible for me to thank all the people who have helped me
during this journey through graduate school, but I would especially like
to thank my advisor Dr. Larry L. Hench for his guidance, advice, encour
agement, patience and understanding, but especially for his patience and
support, without which this dissertation would not have seen the light
of day. His introduction to the strange and wonderful world of Gator
basketball was also a welcome gift!
I would like to thank Dr. David E. Clark, Dr. Eric A. Farber, Dr.
Robert W. Gould, Dr. Joseph H. Simmons and Dr. Jon K. West for their
help, advice and encouragement over the years. I would also like to
thank Dr. C. Jeffrey Brinker and Dr. George W. Scherer for their
helpful, thoughtprovoking discussions and their original contributions
to this field. I am grateful to Mr. Guy P. Latorre for his help and
technical advice. 1 would especially like to thank him for not allowing
me to become the longest serving member of Dr. Hench's technical staff!
It is with great sadness after his sudden recent death that I
recognize the role of Dr. Donald Ulrich in the completion of this work.
He and the Air Force Office of Scientific Research have been totally
supportive in both the funding and the scientific endeavors involved. I
am very grateful for the opportunities that their support provided.
I would finally like to acknowledge a chance encounter on Green
St., Urbana, without which none of this would have occurred, and the
financial assistance of the Elizabeth Tuckerman Scholarship Foundation,
which made graduate school a little easier.
ii
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ii
LIST OF TABLES viii
LIST OF FIGURES x
KEY TO SYMBOLS xxiiii
ABSTRACT xxxiiii
CHAPTER 1 INTRODUCTION 1
PART 1 STRUCTURAL AND TEXTURAL EVOLUTION OF POROUS
SILICA GELS DURING SINTERING AND DURING WATER
ABSORPTION 6
CHAPTERS
2 A CHRONOLOGICAL LITERATURE REVIEW OF THE STRUCTURE AND THE
VIBRATIONAL SPECTROSCOPY OF AMORPHOUS SILICA 6
2.1 The Structure of Amorphous Silica 6
2.1.1 The Categories of the Types and
Structure Concepts of aSilica 6
2.1.2 Structural Models of aSilica 7
2.1.3 TEM Studies of aSilica Structure 18
2.1.4 Molecular Dynamic Simulations of
the Structure of aSilica 19
2.1.5 Molecular Orbital (MO) Calculations of
the Structure of aSilica 20
2.1.6 Bonding and Structure Relationships in
Silica Polymorphs 22
2.2 The Theory of Raman and IR Scattering 30
2.3 Modelling the Vibrational Behavior of aSilica .... 44
2.4 Raman Spectroscopy of aSilica 68
2.5 The Density, Spectroscopy and Structure of
Pressure Compacted aSilica 81
iii
2.6 Raman Spectroscopy of Neutron Irradiated aSilica . 100
2.7 Theoretical Correction of Raman Spectra 101
2.8 Curvefitting the Raman Spectra of Silica Gels 109
2.9 Raman Spectroscopy of Silica Gels 121
2.10 FTIR Spectroscopy of Silica Gels 130
2.11 NMR spectroscopy of silica gels 131
2.12 The Structural Density of Alkoxide
Derived Silica Gels ..... 134
3 STRUCTURAL AND TEXTURAL ANALYSIS OF POROUS SILICA GELS DURING
SINTERING 153
3.1 Experimental Procedure 153
3.1.1 The Production of the Silica Gel Monoliths . 153
3.1.2 Isothermal Nitrogen Adsorption 155
3.1.3 Calculation of Structural Density from N2
Sorption at P/PQ = 0.999 156
3.1.4 Water pycnometry 156
3.1.5 Helium Pycnometry 158
3.1.6 Raman Spectroscopy 159
3.1.7 Thermogravimetric Analysis (TGA) 161
3.1.8 Differential Scanning Calorimetry (DSC) . 161
3.1.9 29Si Magic Angle Spinning Nuclear Magnetic
Resonance (MAS NMR) 161
3.2 Results 161
3.2.1 Structural and Textural Property Measurements 161
3.2.2 The Calculation of Dg from V and Dfa
Using Vp = 1/Db +1/Dg . . 164
3.2.3 Water Pycnometry 169
3.2.4 Helium Pycnometry 175
3.2.5 Textural Properties of HF Catalyzed Silica
Gel Monoliths 186
3.2.6 Thermogravimetric Analysis 193
3.2.7 Raman Spectra of the Silica Gels 193
3.2.8 Curvefitted Raman Peak Positions 224
3.2.9 Curvefitted Raman Peak Areas 235
3.3 Discussion 253
3.3.1 Comparison of the Values of the Structural
Density Dg Calculated from Isothermal N2
Sorption and from H20 Pycnometry 253
3.3.2 The Dependence of the Magnitude of Vp on the
Experimental Techniques Used to Measure V . 254
3.3.3 Helium Pycnometry 262
3.3.4 Comparison to Earlier Work 265
3.3.5 Reason for the similarity of Dgmax for type
OX, 2X and 5X gels 265
iv
3.3.6 The Raman Spectra of the Silica Gels 274
3.3.7 Separation of the Condensation and Viscous
Sintering Processes 279
3.3.8 Thermal Dependency of D., concentration 281
3.3.9 Comparison of Dynasil and Dense Silica Gels 282
3.3.10 Relationship between the W3 and W^ Raman peak
positions and Dg 283
3.3.11 Molecular Orbital Explanation of the
Dependence of d(SiO) on 283
3.3.12 Theoretical Relative Dg Calculation 286
3.3.13 29Si MASS NMR of gels 296
3.3.14 Comparison of 6 Calculated from MASS NMR and
Raman Spectra 300
3.3.15 Explanation of the Increase of Dg to Dgmax at
T 301
smax
3.3.16 Possible Structural Mechanisms of Dg Increase
Below Temov 315
smax
3.3.17 MASS NMR versus Raman spectra between T =
200 and 400C 330
3.3.18 The Magnitude of Dgmax 333
3.3.19 Dependence of Dg of Fused aSi02 on [OH] . 334
3.4 Conclusions 336
4 STRUCTURAL ANALYSIS OF POROUS SILICA GELS DURING THE
ABSORPTION OF WATER INTO THE GEL'S MICROPORES 343
4.1 Introduction 343
4.2 Experimental Procedure 348
4.3 Results 350
4.4 Discussion 363
4.4.1 The Movement of H20 Molecules Through Pores . 363
4.4.2 Water Vapor Absorption 375
4.4.3 D2 Rehydrolysis Rate Analysis in type OX gels 377
4.4.4 The D2 Rehydrolysis Equilibrium Constant Kc
for type OX gels 382
4.4.5 D2 Rehydrolysis Rate Analysis in type B2 gels
[33,175] 386
4.4.6 The Tetrasiloxane D1 Peak 393
4.4.7 The D, Rehydrolysis Equilibrium Constant Kc
for type OX gels 394
4.4.8 SigOH Concentration During Rehydrolysis .... 399
4.4.9 SenThorpe Central Force Function Analysis Of
the Raman Spectra 404
4.4.10 The effect of H20 absorption on the main 430
cm*1 W1 Raman Peak 406
4.5 Conclusions 407
4.6 A Summary of the Structure and Texture of Alkoxide Derived
Silica Gels During Sintering and Water Adsorption . 410
V
PART II THE STRUCTURE OF WATER ABSORBED INTO THE
MICROPORES OF A MONOLITHIC SILICA GEL 413
CHAPTERS
5 DIELECTRIC RELAXATION ANALYSIS OF WATER REMOVAL FROM A TYPE OX
SILICA GEL MONOLITH 413
5.1 Introduction 413
5.2 Theory 414
5.3 Experimental Technique 421
5.4 Results and Discussion 423
5.6 Conclusions 432
6 DIELECTRIC RELAXATION ANALYSIS (DRS) OF WATER ABSORBED IN
MONOLITHIC POROUS SILICA GELS 433
6.1 Introduction 433
6.2 Literature Review 434
6.2.1 Dielectric relaxation 1 (R^ 434
6.2.2 Dielectric Relaxation 2 (R2) 435
6.2.3 Dielectric Relaxation 3 (R3) 436
6.3 Objective 436
6.4 Method 438
6.5 Results 438
6.6 Discussion 446
6.7 Conclusions 453
7 STRUCTURAL ANALYSIS OF WATER ADSORBED IN THE PORES OF ALKOXIDE
DERIVED SILICA GEL MONOLITHS 455
7.1 Introduction 455
7.2 Experimental Procedure 457
7.2.1 Dielectric Relaxation Spectroscopy (DRS) . 457
7.2.2 Differential Scanning Calorimetry (DSC) . 458
7.3 Results and Discussion 460
7.4 Conclusions 474
vi
8 NEARINFRARED SPECTROSCOPY OF WATER ADSORPTION IN A SILICA GEL
MONOLITH
8.1 Introduction
8.2 Experimental Procedure
8.3 Results
8.4 Discussion
8.5 Conclusions
9 DISCUSSION ON THE BEHAVIOR OF WATER ADSORBED INTO POROUS
SILICA GELS
9.1 The Structure of H20 Absorbed into Microporous Silica
Gels
9.2 H+ NMR Analysis of Water Absorbed in Micropores . .
9.3 Structural Explanation of the Magnitude of Wc1/Sa . .
9.4 Structural Explanation of the Magnitude of Wc2/Sg . .
9.5 Explanation of the Observed Changes in Slope of the
e'u(W) Plot
9.6 The Dependence on W/Sa of the Mechanism of Proton
Conduction
9.6.1 The Proton Conduction Mechanism for Wc1< W < Wc2
9.6.2 Proton Conduction Mechanism for W,< W < Wm=v
cZ max
9.7 Summary of the Proton Conduction Mechanisms in Adsorbed
Water
9.8 Dissociation constant of adsorbed H20 versus bulk H20 .
9.9 Magnitude of Drift and Effective Velocity
9.10 Tunneling Theory
9.11 Conclusions and Future Work
APPENDIX RAMAN SPECTRUM THERMAL REDUCTION FLOWCHART
REFERENCES
BIOGRAPHICAL SKETCH
475
475
476
476
481
481
482
482
486
487
488
490
491
496
498
499
500
501
502
503
506
507
522
vii
LIST OF TABLES
Table Page
1. The estimated energy of the formation of planar silicate
rings of order n in aSi02 calculated from Fig. 14. After
[67] 80
2. Textural and structural properties of the type OX silica gel
discs used to calculate their structural density from their
bulk density and pore volume, Dg 1/((1/Db)V ) (Fig. 30),
rH = 1.2 nm 168
3. Textural and structural properties of type OX silica
gelcylinders, rH 1.2 nm, which were used to measure
structural density using H20 pycnometry (Fig. 31) 172
4. Textural properties of silica gel monoliths stabilized at
200C as a function of HF concentration (Fig. 33) 176
5. Table 5. The data used to plot Fig. 34. (a). Structural
density of type OX, 2X and 5X silica gels powders measured
using helium pycnometry, plotted in Fig. 34(a) 181
Table 5 (b). Extrapolated data used to plot Fig. 34(b). . 182
6. Table 6. The textural properties of type OX, 2X and 5X
silica gels. (a). Textural properties of the type OX
cylindrical silica gels characterized by Raman Spectroscopy,
plotted in Figs. 35, 36 and 37 183
Table 6 (b). Textural properties of the type 2X cylindrical
silica gels characterized by Raman Spectroscopy 184
Table 6 (c). Textural properties of the type 5X cylindrical
silica gels characterized by Raman Spectroscopy 185
7. Position, height, width as FullWidthHalfMaximum (FWHM),
and area of the Gaussian peaks curvefitted to the Raman
spectrum of sample OXA stabilized at 400C (Fig. 42) 206
8. A comparison of the properties of densified metalalkoxide
derived silica gels and Dynasil 282
9. Summary of a) Dg changes measured in type OX silica gels in
particular Tp ranges and the Db and [D2]/[Wt] change
viii
322
occurring in the same T ranges, and b) the Dg change caused
by a change in the [D2]/[Wt] of the same magnitude as
measured in the type OX gels in (i) Suprasil with different
Tf [100], and (ii) pressure compacted fused aS102 [133].
10. Properties of the cylindrical silica gel samples used for
H20 absorption studies 352
11. Some textural and structural values of type OX gels at
several stabilization temperatures Tp and water contents W. 411
12. Some structural and textural values of metalalkoxide
derived silica gels and of water absorbed into their pores. 464
13. NIR Transmission Peaks of H20 Molecules Hbonded to Sig0H. 478
14. Activation energies measured for relaxation R1 in type OX
gels at W = 499
ix
LIST OF FIGURES
Figure Page
1. The bulk density Db of different Type I/II and Type III/IV
commercial aSi02 as a function of fictive temperature Tf.
After [38]. Their bulk and structural densities are identical
because Vp = 0.0 cc/g 8
2. The relative orientation of two corner sharing silica
tetrahedra, SiO^, showing the bridging oxygen bond angle, 9,
the siliconoxygen bond length, d(SiO), the OSiO bond
angle, and the tetrahedral angles, 8 and A, which define
the angular orientation of the tetrahedra about their
bridging Si0 bonds. After [56] 15
3. The Si0 bond length as a function of Sec(0) for the silica
polymorphs low tridymite, low quartz, and coesite. The
d(SiO) have a standard deviation < 0.005 . The linear fit
line is the best fit linear regression analysis of all the
data points. After [74] 26
4. A comparison of the experimental d(SiO) in coesite (upper
curves in (a) and (b)) with those calculated for the bridging
d(SiO) in a disilicate molecule, H6Si207 (lower curves in (a)
and (b)). d(SiO) varies nonlinearly with 9 and linearly with
fg 1/(1 + A2), where A2 = Sec(0) is called the
hybridization index of the bridging 0 atom because its state
of hybridization is given by the symbol sp*2. After [76]. ... 27
5. Potential energy surface for the disilicate molecule, H6Si207,
plotted as a function of d(SiO) and 9. The contours
represent increments in energy of 0.005 a.u. = 0.6257
kcal/mole relative to the minimum energy point (1091.76678
a.u.) denoted by the cross. Increasing contour numbers
represent increasing energy. The dashed line represents the
bond lengths and angles for the disiloxy groups in the silica
polymorphs coesite, tridymite, low cristobilite and aquartz.
After [76] 28
6. The principles of Raman scattering, (a) The incident laser
beam, energy E, passes through the sample and the scattered
light is detected to the spectrometer, (b) The Raman spectrum
consists of a strong central peak at the wavelength of the
laser energy E due to the Rayleigh scattering, and the much
weaker Raman shifted lines at Ee1, where ei = hv^ correspond
to the energies of vibrational transitions in the sample in
x
cm'1, where E = 0 cm'1. Stokes Ramanshifted frequencies (Ee)
are positive wavenumber values, and antiStokes Ramanshifted
frequencies are negative wavenumber, (c) The energy level
diagram for Rayleigh and Raman scattering. There are two
energy levels which are separated by an energy e hi/, where
v is the vibrational frequency. The incident laser photon,
energy E, excites the vibrational mode to a shortlived (10'14
sec) electronic "virtual state", which decays with the
release of a photon. When the final vibrational state of the
molecule is higher than that of the initial state, the
released photon energy is Ee, and StokesRaman scattering
has occurred. When the final state is lower, the released
photon has energy E+e, and antiStokes scattering has
occurred. When the initial and final states are the same,
Rayleigh scattering has occurred and the incident and
released photons have the same energy E. After [81] 34
7. The various types of crystal lattice vibrations, (a) The
wavelength of this lattice mode is long compared to the
crystal lattice constant, a, so the mode lies at the center
of the Brillouin zone (k = 0). (b) This mode has wavelength A
2a, and lies at the edge of the Brillouin zone (k = 7r/a) .
The waves in (a) and (b) represent transverse lattice
vibrations for a monatomic chain of atoms, (c) This
illustrates a longitudinal lattice vibration for the same
monatomic chain, (d) For any crystal, there are three lattice
vibrations where all the atoms in a unit cell move in phase
in the same direction. These are the acoustic modes, (e) For
crystals with more than one atom in the primitive unit cell,
there are modes where atoms in the unit cell move in opposing
directions (illustrated for a diatomic chain). These motions
can generate a changing dipole moment and hence interact with
light. These are called optic modes, (f) A typical dispersion
curve in one direction in reciprocal space for a crystal, in
this case with n = 4 atoms in its unit cell. Only long
wavelength lattice vibrations (near k = 0) can be infrared or
Raman active due to the long wavelength of light compared
with crystal lattice spacings, which are marked with dots.
After [81] 36
8. Normal vibrations of a disilicate molecular unit in aSi02.
The axes point along the direction in which the bridging 0
atom moves in the bond bending, stretching and rocking normal
modes. These normal modes correspond to peaks in the Raman
spectra of aSi02. The bondbending axis is parallel to the
bisector of the SiOSi angle, and is assigned to the W3 peak
at 800 cm'1. The bond stretching axis is perpendicular to this
bisector, but still in the SiOSi plane, and is assigned to
the W^ peak at 1060 cm'1 and 1200 cm'1. The bond rocking
direction is orthogonal to the other axes and is normal to
the SiOSi plane. After [85] 46
9. Schematic of the normal modes of vibration in asilica. (a)
The outofphase (highfrequency) and inphase (low
xi
frequency) vibrations of two coupled Si0 stretching motions,
where only Si0 stretching is considered, (b) The type of
motion suggested by various vibrational calculations for
silica polymorphs associated with the W3 Raman band at 800
cm'1. After [94] 55
10. The dependence on the fictive temperature Tf of the Raman peak
frequencies of a sample of GE214 fused asilica. The changes
in the broad network peaks (W.) in various directions are
consistent with reduction in 9 as Dg increases. The much
smaller shift in the positions of the D1 and D2 ring peaks are
consistent with their assignment to regular tetrasiloxane and
trisiloxane rings respectively in an otherwise more
disordered network. After [1123] 66
11. The Raman spectrum of fused asilica at various temperatures.
The dots represent the low temperature spectrum calculated
from the room temperature spectrum after it had been
thermally corrected assuming first order processes, as
discussed in the text. After [115] 70
12. The area of the D2 Raman peak, as a fraction of the total area
of the Raman spectra, versus Db. (a) For a sample of Suprasil
W1 at the indicated Tf. (b) the data from (a) extrapolated to
higher densities and compared to samples of asilica
densified via irradiation with neutrons to the indicated flux
densities. After [100] 75
13. Planar Si0 rings of order n = 2, 3, 4 and 5, with SiOSi
angles 9 given for i> = 109.5, the tetrahedral value [67]. ... 76
14. The dependence of the energy of an sSi0Si= bridge on 9,
estimated using theoretical MO results. This enables
estimation of the energy of formation of various planar rings
having the angles 9n marked in the figure and listed in Table
1. The arrows show the tendencies for the puckering and
unpuckering of silicate rings. After [67] 78
15. Comparison of the thermally reduced Raman spectra (a) of
fused asilica with the imaginary parts of the infrared
derived transverse (b) and longitudinal (c) dielectric
functions. Peaks in e2 = Im(e) and Im(e'1) mark transverse
and longitudinal optical vibrational modes, respectively.
After [88] 79
16. Probability distributions, (a) The probability distribution
of the tetrahedral bond angles, rp, in undensified (dashed
line) and 24%densified (solid line) samples of fused a
silica calculated from the distributions of the isotropic
hyperfine constants, Ajg0. (b) The probability distribution of
defect d(SiO) obtained from the i/i distributions in (a) using
equation (16). After [140] 93
xii
17. Variation in the vibrational peak positions and 9 of Si02 as a
function of compacted density 94
18. Contributions to the background in the Raman spectrum of
porous Vycor. The upper dashed spectra is the experimentally
determined raw Raman spectrum. The lower solid spectra is the
corrected spectrum with the Rayleigh elastic scattering and
the high frequency fluorescent background subtracted [85]. Ill
19. The thermally reduced Raman spectra of a sample of asilica
with 5 wt% H20 dissolved in it, showing the Gaussian peaks
used to curvefit the spectra, and the residual difference
remaining when the curvefitted peaks are subtracted from the
Raman spectra. After [173] 119
20. The Raman spectra of silica gels at different stabilization
temperatures during densification compared to the spectrum of
fused asilica. The large background intensity at Tp = 200C
is due to fluorescence, which is gone by Tp = 400C as the
organics burn out. Spectra I at T = 800C is in a part of the
gel which is still porous, while spectra II is from a fully
dense part of the gel. After [24] 123
21. The relative bulk density, the relative structural density
(calculated from Vp and Dfa) and the first and second DSC
scans, DSC1 and DSC2 respectively, for silica gel A2, made
from TEOS with R = 5 and pH = 0.95. After [5,28,29] 126
22. The temperature dependence of the structural density Dg of two
silica gel samples. Sample A was made with distilled water
with no catalyst added. Sample B was made with distilled
water containing 0.0085% NH^OH. After [9] 135
23. The temperature dependence of the structural density of
monodispersed silica gel powders made by the base catalysis
of TEOS using excess NH^OH [6], After [179] 136
24. The temperature dependence of the shrinkage and structural
density of a 71% Si02 18% B203 7% A1203 4% BaO
borosilicate gel, with R = 5 and pH = 6.8, heated at 2C/min.
After [5,12,29] 140
25. The temperature dependence of the weight loss, shrinkage and
surface area of silica gel sample A2, made from TEOS with R =
5 and pH = 0.95, heated at 2C/min in air. After [5,28,29], 142
26. The temperature dependence of the bulk and structural density
of a silica aerogel made from TMOS using distilled water with
no catalyst, using methanol as a mutual solvent. After [17], 148
27. The dependence on the bulk density of the structural density
of a silica aerogel made from TMOS using acidified water and
methanol, giving a pH 2. After [18] 149
xiii
28.
The temperature dependence of the structural density of
silica xerogels, made from TMOS using acidified water, R = 16
and pH = 1.0, with rH = 1.2 nm, 3.2 nm and 8.1 nm as
indicated. After [183] 151
29. The increase with time at 750C of the bulk density Db of
sample #138, a type OX gel, after heating to 750C in 62 hrs
in Florida air. The open squares () are the experimental
data points, while the solid line is a third order regression
with R2 = 0.990 163
30. The structural density Dg of type OX gels (rH = 1.2 nm)
calculated from V (measured using isothermal N2 sorption) and
Db, using Dg = l/( (1/Db)Vp) as a function of (a) the
sintering temperature and (b) the bulk density Dfa. The open
squares () are the data points, and the solid lines are 3rd
order regressions, giving R2 = 0.6508 and R2 = 0.9117 respec
tively 166
31. The structural density Dg of type OX gels (rH = 1.2 nm)
measured using water pycnometry, as a function of (a) the
sintering temperature, and (b) the bulk density Db. The open
squares () are the data points, while the solid lines are
the third order regressions, giving R2 = 0.8716 and R2 =
0.8513 respectively 170
32. A comparison of the changes observed in Dg of silica gels, (a)
The dependence on Db of the Dg of type OX gels measured using
HjO pycnometry () and calculated from Dg = l/((1/Dfa)Vp) (0).
(b) The dependence on T of the Dg of type OX gels measured
using H20 pycnometry (), Dg = l/((1/Db)Vp) (0) and helium
pycnometry (X) 173
33. The dependence on the HF concentration, [HF] (mole/liter H20),
of the textural properties of the silica gels investigated
here, (a) Db (g/cc) versus [HF]. (b) V (cc/g) versus [HF].
(c) Sg (m2/g) versus [HF] (d) rH (nm) versus [HF] 177
34. The dependence of the structural density measured using
helium pycnometry on (a) T [C], and (b) Db [g/cc], for
sample 0XA, rH 1.2 nm (), sample 2XA, rH 4.5 nm (0) and
sample 5XA, rH 9.0 nm (x). The solid lines in (a) are best
fit 5th order linear regressions 187
35. The dependency on the sintering temperature Tp of the bulk
density, Db, of the cylindrical samples characterized using
the Raman spectrometer. OX (), 0XA (+), 2X (0), 2XA (a), 5X
(x), 5XA (v) 189
36. The dependency on the sintering temperature Tp of the surface
area, Sg, of the cylindrical samples characterized using the
Raman spectrometer. OX (), 0XA (+), 2X (0), 2XA (a), 5X (x),
5XA (v) 190
xiv
37.The dependency on the sintering temperature T of the average
pore radius, rH, of the cylindrical samples characterized
using the Raman spectrometer.
(a), 5X (x), 5XA (v). ...
OX (), OXA (+), 2X (0), 2XA
191
38. The thermogravimetric analysis (TGA) curves of powdered
samples of type OX, 2X and 5X gels heated in flowing dry
nitrogen as 10C/min. The weight loss observed below 180C is
due to the loss of H20 previously absorbed into their pores. 192
39. The raw, unreduced Raman spectrum of Dynasil. (a) 1001350
cm'1, (b) 36003800 cm'1. The peak assignments of aSi02 are
shown 197
40. The thermally reduced Raman spectrum of Dynasil. (a) 1001350
cm'1, (b) 36003800 cm'1. The reduced Raman spectrum, the
curvefitted Gaussian peaks and their peak positions (PP), and
the fitted spectrum calculated from the addition of the
curvefitted peaks are shown 199
41. The raw experimental Raman spectrum of silica gel sample OXA
stabilized at 400C for 400C. (a) 1001350 cm'1, (b) 3600
3800 cm'1 201
42. The thermally reduced Raman spectrum of silica gel sample OXA
stabilized at 400C for 24 hrs. (a) 1001350 cm'1, (b) 3600
3800 cm'1. The reduced Raman spectrum, the curvefitted Gaussi
an peaks and the fitted spectrum resulting from the addition
of these peaks are shown 203
43.The thermally reduced Raman spectra from Fig. 42(a) of sample
OXA stabilized at Tp = 400C from a different angle 207
44. The thermally reduced Raman spectrum from Fig. 42(a) of
silica gel sample OXA stabilized at 400C, along with the
residual intensity left after the curvefitted spectrum is
subtracted from the experimental spectrum, giving x2 =
127,685 208
45. The evolution of the raw, unreduced Raman spectra of sample
OXA, rH = 1.2 nm, during densification via viscous sintering
as T increases from 400C to 900C. (a) 1001350 cm'1, (b)
35003800 cm'1 210
46. The evolution of the thermally reduced Raman spectra of
sample OXA, rH = 1.2 nm, during densification via viscous
sintering as T increases from 400C to 900C. (a) 1001350
cm'1, (b) 35003800 cm'1 212
47. The evolution of the thermally reduced Raman spectra of
sample 2XA, rH 4.5 nm, during densification via viscous
sintering as T increases from 400C to 1000C. (a) 1001350
cm'1, (b) 35003800 cm'1. 214
xv
48. The evolution of the thermally reduced Raman spectra of
sample 5XA, rH 9.0 nm, during densification via viscous
sintering as T increases from 400C to 1150C. (a) 1001350
cm'1, (b) 35003800 cm'1 216
49. This shows that the concentration/unit area of internal pore
surface of the D2 trisiloxane rings, [D2]/[Wt]/Sa, exhibits the
same dependence on Tp for sample OX as for sample 0XA within
the resolution of the curvefitting analysis in their
respective T ranges 221
50. This shows that the concentration/unit volume of the D2
trisiloxane rings, [D2]/[Wt] exhibits the same dependence on
Tp for sample 2X and sample 2XA within the resolution of the
curvefitting analysis in their respective T ranges 222
51. This shows that the ratio of the concentration/unit volume of
the D2 trisiloxane rings and the D1 tetrasiloxane rings,
[D2]/[D.,], exhibits the same dependence on Tp for samples 5X
and 5XA within the resolution of the curvefitting analysis in
their respective T ranges 223
52. The dependence on the sintering temperature of the D1 tetra
siloxane ring curvefitted Raman peak position (PP) for
samples 0XA (), 2XA (+) and 5XA (0). The D1 PP of Dynasil (a)
is shown for comparison 225
53. The dependence on the sintering temperature of the D2 trisil
oxane ring curvefitted Raman peak position (PP) for samples
0XA (), 2XA (+) and 5XA (0). The D2 PP of Dynasil (a) is
shown for comparison 226
54. The dependence on the sintering temperature T of the W2 (?)
curvefitted Raman peak position (PP) for samples 0XA (), 2XA
(+) and 5XA (0). The Dynasil PP (a) is shown for comparison. 227
55. The dependence on the sintering temperature T of the SiOH
curvefitted Raman peak position (PP) for samples 0XA (), 2XA
(+) and 5XA (0). The Dynasil PP (a) is shown for comparison. 228
56. The dependence on the sintering temperature T of the W3 TO
curvefitted Raman peak position (PP) for samples 0XA () 2XA
(+) and 5XA (0). The Dynasil PP (a) is shown for comparison. 229
57. The dependence on the sintering temperature T of the W3 LO
curvefitted Raman peak position (PP) for samples 0XA () 2XA
(+) and 5XA (0). The Dynasil PP (a) is shown for comparison. 230
58. The dependence on the sintering temperature T of the TO
curvefitted Raman peak position (PP) for samples 0XA (), 2XA
(+) and 5XA (0). The Dynasil PP (a) is shown for comparison. 232
xvi
59.
The dependence on the sintering temperature T of the W4 LO
curvefitted Raman peak position (PP) for samples OXA (), 2XA
(+) and 5XA (0) The Dynasil PP (a) is shown for comparison. 233
60. The dependence on the sintering temperature T of the SiOH
curvefitted Raman peak position (PP) for samples OXA () 2XA
(+) and 5XA (0). The Dynasil PP (a) is shown for comparison. 234
61. The dependence on the sintering temperature T of the area of
the W1 curvefitted Raman peak as a fraction of the total Raman
spectrum area for samples OXA (), 2XA (+) and 5XA (0). The
Dynasil peak area (a) is shown for comparison 236
62. The dependence on the sintering temperature Tp of the area of
the D1 tetrasiloxane ring curvefitted Raman peak as a fraction
of the total Raman spectrum area for samples OXA (), 2XA (+)
and 5XA (0). The Dynasil peak area (a) is shown for
comparison 237
63. The dependence on the sintering temperature Tp of the concen
tration/unit area of the internal pore surface of the D1
tetrasiloxane ring, [D1]/[Wt]/Sa, for samples OXA (), 2XA (+)
and 5XA (0) 238
64. The dependence on the sintering temperature of the area of
the D2 trisiloxane ring curvefitted Raman peak as a fraction
of the total Raman spectrum area, (a) For samples OXA () ,
2XA (+) and 5XA (0). The Dynasil peak area (a) is shown for
comparison, (b) For samples OX (), OXA (+), 2X (O), 2XA (a),
5X (x) and 5XA (v). Within the resolution of the curvefitting
analysis the peak areas are the same for the two samples
examined for each type of gel within the T range of each
sample 239
65. The dependence on the bulk density Dfa (g/cc) of the area of
the D2 tetrasiloxane ring curvefitted Raman peak as a fraction
of the total Raman spectrum area for samples OXA (), 2XA (+)
and 5XA (0). The Dynasil peak area (a) is shown for
comparison 241
66. The dependence on the sintering temperature Tp of the concen
tration/unit area of the internal pore surface of the D2
trisiloxane ring, [D2]/[Wt]/Sg, for samples OXA (), 2XA (+)
and 5XA (0) 242
67. The dependence on the sintering temperature Tp of the area of
the 980 cm"1 SiOH curvefitted Raman peak as a fraction of the
total Raman spectrum area for samples OXA (), 2XA (+) and
5XA (0). The Dynasil peak area (a) is shown for comparison. 245
68. The dependence on the sintering temperature of the concentra
tion/unit area of the internal pore surface of the 980 cm'1
surface silanols, [Si0H]/[Wt]/Sa, for samples OXA () 2XA
(+) and 5XA (0) 246
xvii
69.
The dependence on the sintering temperature Tp of the area of
the W3 (TO and LO) curvefitted Raman peak as a fraction of the
total Raman spectrum area for samples OXA (), 2XA (+) and
5XA (0). The Dynasil peak area (a) is shown for comparison. 247
70. The dependence on the sintering temperature Tp of the area of
the W4 (TO and LO) curvefitted Raman peak as a fraction of the
total Raman spectrum area for samples OXA (O), 2XA (+) and
5XA (0). The Dynasil peak area (a) is shown for comparison. 248
71. The dependence on the sintering temperature Tp of the area of
the 3750 cm'1 SiOH curvefitted Raman peak as a fraction of
the total Raman spectrum area for samples OXA (), 2XA (+)
and 5XA (0). The Dynasil peak area (a) is shown for
comparison 249
72. The dependence on the sintering temperature of the concentra
tion/unit area of the internal pore surface of the 3750 cm'1
surface silanols, [Si0H]/[Wt]/Sa, for samples OXA () 2XA
(+) and 5XA (0) 250
73. The dependence on the sintering temperature Tp of the ratio of
areas of the 3750 cm'1 SiOH peak and the 980 cm'1 SiOH peak,
[SiOH]/[SiOH], for samples OXA (), 2XA (+) and 5XA (0) . 251
74. The dependence on the sintering temperature Tp (C) of the
structural density Dg [g/cc] () of a powdered type OX silica
gel, measured using He pycnometry, and the bulk density Db
[g/cc] of monolithic silica gels [169] sintered in humid
Florida air (+) and sintered in a dehydrating atmosphere of
flowing CC14 (0) 264
The dependence on the sintering temperature Tp of the bridging
oxygen bond angle, 8 (0) calculated from the W3 TO and the W4
LO Raman peak positions using equation (11), for samples OXA
(), 2XA (+) and 5XA (0) 289
76. The dependence on the sintering temperature Tp of the Si0
bond length, d(SiO) (), calculated from 8 in Fig. 75 using
equation (2), for samples OXA (), 2XA (+) and 5XA (0). . 290
77. The dependence on the sintering temperature Tp of the calcu
lated relative structural density, which is calculated from 8
and d(SiO) as discussed in the text, for samples OXA () ,
2XA (+) and 5XA (0) 293
78. The dependence on the sintering temperature T for samples
OXA (), 2XA (+) and 5XA (0), of the calculated relative
structural density (from Fig.77) and the experimental
relative structural density, calculated from experimental Dg
data in Fig. 34 by assuming that at Tp = 400C the
experimental Dg is equivalent to an experimental relative Dg
value of 1 294
xviii
79.
The dependence on the sintering temperature Tp of the bridging
oxygen bond angle, 9 [], calculated from the MASS NMR
spectra of a silica gel () [177], the MASS NMR spectra of an
A2 gel (a) [5], the peak positions of the IR spectra of a
type OX gel (X) [207] the W3 TO and L0 Raman peak
positions of sample OXA (+), and the MASS NMR of a type OX
gel (0) 299
80. The dependence, on the sintering temperature Tp for type OX
gels, of the experimental relative structural densities
calculated from Fig. 32(b) and represented by the best fit
linear regressions {Dg = l/((1/Db)V ) [] water pycnometry
[+], He pycnometry [0]), the calculated relative structural
density (a) from Fig. 77, and the D2 trisiloxane Raman peak
area, [D2]/[Wt] as a percentage of the total Raman spectrum
area (X) calculated from Fig. 64 311
81. The dependence on the sintering temperature Tp of the experi
mentally determined relative structural density measured
using He pycnometry (calculated from Fig. 34(a) assuming a
relative Dg 1.00 at T = 400C), and the D2 trisiloxane
Raman peak area, [D2]/[wt] as a percentage of the total Raman
spectrum area (calculated from Fig. 64), for samples OXA, 2XA
and 5XA 312
82. The dependence on the sintering temperature T of the calcu
lated relative structural density (from Fig. 77), and the D2
trisiloxane Raman peak area, [D2]/[Wt] as a percentage of the
total Raman spectrum area and calculated from Fig. 64, for
samples OXA, 2XA and 5XA 314
83. The dependence on their experimental structural density Dg
[g/cc] of the D2 trisiloxane Raman peak area, [D2]/[Wt], as a
percentage of the total area of their respective Raman
spectrum, for silica gel sample OXA (), for fused asilica
with increasing fictive temperature [100], and for pressure
compacted fused asilica [133] 320
84. The dependence on their experimental Dg of the calculated
relative Dg (calculated from the W3 TO and LO Raman peak
positions) for silica gel samples OXA (), 2XA (+) and 5XA
(0), for fused asilica with increasing fictive temperature
[100], and for pressure compacted fused asilica [133], . 324
85. The extrapolated dependence on the hydroxyl concentration,
[OH] (Wt %), of the structural density of Amersil [210], a
Type II asilica, and of Suprasil [211], a Type IV asilica. 335
86. The rate of absorption of water vapor from a reservoir of
deionized water into the pores of type OX gel samples #124,
#141, #127, #136, with rH 1.2 nm, and type 2X gel sample
#139, with rH 4.5 nm 351
xix
87. The evolution of the Raman spectrum (1001350 cm'1) of sample
#127, stabilized at T = 650C (Db 1.28 g/cc, rH 1.2 nm)
as the water content w increases from 0.0 g H20/g gel to W =
Wmax = 0.329 g/g, and then as the gel is then redried by
reheating at Tp = 190C 353
88. The dependence on time t (hrs) of the area of the D2 trisilox
ane curvefitted Raman peak, as a fraction of the total
spectrum area, for samples #124, #136, #127, #141 and #139,
and for a B2 gel [5] 355
89. The dependence on the water content W of the area of the D2
trisiloxane curvefitted Raman peak, as a fraction of the
total Raman spectrum area, for samples #124, #136, #127, #141
and #139 356
90. The dependence on time t (hrs) of the Si0 force function, Kg
(N/m) calculated from the W3 TO and LO Raman peaks using
equation (11), for samples #124, #136, #127, #141 and #139. 358
91. The dependence on the water content W (g/g) of the Si0 force
function, Kg (N/m) calculated from the W3 TO and W4 LO Raman
peaks using equation (11), for samples #124, #136, #127, #141
and #139 359
92. The dependence on time t (hrs) of the bridging oxygen bond, 6
(), calculated from the W3 TO and W4 LO Raman peaks using
equation (12), for samples #124, #136, #127, #141 and #139. 360
93. The dependence on the water content, W (g/g), of the bridging
oxygen bond, 6 (), calculated from the W3 TO and LO Raman
peaks using equation (12), for samples #124, #136, #127, #141
and #139 361
94. The dependence on the water content, W (g/g), of the calcu
lated relative structural density, determined from 6 and
d(SiO) for samples #124, #136, #127, #141 and #139 362
95. The natural log of the D2 trisiloxane curvefitted Raman peak
area, In [D2]/[Wt] plotted against the natural log of the
time of absorption, In t (mins), for samples #136, #127, #141
and #139 380
96. The dependence on the water content, W (g/g), of the area, as
a fraction of the total Raman spectrum area, of the 605 cm"1
D2 trisiloxane and the 980 cm*1 SiOH curvefitted Raman peaks,
for samples # 136 ( and + respectively) and #127 (0 and a
respectively) 398
97. The dependence on log frequency, log f (Hz), of log conduc
tivity G (S/m), log susceptance B (S/m) and log loss tangent,
tan S, of sample #10A for a water content W = 0.467 g/g. . 416
xx
98.
The dependence on log frequency, log f (Hz), of log dielec
tric constant, e' log dielectric loss factor, e", and log
loss tangent, tan 5, of sample #10A for a water content W =
0.467 g/g 417
99. The ColeCole plot [231], otherwise known as a complex plane
plot, of the imaginary part of the complex dielectric
constant, the loss factor e", plotted against the real part
of the complex dielectric constant, the dielectric constant
e", for sample #10A at W = 0.467 g/g. The angle of
suppression, a, of the semicircular plot of relaxation R1
below the xaxis is indicated (not to scale). Relaxation Rg
can be seen as the tail on the low frequency side of
relaxation R1 418
100. The evolution, in sample #10A, of the dielectric constant
spectra, log e'(log f), as the water content W increases from
0.032 g/g to 0.4782 g/g 426
101. The evolution, in sample #10A, of the loss tangent spectra,
log tan S (log f), as the water content W increases from
0.032 g/g to 0.478 g/g 427
102. The dependence of the log of the frequency of the maximum of
the peak in the loss tangent spectra, log f1, on the water
content W (g/g) in sample #10A at 25C 428
103. The dependence of the dielectric constant measured at 13 MHz,
13MHz on t*ie water content W (g/g) for sample #10A at 25C. 429
104. The dependence of the log of the dielectric constant measured
at 1 KHz, 10 KHz, 100 KHz, 1 MHz, and 10 MHz on the water
content W (g/g) for sample #10A at 25C 430
105. The dependence of the shape of the dielectric loss tangent
spectra, log e"(log f), on the material used as measuring
electrodes. Curve A: silver paint, showing relaxation R1 and
the tail of relaxation Rg. Curve B: carbon paint showing just
relaxation R1. Curve C: vapor deposited aluminum showing just
relaxation R1 439
106. The dependency of the log of the characteristic loss tangent
frequency, f51 (Hz) of relaxation R1 on the log of the sample
thickness 1 (cm), i.e. of the electrode separation, using
silver paint electrodes for samples #25 (T = 180), #71 (T =
800C) and #34 (T = 180C), with their pores full saturated
with water, i.e. W = W 440
107. The dependence of the log of the characteristic loss tangent
frequency of relaxation R1, f1, on the log of the water
content W at T = 25C, showing that above Wc2 = 0.275 g/g the
dependence of f51 on W is no longer logarithmic
xx i
443
108. The dependence of the characteristic loss tangent frequency
of relaxation R1, on the water content W at T = 25C,
showing that below Wc2 = 0.275 g/g the dependence of f51 on W
is no longer linear 444
109. The evolution of the susceptance spectra, log B [S/m] (log
f), as the length of the sample, and therefore the measuring
electrode separation, changes from 2.19 to 0.23 cm, for
sample #71, Tp = 180C 451
110. A simple schematic representation of the two models discussed
in the text, (a) Flat pore geometry, i.e. statistical
thickness, (b) Cylindrical pore geometry. Not to scale. . 461
111. The dependence of the log of the characteristic loss tangent
frequency of relaxation R1, f^ (Hz), on the log of the
statistical thickness, W/Sg (g water/1000 m2 = nm) for the
type OX gel samples B180 (which is actually sample #10A),
B650 and B800 at 25C, showing the slight increase in Wfa/S s
W.,/S as the stabilization T increases 465
c' a p
112. The DSC spectra of pure water, type OX gel sample A180 (rH
1.2 nm) with its pores fully saturated with absorbed water,
and type 2X gel sample C45 (rH 4.5 nm) with its pores fully
saturated with absorbed water. The dT/dt = 10C/min in
flowing dry nitrogen 466
113. The relationship between the average cylindrical pore radius,
rH (nm), and the surface silanol concentration, [Sig0H] (#
SigOH/nm2) for the silica gel samples investigated in Chapter
7 467
114. The dependence of the thickness of the bound adsorbed water
for the flat pore geometry model, W^S = Wc2/Sg, and the
cylindrical pore geometry model, Rfa, on the surface silanol
concentration, [Sig0H] (# Sis0H/nm2 ), from the DSC and DRS
analysis 468
115. The dependence of the thickness of the bound adsorbed water
for the flat pore geometry model, W^S s Wc2/Sg, and the
cylindrical pore geometry model, Rb, on the average
cylindrical pore radius, rH (nm), from the DSC and DRS
analysis 469
116. The evolution of the near infrared (NIR) absorption spectra
of type OX gel sample #114 as water is absorbed into its
micropores and the water content W increases from 0.0 g/g to
0.121 g/g 477
117. The change in the wavelength (tm) of the positions of the 2u1,
2u3 and 2v^ NIR peaks as W (g/g) increases in sample #114. . 479
xxii
118. A schematic 2dimensional representation of a structural
model which might explain the changes observed in the
conductivity of H20 adsorbed in the pores of a silica gel as
its statistical thickness, W/Sg, changes. This is a "snapshot"
of what is actually a dynamic system which is in constant
motion because of the short lifetime of Hbonds. The values
of the critical statistical thicknesses are indicated. =
permanent bonds,  = transitionary Hbonds
489
xxiii
KEY TO SYMBOLS
Svmbol
Meaning
Approximately equal to
Equivalent to
[ ]
Concentration, e.g., [OH] = hydroxyl concentration
a
Abbreviation for "directly proportional to"
a
Angle of suppression in ColeCole plots [rads]
ll
to
Born nearestneighbor bondstretching central force function
[N/m]
<*b
Bond polarizability = am/coordination of atom
Molecular polarizability
&
Born nearneighbor bondbending noncentral force [N/m]
\v
Liquidvapor surface tension or free energy [N/m,J/m2]
S and A
Dihedral angles [0]
AE
Activation energy [Kcal/mole] = 1Ksa02
AHf
Heat of formation [Kcal/mole]
AP
Capillary stress [MPa]
apl
Pressure gradient in a liquid
' = K,
Dielectric constant, e' = B/we0
C\l
II
\L>
Dielectric loss factor, e" = G/weQ
l"f 1
The magnitude of maximum of the dielectric loss factor of
dielectric relaxation Rj at fÂ£., where i = 1, 2, 3 or S.
e>R = es
Relaxed, or stationary, dielectric constant at low f < l/rD
e'u = '
Unrelaxed, or infinite, dielectric constant at high f > l/rD
XX iv
*
= K
O
A2
A
A
Tei
*
w
Complex dielectric constant e* (= K*)
Permittivity of free space = 8.854 x 10'12 F/m
Viscosity of a liquid [Pa.s]
Contact angle in the LaplaceYoung equation []
Intertetrahedral =Si0Sis bridging 0 bond angle [], i.e.
the average bridging 0 bond angle representing the V(0)
associated with aSi02, 6 =
Critical bridging oxygen bond angle []
Equilibrium bridging oxygen bond angle [] 144148
Hybridization index
Mean free path [m]
Wavelength [m]
Instantaneous dipole moment vector
Permanent molecular dipole moment
Wavenumber [m"1] = f/c
Laser wavenumber [m'1] = 19436 cm"1 = 514.5 nm
Scattered phonon wavenumber [m"1] = = 1933615436 cm"1
Raman frequency wavenumber [m"1] = 1004000 cm"1
Volume fraction of solid phase Db/Ds
Standard deviation of n values
Relaxation time [sec]
Relaxation time of tan 6 at tan 5 [sec]
Relaxation time of the maximum of the dielectric loss factor
of dielectric relaxation Rj at f ., where i = 1, 2, 3 or S.
Tei VwÂ£j [sec]
Relaxation time at Debye peak [sec], rD = l/wD
Nuclear Correlation Relaxation Time [sec]
Intratetrahedral OSiO angle [], ip = <0Si0
Radial frequency [rad/s] = 2jrf = 1/t
xxv
WD
Radial frequency at Debye peak [rad/sec] = l/rD
Wl
Laser light frequency [Hz] = 27rft = 2%cv^, where 7r = 3.142
W
P
Scattered phonon frequency [Hz] s 2ncv
R
Raman shift frequency [Hz] m 2ttcvr
A
Crosssectional area [m2]
asilica
Amorphous silica s aSi02
a0
Interatomic bond distance
^iso
Isotropic hyperfine constant
AS
As3anmetric stretch vibrational mode
B(f)
Susceptance B at frequency f [S/m]
c
Speed of light = 3 x 108 m/s
Cb
Raman coupling constant
Cn
Coordination number
CPMASS NMR
Cross Polarized MASS NMR
CRN
Continuous Random Network
D
Permeability [m2]
d(OH)
OxygenHydrogen (0H) bond length [run]
d(0..0)
Oxygen to first 0 neighbor distance [nm]
d(Si..Si)
Silicon to first Si neighbor distance [nm]
d(SiO)
SiliconOxygen (Si0) bond length [nm]
A tetrasiloxane ring, whose oxygen breathing mode causes
the peak at 495 cm1 in the Raman spectrum of asilica
)
Cyclic tetrasiloxane ring concentration
[D^/CWJ
Fractional or internally normalized D1 concentration
[D.,]/[Wt]/Sa
D1 concentration/unit surface area of internal pores [#
rings D,,/nm2 ]
tDilo
[D,j] at t = 0 mins
d2
A trisiloxane ring, whose oxygen breathing mode causes the
peak at 605 cm'1 in the Raman spectrum of amorphous silica
xxvi
[D2]
Cyclic trisiloxane ring concentration
[D2]/[Wt]
Fractional or internally normalized D2 concentration
[D2]/[Wt]/Sa
D2 concentration/unit surface area of internal pores [# D2
rings/nm2]
[D2]0
[D2] at t = 0 hrs
[D2]t
[D2] at time t for t > 0 hrs
Db
Bulk density, which includes the open porosity [g/cc]
df
Mass fractal dimension
Df
Fictive density [g/cc], i.e. Dg at a particular Tf
DRS
Dielectric Relaxation Spectroscopy
ds
Surface fractal dimension
Ds
Skeletal, structural or true density of material, which
does not include any open porosity [g/cc]
DSC
Differential Scanning Calorimetry
^smax
Maximum experimental structural density value [g/cc]
dVdrH
Pore volume distribution [cc/g/nm]
dW/dt
Drying rate [g/g/sec]
dW/dtc
Critical drying rate, below which a gel does not crack
f
Frequency [Hz]
f*i
Frequency of the maximum of the tan S spectra, tan 5^ Â¡ of
dielectric relaxation Rj, where i = 1, 2, 3 or S [Hz]
fei
Frequency of the maximum of the e" spectra, e"., of
dielectric relaxation Rj, where i = 1, 2, 3 or S [Hz]
Fb
Fraction of bound H20 adsorbed onto the internal pore
surface
Ff
Fraction of free H20 adsorbed on top of the bound H20
fi
Frequency of mode i [Hz]
fl
Frequency of laser [Hz] = ci/^
fs
Fraction scharacter
ft
Tortuosity factor in the CarmenKozeny equation
xxvii
Fused aSi02 Type I, II, III or IV nonporous amorphous silica
g(w)
Band vibrational density of states (VDOS)
G(f )
Conductivity G at frequency f [S/m]
G(ij)
d(Si..Si) distribution
Gdc
D.C. conductivity [S/m]
Gfi1
Conductivity at f^ [S/m]
Gi
Gruneisen parameter
GR Gs
Low frequency limit of G below 1/r
Gu Go
High frequency limit of G above 1/r
h
Planck's constant 6.626 x 10'34 J.sec
I
Current [Amps]
I(w(,wR)
Experimental Raman intensity (background corrected)
Ip(w)
Stokes intensity, Ip(w) = I(w)
Reduced Raman intensity
IS
Impedance Spectroscopy
J
Flux [volume/(area x time) = m/s]
J()
Instrument transfer function
k
Boltzman's constant = 1.3806 x 10'23 J/K
k
Reaction rate [Mole"1min1 ]
k
Wavevector = 2n/X [m"1]
k' = k[H2O]0
Reaction rate for a pseudofirstorder rate law [min'1]
K* s e*
Complex dielectric constant = K1 + iK2 = Re(K) + Im(K)
Ka = 6
The OSiO bondbending noncentral force function [N/m
1000 dyn/cm]
Kc
Equilibrium constant = [products]/[reactants]
Kn
Knudsen number = A/rH
The OH bondstretching force function [N/m]
xxviii
Ks = a
The Si0 bondstretching central force function [N/m] =
w2 (1/Mg + 1/Mq)
kb
The SiOSi bondbending noncentralforcefunction [N/m]
kt
Isothermal bulk modulus [N/m2]
L or 1
Sample length [m]
LO
Longitudinal optical mode
m
Gram formula weight [g]
M
Molarity [moles/liter s mol dm"1]
M
Atomic mass
MASS NMR
Magic Angle Sample Spinning NMR
MD
Molecular Dynamics
MO
Molecular Orbital
n
Refractive index
n(wR)
BoseEinstein thermal phonon population factor 
[(exp((h/27r)27rcvR)/kT)l]"1 = 3.0063 for uR 104 cm"1
na
Avagadro's number *= 6.02 3 x 1023 atoms/mole
NBO/BO
Ratio of nonbridging oxygen (i.e. SiOH) to bridging oxygen
(i.e. SiOSi) bonds
NMR
Nuclear Magnetic Resonance
OH
Hydroxyl group
OR
Alkoxide group
Os*
Nonbridging oxygen surface atoms
P
Depolarization ratio = I /I_
P/P0
Relative vapor pressure
PP
Peak positions
q,
Vibrational displacement coordinates
Qn
NMR terminology for a Si atom with n bridging 0 atoms
R2
Least squares correlation coefficient
r
Radius of curvature [m]
XX ix
r
Bond directionality ratio = Ka/Ks
R
Molar ratio of [H20]/[silica precursor]
R(f)
Resistivity R at frequency f [m]
R1
The main dielectric relaxation due to the movement of
protons in water absorbed in the pores of a silica gel
Rb
Bound cylindrical thickness [nm]
RDF
Radial Distribution Function
Rf
Free cylindrical thickness [nm]
Rg
Guinier radius of gyration [m]
rH
Average cylindrical pore radius = 2Vp/Sa [m]
Rh
Relative humidity [%]
*m
Molar refraction
rp
Average particle radius [nm]
S
The unit Siemens = fl'1
Sa
Surface area [m2/g] of a porous material calculated from
the N2 sorption isotherm using BET theory
SANS
Small Angle Neutron Scattering
SAXS
Small Angle Xray Scattering
[SiOH]/[Wt]
Fractional or internally normalized SiOH concentration,
i.e. the area of the SiOH peak as a percentage or
fraction of the total area of the spectra
[SiOH]/[Wt]/Sa
SiOH concentration/unit surface area of the internal
pores [# OH groups/nm2]
Si3
Silicon atom in a D2 trisiloxane ring
Si4
Silicon atom in a D1 tetrasiloxane ring
SiOH
The Si0 stretching vibration of an SiOH group at 970 cm
1
SiOH
The 0H stretching vibration of an SiOH group at 3750 cm
1
Sis
Surface silicon atom
XXX
Si OH = SiOH
s s
Surface silanol group
SS
Symmetric stretch vibrational mode
t
Time [sec, min, hr, day, yr, century, millennium, eon]
T
Temperature [ C]
T(t)
Thermal history, time t at temperature T
t1/2
Halflife [mins] = ln2/k for a firstorder reaction
tan 8
Dielectric loss tangent = G/B = e"/e'
I tan 
The magnitude of the maximum of the tan 8 peak at tÂ£ of
dielectric relaxation R1, where i = 1, 2, 3 or S
Tb
Boiling point [C]
Tdb
Temperature at which densification begins by viscous sint
ering in silica gels
TEM
Transmission Electron Microscopy
TEOS
Tetraethoxysilane or silicon tetraethoxide, Si(0C2H5)^
Tf
Fictive temperature [C]
T9
Glass transition temperature [C]
TGA
Thermogravimetric Analysis
T
m
Fusion or melting point [C or K]
TMOS
Tetramethoxysilane or silicon tetramethoxide, SiiOCHj)^
TO
Transverse optical mode
TP
Processing, stabilization or sintering temperature [C]
T
smax
Temperature at which Dgmax occurs [C]
Tv
Vaporization or boiling temperature [C or K]
type OX gel
Silica gel made with no HF, giving rH 1.2 nm
type 5X gel
Silica gel made with 0.075 moles HF/1 of H20, rH 9.0 nm
type 2X gel
Silica gel made with 0.03 moles HF/1 of H20, rH 4.5 nm
V(0)
6 distribution
Vac
The a.c. peaktopeak voltage [Volts]
xxx i
vi
Vibrational quantum number
Vn,
Molar volume [cc/mole]
VP
Pore volume [cc/g] Db'1 Dg'1
Vv
Volume fraction of pores = (1p)
VDOS
Vibrational density of states
W
Water content [g water/g silica gel]
w/sa
Statistical thickness [g H20/1000 m2 = nm]
twt]
Total area under a reduced Raman spectrum except for the
970 cm'1 SiOH, the 495 cm'1 D1 and the 605 cm'1 D2 peaks
W1
Main asilica Raman peak at 450 cm'1
w2
Theoretical asilica Raman peak in 800950 cm'1 region
w3 TO, LO
Symmetric Si0 stretch (SS) peaks at 792, 828 cm'1 in the
Raman spectrum of asilica
W4 TO, LO
Asymmetric Si0 stretch (AS) peaks at 1066, 1196 cm'1 in
the Raman spectrum of asilica
w5
Raman peak of SiOH stretch vibration at 970 cm"1
W6
Raman peak of SiOH stretch vibration at 3750 cm"1
WANS
Wide angle neutron scattering
WAXS
Wide angle Xray scattering
VSa Wc2/Sa
Bound statistical thickness [g H20/1000 m2 = nm]
Wb s Wc2
Bound water content [g H20/g Si02 gel]
Wc1
The first critical water content [g H20/g Si02 gel]
Wd/Sa
First critical statistical thickness 0.088 g H20/1000 m2
s nm
Wc2 s Wb
The second critical water content [g H20/g Si02 gel]
Wc2/Sa VSa
Second critical statistical thickness 0.36 g H20/1000 m2
= nm
VSa
Free statistical thickness [g H20/1000 m2 = nm]
Wf
Free water content [g H20/g Si02 gel]
xxx i i
wi
w_
max
X(f)
Y(f)
Z(f)
Peak assignment of aSi02 structural vibrations in Raman
spectroscopy, where i = 1, 2, 3, 4, or 6
Maximum water content [g water/g silica gel]
Reactance X at frequency f [flm]
Admittance Y at frequency f [S/m = fi1m'1], Y(f) = Gp(f) +
jBp(f), where p = parallel RC circuit
Impedance Z at frequency f [fim] Z(f) = Rg(f) jXg(f), s
= series RC circuit
xxxiii
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
POROUS SILICA GEL MONOLITHS:
STRUCTURAL EVOLUTION AND INTERACTIONS WITH WATER
By
Stephen Wallace
May 1991
Chairperson: Dr. Larry L. Hench
Major Department: Materials Science and Engineering
Monolithic silica gels are produced by the hydrolysis and
condensation of silicon tetramethoxide (TMOS) using acidified water. The
pH and concentration of this water determines the structure of silica
gels, which are fractal, porous materials possessing large surface areas
and small average pore radii. This research elucidates changes in the
structure of silica gels during viscous sintering, and structural
evolution of both the silica gels and water during adsorption into their
micropores.
The changes during densification were probed using Raman
spectroscopy, isothermal N2 sorption, pycnometry and thermogravimetric
analysis. As the temperature, Tp, increases, the structural density, Dg,
increases to a maximum value Dom,. Dom is larger than the D of fused
amorphous silica, which is 2.2 g/cc. Most of the increase in Dg to Dg(nax
is due to weight loss as Tp increases. Some of the weight loss occurs
during the formation of strained, high density, planar D2 trisiloxane
xxx iv
rings by the condensation of adjacent silanols on the pore surface. The
D2 concentration is partially responsible for the increase in Dg. As
densification is completed, Dg decreases from Dsmax to 2.2 g/cc.
Application of the centralforcefunction model for the vibrational
structure of amorphous silica to the gel's Raman spectra shows that the
average bridging oxygen bond angle, 6, is responsible for this decrease
in Dg. Both 6 and the associated skeletal volume are at a minimum at
Dsniax> and as Tp increases further, 6 increases as Dg decreases.
The structure of adsorbed water, and the porous silica
gels into which it is absorbed, are investigated using Raman
spectroscopy, dielectric relaxation spectroscopy and differential
scanning calorimetry (DSC). Surface Dg rings are rehydrolyzed on contact
with water during adsorption. For Dg rehydrolysis at 25C, the reaction
rate 0.000173 (//Dg rings/nm2)'1 min'1 and the equilibrium constant
0.25. The first monolayer of water adsorbed onto the pore surface does
not contribute to the melting peak in the DSC spectra. The proton
conduction mechanism and the relaxation properties of adsorbed water
depend on its statistical thickness.
xxxv
CHAPTER 1
INTRODUCTION
The sintering and resulting densification of alkoxide derived
silica gel monoliths is a complex process. The actual path taken during
processing to produce dry, stabilized or dense monoliths of silica gel
depends on many variables. These include a) precursor and solvent (if
any) used; b) molar water concentration, R, where R = number of moles of
water/number of moles of silica precursor, R 4 is the stoichiometric
ratio for hydrolysis of silica precursors; c) pH, determined by the
catalyst used (The pH controls the relative rates of hydrolysis and
condensation, which in turn control the final gel structure); d) the
specific catalyst used; e) temperature Tp; f) drying method used, i.e.
whether the monolithic gel is dried via i) atmosphere or environmental
control of the relative humidity to produce xerogels, ii) slow evapora
tion at room temperature with no relative humidity control, or iii)
hypercritical drying, producing an aerogel; and g) sintering atmosphere.
For example, in this investigation, a typical monolithic xerogel,
sample type OX, is made from a nitric acid catalyzed tetramethoxysilane
(TMOS) sol with an R ratio of 16 and a HN03 catalyst concentration = 25
cm3 concentrated HN03/1975 cm3 H20. TMOS is also known as silicon tetram
ethoxide or tetramethyl orthosilicate. After drying, this silica gel
will produce a xerogel with a pore volume, V of about 0.45 cc/g and a
surface area, Sg, of about 750 m2/g. The internally interconnected
1
2
microporosity can be modelled as a single continuous cylinder with the
Vp and Sfl of the gel [1,2]. This gives a value of the average cylin
drical pore radius, rh, 20,000 x Vp/Sa = 20,000 x 0.45/750 = 1.2 nm.
The exact shape of the pores in silica gels is unknown, so a "modelless"
pore radius can be used, called the hydraulic pore radius and defined by
Brunauer et al. [3] as Vp/Sa. The hydraulic radius = rH/2 [2].
For the production of monolithic silica gels an acid catalyzed,
high R ratio sol is required. This produces a polymeric, crosslinked,
fractal structure with two levels of particle size and an incomplete
condensation polymerization reaction [4]. The primary particle size has
an average radius, rp, 2 nm, and the secondary particle size, composed
of the agglomerated primary particles, has an average particle radius rp
6.0 nm [4], The structure of the final dry gel is dependent on the sol
structure and contains micropores and both internal and surface silanols
(Sis0H).
The addition of HF as a catalyst drastically decreases the time to
gelation by increasing the kinetic rate of the condensation reaction.
The influence of HF is thought to be due to the basic behavior of F'
ions compared to the acidic H+ groups, i.e. it acts as a Lewis base (or
Bronsted acid) [5]. The sol still has a low pH (pH 1) so the overall
reaction is acidic as opposed to basic. This means that the rate
constant of the hydrolysis reaction is still large relative to the
condensation reaction, and hydrolysis still occurs rapidly. The F* ion
acts as a strong base, catalyzing the condensation reaction. The net
effect is to reduce Sg and to increase V but Sg is reduced by a larger
factor than V This has the effect of increasing rH. The effect of HF
on particle size is not so clear, as the relationship between particle
3
size and pore radius involves both the coordination number, Cn, packing
factor, P.F., the radius, rp, of the particles, and the width of the
particle size distribution. For a given rp, a decrease in the coordina
tion number, Cn, of the particles causes a larger average pore radius,
rH, with no change in particle size.
Silica gels catalyzed by a base have a more compact structure,
with a larger average particle size [5]. Compared to an acid catalyzed
sol, the hydrolysis rate constant of a base catalyzed gel is lower, and
the condensation rate constant is larger. A very high pH, for instance
caused by the addition of an excess of NH^OH to a silicon tetraethoxide
(TEOS) sol, causes the formation of monodispersed, submicron, colloidal
silica spheres, known as Stober spheres [6], These form by the continu
ous agglomeration of condensed silica particles from a high pH silica
sol.
Several authors [719] have recently published data showing values
of the skeletal density, Dg, of metalalkoxidederived silica gels
during sintering which are greater than that of fused asilica. The
skeletal density, Dg, of fused asilica is 2.20 g/cc. Since the reported
values of the skeletal density, Dg (also called the true or structural
density), of the silica gel are larger than the density of asilica
their accuracy has been questioned. The absolute magnitude of the
structural density, Dg, for a given thermal history, depends on the
experimental technique used to measure Dg due to the fractal nature of
the gels [5,20]. This means that the size of the yardstick used, i.e the
molecular diameter in this case, governs the magnitude of Dg. The
dependence of Dg on the thermal history of the gel is related to the
structure of the gel. For example, the reported dependence of the
4
structural density, Dg, on the sintering temperature Tp depends on the
pH of the starting sol. The texture and structure of asilica gel also
depend strongly on the pH.
In Part I of this investigation, the structural and textural
properties of monolithic silica gels will be characterized during
densification via viscous sintering and during the adsorption of water
into the micropores of stabilized gels. Raman Spectroscopy, Isothermal
Nitrogen Sorption, Helium and Water pycnometry, Differential Scanning
Calorimetry (DSC), Thermogravimetric Analysis (TGA) and Magic Angle
Sample Spinning 29Si Nuclear Magnetic Resonance (MASS 29Si NMR) will be
used. The experimentally determined temperature dependency of Dg of
monolithic gels will be explained in terms of these properties. The
Raman spectra of silica gels obtained during processing have been
investigated before [2137] and are qualitatively well understood. The
thermal dependency of Dg will be investigated by quantifying the changes
in the peak positions and areas of the Raman spectra of silica gels as a
function of temperature and other textural variables. These quantified
properties can then be related to the changes in Dg.
The initial hypothesis used to explain the experimentally observed
Dg behavior was that the changes in Dg were related to the changes in
the concentration of the 3membered silicate rings in the silica gel.
The oxygen breathing mode of these trisiloxane rings produces the 605
cm'1 D2 peak in the Raman spectra of amorphous silica [5], The D2 peak
undergoes definite but subtle changes with an increase in the sintering
temperature of the gels during densification. The D2 peak is on the
shoulder of the large main Raman peak at 440 cm'1, so measuring its peak
position and intensity using French curves to draw in the appropriate
5
baseline is not very accurate. The peak position of the D2 peaks will be
shifted from its true value because the main peak distorts the D2 peak
shape. Consequently, to extract quantitative spectral data allowing this
hypothesis to be tested, Gaussian peaks were curvefitted to the baseline
corrected, thermally reduced experimental Raman curves using criteria
discussed in the literature review section on curvefitting.
A chronological critique of the literature concerning the struc
ture and vibrational spectroscopy of asilica is presented in Chapter 2.
The relevance of the literature to Part I is considered in the discus
sion in Chapter 4.
In Part II of this investigation, the structure of water absorbed
into the micropores of stabilized silica gels will be characterized and
the dependence of the conduction mechanism of protons in the adsorbed
water on the statistical thickness of the adsorbed water will be
discussed. Dielectric Relaxation Spectroscopy, Impedance Spectroscopy
and Differential Scanning Calorimetry (DSC) will be used.
PART I
STRUCTURAL AND TEXTURAL EVOLUTION OF POROUS SILICA GELS
DURING SINTERING AND DURING WATER ABSORPTION
CHAPTER 2
A CHRONOLOGICAL LITERATURE REVIEW OF THE STRUCTURE AND
THE VIBRATIONAL SPECTROSCOPY OF AMORPHOUS SILICA
2.1 The Structure of Amorphous Silica
2.1.1 The Categories of the Types and Structure Concepts of aSilica
Bruckner [38,39] wrote a broad review of the properties and
structure of silica. He defined the four categories or types of commer
cially available silica glasses:
a) Type I silica glasses are produced from natural quartz by electrical
fusion under vacuum or under an inert gas atmosphere. They contain
nearly no hydroxyl, OH, groups (<5 ppm) but relatively high metallic
impurities ([Al] 30100 ppm and [Na] = 4 ppm). These include Infrasil,
IRVitreosil, G.E. 105, 201, 204.
b) Type II silica glasses are produced from quartz crystal powder by
flame fusion (the Verneuille process). They contain a much lower
metallic impurity level, but because of the H202 flame, [OH] = 150400
ppm. These include Herasil, Homosil, Optosil and G.E. 104.
6
7
c). Type III silica glasses are synthetic vitreous silica produced by
hydrolyzation of SiCl^ when sprayed into an 02H2 flame. This gives a
very low metallic impurity level, but [OH] = 1000 ppm and [Cl] = 100
ppm. These include Dynasil, Suprasil, Spectrosil and Corning 7940.
d) Type IV silica glasses are synthetic silica produced from SiCl^ in a
water free plasma flame, with [OH] = 0.4 ppm and [Cl] = 200 ppm. These
include Dynasil UV5000, Suprasil W, Spectrosil WF and Corning 7943.
All these different types of silica glasses have slight differenc
es in their properties and therefore characteristic differences in their
structure. Bruckner [38,39] pointed out that the anomalous behavior of
the volumeT curve, which shows minima at 1500C and 80C. This may be
used to decide whether or not the material in question is a glass.
2.1,2 Structural Models of aSilica
Figure 1 shows the bulk, or geometric, density, Dfa, of silica as a
function of the fictive temperature Tf [38]. The bulk density includes
all the porosity, both open and closed, existing in the sample. The
magnitude of the bulk density, Db, for a specific Tf depends on the type
of silica being measured. Types I and II, of natural origin, have larger
densities than Type III, of synthetic origin. Both types reach a maximum
at 1500C of 2.2026 g/cc (Type I and II) and 2.2056 g/cc (Type III).
They tend towards a similar value of 2.2000 g/cc at a Tf of 900C.
Bruckner [38,39] divided the structure concepts of oxide glasses
into 4 groups. Group 1 is based on the Continuous Random Network (CRN)
model due to Zachariasen [40], which was verified using Xrays [41] and
later modified [42]. It is now the generally accepted model for the
structure of silica. Group II is based on the crystallite hypothesis,
BULK DENSITY Db [g/cc]
8
2.2060
2.2050
2.2040
2.2030
2.2020
2.2010
2.2002
Figure 1. The bulk density Dfa of different Type I/II and Type III/IV
commercial aSi02 as a function of fictive temperature Tf. After [38].
Their bulk and structural densities are identical because Vp = 0.0 cc/g.
9
which was also examined by Xray analysis and modified, but has been
rejected as an unrealistic model for the structure of silica [43], Group
III is based on the microheterogeneous structure concept first claimed
as "latent decomposition" in systems with an Sshaped liquidus curve. It
was brought to a thermodynamicalstatistical base of phase separation,
nucleation and decomposition. Group IV includes all those hypotheses
based on geometrical considerations [44], and pure statistical models of
certain partition functions.
Mozzi and Warren [41] performed the classic xray scattering
analysis of the structure of silica, obtaining pair function distribu
tion curves for silica (Fig. 4 in Mozzi and Warren [41]). This repre
sents a structure which is averaged over the whole sample interpreted in
terms of pair functions. Each silicon is tetrahedrally surrounded by 4
oxygen atoms, with an average Si0 distance d(SiO) = 1.62 . Each
oxygen atom is bonded to 2 Si atoms. The 0 to first 0 neighbor distance
d(0...0) 2.65 . These distances have narrow size distributions. The
SiOSi bridging 0 bond angle, 6, shows a broad distribution, V(0),
extending all the way from 120 to 180, with a maximum at 144. The
related Si to first Si neighbor distance, d(Si...Si), also has a broad
distribution, G(ij), extending all the way from 2.78 to 3.24 (Fig. 5
of Mozzi and Warren [41] shows these distributions). This wide variation
in 6 is an important distinction between amorphous and crystalline
silica. It is also an important criterion for any proposed model for the
structure of aSi02. Good agreement with the measured pair function
distribution curve was obtained by assuming a random orientation of the
dihedral angle, $, about the Si0 bond directions, except where prevent
ed by the close approach of neighboring atoms. (The dihedral angle gives
10
the orientation of two neighboring tetrahedra relative to the SiOSi
plane.) This interpretation confirmed Zachariasen's CRN model [40].
Bock and Su [45] applied some of the results from the models of
crystalline silica to yield a semiquantitative description of aSi02.
The truly characteristic part of the electromagnetic spectrum is the
farinfrared region, which can be probed by both IR and Raman spectros
copy [45]. Far IR absorption is a manifestation of the modes of vibra
tion of a disordered structure, which can be used to distinguish a
glassy material from a crystalline material. These modes cannot be
described by any model based on an ordered structure in the crystalline
form. The short range order in the glass was described by assuming that
the average structural unit was aquartz and used the valencebond force
field approximation, giving d(SiO) 0.16 nm and 8 m 150. They
obtained force constant values of Kg 480 N/m (Si0 stretching), Ka
35 N/m (OSiO bending) and KR 5 N/m (SiOSi bending). Although the
selection rules were not adhered to, 15 predicted frequencies were
within the ranges of the spectra of fused aSi02 reported. The Raman
spectra Bock and Su obtained is very poor in comparison to more recent
literature. Bock and Su [45] commented that Wadia and Balloomal's model
[46] is physically unrealistic, but similar to their own, which means
that their own model is also unrealistic!
Gaskell [47] developed a model for the structure of amorphous
tetrahedral materials using ordered units with carefully prescribed
boundary conditions. It gave a reasonable comparison with the observed
radial distribution function (RDF) of an amorphous material. This shows
one of the many problems with trying to decide whether a model is a good
simulation of amorphous material. Even this model, which contains
11
definite local crystalline order, can simulate an RDF. The modern
accepted model of amorphous material is the continuous random network
(CRN) [40] model which contains no crystalline order. This point
illustrates Galeener and Wright's [43] observation that to be any good,
a model must give very good agreement with an RDF, as well as reproduce
other experimental evidence, e.g., Raman spectra, etc.
Gaskell and Tallant [48] reexamined Bell and Dean's ball and stick
inorganic polymer model [49,50,51] of the structure of aSi02 which was
developed to investigate the vibrational spectroscopy of aSi02. They
applied an energy minimization technique with a Keating forcefield to
obtain equilibrium atomic coordinates from the original model and
concluded that the BellDean random structure is an acceptable descrip
tion of aSi02. The relaxed structure gave approximately the correct
values for the density, enthalpy of crystallization and the Xray and
neutron scattering data. The main weakness of the model was the large
surface area to volume ratio intrinsic to the few atoms in the model.
This requires that larger relaxed models of perhaps several thousand
atoms be constructed with improved stereochemical characterization
before further progress can be made in the analysis of random network
models for glass. An improved forcefield function is also required, as
well as better information on the bondangle distributions. Gaskell
obtained values 0 = 144 149 in good agreement with Mozzi and
Warren's [41] value of 144, and a dihedral angle, 6, distribution
showing a non random distribution with peaks visible at 60. This
implied the presence of puckered 4, 5 and 6 membered rings.
Phillips [52] has a different view of the structure of aSi02,
which has been strongly refuted by Galeener and Wright [43]. Phillips
12
does not believe the CRN model can be logically supported, similarly
rejecting the PoraiKoshits and Evstropyev [53] paracrystalline model of
glass structure. Instead he says that glass formation occurs in oxides
not for topological reasons, but for a specific chemical reason, namely
the ability of 0 atoms to form double bonds rather than single bonds at
little expense in enthalpy. Clusters with noncoalescing interfaces
covered with nonbridging surface oxygen atoms, 0g*, form. This suppress
es crystallization and allows the cluster interfaces to fit together
very snugly with little void volume while creating true surfaces in the
usual sense of crystalline boundaries. Phillips said that this, combined
with the fact that for aSi02 the number of structural constraints
exceeds the number of degrees of freedom, means that aSi02 must have a
granular structure. He gave a broad review [52] of the spectroscopic
properties of aSi02 while trying to prove his hypothesis.
Phillips [52] calculated that 20% of the molecules in a cluster
are on the surface, a very large concentration for a defect. He shows
TEM micrographs of aSi02 fibers claiming to show clusters of about 6.0
run diameter, similar to the cluster size calculated to be formed from
his model. This argument reverts to whether or not the researcher
believes that the TEM samples are representative of bulk aSi02. Do the
TEM micrographs show clusters, or are they artifacts of sample prepara
tion or electron beam damage?
Galeener and Wright [43] pointed out that modern diffraction
experiments are able to provide accurate data with high real space
resolution. In practice this provides an extremely fine filter for the
various structural models proposed in the literature. The problem is
that most authors term "good agreement" with experiment as getting peaks
13
in the "right place" in either the reciprocal space interference
function or the real space correlation function. Only very poor models
fail to achieve this. Correct peak shapes and areas must also be
obtained, which requires including the effects of thermal vibration in
the model. A given model fitting experimental diffraction data is no
guarantee that no other models will also fit. Agreement with diffraction
data is a necessary but not sufficient criterion for any structural
model of amorphous solids [43].
Galeener and Wright [43] strongly refuted Phillips [54] model by
showing that it is incompatible with neutron diffraction and Raman
spectroscopic data. Phillips predicted the wrong number of peaks in the
important part of the neutron diffraction pattern, with the wrong shape
and the wrong width. Thus it does not meet Galeener and Wright's [43]
criterion and has to be rejected. Analysis of experimental neutron
scattering data shows that any crystalline structure has to have a
maximum correlation length of 1.0 nm or less if it to reproduce the
experimental amorphous scattering spectra. Phillips [54] claimed a
microcrystallite size of 6.0 nm. Also, since 90% of the 0 atoms in
Phillip's model were in the interior of the Scristobalite microcryst
als, the Raman spectrum of aSi02 should resemble Ecristobalite, which
is not the case. There is no known double bond of Si that is stable at
room temperature. This and other spectroscopic evidence disproves the
assignment of the 495 cm"1 peak to the wagging motion of Si=0 bonds
specified by Phillips' model.
Evans et al. [55] examined several atomic models for aSi02 with
radically different mediumrange structures. They compared the RDF and
the neutron and Xray structure factors computed from each model with
14
experimental data. Despite the differences in mediumrange structure,
all the models provided a reasonable fit to the experimental data but
could not reproduce all the details. They suggested this meant that RDF
are relatively insensitive to the medium range order and that all CRN
models contain too little strain. They also suggested that incorporation
of a granular structure would introduce the strain, putting him in the
paracrystalline model school of thought. The calculation of the vibra
tional density of states for each model and comparison to experimental
Raman spectra was also insensitive to medium range topology. They
concluded that knowledge of the structure of aSi02, a material first
studied extensively over 50 years ago, is essentially incomplete. The
local structure is defined beyond reasonable doubt [41], but the medium
range structure, e.g., the ring statistics, extent of randomness, etc.,
is still a matter of debate.
Galeener [56] looked at the structural models for aSi02 for the
four ranges of order, namely short (SRO), intermediate (IRO, or
medium), long (LRO) and globalrange order (GRO). SRO involves specifi
cation of the bonding environment of each atomic species, essentially
the nearest neighbor (nn) environment, up to 0.3 run. Each Si atom is
surrounded tetrahedrally by four 0 atoms at d(SiO) 0.161 nm, and each
0 atom bridges between 2 Si atoms. There is a small spread in d(SiO), a
small spread in the OSiO angles, rp, (spread 0.75), and a large
spread in 6. Bell and Dean's ball and stick model [4951] contained a
well specified SRO and poorly specified IRO due to the way it was built.
IRO involves specifications of relative atomic positions over
several nm distances, given the SRO. It may take the form of specifica
tion of the dihedral angles, 6 and A, (see Fig. 2) for two corner shar
15
Figure 2. The relative orientation of two corner sharing silica tetrahe
dra, SiO^', showing the bridging oxygen bond angle, 6, the silicon
oxygen bond length, d(SiO), the OSiO bond angle, V>, and the tetrahe
dral angles, 6 and A, which define the angular orientation of the
tetrahedra about their bridging Si0 bonds. After [56].
16
ing tetrahedra, distributions of rings of completed bonds, network
connectivity, or some currently unformulated measure. The planar
cyclotrisiloxane D2 ring is an example, as is the assumption of random
dihedral angles used in the ZachariasenWarren model [40,41] for aSi02.
SRO and IRO specify structure in a volume 1.0 run in diameter.
Morphological LRO accounts for order in noncrystalline structures
on a long range scale, > 1.0 nm. These could be extended voids, chan
nels, spherulites, amorphous microphases, etc. Global range order
accounts for structural order which exists and/or is defined over
macroscopic distances, e.g., macroscopic isotropy, network connectivity,
chemical or structural homogeneity or heterogeneity.
Galeener [56] defines some aSi02 models in the above defined
range of ordering: 1) the Zachariasen model [40]; 2) the Zachariasen
Warren (ZW) CRN model [40,41], same as the well known Zachariasen model
except that d(SiO) is distributed over a narrow range about 0.161 nm (6
is broadly and unimodally distributed from about 120 to 180, with the
most probable value of 144; the dihedral angle is randomly distributed,
having no preferred value); 3) the Lebedev PoraiKoshits [LPK] micro
crystalline model [57], which consists of microcrystallites of cristoba
lite, with connective Si0 bonds between crystallites, and is specified
as noncrystalline (crystallite size is undefined but leads to structural
heterogeneity; this model was rejected by Warren in 1937 [58]); 4) the
Phillips model [59,52,54], rejected by Galeener [43], as discussed
earlier. Galeener [56] points out for model 3) that for 1.5 nm crystal
lites, nearly half of the atoms will be on their surfaces, which should
show up as a peak in Raman spectra, but do not.
17
Galeener [60] pointed out that glasses contain sufficient disorder
that their structure must be defined statistically, as must gases.
Numerous properties of aSi02 vary with preparation conditions, so
presumably does their structure in some statistically significant way.
Statistical structural models are very difficult to prove uniquely. Some
obvious shortcomings of the ZW models are as follows: in real life,
chemical order may occasionally be broken. Point defects are known to
exist in aSi02. Structural parameters are not uncorrelated; d(SiO) and
6 are known from chemical theory to be correlated. Furthermore 8 must be
correlated with d(SiO) 0, rj) and other values of 8 in order for the
ring of bonds to close on themselves. Significant numbers of regular
rings (planar 3fold and puckered 4fold) are believed to exist in
aSi02, and this implies special nonrandom values of 8. These shortcom
ings do not invalidate the ZW model, but rather point out improvements
that could be made in its specific details.
Marians and Hobbs [61] looked at the structure of aperiodic Si02
as a function of network topology, specifically at the ring structure.
They defined rings which are taken to be structurally significant as
those which are not decomposable into smaller rings. They defined a ring
to be indecomposable if there exists no path in the network which
connects any two of its vertices which is shorter than both of the paths
belonging to the ring which connect those two vertices. They applied
this model to the question of how many 3membered rings a network of
corner sharing tetrahedra could accommodate, such that the networks
should be strain free besides the 3membered rings themselves. They
found that large interconnected voids were formed which allowed the
network to form in a strain free manner with a low density. The struc
18
ture consisted of tetrahedra with a 3membered ring through each of two
nonintersecting edges. Topologically then Marians and Hobbs [61] stated
that it is possible to produce strain free structures only if porosity
is included. This describes the structure of silica gel, but statisti
cally a real silica gel would not possess 3membered rings in the
correct topological configuration to make them strain free. Some strain
would exist in the structure, possibly causing Dg values larger than
that of aSi02.
2.1,3 TEM Studies of aSilica Structure
Gaskell and Mistry [62] produced high resolution TEM micrographs
of small aSi02 particles about 15 nm in diameter. Micrographs of solu
tionprecipitated aSi02 had a more regular, ordered appearance than
those of a flame hydrolyzed aSi02. They suggested that regions of local
order could be observed in the micrographs, which would support an
"amorphous cluster" model of the structure. The regions of local order
that they suggested exist are not obvious, and their interpretation
could be different from that suggested, i.e. the structure could
actually be more random than Gaskell and Mistry [62] suggests.
Bando and Ishizuka [63] also examined the structure of aSi02
using dark field TEM images. Bright spots observed in the darkfield
image were interpreted as originating from microcrystallites about 1.7
nm in diameter. Yet again, as for other TEM references, the conclusions
are open to interpretation, because of the difficulty in assigning the
bright spots observed to a particular structural origin. This is due to
the problems in obtaining TEM micrographs of amorphous material, so the
bright spots could just as easily be due to mass thickness contrast.
19
2.1.4 Molecular Dynamic Simulations of the Structure of aSilica
Molecular Dynamics (MD) simulations of structure allow detailed
analysis of the atomistic motion and the complex microstructure that
give rise to the average properties of aSi02. The main disadvantage of
MD is the reliance upon an effective interaction potential, which cannot
effectively model the real binding energy and atomic forces of a
material. Nevertheless, MD simulations of the structure of aSi02 have
yielded reasonably accurate descriptions of the vitreous state. Molecu
lar Dynamics gives too high a defect concentration and too broad a range
of both bond angles, 6 and rf>. This is due to the omission of any
directionally dependent terms in the effective potential, required to
reflect the partial covalency of the system.
Feuston and Garafolini [64] added a small 3body interaction term
to a modified ionic pair potential to simulate the directionally
dependent bonding in aSi02. This improved the modeling of the short
range order around the Si atom, i.e the silica tetrahedra. The model's
RDF improved enough to give fairly good agreement with the Xray and
neutron scattering data on aSi02. Ring size distribution measurements
of the 648 atom aSi02 model gave equal concentrations (31%) of 5 and
6 membered rings, but with concentrations of 3% and 15% for D1 and D2
rings, respectively, which are too high.
Ochoa et al. [65] investigated the failure mode of aSi02 by
applying a uniaxial strain throughout an MD cell. They used a 2body
BornMayerHuggins potential because a 3body potential provided no
improvement in the behavior they investigated. The fracture stress of
the MD aSi02 structure increased as the strain rate increased. At "low"
strain rates below the speed of sound structural rearrangement occurred
20
by rotation of silica tetrahedra to increase 9 in the direction of the
applied stress. The system rearranged itself so that atoms attained new
equilibrium positions through vibrational motions. At "high" strain
rates above the speed of sound this was not possible and atoms were
forced far from their equilibrium positions so that the aSi02 failed by
extension of the Si0 bonds while 9 did not have time to increase.
2.1.5 Molecular Orbital (MO) Calculations of the Structure of aSilica
O'Keeffe and Gibbs [66] used MO theory to model defects in aSiO.,.
MO calculations on model molecules can accurately reproduce structural
configurations in solid oxides. They concluded that Phillips [54] model
of paracrystalline clusters with Si=0 at the internal surfaces was not
correct because the Si=0 bond energy is 380 kJ/mol less stable than two
Si0 single bonds, so Si=0 bonds can be ruled out as a major defect in
aSi02. The strain energy in 2membered siloxane rings eliminates this
configuration as a possibility, while larger rings are not specifically
excluded due to strain energy. The calculated frequencies and the ratio
of calculated frequencies strongly supported Galeener's assignment [67]
of the D1 and D2 bands in the Raman spectrum of aSi02 to be 0 breathing
modes in 4 and 3 membered siloxane rings respectively.
Michalske and Bunker [68] examined the dependence on strain of
siloxane bonds to rehydroxylation, and therefore bondbreaking, by H20
molecules. Molecular Orbital calculations suggested that bond angle
deformation (i.e. strain) is most effective in increasing the chemical
activity of the SiOSi bond. Strain transforms an inert Si0 bond into
a reactive site for adsorption, which consists of a Lewis acidic Si atom
and a Lewis basic 0 atom, while also weakening the Si0 bond.
21
The strainfree bonding configuration corresponded [67] to the
minimum energy value where d(SiO) = 0.163 nm, the OSiO tetrahedral
angle, is 109.5, and d = 144. Molecular Orbital calculations showed
that < 4 Kcal/mole is required to straighten d from 144 to 180 or
decrease 6 from 144 down to 130. Decreasing 6 from 144 to 100
required over 30 kcal/mole, a significant fraction of the total Si0
bond energy of 100 kcal/mole. Increasing or decreasing d(SiO) by 0.01
nm required 30 kcal/mole. Changing \Â¡> by 10 required 25 kcal/mole.
Strained surface defects in dehydroxylated aSi02 exhibited en
hanced reactivity compared to unstrained defects in two respects [68].
First, the strained defects acted as strong acidbase sites which
adsorbed chemicals such as H20 more efficiently than did unstrained
siloxane bonds. Adsorption of electron donor molecules such as pyradine
demonstrated the Lewis acidity of the strained surface defects. Sec
ondly, the Si0 bond in the strained defects were more susceptible to
reactions with adsorbed chemicals, which resulted in bond rupture.
McMillan [69] did a series of abntio M0 calculations to obtain
nonempirical force fields for silicate molecules. He obtained values of
around Ks = 600 Nm'1 for Si0 stretching, Ka = 4050 Nm'1 for OSiO
bending, and KR = 17 Nm'1 for SiOSi bending force constants, similar
to those used in structural model calculations. McMillan's calculations
revealed some low frequency dynamic modes, including the coupled
torsional motions of adjacent SiO^ tetrahedra which might give rise to
the low frequency excitations observed in aSi02. He speculated that
these excitations might explain the asymmetric shape of the main Raman
peak at 430 cm'1, which makes accurate and theoretically supportable
curvefitting of that peak so difficult.
22
2.1.6 Bonding and Structure Relationships in Silica Polymorphs
The variation in refractive index seen in the polymorphs of silica
are usually attributed to the associated changes in density. Revesz [70]
says that the molar refraction exhibits a systematic variation repre
senting differences in the Si0 bond which are related to the magnitude
of the 7r bonding between Si and 0. The Si0 bond is mainly covalent, so
calculation of ionic polarizabilities is not meaningful, and bond
polarizability, ab, can be used instead. This is determined by dividing
the molecular polarizability am by the coordination of silicon, where am
is calculated from the LorenzLorentz equation:
R* = (n2l/n2+2)Vm 7rNAam4/3 (1)
where = molar refraction, n refractive index, Vm = the molar volume
and Na = Avagadro's number. An increase in ab is associated with a
decrease in bond length.
For the crystalline polymorphs of silica, as the density increases
from 2.27 to 2.87 g/cc the 1100 cm"1 peak shifts from 1106 to 1077 cm"1.
The bond strength also decreases, the average 6 decreases from 146.8 to
139, the d(SiO) increases from 0.160 to 0.163 nm, n increases from
1.473 to 1.596, and ab decreases [70].
These changes are related to tt bonding decreasing as the density
increases and the ionic component of the Si0 bond increases concomi
tantly [70], The increase in density can be attributed to decreasing
d7rp7T bonding between Si and 0. The 7r bonding arises from the overlap of
the originally empty Si 3d orbitals with the 0 2p orbital containing the
lone pair of electrons, n bonding increases as 6 increases [71],
23
resulting in increased bond strength, increased ab and an increase in
the Si0 vibration frequency, as well as in decreased bond length. The
ionic component of the bond also decreases.
Revesz [70] gave a value for the ratio of the relative increase in
ab to the relative decrease in bond length, 1, i.e. (Aab/ab)/(Al/l) =
9.3 for Si0. This correlation only applied for the crystalline
polymorphs of silica with densities above 2.33 g/cc, corresponding to
cristobalite. Below 2.33 g/cc, as density increases, ab and d(SiO)
decrease as the Si0 vibration frequency and the bond strength increase.
This is the reverse to the behavior above 2.33 g/cc, which Revesz [70]
said was due to increasing delocalization of 7r electrons. Delocalization
of jt electrons in Si0 rings increases with ring size, but so does the
bond strain, presumably above the value of the equilibrium unstrained
ring. The it bonding and delocalization increase as density decreases.
The directionality ratio r = KQ/KS decreases from 0.199 to 0.163
as the density increases and the bonds become less directional, i.e.
less covalent and more ionic. Multiple bonding of the d7rp7r type for Si
is well established, especially in bonds to 0 [7073]. Overlap between
filled 0 p7r and Si dff orbitals increases as d increases.
Hill and Gibbs [74] examined the interdependence between tetrahe
dral d(SiO) bond length, the nonbonded nearest neighbor d(Si...Si)
separations and the bridging oxygen bond angle, d or
regression analysis of crystalline silica data. They found that d(SiO)
correlates linearly with seed over the entire range of observed angles
(137180). Shorter bonds involve wider angles, so that
d(SiO) = 0.068 seed + 1.526, R2 = 0.74
(2)
24
for d(SiO) = 0.1585 0.1623 ran.
The variance in d(SiO) is small compared to d(Si...Si), so the
Si...Si separation involved in a SiOSi linkage can be approximated by
the linear equation
log d(Si...Si) log 2d(Si0) + 0.81 log sin(0/2).
(3)
Log 2d(Si0) is the intercept = 0.503. It has been proposed [74] that
Si...Si controls the lower limit of 8 at a value = 0.300.31 nm. Values
as low as 0.29 nm fit into this empirical equation, suggesting [74] that
nonbonded interactions change continuously into bonded interactions
without showing a sharp break. A particular "hardsphere" nonbonded
radius for silicon may not be realized in solids.
The d(SiO) bond length also depends weakly on the d(Si...Si)
separation distance. As the Si atoms approach each other as 8 decreases,
d(SiO) increases slightly.
d(SiO) 0.121 d(Si...Si) + 1.982
(4)
for d(Si...Si) = 0.3 0.32 nm.
Newton and Gibbs [75] used abinitio MO theory to calculate
energyoptimized d(SiO) and angles for molecular orthosilicic and
pyrosilicic acids. They conclude that the local bonding forces in solids
are not very different from those in molecules and clusters. An extended
basis calculation for H6SiO^ implied there were about 0.6 electrons in
the 3d orbitals on Si. The bond length and angle correlations were
ascribed to changes in the hybridization state of the bridging 0 and the
25
(dp) irbonding involving all 5 of the 3d atomic orbitals of Si and the
lonepair atomic orbitals of the 0. There was a buildup of charge
density between Si and 0. The atomic charges of +1.3 and 0.65 calculat
ed for Si and 0 in a silica moiety of the low quartz structure conformed
with the electroneutrality postulate and with experimental charges
obtained from monopole and diffraction data for low quartz.
Gibbs [76] reviewed the abinitio calculations of bonding in
silicates. He showed that the disiloxy (SiOSi) group is very similar
in silicates, aSi02 and the gas phase molecule disiloxane with d(SiO)
= 0.162 0.165 nm and 9 = 140 150. d(SiO) shortened nonlinearly
when plotted against 9, but linearly when plotted against either the
hybridization index of the bridging 0 atom, A2 = l/cos
fraction scharacter, fg = (l+A2)'1. It is called the hybridization index
because its state of hybridization is given by the symbol sp1*. Figures
3 and 4 show this relationship for experimental and theoretical data.
Figure 5 shows a potential energy surface for the disilicic acid
molecule, H6Si207, with d(Si0) plotted against 9, on which is superim
posed the experimental bond length and angle data for the aSi02 polym
orphs [76]. The data follow the general contour of the surface, but the
observed d(SiO) are about 0.002 nm longer on the average than that
defined by the valley in the energy surface. The difference may be
related to lattice vibrations at room temperature. The barrier to
linearity of the disiloxy molecule is defined to be the difference
between the total energy of this molecule evaluated for a straight
bridging angle and that evaluated at the minimum energy angle. This is
small, about 3kT at 300 K, so a relatively small amount of energy is
expended in deforming the disiloxy angle from its minimum energy value
26
 Sec 9 []
Figure 3. The Si0 bond length as a function of Sec(0) for the silica
polymorphs low tridymite, low quartz, and coesite. The d(SiO) have a
standard deviation < 0.005 . The linear fit line is the best fit linear
regression analysis of all the data points. After [74].
d (Si O) [A]
27
e [] fs
Figure 4. A comparison of the experimental d(SiO) in coesite (upper
curves in (a) and (b)) with those calculated for the bridging d(SiO) in
a disilicate molecule, H6Si207 (lower curves in (a) and (b)). d(SiO)
varies nonlinearly with 0 and linearly with fg = 1/(1 + A2 ), where A2 =
Sec(0) is called the hybridization index of the bridging 0 atom because
its state of hybridization is given by the symbol sp*!. After [76],
28
en
Figure 5. Potential energy surface for the disilicate molecule, H6Si207,
plotted as a function of d(SiO) and 8. The contours represent incre
ments in energy of 0.005 a.u. = 0.6257 kcal/mole relative to the minimum
energy point (1091.76678 a.u.) denoted by the cross. Increasing contour
numbers represent increasing energy. The dashed line represents the bond
lengths and angles for the disiloxy groups in the silica polymorphs
coesite, tridymite, low cristobilite and aquartz. After [76],
29
to 180. If the bonding force in disilicic acid and the silica polymor
phs are similar, then the disiloxy angles in the latter may be readily
deformed from their equilibrium values. This causes the broad distribu
tion of 8 seen in polymorphs and aSi02 without destabilizing the final
structure.
Gibbs [76] calculated the 8 distributions for 3, h, 5 and 6
membered rings in silicates and siloxanes. The expected increase in the
average 8 and the width of the 8 distribution with ring size is ob
served, showing reasonable agreement with experimental observations.
Janes and Oldfield [723] investigated the bond structure of the
Si0 bond and favored the (dp)7T bonding model, discussed by Revesz
[70], for the Si0 bond in silicates. This involves the atomic dorbit
als of Si and the porbitals of 0 in SiO^ tetrahedra, with the possibil
ity of an admixture of s and p character in the dorbitals as well as
significant overlap with the three Si dorbitals and/or the Si
<7*orbitals. Janes and Oldfield [73] examined the question, given the
existence of (dp) 7rbonding, to what extent is the effect significant;
i.e. does the correlation between d(SiO) and 8 originate from changes
in (dp) 7rbonding? Molecular Orbital calculations showed the possibili
ty of (dp) irbonding but implied only minor structural significance, so
the (dp) 7Tbonding effect facilitated charge transfer, but it was
insensitive to variations in d(SiO) or 8.
Devine et al. [7780] concluded from Magic Angle Sample Spinning
Nuclear Magnetic Resonance (MASS NMR) data of compacted aSi02, in
agreement with Revesz [70] that 8 variation causes charge transfer
effects in the bridging bonds. From the MAS NMR and photoemission
spectroscopy data Devine [79] derived the relationship
30
d(29Si chemical shift,ppm)/d(Si2p3/2 core shift) = 1316 ppm/eV. (5)
When combined with the NMR data on the dependency of the chemical shift
on 6, direct data on the spread in bond charge transfer can be obtained.
Therefore ir bonding magnitude due to 6 variation can also be obtained.
2.2 The Theory of Raman and IR Scattering
Vibrational spectroscopy involves the use of light to probe the
vibrational behavior of molecular systems, using an absorption or a
light scattering experiment. Vibrational energies of molecules and
crystals lie in the approximate energy range 060 KJ/mol, or 05000
cm'1. This is equivalent to a temperature (kT) of 06000 K, and is in
the IR region of the electromagnetic spectrum [81].
The simplest description of vibrations of molecules and crystals
is a classical mechanical model. Nuclei are represented by point masses,
and the interatomic interactions (bonding and repulsive interactions) by
springs. The atoms are allowed to undergo small vibrational displace
ments about their equilibrium positions and their equations of motion
are analyzed using Newtonian mechanics. If the springs are assumed ideal
so the restoring force is directly proportional to displacement (Hooke's
law), then the vibrational motion is harmonic, or sinusoidal in time.
The proportionality constant which relates the restoring force to
vibrational displacement is termed the force constant of the spring.
Solution of the equations of motion for the system allows a set of
vibrational frequencies fj to be identified. Each frequency corresponds
to a particular atomic displacement pattern, known as a normal mode of
vibration. In many vibrational studies the object is to deduce the form
31
of the normal modes associated with particular vibrational frequencies.
This allows vibrational spectroscopy to be used as a structural tool.
The classical model allows a description of the basic features of
vibrational motion. It does not give any insight into why vibrational
spectra are line spectra rather than continuous absorptions, nor into
the interaction of vibrations with light. For this, you must construct a
quantum mechanical model, where Schrodinger's wave equation is con
structed in terms of the vibrational displacement coordinates q.. An
appropriate potential energy function V(q5) is assumed. This gives a set
of partial differential equations from the vibrational wave equation.
Solution of these differential equations gives a set of vibration
al wave functions. Each function describes a vibrational normal mode and
a set of associated vibrational energies. These wave functions and
energies are quantized, so they can take only discrete values determined
by a vibrational quantum number vf, where i = 0, 1, 2, 3, etc. The
quantized energies are usually shown on an energy level diagram as the
vibrational energy levels for the system. In a vibrational spectroscopic
experiment, the system undergoes a transition between vibrational levels
with quantum numbers v, and v. Light is absorbed or emitted with an
energy (AE = hv) corresponding to the separation between the levels.
In a Raman scattering experiment, visible light from an intrinsi
cally polarized monochromatic laser is passed through the sample. About
0.1% of the laser light is scattered by atoms. About 0.1% of the 0.1%
scattered light interacts with the sample in such a way as to induce a
vibrational mode. When this occurs, the energy of the scattered light is
reduced by an amount corresponding to the energy of the vibrational
transition. This type of inelastic scattering is known as Raman scatter
32
ing, while the elastic light scattering with no change in energy or
frequency is known as Rayleigh scattering. The energy of the scattered
light is analyzed using a spectrometer. Raman lines appear as weak peaks
shifted in energy from the Rayleigh line (Fig. 6). The positions of
these Raman peaks about the incident line correspond to the frequencies
of Raman active vibrations in the sample.
In Raman scattering, the light beam induces an instantaneous
dipole moment in the molecule by deforming its electronic wave function.
The atomic nuclei follow the deformed electron positions. If the nuclear
displacement pattern corresponds to that of a molecular vibration, the
mode is Raman active. The size of the induced dipole moment is related
to the ease with which the electron cloud may be deformed, described by
the molecular polarizability am. The Raman activity of a given mode is
related to the change in polarizability during the vibration. In general
the molecules containing easily polarizable atoms, such as I, S and Ti
have very strong Raman spectra. Similar molecules with less polarizable
atoms, such as Si, C and 0, have much weaker spectra. In contrast to IR
spectra, the most symmetric modes give the strongest Raman signals since
these are associated with the largest changes in polarizability.
The number of vibrational modes seen for a molecule is equal to
the number of classical degrees of vibrational freedom, 3N6. N is the
number of atoms in the molecule. For crystals, N is equal to Avagadro's
number, but most of the modes are not seen. This is due to the translat
ional symmetry of the atoms in the crystal. The vibration of each atom
about its equilibrium position is influenced by the vibrational motion
of its neighbors. Since the atoms are arranged in a periodic pattern,
the vibrational modes take the form of displacement waves travelling
Figure 6. The principles of Raman scattering, (a) The incident laser
beam, energy E, passes through the sample and the scattered light is
detected to the spectrometer, (b) The Raman spectrum consists of a
strong central peak at the wavelength of the laser energy E due to the
Rayleigh scattering, and the much weaker Raman shifted lines at Eie^,
where e^ = hi/,, correspond to the energies of vibrational transitions in
the sample in cm'1, where E = 0 cm'1. Stokes Ramanshifted frequencies
(Ee) are positive wavenumber values, and antiStokes Ramanshifted
frequencies are negative wavenumber, (c) The energy level diagram for
Rayleigh and Raman scattering. There are two energy levels which are
separated by an energy e = hi/, where v is the vibrational frequency. The
incident laser photon, energy E, excites the vibrational mode to a
shortlived (10'14 sec) electronic "virtual state", which decays with
the release of a photon. When the final vibrational state of the
molecule is higher than that of the initial state, the released photon
energy is Ee, and StokesRaman scattering has occurred. When the final
state is lower, the released photon has energy E+e, and antiStokes
scattering has occurred. When the initial and final states are the same,
Rayleigh scattering has occurred and the incident and released photons
have the same energy E. After [81].
34
(b)
t RAMAN SPECTRUM
WAVENUMBER [cnf1].
/ I \
/ I \
(c) / I \
/ I \
T
I
j i
AntiStokes
Raman
Raleigh
Virtual
State
Stokes
Raman
n = 1
n = 0
Figure 7. The various types of crystal lattice vibrations, (a) The
wavelength of this lattice mode is long compared to the crystal lattice
constant, a, so the mode lies at the center of the Brillouin zone (k =
0). (b) This mode has wavelength A = 2a, and lies at the edge of the
Brillouin zone (k = 7f/a). The waves in (a) and (b) represent transverse
lattice vibrations for a monatomic chain of atoms, (c) This illustrates
a longitudinal lattice vibration for the same monatomic chain, (d) For
any crystal, there are three lattice vibrations where all the atoms in a
unit cell move in phase in the same direction. These are the acoustic
modes, (e) For crystals with more than one atom in the primitive unit
cell, there are modes where atoms in the unit cell move in opposing
directions (illustrated for a diatomic chain). These motions can
generate a changing dipole moment and hence interact with light. These
are called optic modes, (f) A typical dispersion curve in one direction
in reciprocal space for a crystal, in this case with n = 4 atoms in its
unit cell. Only long wavelength lattice vibrations (near k 0) can be
infrared or Raman active due to the long wavelength of light compared
with crystal lattice spacings, which are marked with dots. After [81].
36
(a)
i 1 1 1 1J H
A.> k = 0
k = Wavevector
(b)
W^sAs
X = 2a k = ^
Transverse
a =Lattice Spacing
(c)
Longitudial
(d)
Acoustic Mode
d = Unit Cell Dimension
(e)
Optic Mode
(f)
3n 3 Optic
Branches
}3 Acoustic
Branches
kmax
Wave vector k =4
d
37
through the crystal. These are known as lattice vibrations. The lattice
waves are described as longitudinal when the nuclear displacements are
parallel to the wave propagation direction. They are described as
transverse when the displacements are perpendicular to the propagation
direction (Fig. 7).
The nuclear displacements give rise to an oscillating dipole
moment, which interacts with light in a spectroscopic experiment. The
frequency of this oscillating dipole wave is defined by the oscillation
frequency of individual atoms about their equilibrium position. Its
wavelength is defined by that of the associated lattice vibrations. In
order for the lattice vibration to interact with light, the wavelength
of the lattice vibration must be comparable to that of light, for
example 514.5 nm. This is much larger than the dimensions of crystalline
unit cells. Therefore only very long wavelength lattice modes can
interact with light in an IR or Raman experiment. In these long wave
length lattice vibrations, the vibrations within adjacent unit cells are
essentially in phase. The number of vibrational modes which may be seen
in IR or Raman spectroscopy is equal to 3N3. N is the number of atoms
in the primitive unit cell. These 3N3 vibrations which can interact
with light are termed the "optic modes." Transverse and longitudinal
optic modes are termed TO and LO modes for short.
Crystal lattice vibrations are usually described by k, the wave
vector. The direction of k is the direction of propagation of the
lattice wave, and the size of k is 2n/\. A is the wavelength of the
lattice wave. The relationship between the frequency of a particular
normal mode and the wavelength of its propagation through the lattice is
known as a dispersion relation. This is usually represented graphically
38
as a dispersion curve y(k) (Fig. 7). Each normal mode is associated with
a branch of the dispersion diagram. In any particular crystallographic
direction in reciprocal space, there are 3N branches. Three of these are
the acoustic branches, which cause the propagation of sound waves
through the lattice. At infinite wavelength, that is at k = 0, the three
acoustic modes have zero frequency, and correspond to translations of
the entire crystal. The remaining 3N3 branches are known as the optic
branches. They can give rise to IR and Raman active vibrations for long
wavelength modes (k 0).
The shortest wavelength A for lattice vibrations is defined by the
lattice constant, a, with the adjacent unit cells vibrating exactly out
of phase. The A of the lattice wave is then 2a, corresponding to k =
7r/a. The phase relations between vibrations in adjacent unit cells
define a region in reciprocal space between k = ir/a and k n/a. This
region is known as the first Brillouin zone. Long A lattice vibrations
with k = 0 are said to lie at the center of the first Brillouin zone.
Just like molecules, crystal lattice vibrations are more completely
described by the quantum mechanical model. The vibrational spectra of
crystals correspond to transitions between vibrational states. The basic
unit of vibrational excitation in a crystal is known as a phonon, by
analogy with the term photon for a quantized unit of light energy.
In a spectroscopic experiment, such as IR and Raman spectroscopy
for probing vibrational modes, we are concerned with transitions between
quantized states, from some initial state, n, to another state, m. The
energy associated with the transition is the difference between the
energies of the two states, AE = E En. The intensity of the observed
line is related to the probability of the transition n + m, described by
39
the Einstein transition probabilities for absorption (B^) and induced
emission (B^) The Einstein coefficient for absorption describes the
case where a system is initially in state n and absorbs a quantum of
energy from an applied radiation field to undergo a transition to a
higher energy state m [82]. The transition probability is maximized when
the energy of the radiation corresponds to AEmn. The set of probabili
ties for transitions between sets of levels are known as the selection
rules for the spectroscopic transitions in the system.
For IR absorption, the oscillating electromagnetic field of the
incident light causes a timedependent perturbation of the system from
its initial state n. This perturbation is responsible for the transition
to the higher energy state m, so IR absorption can be considered as a
timeindependent perturbation followed by a timedependent perturbation.
In Raman scattering, the system is perturbed by the incident beam before
the transition takes place, so Raman scattering can be considered as two
consecutive timedependent perturbations to the system.
In an IR experiment the system absorbs a quantum of light with
energy in the infrared region of the spectrum. This causes the system to
change from a vibrational state with quantum number vn to one with
quantum number v For the timedependent perturbation theory, the
perturbation can be described as an interaction between the oscillating
electric field vector, E, of the light and the instantaneous dipole
moment vector, fi, of the molecule. For a diatomic molecule, the dipole
moment is defined by fi = Qrg. Q is the charge difference between the
atom centers, and rg is the atomic separation. When rg = rQ (the equi
librium bond distance), Â¡i0 is the permanent molecular dipole moment.
40
During a vibration, the atoms undergo small displacements, Ar, in
relation to each other.
The size of the instantaneous dipole moment generated depends on
Ar and /. Vibrations are IR active if there is a dipole moment change
during the vibration and if n = m 1, i.e. if the vibrational quantum
number v changes by one unit. These two conditions are the selection
rules for IR of the harmonic oscillator. For an absorption line, if the
lower state is the vibrational ground state (v = 0), this is the
fundamental absorption line, from v = 0 to v = 1. The intensity of the
transition is a the size of the dipole moment change during the vibra
tion (d/z/d(Ar)). These selection rules can be extended to polyatomic
molecules and condensed phases. In general for a vibration to be IR
active the vibrational motion must cause a change in the dipole moment,
i.e. d/i/dq. # 0, where q5 = the vibrational normal coordinate. This can
occur even when the molecule has no permanent dipole moment.
For crystals, an additional selection rule is introduced by the
translational symmetry of the crystal. The vibrational normal modes are
cooperative lattice distortions. If the mode causes a dipole change
within the unit cell, an electric dipole wave forms within the crystal.
It has a well defined wavelength and wave vector in the direction of
propagation. This dipole wave can only interact with light when its
wavelength is comparable with that of infrared radiation. This occurs
when the wavelength of the electric dipole wave is very large or the
wave vector tends to zero.
In Raman spectroscopy a beam of light is passed through a sample
and the energy of the scattered light is analyzed. Both elastic (Ray
leigh) and inelastic (Raman) scattering is seen. Raman scattering occurs
41
via interaction with the vibrational wave function of the system. The
scattering mechanism can be described by the instantaneous dipole moment
/ijnd induced in the system by the incident light beam:
/i = amE = QmE0cos27rft (6)
where E is the oscillating electric field vector of the radiation with
frequency f and amplitude EQ and am is the molecular polarizability
which expresses the deformability of the electron density by the
radiation field. Since /iind and E are not collinear, am is a second order
tensor. Since the polarizability will in general change during a
molecular vibration, it is commonly expanded in a Taylor series. The
action of the light beam in creating the instantaneous induced dipole
moment is the first timedependent perturbation on the system. In the
second step of the analysis the vibrational wave functions corresponding
to the initial and final states of the system are allowed to interact,
modulated by the induced dipole moment [82].
This treatment results in the selection rules for the vibrational
Raman effect. The Raman intensity for a transition between vibrational
states n and m is proportional to the square of the transition moment
Mm. A vibration is Raman active then, i.e. M + 0, when the vibrational
quantum number changes by one unit between states n and m, and the term
dp/d(Ar) # 0. The first selection rule is relaxed for anharmonic
molecular vibrations, allowing overtone bands to appear in the Raman
spectrum, as for IR absorption. The second selection rule implies that
for a vibrational mode to be Raman active there must be a change in
molecular polarizability associated with the vibration [82].
42
The methods of symmetry and group theory provide techniques for
predicting the IR and Raman activities of all vibrational modes of even
complex molecules and crystals. Molecular symmetry is described for a
set of conventionally chosen symmetry elements, which express certain
spatial relations between different parts of the molecule. For any
molecular system, the set of symmetry operations showing the symmetry of
the molecule forms a mathematical group. This is a special type of set,
satisfying particular combination relations between the elements of the
set. Group theory is the mathematical framework within which quantita
tive descriptions of the symmetry possessed by a structure are con
structed. McMillan and Hess [82] discuss the theory of symmetry and
group theory as applied to molecular structure and spectroscopy.
Knowledge of the symmetry information from group theory then
allows prediction of which vibrations will be IR active and which will
be Raman active. For each symmetry operation found (associated with a
particular vibration), the Cartesian translations of the coordinate
origin caused by each are examined. If the origin shows any translatio
nal (as opposed to rotational) movement for a particular vibration
associated with a symmetry operation, that vibration will be IR active.
This is because for IR activity there must be a change in the dipole
moment, Afi, during the vibration. Since the dipole moment is a vector,
this change can be expressed by the Cartesian coordinates A/x, A/y and
Anz. These belong to the same symmetry species as Cartesian translations
of the origin, so they can be examined to check for IR activity [82].
The condition for Raman activity of a vibrational mode is that
there must be a change in its polarizability am during the vibration.
This polarizability change can be expressed in terms of the second order
43
tensor elements axx, a azz, axy, aÂ¡xz and ayz. Since this tensor is a
linear function of the atomic displacement [83,p.154], the elements of
the tensor transform in the same way as the quadratic combinations of
the Cartesian translations x, y and z of the coordinate origin of the
atom for a particular vibration. Examination of these quadratic combina
tions for a particular molecule or crystal by group theory identifies
the symmetry species of Raman active vibrational modes, and therefore
the vibrational modes themselves [82].
The determination of the symmetry species for the vibrational
modes of a molecule or crystal allows immediate prediction of the number
and type of 1R and Raman active vibrations of the molecule or crystal.
For a crystal structure only those vibrational modes for which all units
cells vibrate in phase can give rise to an infrared or Raman spectrum.
Therefore you need only consider the unit cell symmetry to determine the
number and species of IR and Raman active modes of a crystal [82],
For an amorphous material the selection rules no longer apply. The
theory of which modes will be IR or Raman active is not as well devel
oped. IR and Raman spectroscopies probe the same vibrational modes in
pure aSi02. In IR spectroscopy, the electric field of the IR radiation
couples with the instantaneous dipole moment created by the relative
motions of atoms with opposite charges. Raman spectroscopy probes non
polar modes, which explains why Raman modes involve symmetric vibration
al modes, as these do not involve the dipole creation caused by asymmet
ric charge movement [84]. This supports the assignment of the symmetric
0 breathing mode of the 3 and 4 membered silicate rings to the D, and D1
Raman peaks, respectively. The known theories of the vibrational spectra
of aSiO., are discussed in the next section.
44
2.3 Modelling the Vibrational Behavior of aSillca
Wadia and Balloomal [46] developed a model explaining the Raman
and IR spectra of aSi02 in which the tetrahedral SiO^ units were linked
to fixed walls, and claimed that the model's predictions gave a satis
factory but not very accurate interpretation of the observed spectra.
Bell and Dean [49] pointed out that traditionally there are two
main approaches to the problem of determining atomic vibrational
behavior in glasses. The first one used methods developed in the theory
of molecular spectroscopy, and the second was based on the techniques of
crystal lattice dynamics. The first approach rests upon the implicit
assumption that the vibrational behavior of a small unit of the glass
structure can adequately characterize the entire glass system. The small
unit contains only several molecules [49]. Such a method often gives
quite a reasonable account of the number and position of bands in the
vibrational spectra. However, it can give a description of the detailed
atomic motions only for those vibrational modes of the full glass system
which are intensely localized in regions similar to the units consid
ered. The second approach replaces the glass, not with a small molecular
unit, but with an infinite regular crystalline array. The vibrational
properties of this array are derived using conventional lattice dynamics
procedures. This method gives a fair account of the band positions.
Implicit in the approach is the assumption of an extended wavelike form
for the normal modes of vibration.
Bell and Dean [49] took a third approach to determining the
vibrational behavior of aSi02. They used a physical ball and stick
model of a giant inorganic molecule complying with short range structur
al data obtained from Xray and neutron scattering experiments on
45
aSi02. They calculated the normal mode frequencies and atomic ampli
tudes of vibration of the model using a central Si0 force constant Kg =
400 N m'1 (1 N m'1 1000 dynes/cm). The ratio of the noncentral OSiO
force constant Ka to the Kg was taken as 3/17 0.176. They obtained
frequency distribution histograms for aSi02 which were similar to
experimental Raman spectra, possessing all the main structural peaks.
With the surface nonbridging bonds fixed, they obtained peaks at 400,
500 (shoulder), 750 and 1050 cm'1. This compared with their observed
experimental peaks at 500, 600, 800 and 1100 cm'1.
Detailed analysis of selected normal modes by Bell and Dean [49]
showed that the 1050 cm'1 band in the calculated spectrum was associated
with an asymmetric bond stretching vibration where bridging oxygen atoms
moved parallel to the Si...Si line joining their immediate Si neighbor
(Fig. 8). The modes in the 500 cm'1 (shoulder) and 800 cm'1 regions were
associated with bond bending vibrations in which 0 atoms moved along the
bisectors of the SiOSi angles (Fig. 8). In the 400 cm'1 peak the modes
were associated with the bondrocking motion of bridging oxygens
vibrating perpendicular to the SiOSi planes (Fig.8). Bell and Dean
[49] concluded that neither the purely molecular approach nor that based
on an undiscriminating use of crystal lattice dynamics was likely to be
fully successful in yielding information on vibrational modes throughout
the spectrum. Only a much more flexible scheme, such as that based on an
extended atomic model is capable of reproducing the full range of vibra
tional behavior. Galeener and Wright [43] agree with this method being
the best way to prove a theoretical model of the structure of glass.
Galeener has done a lot of work on the structure of aSi02 and the
interpretation of its Raman and IR spectra. The Raman spectrum of fused
46
Oxygen
Bending = W3
Stretching = W4
Rocking
Figure 8. Normal vibrations of a disilicate molecular unit in aSi02.
The axes point along the direction in which the bridging 0 atom moves in
the bond bending, stretching and outofplane rocking normal modes.
These normal modes correspond to peaks in the Raman spectra of aSi02.
The bondbending axis is parallel to the bisector of the SiOSi angle,
and is assigned to the W3 peak at 800 cm'1. The bond stretching axis is
perpendicular to this bisector, but still in the SiOSi plane, and is
assigned to the peak at 1060 cm'1 and 1200 cm*1. The bond rocking
direction is orthogonal to the other axes and is normal to the SiOSi
plane, i.e. outofplane. After [85].
47
aSi02 (also known as vitreous or melt derived silica) has long been
puzzling because it contains peaks which have not been explained by
vibrational calculations on the favored CRN structural model. Galeener
and Lucovsky [86] demonstrated that a complete explanation of the
vibrational spectra requires incorporation of another type of interac
tion between the tetrahedra. That is the longrange interaction provided
by the Coulomb fields associated with certain excitations of the system.
There are two types of macroscopic modes: transverse and longitu
dinal. In an isotropic medium such as glass, transverse modes are those
in which the average electric vector E is perpendicular to the direction
of periodicity of the wave (Fig. 7(b)). Their resonant frequencies are
determined by poles in K2 s Im(K) where K* K1 + iKj = Re(K) + Im(K) is
the complex dielectric constant of the medium. Longitudinal modes are a
complementary set whose average electric field is completely parallel to
the direction of periodicity (Fig. 7(c)). Longitudinal modes normally
resonate at zero values of K*. In the long wavelength limit [86,87] they
resonate at poles of the dielectric energyloss function Im(1/K*). The
converse statement then follows. Peaks in K2 reveal transverse modes,
while peaks in Im(1/K*) identify longitudinal modes [86,87]. The ob
served poles in Im(1/K*) occur at zeros of K* [86].
Galeener et al. [86,87] investigated the possibility of longitu
dinal response in aSi02 by determining the poles in K2 and Im(1/K*)
and comparing their positions with those of the observed Raman spectra.
KramersKronig techniques were applied to IR reflectivity spectra to
obtain IR values of K* = K1 + iK2, and the latter were used to compute
Im(1/K*) = K2/(K,2+K22) Galeener reported the existence of three TOLO
pairs at 455 and 495 cm'1, 800 and 820 cm"1, and 1065 and 1200 cm"1. They
48
are called optical modes because they appear at sufficiently high
frequencies to obviate the possibility of their being acoustic. Galeen
er's initial interpretation [86] of the 495 cm"1 peak was wrong [87], as
was [5] Walrafen's [88,89] assignment to sSi+ and =Si0" defect centers.
Wong and Angel [90] reviewed the early literature of the paracry
stalline models for the vibrational spectroscopy of aSi02. They pointed
out that the abnormal excess heat capacity of aSi02 is contributed by
the optical modes of very low frequencies.
The lack of translational symmetry in amorphous materials prevents
their vibrational excitations from being described by plane waves
propagating from unit cell to unit cell. The theoretical understanding
of the vibrational properties of random networks is much less complete
than it is for crystals [91]. The principal theoretical approaches
applied to amorphous materials have involved either numerical techniques
to determine the modes of random networks, or attempts to identify
molecular units that retain their integrity to some degree in the
amorphous solid that can be analyzed on their own. Numerical techniques
involve building a ballandstick model of the structure, and the
problem is reduced to diagonalizing a large matrix and finding the
associated density of eigenvalues. With care over the treatment of the
surface, reasonable density of states have been obtained for aSi02
[4951]. This approach reproduced the broad density of states, implying
that aSi02 is best regarded as a giant covalently bonded molecule which
cannot be subdivided into molecular units in any obvious way. The
density of states would contain sharp peaks if the structure could be
decomposed into weakly interacting molecular units.
49
aSi02 consists of a random 3dimensional network of SiO^4' tetra
hedra and these basic tetrahedra retain their integrity in the crystal
line polymorphs of silica. The molecular modes of SiO^' play an impor
tant role in determining the vibrational spectra of aSi02, as does the
magnitude of the bridging 0 bond, 0. 0 determines whether the material
possesses narrow molecular modes or broader solidstate bandlike modes
due to increased effective coupling of the individual tetrahedra. The
transition occurs as 0 increases from 90 to 180 [91] The normal
vibrational modes of AXA tetrahedral molecules are well known [52]. They
consist of a nondegenerate scalar A1 (symmetric breathing) mode, a
doubly degenerate E tensor mode, and two triply degenerate vector
bending and stretching f21,2 modes. All modes are Raman active, but only
the f21,2 vector modes are infrared active. The CRN model leads to the
separation of continuum modes in the glass and this establishes their
connection to the normal modes of AX^ free molecules [91].
Sen and Thorpe [91] developed a simple model to study the vibra
tional density of states of aSi02> They used just the nearestneighbor
central Bornforce, Kg, between Si atoms bonded to 0 atoms, which
allowed them to study the transition from molecular to solidstate
behavior as 0 changes. They showed that because 0 is larger than a
critical angle 0C, where $c = cos"1 (2M0/3MS]) 112.4 for aSi02, effec
tive coupling among the tetrahedra leads to solidstate modes, rather
than molecular modes. Therefore the vibrational characteristics of
aSi02 are determined more by 0 than by the SiO^ tetrahedra. Inclusion
of a small noncentral force does not modify these results, because the
nearneighbor noncentral force constant Ka is small so the high fre
quency optic modes are well represented by this model. is the bond
50
bending noncentral force function acting at right angles to the central
bond stretching force function, Kg (also known as a). Ka must be includ
ed when examining low frequency modes.
Sen and Thorpe [91] developed equations for the dependency on the
atomic masses of silicon and oxygen, M$j and Mq, the central force
function Kg (N/m) and (), of the spectral limits of the two highest
frequency modes in the vibrational density of states of aSi02
Wl2 = (V^) (1 + cos) (7)
w22 = (Kg/Mj,) (1 cos) (8)
w32 (Kg/^) (1 + cos) + 4/3 Kg/Msj (9)
w42 = (Kg/Mjj) (1 cos) + 4/3 Kg/Msi, (10)
where w1, a>2, w3 and w4 are the angular frequencies (rad/sec) of the
spectral limits of the two highestfrequency bands in the vibrational
density of states (VDOS) of aSi02. These limits therefore equate to
four states in the VDOS, which account for four of the nine expected per
formula unit Si02. The remaining five states are acoustical states
driven to zero frequency because Ka = 0 in this model [87,88,91],
Equations (7)(10) (as well as equations (11) and (12)) remain
true if w (rad/sec) is replaced by the wavenumber value (cm'1) of the
frequency, M by the atomic weight of the atom, and Kg by Kg/0.0593,
where Kg (dyn/sec) = 1000 Kg (N/m) [92] Dimensional analysis of equa
tions (7)(10) shows that radians is missing as a dimensional unit, so
the equations do not balance. This is because the assumptions that had
to be made to solve the three body problem used for Sen and Thorpe's
51
model [91] of the vibrational density of states involved removing 9
(units of radians) as an implicit variable [93].
Bell and Dean assign w1 (=W,j) to the bond rocking (R) outof
plane motion of the SiOSi bridging bonds, u>3 (= W3) to the bond
bending (B), or symmetric stretch (SS) motion of the SiOSi bridging
bonds, and (s W4) to the bond stretching (S) or antisymmetric
stretch (AS), motion of the SiOSi bridging bonds [94] (Fig. 8). In Sen
and Thorpe's model [91] the bond rocking (R) motion perpendicular to the
plane of the SiOSi plane does not occur because there is no restoring
force for this vibration, i.e. Ka = 0, so no bond length change is
involved in the vibration.
Galeener [92] developed a method for analyzing the vibrational
spectra and structure of AX2 tetrahedral glasses, based on interpreting
the vibrationalband limits calculated for the centralforce network
model developed by Sen and Thorpe [91]. The model assumed a certain
geometry for neighboring bonded silica tetrahedra which was not periodic
in space but had identical OSiO angles = cos'1 (1/3) = 109.5 and
common SiOSi angles 9. The dihedral angle, 6, was allowed to have any
value. The bonds possessed the types of vibrations known to exist in the
aSi02 structure. These are the bending, stretching and rocking motions
of the 0 atom, using the nomenclature in Fig. 8 [51].
A statistical distribution of 9 is used to simulate disorder in
the model. From his analysis of this model, Galeener concluded that the
centers of the two high frequency bands seen in aSi02, W3 (810 cm"1) and
W^, (1060 and 1200 cm'1) are associated with w3 and w^., evaluated at the
most probable intertetrahedral angle. Galeener [92] therefore developed
expressions for the calculation of the Si0 bondstretching constant,
52
Ks, and the SiOSi angle, 0, from the experimentally determined values
w3 = w3(0) = W3 and w4 = w4(0) = W4, and the masses of the vibrating
atoms
Ks 0.5(w32+w42)M0(1+4M0/3MSi)'1 (11)
cos0 = (w32w42)(w32+w42)'1(l+4M0/3Msi) (12)
Substitution of the W3 and W4 peak positions of aSi02 into
equations (7)(12) yielded quantities that were within 10% of those
given by the calculation based on Born forces and realistic disorder
developed by Bell et al. [49,50,95], even though these expressions
involve the assumption that Ka = 0. Galeener [92] therefore concluded
that the SenThorpe theory was realistic and could be used to analyze
the structure of aSi02.
The splitting of the highestfrequency mode W4 into a wellsepa
rated transverseoptical longitudinaloptical (TOLO) pair is not
accounted for by this theory. The position of the so called baremode,
whose frequency is split by Coulomb interactions into the TOLO pair,
cannot be predicted by any known theory. Galeener [92] showed that the
bare mode lies nearer the L0 frequency than the TO frequency. He applied
equations (11) and (12) to the measured values of W3 LO and W4 LO and
obtained values of Kg 569 N/m and 0 = 130 compared to the Xray
diffraction value of 144 [41]. Galeener [92] obtained values of Kg
444569 N/m and 0 w 126130.
The calculated wavenumber of the lowestfrequency limit is very
similar to the main 450 cm'1 W1 Raman peak. From this, Galeener [92]
inferred that the dominant W1 450 cm'1 Raman peak occurred at the
53
lowfrequency edge of the band whose parentage is the breathing mode of
the isolated molecule. Therefore, the Raman matrix element (or coupling
coefficient) must peak sharply at this position. This demonstrates a
case where the coupling coefficient in Shuker's theory [9697] is not
constant, but is a sharp function of frequency over the band involved,
and peaks near one edge [92],
Raman scattering is known to arise largely from symmetrical
changes in bond length (bond polarization) rather than bond angle [92]
(as opposed to IR scattering which arises from asymmetrical vibrations).
The Raman strength is therefore maximum for the inphase stretching
associated with bendingtype motion at W1. It is reduced for the outof
phase stretching associated with the stretchingtype motion which occurs
at the theoretical W2 band edge. This explains why the main 450 cm'1
peak is so intense and the theoretical peak W2 is not visible in experi
mental Raman spectra. Galeener was therefore able to attribute on a
theoretical basis the main Raman peaks to vibrations of the structural
units of aSi02. These are: 450 cm'1 = = W1, 800 cm"1 = w3 s W3, 1060
and 1180 cm'1 = = W^, while a>2 = W2 was assigned to 990 cm'1. He
derived an expression relating the fullwidthhalfmaximum (FWHM) of the
Raman peaks to the FWHM of 0, i.e A0. The Xray diffraction derived
value of A0 is 35 [41]. Galeener [92] calculated a value from of
Ad 34, which is the same within the resolution of the calculation.
Since the w1 mode is near the W1 peak, the mode of vibration of W1
can be described [88], It involves inphase symmetric stretch (SS)
motion of all the 0 atoms in the glass while the Si atoms are at rest.
This assignment has been supported by the observation of isotopic shifts
for 160 for 180 substitution in aSi02 that are consistent with no Si
54
motion in W1 [88]. Thus W1 was assigned to very strong Raman activity by
a relatively small number of states having SS motion, and should,
therefore, not normally correspond to a peak in the VDOS.
Therefore, the dominant lowest frequency Raman peak W1 involves
the symmetric motion of the 0 atom along a line bisecting the SiOSi
angle, the bending (B) motion [92]. Galeener preferred to call this the
symmetricstretch (SS) motion [92] (Fig. 9(a)). (The W1 peak is IR inac
tive. The low frequency IR peak at 480 cm"1, which does not equate to
the 450 cm"1 W1 or the 495 cm"1 D1 Raman peak, is primarily due to the
rocking motion (R) of =Si0Si= bridging oxygen bonds (Fig. 8), but
includes some Si motion.) The next lower frequency W3 peak is both IR
and Raman active, but is most intense in the Raman mode because it is
mainly a symmetric vibration. W3 involves SS motion of the 0 atom, but
there is some Si motion depending on the ratio of the masses of 0/Si,
the average 6 value and the coordination of the cation Si (Fig. 9(b)).
The high frequency peak is also both IR and Raman active,
though it is a much more intense IR mode because it is an asymmetric
vibration. involves motion of the 0 atom along a line parallel to
Si...Si (the line between the bridged atoms), the S motion in Fig. 8.
Galeener [92] calls this the asymmetricstretch (AS) motion (Fig .9(a)).
Lucovsky [98] presented evidence for the existence of a Raman
active peak in the 900950 cm"1 region. He approached the peak assign
ment from the school of thought involving the intrinsic defect state.
This is used by the optical fibre and Electron Spin Resonance (ESR)
fields, following the ideas of Mott [99] on the chalcogenide amorphous
semiconductors. Lucovsky assigned this peak to nonbridging oxygen atoms
C^~, (which means a chalcogen with a covalent coordination of 1 and a
55
OutofPhase
High Frequency,
(a) Bending or
Asymmetric
Stretching (AS)
\ y\ /
^Si Si
InPhase
Low Frequency,
Bending or
Symmetric
Stretching (SS)
W4TO W4LO
Wt
1060 crrr1 1190 cm'1
450 cm'1
(b)
O
:s
Si s  O
\
\
o
o
Silicon "Cage" Motion,
Involving some SS of the O Atom
W3TO V\fcLO
790 cm*1 810 cm*1
Figure 9. Schematic of the normal modes of vibration in asilica, (a)
The outofphase (highfrequency) and inphase (lowfrequency) vibra
tions of two coupled Si0 stretching motions, where only Si0 stretching
is considered, (b) The type of motion suggested by various vibrational
calculations for silica polymorphs associated with the W3 Raman band at
800 cm'1. After [94],
56
charge state of 1) though he did not actually show a Raman spectra
showing this peak. Lucovsky assigned the 605 cm'1 peak to threecoordi
nated oxygen atoms (C3+) describing the peak as an intrinsic defect in
terms of the valencealternationpair model. Galeener [67,100103] and
Brinker et al. [5] have since shown that this assignment is wrong.
Bell [50] showed that the fit between experimental ballandstick
model and theoretical Raman curves for aSi02 improved after further
refinement of the CRN model. The theory predicted the 1200 cm'1 peak and
slightly exaggerated the size of the 800 cm'1 peak due to too small a
cluster size. It did not predict the correct behavior of the 600 and 495
cm'1 peaks due to lack of some unspecified symmetry in the Si02 network
and the absence of three membered rings respectively.
McMillan [94] comes from the geochemical school of thought,
examining the silicate melt phase, or magma, in igneous processes. He
extrapolates the Raman vibrational spectroscopy of the equivalent glass
phase to the equivalent melt composition. McMillan reviewed the litera
ture of Raman spectroscopy of aSi02 glasses, and their interpretation
in terms of structural models. He pointed out that the first successful
Raman spectra of aSi02 was obtained by Gross et al. [104] in 1929.
McMillan [94] summarized his knowledge of the aSi02 Raman peaks.
These were: a) Two weak, depolarized bands (depolarization ratio p
0.75) near 1060 and 1200 cm'1, b) A strong band at 430 cm'1 which is
highly polarized and also asymmetric, partly due to thermal effects and
partly due to weak bands near 270 and 380 cm'1 which correspond to
maxima in the depolarized spectrum, c) Two weak sharp polarizable peaks
near 500 and 600 cm"1 of controversial origin, attributed to broken
SiOSi bonds, or to small siloxane rings. McMillan [94] dismissed
57
Phillips [52] assignment involving doublebonded Si=0 linkages as not
being supported by abinitio molecular calculations, d) An asymmetric
band near 800 cm'1 with probable components near 790 and 830 cm'1.
McMillan [94] also gave the current literature peak assignments to
structural vibrations. The high frequency bands were assigned either to
asymmetric Si0 stretching vibrations within the framework structure, or
to the TO and LO vibrational components, separated in frequency by the
electrostatic field in the glass. The 430 cm'1 peak was assigned to the
symmetric motion of the bridging oxygen in the plane bisecting the
SiOSi linkages. The 800 cm'1 peak was assigned to the motion of Si
against its tetrahedral 0 cage, with little associated 0 motion.
The vibrational modes of aSi02 are highly localized [94], despite
the macroscopic disorder of the structure, as shown by the well defined
and highly polarizable Raman peaks. This suggests vibrating units with
high symmetry within the glass structure. The vibrational assignments
above were based on the energies (= frequencies) and symmetries of the
observed vibrational transitions. McMillan [94] did not give a detailed
description of the nature and extent of each mode, which is only
possible from a dynamical analysis of the system. The molecular struc
ture of a system defines the relative positions of its constituent atoms
and the interactions between them. If one or more atoms are moved from
their equilibrium position, the interatomic forces restore the system to
its equilibrium configuration. The atomic displacements executed during
this process are described by the equations of motion of the system,
whose solution are its normal modes of vibration. The mathematical
formulation for the dynamics of discrete molecules are well established
58
and the force constants for the system describe the curvature of the
potential energy surface near the equilibrium geometry [94].
For aSi02 the assumed force constants are a function of the
particular model used to describe both the interatomic interactions and
the vibrational motions. Solution of the equations of motion for the
system using appropriate force constants gives the energies of the
vibrational transitions, and their associated atomic transitions. Using
these methods, vibrational calculations have been carried out on aSi02
by considering the amorphous network as a single large network and by
considering small representative units, as discussed earlier. The
validity of such vibrational calculations is critically dependent on the
force constant model used and its relevance to the true interatomic
potential surface. Realistic force constants may be evaluated if this
surface is known analytically, which is not the case for silica [94].
Several methods are available to construct sets of force constants
designed to model interatomic interactions in aSi02. The calculated
vibrational spectra are compared with the experimental spectra as a
criterion for the applicability of that force constant set. However, an
observed spectrum may be reproduced using a variety of force fields. If
the chosen force field does not approximate the true potential surface
then the calculated atomic displacements may not resemble the motions
associated with the true vibrational modes, although the Raman and IR
spectra may have been calculated to within experimental error. From
these considerations, a rigorous correlation of the vibrational proper
ties of aSi02 with its structural properites awaits a better under
standing of its interatomic bonding [94]. The vibrational calculations
performed in the literature [45,46,49,53,91] are subject to these
59
limitations, and the structural assignments to vibrational peaks can not
be taken much further than the general assignments discussed above.
All of these models have included an Si0 stretching force
constant, Kg, with values varying from 300 to 700 Nm"1. Gibbs et al.
[105] carried out an abinitio molecular orbital (MO) calculation for
the SiOH^ molecule, giving Kg 665 Nm'1. This is consistent with most of
the calculations which have reproduced the highfrequency region of the
vibrational spectrum, associated with the Si0 stretching motions.
Inclusion of the nearestneighbor 0...0 interaction, which changes
during Si0 stretching, might lead to slightly lower values.
Most MO calculations have also considered the OSiO and SiOSi
bending forces, Ka and KR respectively. The estimated Ka value has
ranged from 20 to 70 Nm'1, expressed as (l/d(Si0)2){dE/d(d(Si0)2)} ,
where d(SiO) is the Si0 bond length and E is the theoretically
determined energy [94], KB has been estimated at 220 Nm1. Gibbs et al.
[105] calculated a similar value of 100 Nm"1 for Ka, and 818 Nm'1 (as a
function of the 0) for KR for H6Si207 [94].
Revesz [70] discussed the directionality ratio, r, of silica
polymorphs and asilica. The directionality ratio r is a dimensionless
ratio originally mentioned by Phillips [106,p.337], defined as the ratio
of the nextnearestneighbor bondbending noncentral (directed) force,
Â£, to the nearestneighbor central (undirected) bonding force, a, so r =
&/a. The ratio r measures the covalency of a bond. As r increases the
covalency of the bond increases and the ionicity decreases, so the
directionality, i.e. the resistance to bending, increases. The ratio r
governs the vibrational density of states of aSi02.
60
Phillips [106] discussed r for binary crystals of formula ANB8N,
for which a = Kg is the bondstretching force function of the AB bond.
There should be both ABA and BAB bondbending noncentral force
functions in ANB8'N, i.e. Ka and Ka, but Phillips does not distinguish
between them. The ABA bondbending force function KR determines the
resistance to rotation of A around B, while the BAB bondbending force
function Ka determines the resistance to rotation of B around A. These
are identical only if the charge distribution and valency are identical
in A and B, which is unlikely except in pure elements. The ionic radii
also have to be identical to avoid different steric effects such as are
seen in asilica. For diamond, r = 0.7 (which would explain its high
elastic modulus), while r = 0.3 for Ge and Si. These all have just one
value of S [106]. Phillips gives values of r [106] for some ANB8_N crys
tals without discussing whether r involves Kff and KB in each crystal, so
it is unclear from [106] whether r = Ka/Kg or r = KB/Kg in this case.
In aSi02 the OSiO bondbending force, Ka, is larger than the
SiOSi bondbending force, KB, because the 0...0 steric repulsion is
larger than the Si...Si steric repulsion. This is because not only is 0
much larger than Si but Si is tetravalent while 0 is bivalent. The
OSiO bond angle if) 109.5 is very rigid, while the SiOSi bond
angle, 8, is much more flexible, so Ka > KR. The Si0 bond is the most
rigid, so Kg > Ka. Bock and Su [45], McMillan [69,94], Barrio et al.
[107,108], Gibbs et al. [105] and Galeener [92] calculated bond force
function values of the correct order, Kg > Ka > KR. The ratio r can be
Ka/Ks and KB/Kg, and V depends on Ka/Kg while 8 depends on KB/Kg. The
vibrational spectroscopy of silica is determined by Ka/Ks and KB/Kg.
61
Kg, the Si0 bond stretching force constant, is the largest and
consequently the dominant force function, so it is used in all vibra
tional models [45,912,107,108]. Some models also include a bondbending
forcefunction called 6, but they do not explicitly define Â£ as either
Ka or Kg so it is unclear which force function they are talking about.
The next largest influence on the vibrational spectra of silica after Kg
is the next largest force function, which is Ka, so Â£ must be Ka in
these vibrational models. For instance Barrio and Galeener [107,108]
model the vibrational spectra of aSi02 using a Bethe lattice and quote
a value for Â£ of 78 N/m. They define Â£ as the noncentral force con
stant, so Â£ must be the OSiO bondbending force function Ka in this
case.
Revesz [70] calculates r for the polymorphs of silica from earlier
references which give the values of the appropriate force functions.
Revesz said that r is Kg/Kg, where Kg is the force constant of the
SiOSi bending vibrations [70]. He gave a value for aSi02 of r =
0.182. For Ks = 600 N/m, this gives a value of KR = 109 N/m, which is
much too large to be the SiOSi bending force function. On the other
hand this value is very similar to the expected value of the OSiO
bending force function Ka. According to Sen and Thorpe [91], Ka/Ks 0.2
for AX2 glasses, where Ka is the OSiO bending force constant. Sen and
Thorpe [91] disagree with Revesz [70] over the definition of the ratio
r, although they agree that r 0.2 in aSi02. Revesz gives a value for
acristobalite of r = 0.199 calculated from values given by Rey [109],
Examination of [109] shows that Rey gives values for the OSiO bending
force constant, not the SiOSi bending force constant, so Rey [109]
62
disagrees with Revesz. Revesz [70] is therefore wrong in his definition
of the ratio r, and the correct definition is r = Ka/Kg.
Amorphous silica may be considered as a network of SiO^ tetrahedra
polymerized by cornersharing each oxygen between two SiO^ units. Sen
and Thorpe [91] found that the vibrations derived from Si0 stretching
in asilica depend on 6 between the tetrahedra. As this angle is larger
than 112 in aSi02 (144, in fact [41]) the stretching modes of adja
cent tetrahedra become coupled. This causes the highfrequency bands
(1060 cm'1 and 1200 cm'1) of modes where the coupled Si0 stretches are
out of phase, giving the resultant oxygen motion parallel to the Si...Si
line (Fig. 9(a)). A lowfrequency set of modes (the 450 cm'1 W1 peak)
where adjacent Si0 stretching is in phase give the resultant oxygen
motion in the plane bisecting the SiOSi bond (Fig. 9(a)), which agrees
with Galeener et al. [42,55,88,92], This model does not predict the 800
cm'1 Raman peak, which must involve other considerations. Bell and Dean
[51] did reproduce this peak, involving predominantly Si motion (consis
tent with the isotopic substitution experiments of Galeener and Geiss
berger [110]), as a silicon cage motion shown in Fig. 9(b).
Barrio and Galeener [107,108] tried another approach to modeling
the vibrational behavior of aSi02. They used the Bethe lattice [111]
(which had already been done successfully by Sen and Thorpe [91]), an
infinite simply connected network of points, as an approximate disor
dered structure which only uses central bondlength restoring forces.
Barrio included the noncentral (or intrinsic angle restoring) forces by
specifying the positions of bonded atoms over a random distribution of
the dihedral angles at the successive branches. This caused a random and
uncorrelated dihedral angle, 5, as expected in aSi02. They obtained
63
expressions for the vibrational density of states and the polarized
portion of the Raman response. Values of = 154, Kg = 507 Nm'1 and =
78 Nm"1 gave the best fit to the central frequencies of the broad peaks
at 420 and 820 cm"1 and the width of the 420 cm"1 peak.
Barrio and Galeener claimed an improvement in theoretical spectra
to "nearperfect" [107] agreement with the vibrational density of states
(VD0S) produced by the largecluster calculations of Bell and Dean. They
did this by (a) averaging over realistic distributions of 6, and (b)
adding a small component to the frequency to correct for the known
tendency of the Bethe lattice to produce narrow bands. Both group VD0S
calculations are less accurate at < 100 cm'1 because of deficiencies in
the Born Ka forces and at > 800 cm'1 because of neglected Coulomb
forces. The 495 and 606 cm'1 peaks are not reproduced because they arise
from defects in the structure not modeled by the Bethe lattice.
The Born noncentral force Ka is a twobody force which can accu
rately simulate the more accurately simulate the more realistic Keating
threebody noncentral force, except at the lowest frequencies [107].
Phillips [54,59] examined the Raman defect peaks in detail to try
to fit them into his model of aSi02. Isotopic substitution of 160 by 180
showed a complete isotopic shift (e.g., D1 moves from 495 to 465 cm'1)
which implies little or no Si participation in these vibrations. This
conclusion is reinforced by direct measurement of the effect of replace
ment of 28Si by 30Si on the D1 and D2 frequencies. Within the limits of
the experimental resolution [110] nothing happens. These experiments
imply a pure 0 isotope shift for these peaks and require that the
molecular structures responsible contain a high degree of symmetry.
Phillips [54,59] model of aSi02 structure consisted of clusters having
64
the internal topology of cristobalite, a cubic structure with density 5%
greater than aSiO.,. The Si atoms are arranged on a diamond lattice,
with the dominant surface texture of these cristobalite paracrystallites
having a (100) plane. The basic surface molecule is (01/2)2Si=0s*, on
crystallites of about 6.0 nm diameter. He assigns the 495 cm'1 peak to a
vibrational mode of the 0g* atoms normal to the (100) surface normal,
i.e. parallel to the (100) surface plane.
The narrower a Raman peak, the larger the distance over which
structural units causing the peak must possess periodicity, so narrow
Raman peaks imply some structural order over a significant distance. The
problem is discovering the size of the significant distance. Phillips
[54,59] claims that the 6.0 nm periodicity of his clusters is easily
large enough to explain the narrowness of the D1 peak (FWHM 30 cm'1).
This is refuted by Galeener and Wright [43]. Phillips [54] attributed
the D2 peak to a ring mode associated with intercluster crosslinking.
Galeener [103,112] reviewed the Raman and ESR spectroscopic
evidence for the structure of aSi02. He pointed out that the properties
of vitreous silica depend on the thermal history of the sample, often
expressed as the fictive temperature, Tf, and the [OH] concentration.
The primary SiOH Raman peaks appear at W6 = 3700 cm'1 = SiOH vibration,
and W5 = 970 cm"1 = SiOH vibration. He showed that the equilibrium
defect concentrations, [D^] and [D2] are independent of [OH], and
proportional to Tf. On the other hand the relaxation time tQ, i.e the
time it takes the sample to reach the equilibrium defect concentrations
is inversely proportional to [OH] and T. The Arhennius activation energy
for D1 and D2 are 0.14 and 0.40 eV respectively for the tetrasiloxane
and trisiloxane rings causing each peak. These are calculated from the
65
log of the percent area of the total reduced spectrum under D1 and D2
peaks plotted against inverse Tf. Figure 10 shows the observed depen
dence of the peak frequencies on Tf for pure aSi02, with W1 and W3
increasing as Tf increases from 900 to 1500C, and W4 TO and LO decreas
ing. These shifts are in the directions to be expected if the average &
decreased, by an amount estimated to be by about 2, as the aSi02
density increases. The defect peak positions change very little in
comparison due to the rigidity of these small strained ring structures
compared to the larger rings of the bulk structure.
Raman spectroscopy provides information about structural features
of glass which have concentrations greater than about 1% [112], i.e. its
detection limit is > 1%. Electron Spin Resonance (ESR) can probe
structural features associated with defects at much lower concentra
tions, if the defects are spin active. Pure aSi02 shows no detectable
ESR signals, so ESR signals are seen only after the sample is subject to
various kinds of radiation, including Cu Xrays. The most important
of these signals is the E' line whose origin is the spin of an electron
in the unbonded sp3 of a 3bonded Si atom. The number of preexisting E'
defects is inversely proportional to [OH], and are more resistant to
their formation the lower is the fictive annealing T. These defects do
not relate to the nonbridging oxygen defects discussed earlier concern
ing Raman defects.
McMillan [69] summarized the vibrational studies of aSi02. He
discussed a defect peak seen at 910 cm'1 in wet and dry aSi02 samples
which does not scale with any other defect peaks. This band occurred in
the region commonly assigned to the symmetric Si0 stretching vibration
of an =Si0', or hS=0 group.
66
Figure 10. The dependence on the fictive temperature Tf of the Raman
peak frequencies of a sample of GE214 fused asilica. The changes in the
broad network peaks (W) in various directions are consistent with
reduction in 6 as Dg increases. The much smaller shift in the positions
of the D1 and D2 ring peaks are consistent with their assignment to
regular tetrasiloxane and trisiloxane rings respectively in an otherwise
more disordered network. After [1123],
67
Dianoux [20] examined lowfrequency excitations in asilica to
derive the vibrational density of states. He investigated the character
of these vibrational modes through a careful analysis of the inelastic
structure factor of these modes. aSi02 has an average velocity of sound
= 4.1 km/sec, and a Debye frequency fD = 10.3 THz, corresponding to a
Debye T of 494 K. The density of states is thus gjj(f) = 2.75 x 10"3 f2
(where f = frequency in THz) and is essentially independent of tempera
ture [20]. He showed a calculation, in the spirit of the quasicrystall
ine approach, of the elastic and inelastic structure factors for a model
containing 5 connected tetrahedra. He claimed that it reproduced the
gross features of the experimental elastic structure factor S(Q).
Therefore inelastic neutron scattering permitted a microscopic explana
tion for the form of the density of states at low frequencies. This is
exactly the type of broad claim that Galeener and Wright [43] said is
made about structural models based on a rather poor fit to experimental
data, but which in fact has very little basis in reality.
Dianoux [20] also examined the currently fashionable explanation
for the form of the density of states of amorphous materials based on
fractons. Fractons are excitations on a fractal network, i.e. localized
phonons. The theoretical predictions are that the nature of the thermal
excitations of a fractal system should change at a particular frequency
wco, presumably related to the scale range over which the material is
fractal. Below this frequency, the vibrations are phonons which can
propagate and g(w) should vary as w2 as in the Debye model. However,
above this frequency (whose wavelength would correspond to the length of
some characteristic structural unit of the material), g(w) should vary
as the dgl power of w, where dg < 3. He showed by a scaling argument
68
that an anomalous enhancement of the density of states (the socalled
fracton edge) could be expected at the crossover wcQ between the two
regimes. He showed some data for hydroxylated small aSi02 particles
with a fractal dimension df = 2,5 up to a length scale of about 30 nm,
from small angle neutron scattering. The evidence for fractons is not
completely consistent or explained properly yet. Other possible models
must be examined for the correct explanations of observed properties.
2.4 Raman Spectroscopy of aSilica
Stolen [114] measured the low frequency (10120 cm'1) Raman
spectra of aSi02 as a function of T, and confirmed Hass's [1156] find
ings (discussed in the section on the thermal reduction of Raman
spectra). Stolen concluded that the low frequency scattering arises from
harmonic oscillator modes, which contribute to the excess heat capacity
and neutron scattering observed in aSi02. The low frequency, tempera
ture sensitive maximum at 50 cm'1 does not arise from a maximum in the
density of states. Rather it arises from the large occupation number of
low frequency modes, determined by BoseEinstein statistics, along with
a sharp drop in the VDOS at very low frequencies. Stolen [114] also
confirmed that, in contrast to Raman spectroscopy, the same low frequen
cy range in IR spectra is T independent.
Shuker and Gammon [96] extended their own work [97] and obtained
a good low frequency Raman spectrum of aSi02, showing the low frequency
"Bose" peak at 50 cm'1. They showed that the disorder in glass brings
about a breakdown in the Raman selection rule k = 0 and that essentially
all modes of vibration are allowed to participate in the scattering.
This led them to the conclusion that the Raman scattering in disordered
69
materials is first order Raman scattering. It is closely related to the
density of states, which includes a thermal contribution described by
BoseEinstein statistics. This does not include vibrations with intrin
sic symmetry which forbids their coupling to Raman scattering. Raman
scattering is due to the fluctuations in the polarizability as modulated
by the vibrational modes. The BoseEinstein population factor n(w,T) is
an important term in the Raman scattering intensity and can drastically
change the appearance of the spectra. It depends on the T at a given
frequency, and proper account must be taken of this fact. Figure 11
shows the spectra of aSi02 at 300 K and 12 K. At 12 K the peak at 50
cm'1 disappears. In comparison, the main peak at 440 cm'1 and the D1
defect peak at 495 cm'1 do not change significantly in intensity. The
50150 cm'1 peak is therefore due to the thermal population of the lower
states in the room temperature data and not to the vibrational mode. The
Raman spectra must therefore be thermally reduced to look just at the
vibrational modes.
Aside from the thermal factor, there is another important and
rigorously accessible factor, that of the harmonic oscillator amplitude.
It is given by (1/w) and thus is a relatively weak function, but it
still changes the spectra. Shuker and Gammon [96] concluded that Raman
scattering in disordered systems differs from the scattering in crystals
in that it is related to the spectrum of the vibrations in the material
rather than to specific modes of vibration. They showed that the Raman
spectrum is first order. The polarized intensities are some linear
combination of the individual density of states under the simplifying
assumption that the coupling coefficients are constant for the vibra
tions of the same band.
RAMAN INTENSITY
70
WAVENUMBER [cm1]
Figure 11. The Raman spectrum of fused asilica at various temperatures.
The dots represent the low temperature spectrum calculated from the room
temperature spectrum after it had been thermally corrected assuming
first order processes, as discussed in the text. After [115].
71
Walrafen [88,89] produced a high quality Raman spectra for a
Suprasil1 aSi02 fiber from 100 to 4000 cm'1, with good background to
noise ratio. He used a slitless optical fiber laserRaman spectrometer.
This produced wavenumber assignments for all the main vibrational peaks,
which they divided into three groups: (1) bands that arise from vibra
tions of the aSi02 network, including overtones and combinations, i.e.
bands at 440, 800 (+ a shoulder at 825), 1055, 1180, 1600 (+ a shoulder
at 1480), and 2160 (+ a shoulder at 2040 and 2325 cm*1), (2) defect
bands that arise from Si+ and Si0" defect centers in the aSi02 net
work, i.e. bands at 485 and 600 cm'1, and (3) bands from OH groups in
the network, i.e. bands at 3690 cm'1 and unresolved sidebands. The
intensity of these bands was found to be proportional to the [SiOH]
concentration, as is the intensity of the 1.39 pm IR absorbance peak.
This is the OHstretching overtone of the Raman peak at 36855 cm'1 and
the infrared fundamental peak at 2.73 pm.
Stolen and Walrafen [117] looked at the influence of [OH] concen
tration on the 495 and 600 cm'1 Raman peaks. They confirmed the identi
fication of the strongly polarized 3690 cm'1 peak as being due to non
interacting OH units in a dense matrix. The tail is due to hydrogen
bonded OH groups with a distribution of bond strengths. They showed that
the ratio of the intensity of the 3690 peak to the 440 cm"1 peak is
linearly proportional to the silanol concentration, [SiOH]. The 970 cm'1
peak is due to the Si0 stretching vibration of the SiOH silanol
groups. The intensity of the 495 and 600 cm"1 defect peaks are related
to the Tf and the [OH] concentration, though the exact dependency is not
determined. Their results were interpreted to support a model of H20
trapped at broken Si0 bond defects.
72
Galeener and Mikkelson [118] confirmed Stolen and Walrafen [117]
experiments showing that OH concentration can be measured non destruc
tively using the intensity of the 970 cm"1 SiOH peak in the Raman
spectra of aSi02. They extended this work to show that spatial concen
tration distributions could be obtained with a resolution of 50 Â¡jlm.
Mikkelson and Galeener [100] did a more detailed investigation of the
relationship between the Tf, [SiOH], the D2 600 cm*1 Raman peak and the
density of aSi02. The physical properties of aSi02 are strongly
dependent on the thermal history, characterized by the Tf, at which
prior equilibrium was reached and from which a sufficiently fast quench
was made. Since the density of aSi02 at 25C is dependent on Tf, so the
structure must depend on the Tf.
The intensity of the D1 and D2 peaks increases with neutron
irradiation [119] and with increasing Tf [100]. Neutron irradiation with
2 x 1020 n/cm2 causes a sevenfold increase in the D2 peak intensity but
only a twofold increase in the 495 cm'1 intensity. Whether this means
peak height or area under the peak is not clear. Presumably peak area is
measured. The influence of the choice of baseline corrections on the
peak area is also not considered. In other words the area could be
measured by drawing in the shoulder of the peak on which D2 is situated,
and then just measuring the area above this line. The area could also be
measured by removing the effect of the elastic scattering peak and
fluorescence by a baseline correction, and then curvefitting Gaussian
peaks. The relative change in area due to irradiation would be different
for these two different methods. The Gaussian curvefitting method would
give a larger initial peak area, so the measured percentage change in
73
area during irradiation would then be smaller. The specific technique
used must be considered when comparing different peak area data sets.
Mikkelson and Galeener [100] investigated the relationship between
the D2 peak area and Tf. They decided that since the 495 cm1 peak rides
on such a steep portion of the dominant network line at 450 cm1 it was
difficult to assess changes in its intensity accurately, so they focused
on the 606 cm'1 peak. They drew in a baseline under the 606 cm'1 peak on
the main peak's shoulder to determine the integrated peak intensity. The
peak areas were measured gravimetrically from a copy of the chart
recorder scan and normalized against the density of each sheet of paper.
These areas were then internally normalized to the peak intensity of the
450 cm1 line (how is not specified) and converted to percent area of
the total reduced firstorder spectrum. This meant that the spectra had
been thermally reduced, unlike the raw data in Fig. 1 of Mikkelson and
Galeener [100] in which they show the baseline correction to the 606
cm1. This is a contradiction and leads to some confusion about the
consistency of their calculations. Estimated error is 6%.
[OH] was monitored using the 3700 cm1 peak. Mikkelson and Galee
ner [100] found no dependence of the final values for the 606 cm"1
intensity on OH concentration, contradicting Stolen et al. [117], but
rather they found a strong OHdependence of the relaxation times. The
larger the [OH], the shorter the relaxation time. This fact was not
realized by Stolen et al. [117], thus explaining the apparent contra
diction. The equilibrium D2 peak intensity is larger the higher the Tf.
The assumption is made that it is the concentration of structural units,
related to a particular peak in a Raman spectra, that is changing rather
than the Raman crosssection per unit. They present evidence against the
74
assignment of the D2 unit being a broken Si0 bond, which is the micro
scopic mechanism usually used to explain viscous flow in a glass. The
measured value of AE for the 606 cm'1 structure concentration is 0.6
eV, an order of magnitude smaller than the value of AE for viscous flow.
They plotted the equilibrium fractional area of the D2 606 cm'1
peak against Tf (Fig. 12). Mikkelson and Galeener [100] concluded that
since the 606 cm'1 intensity increases with density, it is the vibra
tional signature of a higher density element. Mammone et al. [120]
assigned the D1 Raman peak of aSi02 to randomly oriented fourmembered
rings and the 450 cm'1 main peak to sixmembered rings. The large width
of this peak is due not only to variation of 6 but also to the presence
of 5, 7 and higher membered ring structures in the glass.
Galeener et al. [101] looked at the development of theoretical
models for deducing glass structure from vibrational spectra via the
method of isotopic substitution of 180 for lighter 160 in free standing
films of aSi02. The observed change in vibrational spectra must then be
accounted for only by the known change in mass of the specific atomic
species, or else the structure or force model is clearly inadequate
[101], They showed that the SenThorpe centralforcefunction CRN model
[91,92] can explain and calculate the isotope shifts observed in the
peaks of the Raman spectra of aSi1802. This strongly supports the
structure, force constant approximations and symmetry assignments used
in this model. They concluded that the isotope shifts of D1 and D2 are
consistent with vibration in which there is mainly 0 motion and little
Si motion [101].
75
s 0.20
<
LU
O.
CM
JP 0.16
e
o
to
o
40 0.12
LL
O
<
LU
< 0.08
<
Z
O
 Neutron (n) Irradiation
_ Fictlve Temperature Tp
O
<
DC
U.
0.04
0.00
/2x 10 n/cm
m
20.
5 x 1019n/cm2
1 x1019n/cm2
/
/
I
(b)
2.20 2.22 2.24
BULK DENSITY Db[g/cc]
2.26
?
Figure 12. The area of the D2 Raman peak, as a fraction of the total
area of the Raman spectra, versus Db. (a) For a sample of Suprasil W1 at
the indicated Tf. (b) the data from (a) extrapolated to higher densities
and compared to samples of asilica densified via irradiation with
neutrons to the indicated flux densities. After [100].
76
Figure 13. Planar Si0 rings of order n = 2, 3, 4 and 5, with SiOSi
angles 8 given for = 109.5, the tetrahedral value. After [67].
77
Galeener [67,102,103,113] proposed that the D1 and D2 peaks at 495
cm"1 and 605 cm'1 are due to puckered 4membered silicate rings and to
planar 3membered silicate rings, respectively. They are connected to
the rest of the structure by elongated Si0 bonds. Figure 13 shows the
structure of the rings involved. Puckering of these rings always reduces
9 below the planar value. Figure 14 shows the energy per bridging bond
as a function of 6, showing the energy for each ring and their relation
ship to the equilibrium minimum energy value. The OSiO angle is always
around 109.5, with a narrow distribution. Table 1 lists the energy of
formation of each ring calculated from Fig. 14, showing their stability.
The breathing motion of 0 atoms in planar rings cause the frequency,
sharpness, strong polarization and lack of companion lines of the Raman
defect peaks. D2 rings have a concentration of about 1% in aSi02.
Revesz and Walrafen [121,122] directly contradict Galeener
[67,101103]. They assign the D1 peak at 495 cm"1 to planar 3membered
rings and the D2 peak at 600 cm'1 to planar and puckered 4membered
rings. Galeener's assignment has been proven to be correct [5].
Galeener [88] reviewed the neutron, Raman, and IR vibrational
spectra of aSi02, summarizing his own work in this area. He pointed out
that the Raman and IR spectra provide insight into vibrational modes,
but they do not provide a direct measure of the vibrational density of
states, VDOS or g(w). This is because the coupling coefficient linking
the spectra with the VDOS are not easily obtained and are sometimes
strong functions of w. The HV Raman spectrum did mimic g(w). He obtained
inelastic neutron scattering spectra, which give a direct measure of
g(w) for w > 250 cm'1, as the coupling coefficients varied slowly with
frequency. The data for crystalline and aSi02 were very similar,
78
0 = eNG +10 n
Figure 14. The dependence of the energy of an sSiOSis bridge on 6,
estimated using theoretical MO results. This enables estimation of the
energy of formation of various planar rings having the angles &n marked
in the figure and listed in Table 1. The arrows show the tendencies for
the puckering and unpuckering of silicate rings. After [67].
79
WWW
1 3 4
TO LO TO LO TO LO
Figure 15. Comparison of the thermally reduced Raman spectra (a) of
fused asilica with the imaginary parts of the infrared derived trans
verse (b) and longitudinal (c) dielectric functions. Peaks in e2 = Im(e)
and Im(e"1) mark transverse and longitudinal optical vibrational modes,
respectively. After [88].
80
Table 1. The estimated energy of the formation of planar silicate rings
of order n in aSiO, calculated from Fig. 14. After [67].
Ring order n
Angle en
Energy En
2
70.5
E2 > 5 eV
3
130.5
E3 = 0.51 eV
4
160.5
E4 = 0.16 eV
5
178.5
Es = 0.80 eV
6
190.5
E6 = 1.08 eV
showing that g(w) is very insensitive to the details of longrange
order. Figure 15 compares the reduced Raman spectra with the transverse
and longitudinal dielectric functions, derived from KramersKronig
analysis from IR reflection spectra. Comparison of the K2 and Im(K'1)
spectra revealed the presence of transverselongitudinal optical (TOLO)
splitting of the IR response of aSi02. The TOLO peaks in the IR
spectra correspond to peaks in the associated Raman spectra.
McMillan et al. [123] observed the Raman spectra of an aSi02
sample containing 6.3% H20 by weight dissolved in its structure. They
showed the expected peak at 3665 cm1, due to SiOH, and a new peak at
3600 cm"1, for which they had no intuitive structural interpretation.
2.5 The Density, Spectroscopy and Structure
of Pressure Compacted aSilica
When certain oxide glasses are subjected to an applied pressure, a
large increase in density occurs [124,125]. The density increases with
time, T and with applied shear. The densification process in the rigid
state at low T is fundamentally different from that at T at or above the
glass transition temperature, Tg. The activation energy for the densifi
81
cation process in aSi02 at low T is between 2.7 and 7.0 kcal/mole
[124]. This is much smaller than the activation energies for viscous
flow (180 kcal/mole) or for oxygen diffusion (72 kcal/mole). Density
increases as large as 18.5% = 2.61 g/cc occurred at 80 kb and 600 C in
aSi02 [124]. The bulk density Dfa of aSi02 is 2.20 g/cc (Fig. 1).
Heating the compacted silica to T below the Tg causes the glass to
relax. The density decreases to an equilibrium value, whose magnitude
depends on the thermal and shear pressure history, the initial compacted
density and the annealing temperature.
Crystals undergo reversible volume changes when subjected to high
pressure, which in some cases are interrupted by abrupt changes in
density. Glasses show gradual structural changes resulting in permanent
density increases after the release of the pressure [126]. Arndt et al.
[126] examined the Dg, microhardness, refractive index and IR spectra of
aSi02 as a function of pressure up to 60 kbar and T up to 700 C. In a
plot of refractive index, n, versus density, Db, they observed disconti
nuities at 2.26, 2.32 and 2.50 g/cc. These corresponded to the densities
of the crystalline phases of silica atridymite, acristobalite and
keatite, respectively. They also observed a change in the IR peaks with
density. The 1110 cm'1 peak shifts to 1070 cm'1 and the 796 cm'1 peak
shifts to 801 cm*1 as the density increases from 2.2 to 2.56 g/cc.
Arndt et al. [126] proposed the following structural rearrange
ments to explain the behavior observed during the densification process.
The number of nonbridging oxygens decreases with increasing pressure.
Additional sixmembered rings form by the rearrangement of larger ring
types, mainly in the density regions equivalent to atridymite and
acristobalite. The long range order of the domains built up of one
82
particular ring type, and perhaps of the domains consisting of combina
tions of ring types with different numbers of members, increases.
Mochizuka et al. [127] showed the Raman spectra of compacted
aSi02 with n = 1.56. They explained the observed changes as being due
to decreases in 6 and increases in d(SiO). Ferraro et al. [128] looked
at the insitu IR spectra of aSi02 as a function of pressure. They
showed that the main 475 cm'1 peak decreased to 471 cm'1, the 815 cm'1
peak increased to 825 cm'1, while the 1090 cm"1 peak did not move as
pressure increased to 59 kb. They discussed, for aSi02, the calculation
of the Gruneisen parameters, G., which govern the thermal expansion of a
material, and are determined by
G, = (Kp/fj) (dfj/dP)T, (13)
where KT = the isothermal bulk modulus, f = frequency of peak i, and P
= pressure.
Walrafen et al. [129] subjected an aSi02 sample to 9 GPa hydro
static pressure at room temperature and obtained an 8% densification in
the recovered sample. The Raman spectra showed no shift in the Si0
stretching band peak position, and no change in the defect peaks. The
main peak at 430 cm'1 decreased in width by 18 cm'1 and shifted upward in
frequency by 10 cm"1. No explanation of the observed changes was given.
Arndt [130] extended his earlier work on compacted aSi02 [126],
He subjected samples of Suprasil to pressures of 120 kb at 500C, well
below the atmospheric Tg of 1070C, giving a density of 2.67 g/cc.
Compaction caused the IR 1095 cm1 and 460 cm'1 peaks to decrease in
wavenumber. He attributed this to pivoting of the SiO^ tetrahedra around
83
their common corners to fill up void space in the glass network due to a
decrease in the average bridging 0 bond angle.
Arndt et al. [131] examined the dependence of refractive index on
density for a series of compacted aSi02 samples, and concluded that
neither the LorenzLorentz or the NewtonDrude equations correctly
describe this dependency. The general refractivity formula (Equation 15
of [132]), with only one common overlap parameter b 1.3, gave a good
fit and a realistic physical model for an explanation of n in terms of
atomic parameters. Arndt et al. [131] showed that changes in ring
structure statistics did not change the oxide polarizability, but a
change in Si coordination number from 4 to 6 did.
Seifert et al. [133] examined the Raman spectra of aSi02 perma
nently compacted up to 2.36 g/cc. The Raman spectra were reduced and
curvefitted using Gaussian functions. As Dg increased the intensity of
the D1 and D2 peaks decreased, the W1 and peaks decreased in frequency
and the Wj peak increased in frequency. Seifert et al. [133] noted that
based on Mikkelsen and Galeener's work [100], the change in density they
observed is far too large to be explained by increases in the defect
peak intensity. As the D2 peak intensity decreased slightly the density
increase could not be trisiloxane ring formation.
Seifert et al. [133] noted that silica tetrahedra are basically
incompressible, so permanent compression must be due to rearrangement of
tetrahedra. The change in 6 alone is not enough to explain the high
compressibility of aSi02> For comparable degrees of compression the
change in 6 in aSi02 is only about 25% of that observed in quartz. They
therefore speculate that the lack of periodicity for the relative
positions of the tetrahedra in aSi02 results in a larger compression
84
for a given change in 6 compared with the arrangement in quartz. This
results in a low Poisson's ratio of 0.056 in quartz, and a higher value
of 0.161 to 0.175 in aSi02. Another possible mechanism for permanent
compaction involved the decrease in size and increase in number of
threedimensionally connected holes found in aSi02. Seifert also
suggested that the increase in density may be related to the breaking of
Si0 bonds during the creation of smaller rings, which would also
involve a decrease in the average bridging 0 bond angle, 6.
The intensity of the D2 peak does not change during compaction of
aSi02, while the W1 peak at 450 cm'1 changes significantly [133] The W3
and peak positions shift slightly. 9 calculated from these peak
position shifts using the SenThorpe theory [91] only increases slightly
while the structural density Dg increases from 2.204 to 2.252 g/cc. This
means that d(SiO) and 9 are changed only slightly while the structural
component causing the W1 peak is changing significantly. If W1 is
assigned to the dihedral angle [134], compaction occurs via rotation of
the silica tetrahedra around the bridging oxygen bond without 0 chang
ing. If W1 is assigned to the width of the 9 distribution, then the
narrowing of W1 is due to the width of the 9 distribution decreasing
without the average 9 changing.
Grimsditch [135] also looked at the Raman spectra of compacted
aSi02 at up to 17 GPa, and noted that under pressure aSi02 exhibits
anomalous physical properties. As pressure increases reversibly up to
2 GPa, the bulk modulus decreases, then increases above this pressure.
Under pure hydrostatic pressure irreversible changes in density only
occur above 12 GPa, although shear stresses lower this threshold. He
found reversible changes up to about 9.5 GPa. A sample compressed to
85
17.5 GPa showed large permanent changes in the Raman spectra. The main
450 cm'1 peak narrowed and shifted to 500 cm'1, and the D2 peak intensity
increased and shifted to 615 cm'1. He attributed this spectrum to a new
form of aSi02, which he labeled an "amorphous polymorph."
McMillan et al. [136] found that on heating an aSi02 sample to
530C at 3.95 GPA, the density increased to 2.328 g/cc and the 430, 492,
1060 and 1200 cm'1 peaks moved to 470, 498, 1020 and 1150 cm'1, respec
tively. An Xray investigation of a densified (2.555 g/cc) aSi02 sample
showed that d(SiO) and d(0...0) remained constant at 0.162 and 0.264
nm, but that d(Si...Si) decreased from 0.307 nm to 0.302 and 9 decreased
from 142 to 137, which is associated with a narrower 9 distribution.
McMillan et al. [136] made the distinction between aSi02 densi
fied at low and high T (>400C). The low T compaction process involved
smaller shifts in peak positions and smaller decreases in FWHM values.
This involves little or no change in Si0 bond length, 9 angle average
or distribution. This could be explained by tetrahedral rotation, i.e.
change in the dihedral angles, with no change in the ring statistics.
The high T compaction process involved the Raman spectra changes
discussed above. It would be consistent with changes in ringsize
distribution, via bond breakage, to smaller average rings and associated
smaller average 6 values and longer average Si0 bond lengths. This
means the 3membered D2 ring would change least, if at all, the D1 peak
slightly more, and the main peak the most, as is seen.
Wong et al. [137] showed that the 800 cm'1 Raman peak of quartz
also increases in frequency as a function of pressure. They measured
accurate frequency shift data as a function of pressure, which they said
could be used as calibration for high pressure measurement.
86
Hemley et al. [138] examined the in situ Raman spectra of aSi02
in a high pressure diamond anvil. They found that up to 8 GPa (= 80
kbar) reversible structural changes caused the Raman peaks to narrow,
the density of states of the lowfrequency modes to decrease, and the
peak frequency to shift as expected. The 440, 492, 850 and 1060 cm'1
peaks shift to 530, 493, 860 and 1052 cm'1. They associated these
changes with a significant increase in the intermediate range order
associated with changes in the magnitude and distribution of 6 brought
about by elastic deformation of 6membered rings. Above 8 GPa irrevers
ible changes in the structure and Raman spectra occurred due to changes
in ring statistics. The D1 and D2 peaks were observed to increase in
frequency and very slightly in intensity until they merged with the 430
cm'1 peak as it increased in frequency as the pressure increased. This
contradicts Seifert's observation that the D1 and D2 peaks decrease in
intensity. Hemley et al. [138] claimed that the D1 and D2 peaks in
creased in intensity due to bond breakage increasing the concentration
of the smaller rings.
Above 30 GPa the defect peaks rapidly broaden and lose intensity.
This suggests a gradual breakdown in intermediaterange and perhaps
shortrange order. This is due to the formation of 2membered and
puckered 3membered rings, and individual tetrahedra deformation and
coordination number changes, respectively [138],
The shape of Raman spectra of aSi02 compacted above 8 GPa there
fore depends whether the spectra are from insitu or quenched samples.
The insitu spectra display characteristics of a more compact structure
than the quenched samples, due to a structural relaxation effect
occurring during quenching. This can be explained by two mechanisms: 1)
87
there are two compaction mechanisms occurring simultaneously. One is
reversible (partially or totally) and can relieve the strain on release
of the pressure, as shown by the movement of the insitu peak from 600
cm'1 to about 510 cm"1 in the quenched spectra. The other is irreversible
(bond breakage to form smaller rings) and does not change on release, 2)
there is one viscoelastic compaction mechanism which has an elastic
component allowing changes in the Raman spectra on release of pressure
and a plastic component causing permanent deformation. The elastic
component is present below 8 GPa, as compaction is completely revers
ible. Above 8 GPa permanent compaction starts. The elastic component is
still present since the density of the insitu sample is larger than the
density after quenching has allowed some relaxation to occur.
Devine et al. [7780] examined the creation, by laser irradiation,
of compacted aSiO., of up to 3.00 g/cc in thin films (25420 nm) of
aSi02, prepared by thermal oxidation of Si. The compacted highdensity
aSi02 films were stable at room temperature, but annealed at 950C to
2.2 g/cc. They concluded that the same compaction mechanisms operated as
in hydrostatic pressure compaction, due to ring collapse forming smaller
rings and not due to laser damageinduced defects.
Walrafen et al. [134] showed there exists an angle and bond length
correlation for all cases of structural modification of aSi02 which
they reviewed. These included applied stresses, both compressive and
tensile, and particle bombardment by neutron and alpha particles. A
decrease in the mean equilibrium 9 produces a corresponding increase in
both the mean equilibrium d(SiO) and the mean equilibrium dihedral or
tilt angle, 6 (and A), between adjoining silica tetrahedra that share a
common bridging 0 atom.
88
These changes correlate to the following changes in the Raman
spectra of aSi02. The 800 cm1 peak, which is due to the symmetric
stretching vibration of the nonlinear SiOSi bridge, increases in
frequency as 9 decreases. The 1060 and 1200 cm1 peaks, due to Si0
stretching, decrease in frequency when d(SiO) increases. An increase in
8 is inferred to correspond to an intensity decrease of a contour
component peaking near 200300 cm'1. This is visible as an asymmetric
lowfrequency narrowing of the main Raman peak at 450 cm1. The dihedral
angle increases, as does d(SiO), when 9 decreases. This relieves the
stericlike repulsive forces that arise between the Si atoms in the
bridging SiOSi bond and the secondneighbor 0 atoms as they approach
each other when 6 decreases. The same correlations have been seen for
quartz. Walrafen made no definitive statements of the effects of
pressure on the defect peak concentrations. The differing effects of
tensile versus compressive forces on the aSi02 structure as exhibited
by Raman spectra is not clearly discussed by Walrafen et al. [134].
Devine et al. [139] used MASS NMR to determine that a compacted
aSi02 sample densified to 16% to 2.55 g/cc had an average 9 value of
138 compared to the undensified sample value of 143. This was calcu
lated from a shift from 107.4 (h143) ppm to 104.5 ppm (=138). Devine
et al. [139] concluded that the reduction in 6 is due to the decrease in
the 0..0 separation, d(0..0), from 0.312 nm to 0.290.30 run, rather than
a decrease in the Si0 bond length. The remnant plastic densificacin
involved modification of the intrinsic ring structure of aSi02.
Devine et al. [140] refined their earlier work [139] on the struc
ture of compacted aSi02< The frequency of the Si0 stretching modes at
89
1060 and 1200 cm'1 is determined by equation (10), from Sen and Thorpe's
[91] central force model. Differentiation of equation (10) yields
dw4/w4 = [ (1/4sin0d0)/((lcosi)+(4m0/3mS].)) ] + dKs/2Kg. (14)
Dimensional analysis of this equation shows that all the units cancel
except for d6, which must have the unit of radians if w is in rad/sec.
Therefore equation (14) is also, like equation (10) from which it is
derived, not dimensionally balanced. This is because 9 should be
included as an implicit variable [91], so that d6 would appear as the
fraction d9/6, like dw4/w4 and dKs/2Kg. The implications with regard to
interpretation of the results of applying experimental values of w to
Sen and Thorpe's model are unclear.
Devine et al. [140] examined this question, and noted that for a
reversible densification of 22% at room temperature dw4/oJ4 = 0.0076 =
8 cm'1 for the 1060 cm'1 peak, and that for an irreversible densifica
tion of 22% dw4/w4 = 0.039 & 42 cm'1. They claimed that substitution of
these values into equation (14), and neglecting the terms in dKg, leads
to values of d9 in the correct sense but an order of magnitude smaller
than that found by Xray or NMR. The assumption that the terms in dKg
can be ignored, presumably because Devine is assuming that Kg is not
strongly dependent on 9, is correct for this model because no bond
restoring force is included in the model, and Kg is constant for all
values of 9. This is unrealistic in reality as the (dp)n nature of the
Si0 bond causes the bond to be approximately 50% covalent, depending on
9, and consequentially partially directional in nature. The magnitude of
the restoring force is therefore proportional to 6.
90
Substituting the values for du>4/w4 from above in equation (14),
and assuming 9 144= 2tt x 144/360 = 2.513 radians, gave values of d9 =
0.0665 for 0.0076 and d9 0.341 for 0.039. As d9 has to have an
absolute value, while dw^/w^ is a fractional ratio, c19 must have a unit.
As u) is in rad/sec, 69 must be in radians, so d0 0.0665 x 3 60/27T =
3.8 and d9 = 0.341 x 360/2tt = 19.5. These values of 69 are about 2
times too large, as 69 is about 9 for 22% permanent densification,
according to Devine's [141] own calculations using equation (10). Devine
et al. [140] therefore contradicts their own calculations [141]. If
Devine et al. thought that the unit of 69 was degrees, then their state
ment about the values of 69 being an order of magnitude too small would
make sense, as 0.341 is about an order of magnitude smaller than 9.
Therefore, according to the arguments presented above, the unit of 69 is
radians so Devine et al. appear to be wrong. Otherwise it is not clear
what values of 69 Devine et al. calculated.
Substitution of W4 (cm'1) for w4 (rad/sec) in equations (7)(12)
means that Kg must be replaced by Kg/0.0593 [92]. Differentiation of
equation (10) with this substitution gives
dW4/W4 [O.O593(1/4sin0d0)/((lcos0) + (4mo/3mSl.))]+O.O593dKs/2Ks. (15)
i.e., the 0.0593 factor ends up in both functions on the right hand side
of the equation. But for 22% plastic densification the ratios dW4/W4 and
dw4/w4 are both equal to 0.039, as they are the same variable in
different units. Therefore the left hand side of the equation doesn't
change, while the right hand side decreases by a factor of 0.0593. This
91
is another example of the fundamental problems caused by the assumptions
made in the central force theory.
Devine concluded that, to explain his calculations, large compet
ing changes must be occurring in the force constants. Due to the errors
in his calculations, discussed above, d is only about two times too
large and not an order of magnitude too small so the changes occurring
in the force constants are relatively small. This means that SenThorpe
analysis of Raman spectra is suitable for quantitative analysis of
structural variations in aSi02. Devine explained the inaccuracies of
the model as being due to OSiO angle variations.
Devine et al. [140] measured the hyperfine splitting of the
electronspinresonance, ESR, spectrum produced at defects involving the
weakly abundant 29Si (4.9 atom.%) nuclei, by gamma irradiation. This can
be used to examine the defect OSiO tetrahedral bond angle, ip, and
d(SiO) distributions of compacted aSi02. The hyperfine splitting
measurements sense the variation in the relative 3s and 3p character
density of the localized electron on the defect site, which change due
to change in 9. The ESR spectra gave the probability distributions of
the isotropic hyperfine constant, Ajso, from which the defect tetrahe
dral bond angle, ip, distribution was obtained, ip is the angle between
the lone electron orbital and one of the Si0 backbonds in the defect
tetrahedra. For fused aSi02 this angle is already increased by Io
relative to the ideal tetrahedral angle of 109.47, and increases by a
further 1.1 due to 24% densification. Figure 16 shows the ip distribu
tion calculated from Aiso. An analysis of silica polymorphs [75] gave
the empirical relationship relating d(SiO) to the triple angle average
92
of the three OSiO angles, common to the bond, in the tetrahedra,
<0Si03,
d(SiO) = 2.17 0.0051(
The distribution in $ was converted into a distribution in <0Si03
and equation (16) was used to deduce the d(SiO) distribution shown in
Fig. 16. The 24% increase in densification produced an increase in V and
d(SiO) associated with the 0 vacancy defect of 0.36% [140],
The recalculation of Devine et al's data [140] above showed that
the high frequency Raman peak shift, associated with an increase in
d(SiO), caused too large a decrease in 6, according to the central
force model. The increase in d(SiO) associated with an increase in i/>
therefore goes some way to explain this discrepancy, as both the
increase in and the decrease in 6 during compaction cause d(SiO) to
increase. Some of the (Si0) increase was due to rÂ¡>, so not all the
shift contributes to an increase in 6, and the increase in 6 calculated
using the SenThorpe central force model should be smaller. Another
possible contribution to the increase in d(SiO) is the dependency of
the central force Ks on .
Using the relationship between d(SiO) and 6 [74]
log [2d(Si0)] = 0.504 0.212 log sin(0/2), (17)
and the values of d(SiO) obtained above, Devine et al. [140] calculated
that in the undensified aSi02 sample 6 139.6 (compared with 144
from Xray data) and 134.5 in the 24% densified sample. So densifica
93
(a)
Figure 16. Probability distributions, (a) The probability distribution
of the tetrahedral bond angles, i>, in undensified (dashed line) and 24%
densified (solid line) samples of fused asilica calculated from the
distributions of the isotropic hyperfine constants, Aiso. (b) The proba
bility distribution of defect d(SiO) obtained from the if) distributions
in (a) using equation (16). After [140],
94
COMPACTION (%
Figure 17. Variation in the vibrational peak positions and 6 of Si02 as
a function of compacted density, (a) Experimental data of the positions
of the IR and Raman peak positions in densified asilica and quartz as a
function of percentage compaction. The y axes are the peak positions in
cm"1. After [141]. (b) The dependence of 6 on the density of asilica
and aquartz as determined from the experimental data in (a) from the
1070 cm"1 peak using equation (10) with Kg = 422 N/m. The same data for
aquartz is shown for comparison. After [141]. (c) The dependence of 6
on molar volume change in aquartz and asilica. After [133].
95
CD
<
FRACTIONAL VOLUME CHANGE
Figure 17continued
96
tion produced at the defect site a reduction in 6 of 5.1, which is
associated with an increase in r[i and an increase in d(SiO) and is
similar to the mean value of 6 measured by Xray and NMR studies.
Devine reviewed all the available data (Refs. 3, 915 of [141]) on
the dependence on Dg of the IR and Raman spectra peak positions of
compacted samples of aquartz and aSi02 (Fig. 17(a)). Figure 17(a)
shows that essentially linear variations with Dg are observed and that
the W3 800 cm'1 peak varies the most. He showed, by differentiation of
the Sen and Thorpe model [91] equations, that, assuming 0 *= 144:
dWj/W, 1.54 dfl (18)
dW2/W2 0.16 dB (19)
dW3/W3 0.31 d6 (20)
dW4/W4 = 0.11 di. (21)
dWj is the fractional shift in peak position Wj. Devine [141] measured
the slopes of the peak positions versus Db in Fig. 17(a), giving
dW,/, 7 0.0096/% (22)
dW3/W3 7 0.0093/% (23)
dW4/W4 7 = 0.0033/%. (24)
7 is the fractional change in density, dDb/Db. He argued that W4 was the
most representative of the central force model and the least sensitive
to noncentral forces, and compared the experimental variation of W1 and
W3 in equations (22) and (23) to W4. This gave
97
(dW^J/dW*/^) = 2.9 (25)
(dW3/W3)/(dW4/W4) = 2.8. (26)
He assumed that the variation in 6, d0, was proportional to minus the
fractional densification, 7 = dDb/Db, so that the theoretical equations
(18)(21) could be compared to equations (25) and (26). The values
predicted from the Sen and Thorpe model [91] are 14 and 2.8. This
suggests that the bond angle 9 dependence of W3 and its associated
pressure dependence are represented by the central force model although
its absolute magnitude is not. The W1 peak is neither represented in its
position nor its pressure dependence by the pure central force model.
Ferrieu and Devine [142] calculated the change in refractive index, dn,
with the change in fractional dens if ication, 7 = dDb/Db [126] for
aSi02. This gave dn/7 = 0.00429/%.
Devine [141], using the equation for W4 from the central force
model and the data in Fig. 17(a), calculated 9 variation during the
densification of aSi02. Figure 17(b) shows these data for elastically
deformed aquartz and plastically densified aSi02. For aSi02 9 de
creased by about 12 for a 30% density increase, while for aquartz 9
decreased by about 27 for 30% densification. This indicates that 6
decrease during densification is 2.3 times larger in elastically
densified quartz than in plastically densified aSi02. Therefore the
decrease in 6 in plastic densification is smaller than in elastic
densification. This is consistent with the picture of plastic densifica
tion in which 6 decreases and structural reorganization occurs. The
structural reorganization permits a partial relaxation of the initial
98
decrease in 9. In Fig. 17(c), Seifert et al. [133] present similar data
showing the decrease in 9 (calculated from Raman spectra of compacted
silica) with the increase in Dg.
Arndt et al. [143] examined the dependency of Dg and n of compact
ed aSi02 on time and T during annealing. The optical effects observed
during annealing as structural relaxation occurred are quite different
from those observed during compaction, when n is linearly proportional
to density, or in other silicate glasses. During annealing n is not
linearly proportional to density, but goes through a deviation with a
minimum. For a large enough starting compacted density value n can drop
below the value of fused aSi02, at a density which depends on the
initial compaction density of the sample being annealed. The optical
behavior during annealing appears to be solely a function of the extent
of volume relaxation. The nonlinear ndensity behavior can be interpret
ed in terms of polarizability using the general refractivity formula
[131]. This showed that the polarizability changes during annealing as
the density changes. This does not occur during the initial compaction
process. Arndt et al. [143] could not explain this phenomena.
Review of the literature on the spectroscopy and structure of
pressure compacted fused silica shows that direct contradictions exist
concerning the changes occurring to the Raman spectra during compaction.
There is no consensus opinion as to how W3 and behave, or the magni
tude of their changes, as a function of Dg. Only Seifert et al. [133]
reports the curvefitted changes in peak positions and areas as a
function of Dg, but they obtained Raman spectra on the fused silica
samples after removal from the compaction apparatus. Hemley et al. [138]
99
showed that the insitu Raman spectra of compacted fused silica are very
different from the Raman spectra obtained after removal.
2.5.1 Raman Spectroscopy of aSiCU Under Tensile Stress
Walrafen et al. [144] examined the tensile stress dependence of
the Raman transmission spectra of a stressed aSi02 optical fibre up to
3.34 GPa. They used the same elastic scattering baseline template for
each spectra obtained, but performed no thermal reduction. The D1 peak
was baseline corrected using a French curve to follow the main peak
shoulder on which the smaller peak is situated. They concluded that the
D1 peak increased in intensity, which visually it does. They did not
show the main and D1 peak positions, or consider the effect of movement
of the main peak on D1 peak shape and intensity, so this conclusion is
questionable. The main peak, the D2 peak and the 800 cm"1 peak do not
change in intensity with applied tensile stress, but the main peak
increased in width. They explain their observations in terms of revers
ible Si0 bond elongation and aSi02 network distortion, with no chemi
cally active sites created by a large tensile stress.
Kobayashi et al. [145] examined the effect of tensile stress on
the Raman spectra of aSi02 fibers. They concluded, in direct contradic
tion to all other work, that the 6 angle and d(SiO) are not affected by
the applied stress. The observed changes in the main 450 cm'1 peak are
due to changes in the OSiO bond angles.
Tallent at al. [132] and Michalske et al. [146] examined the Raman
spectra of aSi02 fibers under tensile stress, and observed that the
443, 491, 604, 792, 832, 1055 and 1187 cm"1 peaks shifted to 426, 486,
600, 769, 811, 1016 and 1164 cm"1 respectively at 10.3 GPa. This con
100
firms earlier work showing that tensile stress does not cause changes
exactly opposite to compressive stresses, as the 1050 cm'1 peak shift is
not in the opposite direction to the other peaks shift.
2.6 Raman Spectroscopy of Neutron Irradiated aSilica
Bale et al. [147] examined the structure of neutron irradiated
aSi02 using Xray diffraction. They concluded that despite the increase
in density that occurs on irradiation, there is a decrease in order as
indicated by RDF analysis. The increase in density is caused by the
average 6 decreasing slightly along with an increase in the density
fluctuations in the material. The irradiation induced scattering centers
caused by the fast neutron scattering have a radius of gyration of at
least 4 nm. They are amorphous rather than crystalline in nature.
Bates et al. [119] also examined irradiated aSi02, and confirmed
the conclusions of Bale et al. [147]. The density of fully irradiated
samples of aSi02 and quartz was 2.25 g/cc. The D2 trisiloxane peak area
increased significantly while the D1 tetrasiloxane peak area increased
only slightly during irradiation. Learmans [148] reviewed the properties
of irradiated aSi02, giving a density value of 2.265 g/cc for irradiat
ed quartz and aSi02, called the metamict state. MAS NMR analysis of
metamict aSi02 shows that 6 = 134, which Chan et al. [149,150] attrib
ute to the formation of D2 trisiloxane rings.
Gokularathnam [151] investigated the structure of a sample of
fused aSi02 after a fast neutron irradiation to a total flux of 1020
neutrons/cm2 using Pair Distribution Function (PDF) and Distribution
Distance Function (DDF) analysis of Wide Angle XRay Scattering (WAXS)
spectra. He showed that after irradiation d(SiO) increased from 1.62
101
to 1.65 , the tetrahedra were essentially preserved, V(0) shifted to a
smaller average value = 138 with a slightly narrower FWHM as the Silst
Si distance distribution broadened, while the remaining DDF's also in
creased in width. The decrease in 6 to 138 correlates with the large
increase in the D2 peak observed by Bates et al. [119] .
2.7 Theoretical Correction of Raman Spectra
Hass [115,116] examined the temperature dependence of the Raman
spectra of aSi02 (Suprasil) from 12300 K. The 300 K spectra showed a
broad peak centered around 50 cm'1 (Fig. 11) called the Bose peak. As T
decreases the Bose peak decreases in intensity significantly (Fig.11)
while the rest of the aSi02 Raman spectrum shows only a slight T
dependence. Hass explained the T dependence of the Raman spectrum in
terms of the firstorder StokesRaman intensity being proportional to
l+nQ, where nQ = l/[exp( (h/27r)wp/kT)1] is the BoseEinstein T dependent
population factor corresponding to an excitation of frequency wp. The
BoseEinstein factor is the mean occupation number at T for a normal
mode with frequency wp. At 300 cm"1, the term l+nQ decreases from 1.31 to
1.0 as T drops from 300 to 12 K, while it decreased from 4.68 to 1.0 at
50 cm'1, a significantly larger decrease. Hass [116] was able to derive
the 12 K spectrum of fused aSi02 from the 300 K spectra (the dots in
Fig. 11) without the large broad peak at 50 cm'1. This is consistent
with the infrared spectrum, which does not show any maximum near 50 cm'1
and has been observed to be essentially independent of T [116,152].
Shuker et al. [97] outlined a calculation leading to an equation
for Raman spectral scattering intensity in terms of the density of
states of the vibrations in amorphous materials. Shuker assumed that a)
102
the vibrations were harmonic, b) the vibrations coupled to light through
the displacement dependence of the electronic polarizability of the
material, and c) the coherence length of the normal modes was short
compared with optical wavelengths. The latter assumption of short
coherence lengths yielded the breakdown of the usual wavevector
selection rules. This allowed the light scattering process to occur from
essentially all the modes of the material, and was the only assumption
they make that was different for glasses compared to crystals.
Shuker et al. [967] developed general expressions for the
vibrational Raman scattering from both amorphous and crystalline solids.
The distinction between crystals and amorphous materials lay in the size
of the region over which the correlation function extended. For crystals
momentum selection rules gave rise to the discrete set of lines seen in
crystal spectra. In amorphous materials the translational symmetry which
characterized crystals is lost, causing the correlation functions to be
localized. This means that all the modes of the material could contrib
ute to the light scattering spectrum, but with an unknown weighting
factor. This factor is composed of the optical coupling tensor and the
mode volume, for each particular mode. The normal vibrations fall into
bands having similar microscopic motions, frequencies, optical coupling
and correlation ranges, i.e. stretching, bending and rocking bands.
The sum over all modes then breaks into a set of sums over the
modes in the bands, and the discrete sums are replaced by the density
ofstates for each band. The density of states give the number of modes
per unit frequency. With these assumptions the Raman spectral line shape
are a the polarization dependent coupling constant Cb, the BoseEinstein
103
occupation number, the band vibrational density of states for band b,
gb(w) and the inverse of the Raman frequency shift, w,
I(w) = EbCbw'1[l+n(w)]gb(w) (27)
The BoseEinstein number is the T factor, which is [l+n(w,T)] for the
Stokes spectra and n(w,T) for the antiStokes spectra. This expression
showed how the density of states of amorphous materials contributes to
the shape of the scattering spectrum. Even with the extreme assumptions
of assigning frequencyindependent coupling constants (which Galeener et
al. showed to be incorrect [92,153]) and correlation ranges to whole
bands, the spectrum is very complicated due to overlapping bands and
differing coupling constants.
Equation 27 was used [96] to produce a reduced Raman spectrum,
(w[n(w,T)+l]'1)I(u;), free of spurious structure due to thermal popula
tion effects. The only problem was obtaining the actual T of the sample,
which can be quite high and uncertain due to localized heating because
of the high local power densities of the laser used to obtain the Raman
spectra. Shuker's theory was still not complete as it was missing the
expected inverse fourthpower dependence on wp, the frequency of the
scattered phonon. It also did not provide a procedure for theoretically
investigating the magnitude of the coupling constant Cb or its assumed
lack of dependence on frequency.
Kabliska et al. [154156] extended Shuker et al.'s [96,97] expres
sion (equation 27) to include two more correction factors:
1) The dispersion of the instrument transfer function, J(w). This
is the broadening factor removed from a spectral peak by deconvolution.
104
In practice this is very difficult to determine. It is usually modelled
by a theoretical function, or is ignored completely as it has only a
small effect if the detector is linear in the frequency range being
measured.
2) The adependence of an induced dipole scatterer on frequency,
which is contained in the coupling coefficient and was assumed to be
constant by Shuker. In fact it has a significant effect and should be
included [154,156],
In an amorphous material all vibrational modes can contribute to
the first order Raman scattering. In a crystal the constraint of k
vector conservation allows only certain phonons near k = 0 to contrib
ute. The Raman spectra of an amorphous solid is then an approximate
measure of its density of vibrational states. An approximate density of
states is therefore obtained by multiplying the raw data by
J(w)1(w)(u;4)[n(w,T)+ir1 (28)
for the Stokes spectra. It is called an approximate density of states
because the coupling coefficient Cb is not in reality band or frequency
independent, as assumed by Shuker et al. [97]. This correction factor
(equation 28) is used in the literature to produce a thermally indepen
dent spectra which can be used for theoretical and experimental analysis
[85,116,154164]. Support for this theory is provided by the T indepen
dence of the approximate density of states calculated by use of equation
(28) [115,155]. The true density of states of an amorphous solid is
expected to change very little with T.
105
Bell et al. [95] did a theoretical calculation of the Raman
scattering intensity, using a bond polarization approximation, for
aSi02. In the semiclassical description of the Raman effect, an inci
dent light beam of frequency wl and given polarization, p, scattered by
a solid with fundamental vibrational frequencies wp, acquires components
with frequencies a^fWp and polarization p. The intensities of the
scattered components is given by
Ip^w) = [ (n+0.50.5)/2w]Ipred(w) (29)
where Ipred(w) is the reduced (T independent) scattering intensity. For
unpolarized incident light scattered perpendicular to the direction of
propagation
red(w) = g(w)
[7G2 + 45A2]
(30)
red(w) = g()
[6G2],
(31)
where g(w) is the fundamental vibrational frequency of the solid, and A
and G are invariants of the polarizability tensor. The evaluation of
Ipred required the calculation of the frequency spectrum, the normal mode
displacement amplitudes and the polarizability change amplitudes. Rather
limited agreement between theoretical and experimental versions of the
frequency spectrumscattering intensity relationship was obtained, due
to poor experimental data and the poor aSi02 model used [95].
Long [157] discussed the theory of Raman scattering in some
detail. He used both classical and quantum mechanical routes to derive
the basic equations for the intensity of the scattered light from an
106
assembly of randomly oriented molecules from first principles. Orcel [4]
also discussed this theory in some detail. Long [157] showed that the
intensity of Raman scattering is proportional to the concentration of
the scattering species. In principle, concentration can be measured
provided there is no departure from a linear law as a result of intermo
lecular interactions. He also showed that it is theoretically possible
to calculate the T of the section of sample actually interacting with
the probing laser by measuring the ratio of intensities of the same peak
for the Stokes and antiStokes spectrum. The intensity of Raman scatter
ing is T dependent, but the dependency is different for Stokes and anti
Stokes. The magnitude of the ratio for a particular peak is given by
(i/li/R)4/(^l+^'R)4[exp{hcz/R/kT} ]
(32)
from which T can be calculated. This equation has been used in experi
ments to measure T [85,116,163].
Galeener and Sen [153] extended this theory to obtain a corrected
reduced Raman spectrum
lPred s (Ip(wl,w)/(ul+wp)4[n(wp)/wp]) Sfa CPb(w)gb(w)
(33)
which may be compared with the infrared derived quantity
wK2(w) Eb Db(w)gb(w)
(34)
Equations 34 and 35 describe the scattering intensity due to harmonic
vibration in a macroscopically isotropic disordered sample which has no
107
longrange order, and is related to a single set of densities of
vibrational subband states.
Walrafen et al. [1589] discussed the application of thermal
reduction techniques to the Raman spectra of other covalent M02 oxides,
specifically BeF2>
Almeida [160] pointed out that the Raman spectra of most inorganic
glasses are enhanced at low frequencies. They exhibit a weakly polarized
or depolarized peak near 50 cm'1. In addition to intrinsic Raman active
vibrational modes of low frequency the Raman spectra are enhanced due to
the BoseEinstein thermal phonon population, as discussed above, an
increase in the Raman scattering intensity proportional to (wl w)4,
where wl is the frequency of the laser line, and the elastically scat
tered radiation wing, due to Rayleigh and, sometimes, Mie and Tyndall
scattered stray light.
The peak around 50 cm'1, called the Boson peak, is not due to just
the thermal population increase with decreasing phonon frequency [160],
To put the raw Raman spectra in a form suitable for comparison with the
VDOS, consideration of the above effects alone is not enough to remove
this peak. The raw data must also be multiplied by the harmonic oscilla
tor factor w to completely remove the Boson peak. Therefore the Boson
designation is not entirely adequate. Almeida showed that certain Raman
active low frequency modes contribute towards the Boson peak. These
modes are intensified for glasses containing ions of large polarizabil
ity.
The literature dealing with the correction factors required to
reduce the experimental Raman spectra includes errors and inaccuracies
in some references. Analysis of this literature led to the use of the
108
following equation in this study to thermally reduce the raw, baseline
corrected spectra before curvefitting
Ired + 1]'1>
(35)
Wwl>wR>
IWpUj)
[rad/s]
c [m/s]
fl cl/l
u{ [m'1]
wR [rad/s]
[m'1]
wp [rad/s]
[m'1]
n(wR)
h
k
T (K)
[N.B. cm'1
= reduced Raman intensity
= experimental Raman intensity (background corrected)
= laser frequency = 2nÂ£ s 2?rfl *= 2vcv^, where tt = 3.14159
= speed of light = 3 x 10 m/s
= frequency of laser [Hz]
= laser wavenumber = 19436 cm*1 s 514.5 nm
= Raman shift frequency = 2nci>R
Raman frequency wavenumber = 1004000 cm'1
scattered phonon frequency = 2ircisp
= scattered phonon wavenumber = s 1933615436 cm"1
BoseEinstein thermal phonon population factor
[(exp((h/2x)27rcvR)/kT)l]'1 = 3.0063 for uR = 104 cm'1
= Planck's constant = 6.626 x 10'3^ J.s
= Boltzman's constant = 1.3806 x 10'23 J/K
= Temperature
must be multiplied by 100 to convert to m*1.]
2.8 Curvefitting the Raman Spectra of Silica Gels
Hawthorne et al. [165] discussed in detail the theory of what they
calls "spectrum resolution methods," i.e. curvefitting. The general
philosophy of curvefitting involves using the physical/chemical knowl
edge of the experiment to set up a mathematical description of the raw
109
data of the experiment. These are composed of a series of separate
spectral bands which together with a random noise component constitutes
the observed envelope of curves. The variable parameters of the model
are then changed to minimize the deviation between the calculated
spectrum and the observed spectrum, using a computer to speed up the
process. If the fit or agreement is statistically acceptable, then this
model is taken as being a possible description of the experimental
situation. Hawthorne et al. [165] pointed out that the procedure of
curvefitting is frequently called deconvolution, and that this is wrong.
Deconvolution is a specific mathematical operation in Fourier analysis
used to reduce spectral line width due to instrument broadening.
When H20 is incorporated into fused aSi02, silanol groups, SiOH,
are formed, as opposed to the discrete H20 molecules found in crystal
line quartz [166]. The vibrational frequencies of the OH groups in fused
aSi02 are sensitive to their environment because the OH vibrations are
decoupled dynamically from the Si versus OH vibrations.
Hartwig [167] investigated the Raman spectra of SiOH groups in
aSi02. The depolarized and polarized spectra of the 0H peak at 3690
cm"1 exhibit different line shapes. This suggests that the 0H band is a
superposition of scattering resonances, with each resonance having a
different scattering tensor. Hartwig used three Gaussian peaks to
curvefit this band, the minimum number required to give a reasonable
fit, at 3630, 3670 and 3700 cm"1.
Curvefitting decomposition of the fundamental Raman and IR SiOH
vibrations in aSi02 by Stone et al. [166] and Walrafen et al. [168]
produced peaks at 3510, 3620, 3665 and 3690 cm'1. These are close to
Hartwig's assignments, and are assigned to 0H groups in different
110
Hbonding geometries, besides the 3690 cm'1 peak due to isolated SiOH.
However McMillan et al. [123] concluded that there was no evidence for
unresolved component bands, and that the asymmetry in the band was due
to a continuous range in Hbonded environments. These peak assignments
are also discussed in some detail by Orcel [4] and Wang [169].
Murray et al. [85] discussed the problems associated with mesopo
rous materials when measuring Raman spectra. They tried to obtain
quantitative peak areas using curvefitting. For porous Vycor, with an
average pore radius of 4.0 nm, the elastic scattering, e.g., Rayleigh
scattering, is approximately 150 times more intense than that from dense
Suprasil. In turn scattering from Suprasil is about 50 times larger than
the Rayleigh scattering from air at S.T.P. The elastic peak in Vycor is
8 orders of magnitude more intense than the peak heights of the aSi02
bulk phonons. The background in the Vycor Raman spectrum due to the
highfrequency tails of the elastic peak is comparable in intensity to
the Raman scattering at 50 cm'1. As the pores in silica gels are of a
similar size, and the effective Tf due to the method of manufacture is
even larger, the elastic peak is expected to be even more intense for
silica gels. This causes severe problems when trying to perform back
ground corrections on the raw spectra.
Two contributions to the background which must be removed to
obtain just the Raman scattering must be considered [85]. They are: a)
the Rayleigh elastic scattering peak, centered around the laser wavenum
ber, and b) the high frequency background. This is shown in Fig. 18
which has contributions from both fluorescence (due to surface organics
and perhaps adsorbed H20 [170]) and an intrinsic electronic surface
effect [85]. Murray et al. [85] measured the shape of the elastic peak
INTENSITY
in
l^ 1 i 1 i i i i i i ii
0 200 400 600 800 1000 1200
WAVENUMBER [cm*1]
Figure 18. Contributions to the background in the Raman spectrum of
porous Vycor. The upper dashed spectra is the experimentally determined
raw Raman spectrum. The lower solid spectra is the corrected spectrum
with the Rayleigh elastic scattering and the high frequency fluorescent
background subtracted. After [85].
112
from a metallic sample with no Raman emissions. This was then scaled by
the peak height ratio of the elastic peak in her Vycor sample to obtain
the shape of the tail under the main peak at 450 cm'1. The elastic peak
was then subtracted from the raw spectra.
The spectral line shape of the high frequency background was
obtained by subtracting two Vycor spectra, one with a larger background
than the other [85]. This assumed that for samples with backgrounds of
different intensity, the backgrounds possessed the same general shape,
i.e. roughly parabolic, but a different magnitude. This assumption is
reasonable. The line shape of the background shape obtained was approxi
mated by a smooth curve and fit to the spectrum near 1700 cm'1.
Mysen et al. [162] devised a method for curvefitting complex Raman
spectra where the line shapes and quality of the fits are determined
statistically after correction for the temperature and frequency
dependence of the raw data. In the fitting routine which they used, the
intensity, halfwidths and position of all symmetric Gaussian bands were
treated simultaneously as unrestrained variables. The number of lines
fitted to a spectrum was treated statistically by: a) numerical minimi
zation of the sum of the squares of the deviations (x2) between the
intensities at each wavenumber of the observed and calculated Raman
envelopes, and b) by maximizing the randomness of the residuals. The
number of lines fitted to individual spectra was limited to the point
where additional lines did not result in a statistically significant
improvement of x2 or in the randomness of the residuals. Using this
curvefitting technique, Mysen et al. [162] looked at the region between
970 and 1350 cm"1 for aSi02. They found that the 1060 cm'1 peak was
fitted by one Gaussian peak, while the 1200 cm'1 peak was fitted best by
113
two Gaussian peaks at 1162 and 1213 cm1. This differs from the usual
interpretation of this peak which is assigned to the single W4 LO Si0
asymmetric stretch vibration and is fitted by one Gaussian peak.
Seifert et al. [163] used the same method as Mysen et al. [162] to
curvefit the region between 700 and 1350 cm'1. They showed that Raman
peaks are Gaussian in shape rather than Lorentzian, and used 7 peaks to
curvefit the thermally reduced aSi02 Raman spectra in this region. The
central portion of the 800 cm'1 peak was fitted by two peaks, at 791 and
828 cm"1, as expected from theory. Two additional peaks at 732 and 881
cm"1 were used to fit the wings of this peak. The region between 900 and
1350 cm'1 was fitted in the same way as Mysen et al. [162],
The distribution of the SiOSi bond angle, 6, in aSi02 is
asymmetric, as shown by Mozzi and Warren [41], Seifert et al. [163]
hypothesized that this asymmetry may be explained by the existence of
more than one 3dimensional unit. Mysen et al. [162] claimed that high
resolution TEM may indicate that aSi02 consists of at least 2 distinct
structures. The Raman spectra cannot easily be interpreted unless
concepts such as TO and LO splitting involving long range order are
invoked. The TO and LO splitting do not aid in explaining results which
indicates that more than one average 0 may be present.
Seifert et al. [163] suggested that the Raman spectra may be
interpreted on the basis of two structural units which differ in 6.
Seifert et al.'s [163] analysis used two Gaussian peaks, at 1160 and
1210 cm"1, to curvefit the LO 1180 cm'1 peak. They used these two
peaks, and the W3 TO (793 cm'1) and W4 LO (829 cm"1) peaks to analyze
theoretically the two structural units using the SenThorpe [91]
centralforce model. The two units had 6 values of 132 and 127 and
114
force constants Kg of 570 N/m and 537 N/m respectively. The unit with a
smaller average 6 was associated with the smaller force constant. This
implied larger Si0 distances in the unit with the smaller 8. Such an
inverse relationship between d(SiO) and 8 has been found theoretically
by Hill and Gibbs [74] in crystalline silica and silicates. A bimodal 8
implied a bimodal dihedral angle, although the bimodal angles are
strongly overlapped in both angle distributions. This leads to one
asymmetric envelope with no intermediate minimum because the difference
in average 8 for the two units is only 5. These frequency distributions
would be strongly skewed toward the lower 8. Seifert et al. [163]
suggested that the two units may be two types of trisiloxane rings where
puckering in one of them leads to a 9 maximum 510 smaller than the
other one.
Seifert et al. [163] also suggested that the anomalous behavior of
the compressibility of aSi02 at 300 K and the two step densification
process at T < Tg are related to the two different ring sizes. As
pressure increases, unit I, with 8 = 132, is continuously transformed
into unit II, with 8 = 127, so above 30 kbar the compressibility of
aSi02 is controlled mainly by the smaller compressibility of the
smaller unit. This is related to the decrease in compressibility as the
average 8 decreases, so glasses containing larger concentrations of 3
and 4 membered rings will be less compressible.
Walrafen et al. [171] curvefitted aSi02 Raman spectra using the
constraint that only the components that correlate with a feature in the
spectrum such as a peak, shoulder or foot were used. The uncorrected raw
experimental spectra was transferred to a straight horizontal baseline
and deconvoluted using a Du Pont 310 analog computer. Ten Gaussian peaks
115
were fitted between 01300 cm'1, with an integrated residual of 1%. The
spectra had not been thermally reduced, so the low frequency peak at 50
cm'1 was present. Peaks were obtained at 55, 105, 235, 370, 460, 495,
610, 685, 795 and 830 cm"1. The 495, 610, 795 and 830 cm1 peaks all
correlated with known peaks. The 55 and 105 cm'1 peaks fit the Boson
peak, which is not significant in thermally reduced Raman spectra, so
these peaks would not be needed for curvefitting in investigations using
reduced Raman spectra. The 685 cm'1 peak is a baseline background
correction required to obtain a good fit. The 235, 370 and 460 cm'1
peaks are the minimum number of peaks require to give a fit to the main
450 cm'1 peak of this uncorrected Raman spectrum. Walrafen et al.
[166,171] stated that the 235 cm'1 peak correlates with a weak shoulder
near 280 cm"1. In reality this shoulder almost has to be imagined to see
it, Walrafen et al. say that it corresponds to a fundamental IR peak
[171], but they do not give the frequency of this vibration. They do not
assign the 370 and 460 cm'1 peaks to any specific structural vibrations.
This is not surprising as the specific vibrations causing the 460 cm'1
peak are still not known with any certainty.
Walrafen et al. [172] examined the Raman spectra of hypercritical
ly dried silica aerogels. They observed that, compared to fused aSi02,
the 800 cm'1 peak had shifted to 850 cm'1 and the 1060 and 1200 cm1
peaks to 975 and 1120 cm'1, respectively. The increase in the 800 cm"1
peak was interpreted to mean that the Si0 force constant is smaller
resulting from greater repulsion produced by a decrease in the equilib
rium 6. The decrease in the high frequency peaks means that Kg is de
creased due to an increase in d(SiO) [172].
116
A Raman correlation exists for fused aSi02 [172], which says that
a decrease in the main equilibrium 9 is accompanied by an increase in
the mean equilibrium d(SiO) and by an increase in the mean equilibrium
dihedral angle between the silica tetrahedra. This means that the 800
cm'1 peak moves to higher frequency as 9 decreases, that the 1060 and
1200 cm'1 peaks decrease in frequency as the Si0 bond lengthens, and
that the Raman intensity below 450 cm'1 decreases as the dihedral angle
increases. The Raman data for aerogels follows this Raman correlation
relating the 9 decrease to increases in d(SiO) and S.
The Raman spectra did not show a D2 peak, as for xerogels below
200C. Walrafen interpreted the D1 behavior of these aerogels as sup
porting Galeener's assignment of D1 rings to cyclic tetrasiloxane rings.
Mysen et al. [164] examined the effect on the Raman spectra of
aSi02 of dissolving up to 10% molecular H20 (and D20) in the aSi02
under pressure. They baseline corrected, thermally reduced and statisti
cally curvefitted the Raman spectra using Gaussian functions. This gave
quantitative data on the peak intensity and position as a function of
the concentration of H20 dissolved in dense aSi02. They used 1 peak for
the main 450 cm'1 peak, 2 peaks for the 1200 cm'1 peak, and 2 peaks for
the 970 cm'1 SiOH peak. Addition of the H20 caused the main and D1 peaks
to amalgamate so two separate peaks were no longer distinguishable.
The relationship governing a peak position shift due to deuterium
isotopic substitution is
WS0h/WS0D ^mS)0H/mSi0D^ 102
(36)
117
where w peak wavenumber, and m = gram formula weight. Based on the 970
cm'1 peak position shift to 955 cm'1 due to deuterium substitution, Mysen
et al. [164] confirmed this peak assignment as being due to SiOH. They
also suggested that two geometrically different SiOH bonds exist in the
quenched hydrated aSi02 melts they investigated. Two peaks were needed
to give a good fit when curvefitting the 970 cm'1 peak which both
shifted by 15 cm'1 on substitution by deuterium.
Dissolving H20 in aSi02 [164] also caused a peak at 1600 cm'1,
which is assigned to the HOH bending motion, and therefore indicates
the presence of molecular H20 in the aSi02. Curvefitting the SiOH peak
between 3000 and 3800 cm'1 required 4 peaks, which have been assigned to
symmetric and antisymmetrie stretching of OH groups in H20 (3310 and
3540 cm'1) and SiOH (3595 and 3660 cm'1). The corresponding OD stretch
bands in the 20002800 cm'1 region were inferred from the relationship
between oscillator mass and frequency for a twoatomic group:
w = (K/2jtc) 1/2 (1/Mh + 1/Mp) 1.3744 (37)
where, K = bond force constant, w = frequency, and M = atomic mass.
This agrees well with experimental results. The intensities of SiOH
stretch bands increase with enhanced interaction between OH groups and
neighboring hydrogen [164]. This introduces error into any calculation
of OH or H20 concentrations from peak intensity due to unknown effects
on peak intensity of hydrogen bonding. Bearing this in mind, Mysen et
al. [164] found that molecular H20 first appeared at 1.5% H20 addi
tion, and then increased linearly in concentration as the H20 content
increased, but not as fast as the [SiOH] concentration. The presence of
118
molecular H20 in aSi02 glass therefore does not mean that all the SiOH
groups that can form have formed. The relative proportions of H20 as OH
in Si02(0H)2 (or Si03(0H).j) and molecular H20 can be calculated from the
Raman spectra using these equations
A
A
A
X
SIOHqjSi'OH + AHOHaHOH =
SiOH^SiOH y OH
"" AH20
HOH^HOH y H20
AH20
i y H20 i y =1
SiOH ^ aH20 ^ ASi02 L
(38)
(39)
(40)
(41)
Asi0H is the ratio of the integrated intensities (950 + 970)/(950 + 970 +
1600). aSl0H and aH'0H are the normalized Raman crosssections for the
SiOH stretch vibrations (970 + 970 cm"1 bands) and HOH bending (1600
cm"1) vibration. The XH2Q0H and XH2QH2o are the mole fractions of H20 in
the hydroxylated silicate unit and molecular H20 respectively. XS]._QH is
the mole fraction of the hydroxylated silicate units assuming 20H/S.
Xg^Q2 is the mole fraction of anhydrous, threedimensional network units
in the melt. X2H2Q is the mole fraction of H20 in the quenched melt. The
ratio 0H/H20 that Mysen calculates from these equations increases with
pressure, and is also temperature dependent.
Mysen et al. [173] extended earlier curvefitting work [162164] to
include the complete range of Si0 structural vibrations in the Raman
spectra of aSi02, i.e., from 300 to 1800 cm"1. Using thermally reduced
spectra of aSi02 containing 3 wt.% H20, the same criteria was used as
[162164] to obtain peaks at 440, 484, 589, 787, 823, 967, 968, 1060,
1193, 1239, and 1621 cm"1. Figure 19 shows the curvefitted spectra. The
484 cm"1 peak is the D1 peak buried under the main peak. The 589 cm'1 is
119
Figur 19. The thermally reduced Raman spectra of a sample of asilica
with 5 wt% H20 dissolved in it, showing the Gaussian peaks used to
curvefit the spectra, and the residual difference remaining when the
curvefitted peaks are subtracted from the Raman spectra. After [173].
120
the D2 peak. The 787, 823, 1060, 1193 and 1239 cm'1 peaks have been dis
cussed above. The 967 and 968 cm*1 peaks are used to fit the SiOH peak
present due to the dissolved H20, and are the minimum number of peaks
required. The tall narrow peak is due to isolated silanol peaks, while
the broader, lower frequency peak is due to Hbonded silanol groups, in
direct correlation with the above analysis of the SiOH peak at 3690
cm"1. The 1621 cm'1 peak is due to molecular H20, present when the H20
content is large enough.
Yokomachi et al. [174] looked at the 1.39 /zm IR absorption band
(which is the first overtone of the 0H stretching vibration of adjacent
SiOH Hbonded to each other (equation (42)) in pure aSi02 fibers. They
examined the peak's T dependence and found four curvefitted peaks, from
which they concluded that the surroundings of SiOHgroups and their
state of existence is hardly changed by the method of synthesizing the
aSi02. They pointed out that SiOH groups form Hbonds, which lengthens
the bond length of the OH group which is participating in the Hbond,
and also lowers its oscillation frequency. Hbonds weaken as T increas
es, which increases the high frequency part of the SiOH peak as the OH
bond length decreases. They assigned the four curvefitted peaks 7070,
7204, 7250 and 7350 cm'1 of the 1.39 /zm peak to, in order of increasing
wavenumber, the bonds a, d, c and b respectively, as shown in equation
(42).
Si
\
0
t
H
H in phase, c / \
\ b / 0 Si (42)
H 0 Si Si 0 /
\ /
H
a
f.?
A
121
2.9 Raman Spectroscopy of Silica Gels
Bertoluzza et al [2123] were the first to look at the Raman
spectra of alkoxide derived silica gels. They examined the evolution of
the structural features of the aSi02 structure as a function of T and R
ratio. They noted the appearance of the D2 defect band at 200C, as
opposed to fused aSi02 which contains D2 rings at all Tf. The peaks in
the Raman spectra due to adsorbed H20 were not recognized as being
independent of the intrinsic structure of the gel, or that removing H20
under vacuum would give a cleaner spectra. Peak identification was made
with the help of D20 substitution [22].
Their conclusion [23] that defects originated from different
starting conditions is not substantiated by the experimental evidence.
Differences can be in fact be explained by differences in Tf and Sg of
the gels. The misunderstanding about H20 peaks persisted i.e. the
exposure or storage of samples between spectra is not discussed with
regard to possible H20 adsorption, and subsequent changes in [D2].
Krol et al. [2427], in an elegant series of papers, made specific
peak assignments and differentiated between dry and wet samples. She
also made the clear distinction between two processes that occur during
densification: a) The condensation of adjacent surface SiOH groups
forming siloxane SiOSi bonds, including the formation of surface D2
trisiloxane and D1 tetrasiloxane rings, and b) pore collapse. Figure 20
shows the Raman spectra of an alkoxide derived gel as a function of T.
Krol et al. [26,27] looked at the Raman spectra of gels made using
HF as a catalyst, with up to 16 g F/100 g of Si02 being incorporated
into the Si02 structure. 2 g F/100 g of Si02 was the minimum detectable
concentration by Raman spectroscopy as a SiF peak at 935 cm'1. This is
122
well above the concentration of F incorporated into the gels examined in
the present investigation.
Brinker and his coworkers [2835] also used Raman spectroscopy in
his investigation of the structural evolution of alkoxide derived silica
gels. They confirmed earlier work showing that no D2 three membered
trisiloxane rings are formed in gels during gelation or drying up to
about 150C [30]. This implies that D2 rings are metastable, unlike the
D1 four membered tetrasiloxane rings which are present in the silica gel
structure during gelation, according to Raman spectroscopy. They also
confirmed the rapid initial increase in [D2] with Tp along with the
associated decrease in [SiOH] (3750 cm'1), and the subsequent decrease
in both [D2] and [SiOH] during viscous sintering for Tp > Tgmax.
Isotopic substitution of 180 for some of the 160 in surface SiOH
groups confirmed that the surface silicate rings assigned to D1 and D2
are formed by condensation of the SiOH groups. Exposure of a silica gel
stabilized at 650C to H2180 in a Rh = 100% atmosphere for 24 hrs caused
the D2 peak to decrease to a level comparable to that in conventional
aSi02. Reheating the gels to 650C increased [D2] to previous levels,
and decreased the frequencies of the D1 and D2 peaks to 486 and 599 cm'1.
This proved that 180 originating as a surface silanol can be incorporat
ed in both defects and that the defects form reversibly on the silica
gel pore surface. The closest OH distance between neighboring SiOH
sharing a common siloxane bond is 0.32 nm, which is 0.05 nm longer than
typical H bonds involving 0H0. Consequently even neighboring silanols
should appear spectroscopically as isolated silanols.
INTENSITY
123
FREQUENCY [cm1] FREQUENCY [cm1]
Figure 20. The Raman spectra of silica gels at different stabilization
temperatures during densification compared to the spectrum of fused
asilica. The large background intensity at Tp 200C is due to fluo
rescence, which is gone by Tp = 400C as the organics burn out. Spectra
I at Tp = 800C is in a part of the gel which is still porous, while
spectra II is from a fully dense part of the gel. After [24].
124
Brinker presented strong evidence and arguments confirming
Galeener's assignment of the D1 and D2 defect peaks in Raman spectra of
silica gels and aSi02 to the oxygen breathing modes of small rings
containing three and four silica tetrahedra respectively. These are
known as D2 trisiloxane and D1 tetrasiloxane rings [30,31]. The Raman
spectra of densified gels heat treated near Tg are very similar to that
of fused silica. The structure of aSi02 made by these two different
ways is identical except for the differences due to Tf and [OH] [31].
Brinker et al. [31] discussed the relative concentrations of the
Raman active D1 and D2 peaks in neutron irradiated aSi02 and the
related increase in density. They suggested that [D^ and [D2] in
irradiated Si02 are similar to that of the A2 gel heated to 680C, which
gave the largest [D.j] and [D2] peak areas. They speculated that perhaps
a similar increase in gelderived Si02 density might be seen.
The relationship between the neutron flux density, the structural
density Dg and [D2] is not linear [100,119]. A flux of 2 x 1020 n/cm2
gives a D2 peak area of 18% percent of the total spectrum area (i.e.
[D2]/[Wt] = 0.18) and Dg = 2.2518 g/cc. The D2 peak of an A2 gel heated
to 680C is about the same height but is narrower than the D2 peak of
the irradiated silica sample [31,119], so [D2]/[Wt] is significantly
less than 0.18. The maximum structural density Dgmax of Brinker et al.'s
[5] A2 gel 2.35 g/cc (Fig. 21) at 680C which is significantly larger
than 2.2518 g/cc. Compared to this irradiated silica sample, Dgmax of an
A2 gel is larger while [D2]/[Wt] is smaller. This data contradicts
Brinker's suggestion [31]. The relationship between [D2] and Dg in A2
gels does not appear to be the same as in neutron irradiated asilica.
125
Brinker et al. [31] also pointed out the relative differences in
stability with respect to H20 and T that exist for D1 and D2 rings. The
less strained cyclic tetrasiloxane D1 ring is more stable, and therefore
less sensitive to large changes in T or H20 content.
The heat of formation of the D1 tetrasiloxane ring is calculated
to be weakly exothermic and therefore will be formed more easily than
the D2 trisiloxane ring. From combined DSC and TGA experiments, the
calculated net heat of formation, AHf 19 kcal/mole, of siloxane bonds
in the T region 350650C is significantly exothermic. AHf 19
kcal/mole is close to a MO calculation of the endothermic heat of
formation of 3fold rings, which is 23 kcal/mole [33]. This positive AHf
reflects the energy required to reduce 6 from 144 to 130. The reduc
tion in 9 is accompanied by charge transfer from Si to 0, which makes
the Si0 bond more ionic [35]. Structure induced charge transfer due to
decreasing 6 increases both the Lewis acidity of Si and the Lewis
basicity of 0. This in turn increases the susceptibility of siloxane
bonds to bond breakage by rehydroxylation by H20. MO calculations [35]
have established that the optimized geometry for the cyclic trisiloxane
molecule, H6Si303, is planar with D3h symmetry and $ = 136.7. This
significantly less than the average 6 value in aSi02.
Therefore D2 form by dehydroxylation of the pore surface at T >
200C. Based on their calculated value of the concentration of Q4 Si
sites in surface D2 rings, Brinker et al. estimated the maximum surface
concentration of the D2 species to be 2/nm2 [175] They suggested that
the D2 rings form at the surface due to the decreased constraints of the
matrix, and that once formed, the very high viscosity provided by the
matrix preserves the defect until it is exposed to H20 or high T. If
126
PROCESSING TEMPERATURE Tp[C]
Figure 21. The relative bulk density, the relative structural density
(calculated from Vp and Db) and the first and second DSC scans, DSC1 and
DSC2 respectively, for silica gel A2, made from TEOS with R 5 and pH =
0.95. After [5,28,29].
HEAT CAPACITY Cp[cal/g/C]
127
this is the case, we can ask "why would not the same decreased con
straints that allow their formation also allow their destruction?"
Conversely, "if the very high viscosity preserves the defect, why
shouldn't the same high viscosity preserve the original structure and
prevent D2 formation?"
29Si magic angle sample spinning (MASS) NMR spectroscopy provided
a new tool for in situ investigations of the local environment of Si in
condensed systems. The linear relationship between the 29Si chemical
shift, 6, of Q4 resonances and 6 is S(ppm) = 0.5889(0) 23.2 (correla
tion coefficient = 0.982), which provided a method of determining 6.
Brinker et al. [35] ran MASS and cross polarized MASS (CPMASS) spectra
on alkoxide derived gels (a) heat treated to different T, and (b) heat
treated and then exposed to a saturated H20 atmosphere. MASS NMR can
only be performed on powders. The heat treated samples were cooled in
dry 02, evacuated, and sealed in glass ampoules in vacuum. As they do
not mention grinding the gels for the MASS NMR, they presumably were
powder to start with. Presumably, then, all the samples Brinker et al
use are powders or they would state that they are monoliths.
Three prominent peaks at chemical shifts of about 91, 101, and
110 ppm in the MASS and CPMASS (cross polarized MASS) spectra of the 50
and 200C gels and in the rehydrated 200 and 600C gels corresponded to
Q2, Q3 and Q4 silicon sites respectively. Terminal 0 associated with Q2
and Q3 Si are bonded to H (OH groups) as shown by the 1H CPMASS spectra
in which the intensities of the Si resonances of the Q2 and Q3 sites are
enhanced relative to those associated only with the bridging 0 (Q4
sites). Brinker et al. [35] therefore concluded that the average
environments of Q4 silicons in 50C and 200C dried gels, 1100 C
128
densified gels and all the rehydrated silica gels are similar to those
in fused aSi02 as they had identical Q4 shifts. 8 147149 for all
these gels, as calculated from the 8 dependency on S for the Q4 value of
110 to 111 pm displayed by these samples.
The MASS spectrum of gels heat treated to 600 C were quite
different. They were curvefitted with Q2 (91 ppm) and Q3 (101 ppm)
peaks as well as a peak at 105 ppm which was required to obtain a good
fit. This peak was interpreted to be a Q4 peak with 8 = 139. Exposure
of the 600 C peak to H20 vapor caused the peak to shift back to its
original value (111 ppm) in the 50 and 200 C samples. The relative
intensity of the D2 peak correlated well with this NMR data. The NMR
data unambiguously associated the formation of the species responsible
for D2 with the presence of Si sites with reduced values of 8, and
conversely the elimination of this species with an increase in 8.
Brinker therefore definitively identifies the D2 species as a cyclic
trisiloxane, as originally proposed by Galeener [67].
For the 350650C temperature interval in which the D2 species
primarily formed, the average heat of formation of a siloxane bond was
calculated to be 0.88 eV = 20 J/g *= 4.7 cal/g. This is similar to the
calculated strain energy of 3membered rings. As the heat of formation
of unstrained siloxane bonds by the condensation of silanols is close to
zero, all of the associated strain energy is a result of ring closure.
The strain is associated with D2 formation. All the strained species are
Si as the Q3 and Q2 peak positions are unaffected by the formation or
elimination of D2 species [35].
The reduction in D2 intensity relative to the populations of the
higher order rings on exposure to H20 is due to D2 ring rehydrolysis
129
(equation 44). Most of the 3membered rings are present in surface
sites, where they are directly exposed to adsorbed H20. Some of the four
membered D1 rings, shown to be present before gelation by the Raman
spectra, are also present in the bulk aSi02 structure so they are
inaccessible to H20 molecules. Strain in the D2 rings makes them more
susceptible to hydrolysis than unstrained, higherorder rings. Lack of
strain in D1 rings makes them less susceptible to hydrolysis.
Mechanistically, normal unstrained siloxane rings are hydrophilic
and resistant to hydrolysis [1]. Si atoms which are tetrahedrally
coordinated by 0 lack the acidity to interact with the basic lonepair
electrons in the 0 in H20. The lonepair electrons in the Si0Si bridge
lack the basicity to interact with the protons in H20. However, reaction
studies suggest that changes in the tetrahedral geometry around Si
activate empty dacceptor orbitals, making the Si more acidic [35]. MO
calculations suggest that decreasing 6 transfers electron density into
the lone pair orbitals of the bridging oxygen, making the 0 more basic
and the Si more acidic. The increased polarity and enhanced acid/basic
properties of the strained Si0 bonds promote the adsorption of H20 on
the bond and the subsequent bond hydrolysis.
Mulder et al. [36,37] proposes the existence of a third defect
peak in the Raman spectra of silica gels, the so called "D0" peak at 490
cm'1. They attributes this peak to the symmetric stretch vibration of
three 0 atoms symmetrically bonded to an SiOH group. This would be seen
in the wet gel or a gel with a large concentration of Sig0H groups. It
would gradually disappear as T increases and the [SiOH] decreases, to
be replaced by the D1 peak at a very similar peak position, as the
4fold rings are formed. This peak assignment is questioned by Brinker
130
et al. [35], who presents strong evidence for the incorrectness of
Mulder's assignment and data interpretation.
The Raman spectra of alkoxide derived gels heated to T < 350C
exhibit an intense background, due to fluorescence, which is non linear
between 1004000 cm'1. This background swamps the Raman peaks and makes
curvefitting very difficult due to the very poor S/N ratio and the
difficulty of removing the background signal. This very intense and
broad scattering background is usually attributed to organic fluores
cence caused by the laser [170], which reduces in intensity with time of
exposure to the laser. Careri et al. [170] proposed that the intense
scattering background observed on oxide surfaces is in fact due to the
presence of H20 molecules tightly Hbonded close to some Lewis sites.
2.10 FTIR Spectroscopy of Silica Gels
Almeida et al. [176] examined the FTIR specular reflectance
spectra, measured 20 offnormal, of an alkoxide derived silica xerogel
using KramersKronig analysis. (They noted that the reflection peaks of
aSi02 are always shifted to higher frequencies relative to the trans
mission peaks od aSi02, so care must be taken when comparing reflection
and transmission peaks.) Compared to the reflection spectra of fused
aSi02, the dominant reflection peak of the gel is red shifted to
smaller wavenumbers, from 1125 cm'1 (fused aSi02) to 1088 cm'1. The 811
cm'1 peak also decreased from the fused aSi02 value of 817 cm'1, which
is the contradictory direction from that expected. After heating the gel
to 400C the reflectivity spectrum showed small upward frequency shifts
in the dominant band, along with a reduction in surface area from 400
m2/g for the dry gel to 20 m2/g for the 400C gel. The frequency of a
131
peak decreases as Kg or 9 decrease. When 6 decreases the 800 cm'1 Raman
peak increases in frequency, and the 1060 and 1200 cm"1 Raman peak
decrease in frequency. There is an inverse cubic correlation between Kg
and d(SiO) so as Ka increased d(SiO) decreased by the cube root of the
percentage increase of Ka. Based on this, and assuming the main peak
trend (from 1125 to 1088 cm'1) is the true difference between fused
aSi02 and silica gel, then either or 9 or both of them have de
creased in the dry gel compared to the fused aSi02 [176]. If 9 and/or
Ka decreased, then d(SiO) increased, and peak vibration frequencies
correspondingly increased, as is seen by Almeida et al. [176]. Heating
the gel caused the gel to become more like fused aSi02 as the 1088 cm'1
peak increased in frequency and 9 and Kff changed accordingly [176],
2.11 NMR spectroscopy of silica gels
Vega et al. [177] investigated the chemical evolution of alkoxide
derived silica gels using 29 Si NMR. The extent of crosslinking was
found to increase very slowly after gelation. This implied that if the
physical properties of the gel were determined by the topology of the
aSi02 network, very small increments in the crosslinked density would
have a profound effect on the physical state. On the other hand,
interchain linking could also be provided by Hbonding of water mole
cules .
29Si NMR analysis of otherwise identical silica gels made with R =
4, 8 and 16 showed that increasing R increased both the shortterm and
longterm condensation rate. R is the ratio of number moles of water to
the number of moles of silica precursor. The Q4 peak appeared more
132
quickly and increased in intensity more quickly the larger R. The
spectra of the dry gels were very similar for all values of R [177].
The degree of polymerization found by MAS NMR in the dry gels
[177] corresponded to Q*:Q*:Q^ ratios between 1:5:6 and 0:6:6. For every
12 Si's, 5 or 6 carried one OH and 1 or 0 carried two OH's, so there is
a low degree of crosslinking. The final [SiOH] for these particular dry
gels was between 0.5 and 0.6 SiOH per Si atom, similar to SiOH/Si = 0.63
estimated for aged wet gels. Of course [SiOH] will change as the
composition, R ratio, pH, etc. of the silica sol change. The changes
that took place in the viscoelastic properties of these drying gels
therefore resulted from a molecular mechanism requiring the formation of
relatively few SiOSi bridges.
Vega et al. [177] examined the 1H MAS NMR of drying silica gels
containing H:Si ratios going from 2.4 (pores not fully saturated) to 0.6
as the water was removed. An H:Si ratio of 0.6 was for the fully dry
gel, i.e. all free water removed for T used to dry the gel, and all the
H existed as SiOH. The 2.4 H:Si ratio had 0.9 water molecules (contain
ing 2 H per molecule) per Si atom, as well as 0.6 OH per Si atom.
When the gel was dried to a H:Si ratio of 1.0 or less, the 0.6
SiOH and the residual H20 molecules were rigidly bound in the gel frame
work. On the other hand, when the moisture content was higher than 1.5
OH per Si atom, all the protons of the H20 molecules and the SiOH groups
constituted one liquid state. In this liquid state the H atoms exchanged
rapidly between the free H20 and all the bound SigOH groups.
The SiOH groups caused three MAS peaks at 3, 2, and 1.2 ppm shift.
These were due to OH that was Hbonded to 0, OH that is Hbonded to
neighboring OH groups (SIOH or residual H20), and isolated OH, respec
133
tively. The ethoxide (0C2H5) to Si ratio was less than 0.02 for R = 16,
so the surface SiOC2H5 concentration was low.
The 29Si MAS NMR data showed [177] that for an R = 16 gel the Q4
peak position shifts from 112 ppm = 150.8 to 109 ppm = 145.7 as the
H20 was removed during drying, while the Q3 peak did not shift. Since
the chemical shift depends on 9, the aSi02 network undergoes a stage
of strain when the H20 content passes a critical concentration, associ
ated with the fundamental changes in the Hbonding scheme discussed
above. The critical H:Si concentration is at about 1.0. The reduction in
9 from 150.8 to 145.7 was associated with the large capillary forces
experienced by the gel as the last H20 is removed from the pores.
The ratio of 0.6 OH/Si is equivalent to about 9 OH/nm2. The
surface silanol concentration of silica gels is 4.9 OH/nm2 so about half
of the OH groups are evenly distributed throughout the bulk of the gel
with an average protonproton distance of about 0.5 nm. The high [OH]
will contribute to the low Ds, the high thermal expansion and the low
elastic modulus observed in dry silica gels.
Aujla et al. [178] calculated the 9 distribution in aSi02 from
the 29Si MASS NMR lineshape using the linear relationship between the
29Si MAS NMR chemical shift and 9. aSi02 made via the hydrolysis of
SiCl^ and from colloidal aSi02 both have large [SiOH] in the form of Q2
(Si02(0H)2) and Q3 (Si03(0H)) groups. Aujla [178] showed that at low
sintering T (Tp = 250C) these aSi02 samples have much narrower FWHM
and fewer large angles in 9 distributions than Suprasil. Their distribu
tions became very similar to Suprasil after sintering at 900C. The
narrowness of the distributions is interpreted as a more ordered
situation [178] for the aSi02 samples prepared by different techniques.
134
They converge on a single structure if heated to a sufficiently high T
which is below the softening points of the materials.
2.12 The Structural Density of Alkoxide Derived Silica Gels
Yamane et al. [7] was among the first to publish data on the
physical properties of monolithic (i.e. geometric nonfragmented
samples) pieces of dried silica gel made from basecatalyzed tetrameth
oxysilane (TMOS). The bulk and skeletal densities, Dfa and Dg, surface
area, Sa, pore volume, V average pore radius, rH, pore size distribu
tion, dVp/drH, and drying rates were measured. Dg varied from 1.98 and
2.06 g/cc for the dry gels, depending on the pH of the starting sol. No
estimate of their accuracy was made. It was not specified whether H20 or
helium pycnometry was used. The Sg, Dg and Db of the dry gels increased
as the silica sol pH increased from 7.42 to 8.54 during NH^OH addition.
Decottignies et al. [8] discussed the manufacture of dense aSi02
from hot pressed powdered silica gel made from neutral (no catalyst
added) TMOS. They had Db = 2.21.g/cc, similar to that for fused aSi02.
Yamane et al. [9] published further work on the synthesis of
monolithic dense silica gels made from basecatalyzed TMOS derived gels.
They gave specific values of Dg, using the same technique as in [7] i.e
pycnometry, but again the type of pycnometry was not specified. Figure
22 shows the dependence of Dg on T, with an 18 hrs hold at each T, for a
neutral sol and an ammoniated sol. The maximum value is 2.23 g/cc,
occurring at the maximum Tp = 900C. It is not clear whether Dg would
have increased or decreased if T was increased further.
P
Sacks et al. [179,180] examined the sintering behavior of compacts
of aSi02 particles made from basecatalyzed tetraethylorthosilicate
o o
135
Figure 22. The temperature dependence of the structural density Dg of
two silica gel samples. Sample A was made with distilled water with no
atalyst added. Sample B was made with distilled water containing
.0085% NH40H. After [9],
STRUCTURAL DENSITY DS [g/cc]
136
Figure 23. The temperature dependence of the structural density of
monodispersed silica gel powders made by the base catalysis of TEOS
using excess NH^OH [6]. After [179],
137
(also known as tetraethoxysilane or silicon tetraethoxide), TEOS, using
the Stober process [6]. This utilizes high pH ammoniated H20 to precipi
tate monodispersed spherical aSi02 particles. The particles had an
average diameter of about 500 nm, giving Sg 7 m2/g with the fullwi
dth halfmaximum (FWHM) of the pore size distribution 50 nm. Figure 23
shows the thermal dependency of Dg of the aSi02 Stober particles. Dg is
roughly oc T as Dg increases from 2.05 to 2.30 g/cc between 25C and
1050C. Dgmax occurs at 1050C. The silica powder compacts had not fully
densified at 1050C, so it is not clear whether Dg would increase or
decrease if the compacts were completely densified with no internal
porosity. The increase in Dg above that of fused aSi02 was attributed
to structural rearrangement leading to a more ordered, dense packing of
Si02 tetrahedra [1,168,180],
Brinker et al. [10] investigated the evolution of Dg of acid
catalyzed TEOS derived silica gels, called A2 gels. A2 gels are made
using a different technique from the gels investigated in the present
study. Brinker et al. [10] used a two step acidcatalyzed hydrolysis
technique, the first step consisting of hydrolysing TEOS with R = 1
under acidic conditions. This was followed by: a) the addition of H20
plus acid to give gel A2 with a sol pH = 0.95, or b) the addition of H20
plus base to give gel B2 with a sol pH = 7.2 and an overall R ratio of
5. The specific manufacturing technique used to make the gels had an
effect on the resulting Dg values due to the different aSi02 structures
formed for different starting sols and/or conditions. This is true for
all the investigations discussed here where the gels are made under
different conditions. This is because the most important property of
gels, and the most important influence on all alkoxidederived gel
138
properties, is that the structure and properties of the gel depend
strongly on the starting conditions, the sol composition and pH, the
ageing T, time, and pore liquor composition, the drying technique, etc.
All these variables can have a slight or drastic influence on the final
structure of the dry and stabilized gel, and therefore the physical
properties, including Dg and its evolution during densification. This
must be kept in mind when comparing alkoxide derived gels.
Brinker et al. [10] examined specifically the shrinkage of an
acidcatalyzed gel, gel A2, and a basecatalyzed aSi02 gel, gel B2, in
the T range 400550C. They noted that gel A2 exhibited increased
shrinkage, compared to gel B2, and that the associated weight loss was
very small. Gel A2, as determined by small angle Xray scattering
(SAXS), was the most ramified, least highly crosslinked gel of those
compared. In this T range Dg of gel A2 increased by 25 %, and showed an
exothermic peak on a DSC scan. Brinker associated the size of the
exothermic peak, which occurred at the same T as the inflection in the
shrinkage curve, with the magnitude of the excess free volume present in
the gel [28]. The exotherm was larger for gels prepared under conditions
favoring growth of weakly crosslinked polymers in solution. They
attributed the increase in Dg to structural relaxation, but gave no
specific values for Dg. They defined structural relaxation as the micro
scopic motion of atoms or polymer fragments which result in reduced
excess free volume and increased Dg associated with a DSC exotherm.
Excess free volume, which can reduce Dg [11], is difficult to
distinguish from the effect of the incorporation of hydroxyl groups, as
they have the same effect on Dg. Excess free volume relaxes exothermica
lly at T near Tg with an accompanying increase in viscosity, rÂ¡. The
139
observation of isothermal increases in viscosity with no accompanying
dehydration provides indirect evidence [11] in support of excess free
volume causing the observed changes in Dg.
The heat of formation, AHf, of SiOSi bonds is very sensitive to
9. AHf is a minimum at 6 & 144 in aSi02 and 4 kcal/mole [28], The
heat of formation for 2membered and 3membered rings, 9 91 and 138,
is 55 and 23 kcal/mole respectively. From an analysis of DSC and TGA
data, Brinker et al. [30] calculated that the average AHf of the SiOSi
bonds formed by condensation during sintering was 19.3 kcal/mole. This
inferred that the majority of bonds formed during dehydration above
545C are highly strained due to 3membered silicate ring formation, so
the dehydrated gel network is metastable. Above Tg it dissociates
exothermally to form more stable bonds as the bond angle increases to
the stable value, as shown by the exotherms observed above 660C.
During drying the structure is influenced by the solubility of
aSi02 in the liquid in which the gel was aged and dried [29], which
governs the extent of Ostwald ripening. In alkoxide derived gels
condensation begins before hydrolysis is complete, resulting in highly
ramified, fractal structures rather than dense colloids. Few bridging
bonds are broken and reformed during solvent removal so the structure of
the dry, porous xerogel bears some relation to the structure at the gel
point. This means that the structural starting point after drying may
vary significantly depending on the original gelation conditions.
Colloidal gels, composed of a fully crosslinked skeleton, are analogous
to porous glass and their densification behavior is described accurately
by viscous sintering models. The same model does not describe the
sintering behavior of alkoxide derived gels, due to the metastable
140
PROCESSING TEMPERATURE Tp[C]
Figure 24. The temperature dependence of the shrinkage and structural
density of a 71% Si02 18% B203 7% Al203 4% BaO borosilicate gel,
with R = 5 and pH = 6.8, heated at 2C/min. After [5,12,29].
STRUCTURAL DENSITY Ds[g/cc]
141
nature of these gels influencing both their densification kinetics and
their thermodynamic properties.
Brinker et al. [29] discounts the possibility that the shrinkage
observed for metal alkoxide derived gels in intermediate T ranges is due
to rearrangement of primary particles or secondary agglomerates to
higher coordination sites. They demonstrated that this shrinkage can
result exclusively from skeletal densification for the borosilicate gels
they investigated. Skeletal densification is the densification of the
solid phase comprising the porous gel toward that of the corresponding
meltprepared glass. Figure 24 shows the shrinkage and Dg of a borosili
cate gel, pH = 6.8, R = 5, 71% Si02 18% B203 7% A1203 4% BaO, as a
function of T. If particle rearrangement was occurring Dg would not
increase, as it does in Fig. 24 where Dg increases by 27%, accounting
for the 23% gel shrinkage seen in the same T range. During the region of
largest Dg increase up to 500C, the surface area hardly changes, so
viscous flow is not occurring.
Brinker et al. [28,29] measured the skeletal density Dg of an A2
gel as a function of T (Fig. 21) calculated from the bulk density, Dfa,
and the pore volume, V measured from isothermal N2 sorption at P/PQ =
0.999, using the equation
Vp 1/Db 1/Dg. (43)
This assumes no closed porosity. The initial decrease in Dg was due to
the loss of surface hydroxyls, organics and physisorbed H20 [29]. The
subsequent changes in Dg are due to skeletal densification, structural
relaxation and viscous sintering. Figure 21 shows a maximum relative Dg
142
PROCESSING TEMPERATURE Tp[C]
1100
1000
900
800
700
600
Figure 25. The temperature dependence of the weight loss, shrinkage and
surface area of silica gel sample A2, made from TEOS with R = 5 and pH =
0.95, heated at 2C/min in air. After [5,28,29],
SURFACE AREA SA [m2/g]
143
of 1.08 s 2.38 g/cc at 700C for an acid catalyzed silica gel with an
average pore radius rH of about 1.0 ran, and a fractal dimension = 1.9,
inferring a weakly crosslinked gel. For this silica xerogel, gel A2,
bulk densification occurs by viscous sintering between 800900C, while
skeletal densification occurs exothermally between 450600C with little
associated weight loss (Fig. 25). The repeat DSC scan in Fig. 21 showed
that this densification process was irreversible. Exposure of the gel to
H20 caused the reappearance of the exothermic peak due to rehydroxylat
ion of the strained surface silicate rings.
Silica gels are known as silica xerogels when dried at ambient
pressure by T control. Dg of alkoxide derived xerogels dried at 200C is
lower than that of fused silica due to the weakly crosslinked, hydroxyl
ated network at the gelation. The low Dg values are attributed to in
creased [OH] and [OR] content and greater free volume [29]. In other
words the structure of the silica gel, and therefore the magnitude of Dg
is a function of the starting gel conditions, which govern the degree of
crosslinking, bridging oxygen bond formation, hydrolysis etc. This is
measured by the ratio of the number of Si atoms to the number of
bridging oxygen bonds. The average number of OH + OR remaining in dry
gels can be as high as 1.46/Si atom, resulting in reduced crosslinking
and a reduction in Dg.
The increased [OH] and [OR] (i.e. decreased crosslinking) and
greater excess free volume, which cause the reduced Dg values, may be
described by an affective Tf for the gel [29]. The metastable silica
structure locked in during gelation is retained to higher T for higher
heating rates. This infers that the magnitude of the Dg value measured
for a specific T depends on the thermal history of the gel up to that
144
point. In silica xerogels, skeletal dehydration occurs below 500C, as
above 500C only isolated surface silanols, Sis0H, remain, which Brinker
et al. [29] say do not affect skeletal density. Since OH groups must
contribute to the skeletal volume used to calculate D of the aSiO,,
they must effect Dg. Presumably therefore Brinker et al. [29] mean that
since the OH groups are isolated groups on the surface they are too far
apart to react, so they do not affect Dg via further condensation above
500C.
The initial Dg increase observed in Fig. 21 occur as a consequence
of the loss of the high hydroxyl, [OH], and organic, [OR], content and
excess free volume. This causes skeletal densification to occur by both
increased crosslinking and structural relaxation towards the configura
tion characteristic of the metastable liquid [29], The structure densit
ies by crosslinking and structural relaxation. Crosslinking happens
mainly at the lower end of the densification T range (300450C) with a
relatively large associated weight loss. Structural relaxation occurs in
the lower rÂ¡ region at the higher end of the densification T range
(450600C) with little associated weight loss (Figs. 21 and 25).
By analogy to melted glass, structural relaxation is expected to
occur near the Tg of the skeleton, i.e. at sufficiently low rj to allow
diffusive motions of the network. This presumably occurs at a relatively
high T, 5001000C, and the skeleton will densify exothermally with no
associated weight loss. Comparison of the Raman spectra of dry gels with
that of high Tf fused aSi02 infers that their Tf value, which is a
measure of the excess free volume present in a system, is extremely
high. Due to the open structure frozen in at gelation, a dry gel will
have a very high effective Tf [28] This will broaden the T range of the
145
associated Tg, effectively lowering Tg for that gel. This allows struc
tural relaxation, which occurs at the viscosity associated with Tg, to
occur at a low T compared to fused aSi02. The Tf value drops rapidly
during the initial stages of sintering but still causes a large effec
tive decrease in rÂ¡. Therefore structural relaxation occurs at a rela
tively low T, and continue to occur as T rises and the gel Tg rises due
to the associated Tf decrease.
The Sg decrease accompanying skeletal densification can be ac
counted for [28] by the contraction of the skeleton according to
^s(initial)/^s
and does not result from sintering of open pores. This equation cannot
be used for fractal gels unless the same molecule is used to measure Dg
and Sg because the their magnitude depends on the size of the molecule.
N2 was used to measure Dg and Sa in this case. The observed dependency
of Dg on T is thus explained in terms of structural relaxation, viscous
sintering and a high effective Tf. For acidcatalyzed alkoxide derived
gels, the network structure formed is a product of condensation reac
tions which occur in solution before gelation and during the gelto
glass conversion. This leads to metastable, hydroxylated, open networks
which may be retained to elevated T and therefore influence Dg [29].
For a multicomponent gel, Brinker et al. [12] present evidence
which they said shows that skeletal densification can account for all
observed shrinkage in the gel between 150 and 525C, due to condensation
polymerization and structural relaxation. The extent of skeletal
densification will depend on the openness of the gel structure initial
146
ly. This depends on the starting sol and probably on the method of
drying which controls the drying stress described by the LaplaceYoung
equation [181]. Thus, gel shrinkage depends on the composition of the
sol and on the structure of the original gel [14]. Brinker et al. [12]
concluded that capillary contraction contributed 3% to the total
observed shrinkage below 150C, skeletal densification contributed 33%
to the total shrinkage from 150525C, and viscous sintering accounted
for the remaining 63% of the total shrinkage above 525C for the
borosilicate gel investigated. The contributions might be different for
other gel systems. Skeletal densification occurs without dramatically
changing the local environment of the basic structural units as the
skeletal matrix shrinks isotropically while maintaining the original
coordination number of the units which comprise it. Therefore the
dimensional motion required for skeletal densification is very small,
explaining how this process can occur at relatively low T.
Brinker et al. [13] analyzed the isothermal sintering of alkoxide
derived gels and observed a substantial increase in viscosity with time.
Some of the increase in viscosity was caused by the continual loss of
hydroxyls as H20. This is revealed by the shift of Tg for these samples
in a DSC. Some of the viscosity increase resulted from changes in the
microstructure, represented by the decrease in Sg. Structural relaxation
accounts for the remaining portion of the increase in viscosity. The
volume relaxation needed to achieve that effect in region III, where
there is large shrinkage due to viscous flow with little weight loss,
would be a tiny fraction of the relaxation that is observed in region
II, where little shrinkage and large weight loss occurs compared to
region III.
147
Further analysis of gel sintering data showed that extensive gel
shrinkage which is accompanied by weight loss is expected to result
primarily from condensation reactions within the skeleton [14], as
opposed to structural relaxation. This would cause Dg to increase if the
structural volume decreases faster than the weight loss. The condensa
tion reaction of isolated SiOH would cause the formation of surface D,
rings. The subsequent decrease in Dg observed for some silica gels,
including those in this investigation, is related to changes in bulk
density, i.e the viscous flow regime.
Dos Santos et al. [15] investigated the structural properties of
silica aerogels made by drying hypercritically in an autoclave using
SAXS, isothermal N2 sorption, density and TEM techniques. They calculat
ed values of Dg 2.2 g/cc, and concluded that these were unrealistic
due to the model used to calculate the data from the SAXS data. Boonstra
at al. [16] also measured the Ds of silica aerogels using He pycnometry,
and found values of 2.152.2510.05 g/cc, but there was no correlation
between Dg and the sol composition or dried gel properties. They con
clude that about half of the surface is covered by 0CH3 groups.
Phalippou et al. [17] measured the Dg of dried silica aerogels,
made from TMOS and methanol with no catalyst. They confirmed the conclu
sion of Dos Santos et al. [15] that the particles in aerogels detected
by SAXS are silica particles, as opposed to pores, whose skeletal
density range from 1.5 to 2.2 g/cc, depending on the starting sol. The
Dg and Db of the aerogels increased as pH increased, as reported by
Yamane et al. [8], and is related to the degree of internal particle
hydration, governed by the catalyst (which controls the pH), and the
degree of excess free volume. Dg and Db also increased as the volume %
148
TIME t [min.]
Figure 26. The temperature dependence of the bulk and structural density
of a silica aerogel made from TMOS using distilled water with no
catalyst, using methanol as a mutual solvent. After [17].
STRUCTURAL DENSITY Ds [g/cc]
149
BULK DENSITY Db [g/cc]
Figure 27. The dependence on the bulk density of the structural density
of a silica aerogel made from TMOS using acidified water and methanol,
giving a pH = 2. After [18].
150
of TMOS in the sol increased [17]. Figure 26 [17] shows the expected
increase in Dg with time at 1050C for a neutral TMOS derived aerogel,
with a maximum value of 2.20.04 g/cc, when Db = 1.2 g/cc. Yet again it
is not clear if D would increase or decrease as D. and increases
s bp
further.
Lours [18] measured the Dg of silica aerogels as a function of Db,
and obtained the data shown in Fig. 27. The aerogels were made from
nitric acid catalyzed TMOS in methanol, pH 2. Figure 27 shows an
initial increase in Dg with little change in Db, followed by a conver
gence of Dg and Db at 2.2 g/cc. Dg is calculated from Db, measured using
Hg pycnometry, and the apparent V calculated from the SAXS data. The
two distinct slopes of the curve indicate two densification regimes, so
the sintering of silica aerogels occurs in two sometimes overlapping
phases, depending on the texture of the gel. At lower T, 500800C, the
dry gel undergoes a diffusion controlled contraction leading to densifi
cation of the matrix (presumably corresponding to Brinker's concept of
structural relaxation). At higher T viscous flow sintering leads to
elimination of the porosity. The very low Dg values measured here by
SAXS correspond to 310 nm particles containing open porosity. These
would be penetrated by He pycnometry giving the correct Dg, but is seen
by SAXS only as fluctuation residues [18]. Dg of aerogels seen by SAXS
and He pycnometry progressively coincide at later densification stages
after elimination of microporosity [18].
Esquivias et al. [19] investigated the Dg of xerogels using wide
angle Xray scattering (WAXS). They obtained values of Dg 2.09 g/cc,
less than that of fused aSi02. They said this was explained by RDF
analysis as being due to a small particle size distorting the short
STRUCTURAL DENSITY Ds [g/cc]
151
Figure 28. The temperature dependence of the structural density of
silica xerogels, made from TMOS using acidified water, R = 16 and pH =
1.0, with ^ = 1.2 ran, 3.2 nm and 8.1 nm as indicated. After [183]
152
range order, and was affected by the surface defects. This yielded a
longer average bond length and a distortion in the aSi02 network.
Orcel et al. [182] measured the Dg of silica gel, using He pycno
metry on powdered samples, as a function of % Ce in the system and T.
For 1% Ce, Dg 2.0 g/cc at 200C, increased to 2.3 g/cc at 800C and
decreased to Dg of the corresponding melt derived glass. Vasconcelos
[183] obtained a very similar dependency of Dg on Db for pure silica
gels made from TMOS using helium pycnometry on powdered gels (Fig. 28).
Dg 2.13 g/cc at 200C, 2.32 g/cc at 800C and 2.2 g/cc at 1200C.
In summary, the structural density Dg of silica gels depends in a
complex interdependent manner on many factors. These include starting
sol composition, pH, R, T, drying method, thermal history, etc. Values
of Ds > 2.20 g/cc have been measured [9,12,28,29,179,183] but are ques
tioned because they are larger than Dg of fused aSi02. The Dg of base
catalyzed silica gels increases to Dsmax >2.2 g/cc (Figs. 2224) during
densification, but it is not clear whether Dg would remain >2.2 g/cc or
decrease to 2.2 g/cc if the gels were heated to higher T than in Figs.
2224. The Dg of acidcatalyzed silica gels increases to Dgmax >2.2 g/cc
during densification, but decreases to Dg = 2.2 g/cc at full densificat
ion (Figs. 21 and 28).
CHAPTER 3
STRUCTURAL AND TEXTURAL ANALYSIS OF POROUS
SILICA GELS DURING SINTERING
3.1 Experimental Procedure
3.1.1 The Production of the Silica Gel Monoliths
The initial concepts, ideas, techniques, and processes leading to
the development of the successful mixing, casting, ageing, drying,
stabilization, dehydration and sintering to full density of monoliths of
metal alkoxide derived silica gels were developed at the Department of
Material Science at the University of Florida, Gainesville, Florida by
Dr S.H. Wang [169] in the laboratories of, and under the guidance of, Dr
L.L. Hench, in 19821986. These techniques were improved, refined and
simplified by members of Dr Hench's research group, including E. Akomer,
G.P LaTorre, R. Nickles, Dr J.L Nogues, Dr G.E. Orcel, D.E. Parsell, Dr
S. Park, M.J.R. Wilson, Dr B.F. Zhu and the author (SW) in 19841989.
The silica gels used in this study were made with the standard process
ing technique which was the final product of this research program.
Dried porous and/or dense monolithic silica gels can be made easily and
reliably by following the processing recipies. This standard method
removes the experimental variables that exist due to the use of differ
ent processing techniques. The standard processing technique is dis
cussed in detail by Wang [169], Orcel [4], Wilson [181], Elias [184] and
Vasconcelos [183]. Consequently, only a brief description of the method
for making standard silica gel monoliths will be given here.
153
154
The silica gel is made using nitric acid (HN03) as the catalyst.
It is called sample type OX throughout this study and is the gel to
which others are referenced. A large quantity (1975 cm3) of chilled H20
is poured into a large glass beaker containing a magnetic stir bar on a
magnetic stir plate. 25 cm3 of concentrated HN03 is slowly added to the
H20 while stirring continuously. After the acid had been allowed to
completely ionize, 1000 cm3 of TMOS is slowly poured into the acidified
H20 over a 10 minute period. This gives a sol composition of
225:3710:13.5 moles of TMOS:H20:HN03. TMOS is very dangerous and must be
handled with great care under a hood. A polycarbonate measuring cylinder
is used to measure the TMOS, as it reacts with polystyrene containers.
The sol, which by now consists of silicic acid, SiiOH)^, in
solution in a H20/methanol solvent (the mother liquor), is covered and
stirred for 1 hour, before casting into molds of the required shape and
sealed to prevent evaporation. Gelation takes 2 days at 25C. The cast
gels are then sealed in their casting containers and aged at 80C in
their own pore liquor for 36 hours. After ageing the gels are carefully
transferred to Teflon drying containers, covered with pure H20, sealed
in the containers with lids containing controlled septum sizes and dried
by heating at 3C/hour to 180C. The resulting type OX dry gels are
slightly translucent monoliths with Db 1.05 g/cc, Vp 0.45 cc/g, Sa
750 m2/g, rH 12 , [Si0H]g 5 0H/nmz and a fractal dimension D 2.4
[4] Dry is defined to mean no physisorbed H20 remaining in the micropo
res of the silica gel after heating to 180C in air [1],
The addition of hydrofluoric acid, HF, to the sol of the funda
mental silica gel composition, type OX, changes the structure of the
gel, as discussed in the introduction. The HF is added to the sol, after
155
the HNOj has been added, in the form of a 3% solution of HF in H20. The
HF catalyzed gels are cast, aged and dried in exactly the same way as
the HN03 type OX gels. The basic HF sol composition, known as type IX,
contains 225:3710:13.5:1 moles of TMOS :H20:HN02:HF, equivalent to 0.015
moles of HF/liter of H20. Sample types 2X and 5X, used in this study,
contain 0.03 mol/1 and 0.075 mol/1 of HF respectively. All the other
components have the same concentration as the type OX sample. The molar
TM0S:H20:HN03:HF ratio of silica gel sample type 2X 225:3710:13.5:2,
and of type 5X = 225:3710:13.5:5. At 200C, for type 2X, the average
cylindrical pore radius rH = 4.5 nm, and for type 5X, rH = 9.0 nm.
Most of the dry gels, including the ones characterized in the
Raman spectroscopy study, were densified by sintering in a box furnace
using a digital T controller. The furnace atmosphere was Florida air,
with the associated high humidity. Dry helium was used for two of the
Raman samples, 2XA and 5XA. The Raman samples were sintered by heating
at 5C/hr, then holding for 12 hours at each holding T before being
furnace cooling.
3.1.2 Isothermal Nitrogen Adsorption
The isothermal N2 sorption measurements of all the silica gel
samples were performed on an automatic N2 sorption instrument, the
Autosorb 6, made by Quantachrome Corp., Syosset, N.Y. The instrument
measures the volume of gaseous nitrogen adsorbed at a specific relative
pressure P/PQ at the boiling point of liquid N2 77.36 K (195.79C) over
a range of relative pressures from P/PQ = 0.001 to 0.999.
Type OX silica gels give a type I N2 sorption isotherm, with a
type E hysteresis loop [185]. This is typical of a microporous material.
156
All the reported values of the surface area, Sa (m2/g), of the silica
gels were calculated from the isothermal N2 sorption data between P/PQ 
0.050.20 using the BET theory [2], with an R2 correlation coefficient >
0.999. All the reported values of normalized pore volume, Vp (cc/g), of
each monolith was calculated from the volume of liquid N2 adsorbed at
P/P0 0.999, unless otherwise stated. The average pore radius, rH =
20000*Vp/Sa [] was calculated from the measured Sa and Vp by assuming
that all Sg and Vp are due to one continuous cylindrical pore.
3.1.3 Calculation of Structural Density from N2 Sorption at P/PQ = 0.999
Some type OX silica gels cylinders were polished so their faces
were parallel. Their diameter ( 1.4 cm) and height ( 0.5 cm) were
carefully measured and their volume calculated. The gels were dried at
180C in 0.1 Torr of vacuum to remove all the physisorbed H20 without
removing any silanols [1], and the dry weight measured. Db was calcu
lated. The normalized Vp was measured in the automatic N2 sorption
instrument using a sample holder designed to hold large samples. Dg was
calculated using the relationship Vp = 1/Dg1/Db. The accuracy of Dg
values measured using this technique was estimated to be 0.01 g/cc.
3.1.4 Water Pvcnometry
Geometric cylinders of silica gel, approximately 4.0 cm high and
1.4 cm in diameter, were heated at different T and time combinations to
give a range of samples with different bulk density, Db, values. The
samples were then furnace cooled to 150C, removed and immediately
weighed. The volume was then calculated from the height and diameter and
Db calculated from the dry weight. The skeletal volume was measured in a
157
pycnometry bottle using H20 as the immersion liquid. Immersing the gels
directly into H20 in the bottle could cause sample fragmentation due to
the capillary stresses generated by the micropores. This was especially
true for gels heat treated at < 400C, due to their low strength. Even
if the gels did not crack, a small bubble of air was sometimes trapped
in the center of the gel cylinder by the invading H20. This could also
cause brittle failure due to the pressure created by the trapped air.
To prevent these problems the pores were saturated with H20 by
leaving each gel in an atmosphere saturated with H20 giving a relative
humidity Rh = 100%. This was done by placing the gel in a small open
petri dish, which was placed in the center of a larger petri dish.
Deionized H20 was placed around the small petri dish in the large petri
dish and a lid placed on the large dish. The H20 reservoir caused the
atmosphere above the gel to saturate with H20 so the micropores in the
gel also became saturated via water vapor diffusion and condensation.
The type OX gels had to be exposed to the saturated atmosphere for
3 days to ensure the pores were completely filled with H20. In other
words type OX gel had to be exposed to an Rh = 100% atmosphere for three
days before soaking the gel in liquid H20 did not increase its weight.
Gels with larger rH required a shorter time to saturate. In addition, as
rH increases the capillary stresses created by the absorption of bulk
liquid into a gel decreases. Consequently gels with larger rH can be put
directly into water with less change of cracking.
The volume of the gel structure was measured using deionized H20
in the glass pycnometer at 24C. This was repeated 4 times for each
sample, giving a standard deviation of 0.001 g/cc. The Db of the H20
adsorbed into the micropores of the gel was assumed to be the same as
158
bulk HgO at 24C = 0.9973 g/cc. The skeletal volume of the silica gel
was calculated from the volume of H20 displaced in the pycnometer. Dg
was calculated from the dry weight and skeletal volume of the gel.
3.1.5 Helium Pvcnometrv
A helium micropycnometer (made by Quantachrome Corp., Syosset,
N.Y.) was used to measure the skeletal volume of the silica gel sample
at ambient T. It was not possible to measure the skeletal volume of
monolithic silica gel samples because a stable equilibrium pressure
could not be obtained in the micropycnometer sample cell. This was
because the micropores in the gel are so small that helium diffusion at
1 atmos. is of the Knudsen type i.e. the mean free path of the diffusing
gas is larger than the average pore size. Interaction with the pore wall
is the dominant effect and the distance the helium has to diffuse in a
monolith is too large for an equilibrium pressure to be reached in the
30 seconds available for the measurement in this pycnometer. The samples
had to be ground to a powder fine enough for the diffusion distance to
be small enough that a stable pressure reading could be obtained in less
than 30 seconds. The samples were ground in a mortar and pestle.
The He pycnometer could hold a maximum of 2 cm3 of material. A
measurement procedure was used which allowed the sample to come in
contact with the atmosphere as little as possible. For each silica gel
sample about 5 gm of sample were initially ground to a fine powder. This
was heated to 200C in an aSi02 crucible with a lid, held for 12 hrs
and then quickly transferred to the sample holder cup of the helium
micropycnometer. The dry weight of the silica gel powder was measured
159
before it was sealed in the instrument sample cell, when the sample cup
was still too hot to touch.
The sample was allowed to equilibrate thermally in the sample
holder in the helium pycnometer under a slow flowing dry helium atmo
sphere purge. After about 1 hour, the measurements required to measure
the skeletal volume of the sample were performed. The skeletal volume
was calculated from the calibration values for the instrument being
used. Dg was calculated from the dry sample weight and the skeletal
volume. Afterwards the sample was returned to the furnace and heated in
air to 300C, held for 12 hrs, furnace cooled, transferred to the sample
holder cup, weighed, sealed in the instrument, thermally equilibrated,
the skeletal volume measured, removed, etc. The procedure was repeated
until no further changes in Dg were measured for a T increase of 150C,
when pore closure and densification is complete. The standard deviation
of Ds was calculated to be < 0.004 g/cc.
3.1.6 Raman Spectroscopy
The Raman spectrometer consisted of a SpectraPhysics Argon ion
laser, a sample support stage, a scatteredlightgathering lens and a
ISA Ramanov U1000 double beam monochromator connected up to an RCA
photomultiplier tube. No polarizer was available for use. The slit width
was set to 250 /jM with a 2 cm'1 step interval. An integration time of 1
second was used to keep the total measurement time as short as possible,
about 20 minutes. The sample was aligned relative to the monochromator
to maximize the throughput intensity. The monochromator was controlled
by a SpectraLink control box which allowed the system to be controlled
from an IBM PS/2 50 computer using a custom written BASIC program. The
160
output from the photomultiplier tube was also connected to the control
unit, so the digitalized spectrum could be saved directly as an ASCII
file on a disc without the need of an analog recording device.
The Raman spectra of the silica gel monoliths were measured in a
perpendicular geometry, i.e. the spectrometer was at 90 to the laser.
The laser was set at 0.5 W at a wavelength of 514.5 nm (in the green
section of the electromagnetic spectrum). The sample was probed approxi
mately 1 mm below its surface to keep the signal intensity as large as
possible to give the highest S/N ratio possible. The ascast surfaces of
these samples were optically flat, so there was no scattering at the
point of entry of the laser into the gel.
Three sample types were characterized using Raman Spectrometry.
These were sample types OX, 2X and 5X, as discussed above, in the form
of monolithic cylinders approximately 4.0 cm height and 1.0 cm in
diameter. Two examples of each sample type were characterized using
Raman spectroscopy. These were samples OX and 0XA for type OX, samples
2X and 2XA for type 2X, and samples 5X and 5XA for type 5X gels.
After collection, the raw spectra were thermally reduced to allow
for thermal population effects and baseline corrected to remove the
elastic scattering peak and background fluorescence, as discussed in the
literature review. The reduced spectra were curvefitted with Gaussian
peaks using a least squares fit algorithm from a commercial software
program (Spectra Calc V2.20, Galactic Industries Corp., Salem, NH). This
gave theoretically supportable fitted peaks for all the important
experimental peaks, with a peak position resolution of 1 cm'1, and peak
areas estimated to be accurate to 23%.
161
3.1.7 Thermogravimetric Analysis (TGA
About 20 rag of each powdered sample was dried at 150C before
being run on a TGA in a flowing dry oxygen atmosphere from 25C to
1100C. The TGA spectra were recorded digitally for analysis.
3.1.8 Differential Scanning Calorimetry (DSC)
Powdered silica gel samples were predried in the same way as for
the TGA. About 15 mg were run in a copper DSC sample pan, left unsealed
so evolving gases could escape, from 25C to 700C. Powdered fused
silica was used as a reference material. The DSC spectra were recorded
digitally for analysis.
3.1.9 29Si Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR^
Type OX silica gel samples, heat treated to 180C and 810C, were
ground to produce fine powders. Each sample was run in a MASS NMR
spectrometer [186] using an air bearing spinning at 5 KHz. The spectra
were recorded digitally.
3.2 Results
3.2.1 Structural and Textural Property Measurements
Physical properties are usually presented graphically as a
function of temperature, T, and the holding time is the same for each T.
The density of a gel is a function of its thermal history T(t), i.e. of
both T and time. If the holding time is different for the sample
measured at each T, each sample's thermal history must be considered
when comparing different sets of data on T dependency of physical
162
properties. An example of the magnitude of the influence of time is
demonstrated in Fig. 29. This shows the change with the isothermal
holding time of the Db for a type OX monolithic silica gel at 750C, rH
as 1.2 nm. In 10 hrs Db increased by 4.0%, in 24 hrs by 5.6%, and in 280
hrs by 17.5%. These are significant, nonlinear, increases.
The variation of viscosity, rÂ¡, of a metal alkoxide derived silica
gel with T is an activated process, but it does not show the straight
line expected from the classic Arrhenius In i) v's 1/T plot. This is
because silica gels have a metastable structure and structural relax
ation as well as viscous sintering occurs during densification [5]. The
importance of T(t) is that the T at which the changes associated with
viscous sintering start can change dramatically depending on T(t) of the
sample up to that point [5,1013].
This means that when a physical property is plotted against T,
some idea of the time scale and heating rates involved, i.e. the T(t) of
each sample, are required so comparison can be made to other data. Even
if the heating schedule is the same for each sample, very different
shrinkage rates can be obtained for supposedly identical samples. Proof
of this was provided by observing a batch of type OX gels during
sintering to full density. The gels were all from the same processing
batch and were all processed in exactly the same way. They were densif
ied in air in a box furnace, using a digital T controller. Visual
observation through a fused aSi02 window in the furnace showed that
some of these identical gels started to foam at different T.
BULK DENSITY [g/cc]
163
TIME AT 750C IHRS]
Figure 29. The increase with time at 750C of the bulk density Dfa of
sample #138, a type OX gel, after heating to 750C in 62 hrs in Florida
air. The open squares () are the experimental data points, while the
solid line is a third order regression with R2 = 0.990.
164
Even before sintering, supposedly identical gels from the same
batch can show variation in Sa, Vp and rH. A batch of 10 gels dried
together showed a sample to sample variation of 6.5% in rH, compared to
an internal variation for one gel of 3% [185]. This means that if a
second gel is made and sintered in identical fashion to the first gel,
the structure and texture of the second sample are unlikely to show
exactly the same dependency on T as the first sample.
Process variables, like the liquid in which the gel is immersed
during drying or the atmosphere used during sintering, will all influ
ence the rate of change of a property. This is well known. The size of
the sample will also have a strong influence on the gel properties
during ageing, drying and sintering [5], Similarly the reduction of a
gel from a monolith to a powdered form increases the T at which viscous
sintering begins by as much as several hundred C, all other factors
being equal. As the samples used to measure Dg using nitrogen adsorption
and HjO pycnometry were monoliths, while those used for helium pycnome
try were powders, this must be taken into account.
3.2,2 The Calculation of D_ from Vp and Db Using Vp 1/D^ + 1/Th
As one of the objectives of this study was to confirm the values
published in the literature on the changes in Dg during sintering, three
different methods were used to measure Dg. The first technique involved
calculating Dg from Db and Vp (using equation (43)) for the cylindrical
samples used in the impedance spectroscopy studies. The problem, as
discussed above, is that the samples had different thermal histories.
Thus, there is a large distribution in the calculated Dg values when
they are plotted against T in Fig. 30(a).
165
A solution to the problem of comparing samples with different
thermal histories is to use an independent variable which accounts for
the thermal history of each sample. The bulk density Dfa is a good choice
to fulfill this requirement. Similar values of Dfa can be obtained with
very different combinations of heating rate and time at T. This allows
samples with very different thermal histories to be compared.
Using Dfa for comparison is a reasonable idea, but T is the domi
nant variable of thermal history, as it is in the exponential portion of
the Arrhenius function. Time does not have such a strong influence, so
the properties of samples with different thermal histories can be
plotted as a function of T and still be compared. For porous silica gel
monoliths other variables can also have a strong influence, and must be
considered when interpreting results. These include structural differ
ences, rH, [OH], Sg, sample size, etc.
Figure 30(b) shows that Dg exhibits a smoother dependency on Db
for the type OX gel samples. The correlation of the Dg dependency on Db
compared its dependency on T can be measured by linear regression. The
R2 correlation coefficient, calculated from the least squares fit of the
regression, gives a direct measure of the dependency of the dependent
variable on the independent variable. A third order regression fitted to
the N2 sorption data gives a correlation of R2 = 0.651 for Dg on T (Fig.
30(a)), while R2 = 0.912 for Dg on Db (Fig. 30(b)). So, statistically as
well as visually, Dg shows a better correlation on Db than on T.
Table 2 lists the textural properties of these samples. Since
these samples were not originally made to investigate the Dg variation,
and this data was originally plotted without knowing what the dependency
should be, no predetermined bias could influence the results. This means
STRUCTURAL DENSITY, Ds [g/cc]
166
SINTERING TEMPERATURE, Tp PC]
Ds = 1/((1/Db)Vp) R2 = 0.6508
Figure 30. The structural density Dg of type OX gels (rH = 1.2 ran)
calculated from Vp (measured using isothermal N2 sorption) and Db, using
Dg l/((1/Db)Vp) as a function of (a) the sintering temperature and
(b) the bulk density Du. The open squares () are the data points, and
the solid lines are 3r order regressions, giving Rz = 0.6508 and Rz =
0.9117 respectively.
STRUCTURAL DENSITY, Ds [g/cc]
167
BULK DENSITY, Db [g/cc]
Ds = 1/((1/Db)Vp) R2 = 0.9117
Figure 30continued
Table 2. Textural and structural properties of the type OX silica gel
discs used to calculate their structural density from their bulk density
and pore volume, Dg = l/((1/Db)V ) (Fig. 30), rH = 1.2 nm.
T (C)
rH ()
VD (cc/g)
sa (mVg)
Db (g/cc>
Ds (g/cc>
180
15.45
0.530
686
1.020
2.220
180
14.16
0.521
736
1.041
2.275
180
13.77
0.511
742
1.056
2.295
180
12.52
0.464
742
1.134
2.395
400
11.42
0.404
708
1.213
2.380
600
13.15
0.405
615
1.218
2.400
600
13.69
0.392
572
1.256
2.470
650
13.83
0.344
498
1.322
2.426
650
11.26
0.312
555
1.375
2.409
650
13.17
0.271
412
1.424
2.321
800
11.36
0.198
348
1.571
2.280
830
14.38
0.200
278
1.565
2.278
850
14.95
0.141
189
1.697
2.231
169
that the results, showing a maximum Dg value, Dsmax, 2.43 g/cc at Db =
1.25 to 1.4 g/cc, are supportable even though Dsmax is 10% larger than
the density of fused silica. The magnitude and dependency of the change
in Dg during sintering warranted further investigation to confirm the
initial measurements and to understand what is happening.
3.2.3 Water Pvcnometrv
Water pycnometry was used to confirm the Dg variation observed in
Fig. 30. A series of cylindrical, type OX silica gels were made and
sintered at different T. These cylindrical samples were w X A cm in
diameter and 4.0 cm high. Figure 31(a) shows Dg measured by H20 pycnome
try plotted against T, from the values listed in Table 3. As in Fig.
30(a) there is a broad distribution in Dg at a particular T. A second
order regression gives a correlation of R2 = 0.872. Replotting Dg as a
function of Db in Fig. 31(b) shows that Dgmax = 2.260.01 g/cc and occurs
at Db = 1.3 to 1.4 g/cc, which is similar to the Db range for Dsmax
measured using N2 sorption (Fig. 30(b)). A third order regression gives
a correlation of R2 = 0.851. This, surprisingly, is slightly lower than
the thermal correlation despite the large distributions visible in Dg at
a particular Tp (Fig. 30(a)).
The type OX silica gel samples measured by both these techniques
were monoliths with rH = 1.2 nm. Figure 32(a) shows, for comparison, Dg
calculated from H20 pycnometry and N2 adsorption as a function of Db.
The overall shape of the curves is very similar. However, they have
different absolute magnitudes until densification is complete.
Silica gels show the changes in Dg observed in Figs. 30 and 31
during densification despite being rehydrated by the H20 absorbed during
STRUCTURAL DENSITY, Ds [g/cc]
170
SINTERING TEMPERATURE, Tp ['Cl
WATER PYCNOMETRY R2 = 0.8716
Figure 31. The structural density Dg of type OX gels (rH = 1.2 nm)
measured using water pycnometry, as a function of (a) the sintering
temperature, and (b) the bulk density Db. The open squares () are the
data points, while the solid lines are the third order regressions,
giving R2 = 0.8716 and R2 = 0.8513 respectively.
STRUCTURAL DENSITY, Ds [g/cc]
171
BULK DENSITY, Db (g/ccl
WATER PYCNOMETRY R2 = 0.8513
Figure 31continued
172
Table 3. Textural and structural properties of type OX silica gel
cylinders, rH 1.2 nm, which were used to measure structural density
using H20 pycnometry (Fig. 31).
T (C)
Ds (g/cc)
Db (g/cc)
VD (cc/g)
Sa (mVg)
180
2.1570
1.060
0.480
799.6
180
2.1716
1.089
0.458
763.0
180
2.1791
1.090
0.459
764.2
180
2.1799
1.104
0.447
744.6
300
2.2097
1.119
0.441
734.9
300
2.2244
1.133
0.433
722.4
650
2.2430
1.210
0.381
634.4
400
2.2208
1.227
0.365
607.8
400
2.2208
1.227
0.365
607.6
400
2.2427
1.239
0.361
602.0
650
2.2641
1.270
0.346
576.6
650
2.2669
1.316
0.319
531.2
650
2.2557
1.400
0.271
451.6
650
2.2487
1.439
0.250
417.0
800
2.2379
1.566
0.192
319.5
800
2.2286
1.623
0.167
279.1
800
2.2427
1.643
0.163
271.5
800
2.2411
1.659
0.157
261.2
800
2.2120
1.672
0.146
243.3
800
2.2170
1.687
0.142
236.2
950
2.2060
2.206
0.000
0.0
STRUCTURAL DENSITY, Ds [g/cc]
173
BULK DENSITY, Db [g/cc]
WATER PYCNOMETRY 0 Ds = 1/((1/Db)Vp)
Figure 32. A comparison of the changes observed in Dg of silica gels.
(a) The dependence on of the Dg of type OX gels measured using H20
pycnometry () and calculated from Dg = l/((1/Dfa)V ) (0). (b) The
dependence on T of the Dg of type OX gels measured using H20 pycnometry
() Dg 1/((1/Db)Vp) (0) and helium pycnometry (X).
STRUCTURAL DENSITY, Ds [g/cc]
174
0.1
H20 PYCN.
0.3 0.5 0.7 0.9
(Thousands)
SINTERING TEMPERATURE, Tp CC]
0 Ds = 1/((1/Db)Vp)
1.1
X He PYCN.
Figure 32continued
175
the measurements, so the structures of silica gels heated to different T
do not all revert to the same structure when rehydrated by H20 adsorp
tion. This means that because D continues to increase to >2.2
s smax
g/cc during sintering despite all the surface D2 rings being rehydroxyl 
ated, the concentration of D2 rings, [D2] can only make a relatively
small contribution to the magnitude of Dg and the changes occurring to
the internal bulk aSi02 structure make a relatively large contribution
to the magnitude of Dg.
3.2.4 Helium Pvenmetry
Helium pycnometry was used to confirm the Dg data plotted in Figs.
30, 31 and 32(a). These measurements were made on powdered samples, in
contrast to the cylinders used above, since it was not possible to
obtain stable pressures in the He pycnometer using monoliths.
During the helium pycnometry experiments, three different powdered
silica gel types were examined, types OX, 2X and 5X. Type OX is the HN03
catalyzed gel made in the same way as the cylinders used for the N2
sorption and the H20 pycnometry samples. Types 2X and 5X were the HN03 +
HF catalyzed gels made as discussed in the experimental procedure. The
addition of HF to HN03 acid catalyzed silica gels changed the texture of
the gel. Figure 33 shows the dependence of the texture, i.e. Db, V Sg
and rH, of the asdried gels on the molar concentration of the HF added
to the sol. As [HF] increases, Db and Sg decrease asymptotically and Vp
increases asymptotically. The linear increase in the average pore radius
(rH = 20000 x Vp/Sa) with [HF] as opposed to the nonlinear increase
which might be expected, is fortuitous and occurs because Vp increases
at the same rate that Sg decreases, i.e. Vp increases by a factor of
176
Table 4. Textural properties of silica gel monoliths stabilized at 200C
as a function of HF concentration (Fig. 33).
Gel type
OX
IX
2X
4X
5X
[HF] (mol/1)
0.00
0.015
0.030
0.060
0.075
Db [g/cc]
1.066
0.788
0.686
0.608
0.572
rH [nm]
1.21
2.58
4.45
7.45
8.98
Sa [mz/g]
765
618
447
314
286
VD [cc/g]
0.4643
0.7950
0.9932
1.1698
1.2850
Db [g/cc]
1.061
0.791
0.684
0.613
0.572
Ds [g/cc]
2.0925

2.1344

2.1647
2.77 while Sg decreases by a factor of 2.67 as [HF] increases from OX to
5X (Table 4), the rate of increase of Vp is the same as the rate of
decrease of SgI so rH increases linearly. The exact mechanism causing rH
to increase linearly with [HF] is unknown. Table 4 lists the textural
values at 200C as a function of [HF].
The purpose of measuring the Dg of HF catalyzed gels was to
investigate the change in the dependency of Ds, on Db and T, when the
gels have different starting values of Sg and V The average pore size
of the gels was characterized by the average cylindrical pore radius rH.
Figure 34(a) shows the dependency of Dg on T, as measured by helium
pycnometry, for gel types OX, 2X, and 5X. Table 5(a) lists the actual
values. When fitted with fifth order polynomials, the least squares
correlation coefficient R2 was 0.997, 0.990 and 0.996 for the type OX,
2X and 5X gels respectively. The average pore radius at 200C of type OX
gels 1.2 nm, of type 2X gels 4.2 nm, and of type 5X gels ^ 9.0 run.
The powdered gels were held for 12 hrs at each T.
BULK DENSITY AT 180'C, Db [g/cc]
177
Figure 33. The dependence on the HF concentration, [HF] (mole/liter
H20), of the textural properties of the silica gels investigated here,
(a) Db (g/cc) versus [HF]. (b) Vp (cc/g) versus [HF]. (c) Sg (mz/g)
versus [HF]. (d) rH (nm) versus [HF].
PORE VOLUME AT 180'C, Vp (cc/g)
178
HF CONCENTRATION, [HF] (mole/litre H20)
Figure 33continued
SURFACE AREA AT lBOC, Sa (mVg)
179
HF CONCENTRATION, IHF] (mole/litre H20)
Figure 33continued
CYLINDRICAL PORE RADIUS AT 180*C (nm)
180
HF CONCENTRATION, [HF] (mole/litre H20)
rH (nm)
Figure 33continued
181
Table 5. The data used to plot Fig. 34. (a). Structural density of type
OX, 2X and 5X silica gels powders measured using helium pycnometry,
plotted in Fig. 34(a).
Gel type
OX
2X
5X
rH (nm)
* 1.2
4.5
9.0
T (C)
Ds (g/cc)
200
2.0925
2.1344
2.1647
250
2.1124
2.1613
2.1673
300
2.1339
2.186
2.1849
350
2.1799
2.1945
2.1990
400
2.2237
2.2218
2.2196
450
2.2529
2.2559
2.2366
500
2.2698
2.2671
2.2609
550
2.2900
2.2712
2.2625
600
2.2925
2.2846
2.2763
650
2.3019
2.2935
2.2946
700
2.2991
2.3009
2.3005
750
2.2977
2.3138
2.3073
800
2.3011
2.3172
2.3097
850
2.2851
2.2998
2.3039
900
2.2796
2.293
2.3005
950
2.2557
2.2838
2.2979
1000
2.2282
2.2654
2.2855
1050
2.2310
2.2303
2.2590
1100
2.2339
2.2309
2.2155
1150
2.2321
2.2295
2.2129
182
Table 5 (b). Extrapolated data used to plot Fig. 34(b).
type
OXA
2XA
5XA
rH
(nm)
1.2
4.5
9.0
T
(C)
Db
[g/cc]
Ds
[g/cc]
Db
[g/cc]
Ds
[g/cc]
Db
[g/cc]
Ds
[g/cc]
200
1.120
2.0925
0.720
2.1344
0.580
2.1647
400
1.145
2.2237
0.727
2.2218
0.586
2.2196
500
1.184
2.2698
0.742
2.2671
0.582
2.2609
600
1.257
2.2950
0.768
2.2846
0.593
2.2763
700
1.375
2.3011
0.788
2.3009
0.604
2.3005
800
1.466
2.2950
0.835
2.3172
0.617
2.3097
840
1.557
2.2800




880
1.764
2.2450




900
2.195
2.2282
1.065
2.2930


950
1.477
2.2654
0.661
2.2979
1000
2.190
2.2303
0.921
2.2590
1100
1.614
2.2286
1120
2.196
2.2129
183
Table 6. The textural properties of type OX, 2X and 5X silica gels. (a).
Textural properties of the type OX cylindrical silica gels characterized
by Raman Spectroscopy, plotted in Figs. 35, 36 and 37.
T (C)
Db E s/cc 3
Ds [g/cc]
Sa [m2/g]
rH [nm]
Sample OX (sintered in Florida air)
350
1.162
2.1799
669.5
1.2
400
1.162
2.2237
684.8
1.2
500
1.183
2.2698
674.4
1.2
600
1.214
2.2925
645.9
1.2
Sample 0XA (sintered in Florida air)
400
1.145
2.2237
706.5
1.2
500
1.184
2.2698
672.9
1.2
600
1.257
2.2950
599.3
1.2
700
1.375
2.3011
487.2
1.2
800
1.466
2.2950
412.5
1.2
840
1.557
2.2800
341.2
1.2
880
1.764
2.2450
205.8
1.2
900
2.190
2.2282


184
Table 6 (b). Textural properties of the type 2X cylindrical silica gels
characterized by Raman Spectroscopy.
T (C)
Db Cg/cc]
Ds [g/cc]
Sa [m/g]
rH [nm]
Sample 2X (sintered in Florida air)
350
0.795
2.1945
361.0
4.44
400
0.791
2.2218
352.4
4.62
500
0.800
2.2671
373.9
4.33
600
0.836
2.2846
350.6
4.33
780
1.046
2.3138
259.4
4.04
800
1.089
2.3172
240.9
4.04
900
1.351
2.2930
179.4
3.39
970
2.199
2.2303
3.4
3.81
Sample 2XA (sintered in helium)
400
0.727
2.2218
400.7
4.62
500
0.742
2.2671
403.1
4.50
600
0.768
2.2846
399.4
4.33
700
0.788
2.3009
397.0
4.20
800
0.835
2.3172
379.2
4.04
900
1.065
2.2930
296.9
3.39
950
1.477
2.2654
157.1
3.00
1000
2.190
2.2303
4.3
3.81
185
Table 6 (c). Textural properties of the type 5X cylindrical silica gels
characterized by Raman Spectroscopy.
T (C)
Db tg/cc]
Ds [g/cc]
Sa [m2/g]
rH [nm]
Sample 5X (sintered in Florida air)
350
0.587
2.1990
278.0
8.98
400
0.585
2.2196
283.9
8.87
500
0.580
2.2609
288.8
8.87
600
0.605
2.2763
273.4
8.87
780
0.615
2.3073
277.0
8.60
800
0.642
2.3097
261.3
8.60
900
0.677
2.3005
248.2
8.40
1000
1.026
2.2855
143.8
7.47
1070
2.194
2.2155
2.5
3.52
Sample 5XA (sintered in helium)
400
0.586
2.2196
279.6
8.98
500
0.582
2.2609
287.7
8.87
600
0.593
2.2763
281.4
8.87
700
0.604
2.3005
275.3
8.87
800
0.617
2.3097
276.2
8.60
950
0.661
2.2979
256.6
8.40
1000
0.729
2.2855
228.4
8.18
1050
0.921
2.2590
172.3
7.47
1050
0.921
2.2590
172.3
7.47
1100
1.614
2.2286
61.8
5.44
1120
2.196
2.2129
2.0
3.52
186
Figure 32(b) shows Dg for type OX gels as measured by the three
different experimental techniques. The H20 pycnometry and N2 sorption
samples were monoliths, so they densified (i.e. Vp = 0.0 cc/g) at 900C
and their Dg versus T graphs converge both to 900C. The He pycnometry
sample was a powder so it densified at 1000C and its Dg does not finish
decreasing and stabilize until 1000C, because the [Sig0H] of the powder
decreases more rapidly than the monolith. If the He pycnometry sample
had been a monolith it would also have densified at 900C.
The Dg of a type OX gel powder doesn't stabilize (i.e. reach a
constant value, which occurs at the Tp where densification is complete,
and does not change when T is increased above this T as seen in Figs.
32(b) and 34(a)) until Vp = 0.0 cc/g at 1000C, while Dg of type OX gel
cylinders stabilize when Vp = 0.0 cc/g at 900C. This means that the T
at which De starts to decrease, after Dem,v is reached at T during
sintering, is determined by the same factors that determine the depen
dency of Vp and Db on T.
Since powdered gels were used in the He pycnometry Dg measure
ments, their Dfa could not be measured directly, so Db was measured from
the dependency on Tp of the Db of the cylindrical Raman samples 0XA, 2XA
and 5XA in Fig. 35 for each T at which D was measured for type OX, 2X
r
and 5X gels, respectively, in Fig. 34(a). Dg could therefore be plotted
as a function of Db in Fig. 34(b). Table 5(b) lists these data.
3,2.5 Textural Properties of HF Catalyzed Silica Gel Monoliths
Figure 35 shows the T dependence of Dfa for the monolithic silica
gel samples characterized in the Raman spectroscopy experiments. The
expected increase in the T at which viscous sintering starts for each
STRUCTURAL DENSITY, Ds [g/ccl
187
(Thousands)
SINTERING TEMPERATURE, Tp [*C]
OXA 0 2XA X 5XA
Figure 34. The dependence of the structural density measured using
helium pycnometry on (a) Tp [C], and (b) Db [g/cc] for sample OXA, rH
1.2 nm (), sample 2XA, rH 4.5 nm (0) and sample 5XA, rH 9.0 nm
(x) The solid lines in (a) are best fit 5th order linear regressions.
Figure 34continued
OXA
2.14
STRUCTURAL DENSITY
Ds [g/cc]
188
BULK DENSITY, Db [g/cc]
189
(Thousands)
SINTERING TEMPERATURE, Tp PC]
Figure 35. The dependency on the sintering temperature Tp of the bulk
density, Db, of the cylindrical samples characterized using the Raman
spectrometer. OX (), OXA (+), 2X (0), 2XA (a), 5X (x), 5XA (v).
SURFACE AREA, Sa (m*/g)
190
(Thousands)
SINTERING TEMPERATURE, Tp PC]
Figure 36. The dependency on the sintering temperature Tp of the surface
area, Sg, of the cylindrical samples characterized using the Raman spec
trometer. OX (), OXA (+), 2X (0), 2XA (a), 5X (x), 5XA (v).
AVERAGE CYLINDRICAL PORE RADIUS, rH [A]
191
(Thousands)
SINTERING TEMPERATURE, Tp PCI
rH = 20000 x Vp/Sa
Figure 37. The dependency on the sintering temperature Tp of the average
pore radius, rH, of the cylindrical samples characterized using the
Raman spectrometer. OX (), OXA (+), 2X in humid air (0), 2XA in dry
helium (a), 5X in humid air (x) 5XA in dry helium (v).
192
SINTERING TEMPERATURE, Tp [CJ
Figure 38. The thermogravimetric analysis (TGA) curves of powdered
samples of type OX, 2X and 5X gels heated in flowing dry nitrogen at
10C/min. The weight loss observed below 180C is due to the loss of
water previously absorbed into their pores.
193
sample, due to different rH and Sfl values, can be seen. Samples 2XA and
5XA were sintered in dry helium, while samples OX, OXA, 2X and 5X were
sintered in humid air. The observed differences between 2X and 2XA, and
5X and 5XA were due to these differences in sintering atmospheres.
Figures 36 and 37 show the T dependency of the Sg and rH of these silica
gel cylinders, demonstrating that it is possible to make Type VI Gelsil
monoliths with large Sg (> 200 m2/g) stable up to almost 1000C. The
thermal stability of porous gelsil samples is discussed elsewhere
[4,169], Table 6 lists the textural values of the cylindrical silica
gels used in the Raman spectroscopy characterization experiments.
3.2.6 Thermogravimetric Analysis
Figure 38 shows the TGA curves for type OX, 2X and 5X gels. The
total weight loss of each gel type increases as Sg of the gels increas
es, OX > 2X > 5X. The weight loss occurs in three stages. Below 180C
weight loss occurs due to loss of adsorbed H.,0 from the pores. Between
200C and 600800C (depending on the sample), it occurs due to: a) the
oxidation of residual alkoxide groups, and b) the loss of internal and
surface OH as H20 via the condensation polymerization reactions occur
ring during structural relaxation. Above 600800C, the observed
decrease in weight occurs due to OH loss during the condensation
polymerization reaction occurring during the viscous flow accompanying
the sintering process which produces full densification.
3.2.7 Raman Spectra of the Silica Gels
The processes involved in the raw data manipulation, baseline
correction and curvefitting of the experimental Raman spectra are
194
discussed in the introduction and discussion sections. The specific
procedure used to achieve baseline corrections, thermally reduce and
curvefit the experimental Raman spectra is discussed in Appendix A.
Setting up the curvefitting model used to quantify the changes in
the recorded Raman Spectra involved [165]:
a) Data reduction procedures. This involved, in the present
investigation, interpolation, smoothing and truncation of the spectra to
1001350 cm'1 before any baseline correction was done, using a commer
cial software package called Spectra Calc V2.20 (Galactic Industries
Corp., Salem, N.H.). The thermal reduction of the baseline corrected
spectra, which is also discussed in the literature review, also comes
under this heading.
b) Background modeling. The background in the Raman spectra are
slightly nonlinear but can be described by a linear background.
The elastic scattering, or Rayleigh, peak in the Raman spectra of
the silica gel measured in this investigation could not be fitted by a
Gaussian function. When this was attempted on a Lotus 123 spreadsheet,
the tail of the elastic peak in the Raman spectrum did not have the same
shape as a Gaussian curve. It turned out this was irrelevant because the
thermal reduction reduced the intensity of the low frequency section of
the spectra by such a large factor that the inelastic peak no longer
made a significant contribution to the Raman spectra intensity and could
be ignored during curvefitting.
As discussed in the literature review, Murray et al. [85] obtained
the shape of the background correction by a subtraction technique. The
background correction shape obtained when the same subtraction technique
was performed for two gels, heat treated at different T to give differ
195
ent background intensity, could be fitted by a y = mx01 + c function.
This equation gives a very rapid initial rise in intensity, followed by
a very rapid leveling off to a horizontal line, just like the background
shape obtained by subtraction. Therefore the high frequency background
in silica gels could be modeled quite accurately by a horizontal
straight line of intensity equal to the Raman spectra magnitude at 1350
cm'1. This could be subtracted out directly using Spectra Calc, and
thereby removed the fluorescence, the background scattering and the
intrinsic surface effects.
c) Modeling the band shape. One of four distribution functions is
usually used, i.e., Binomial, Poisson, Gaussian or Lorentzian. The
Gaussian function has been found to give the best fit to Raman peaks
[165], This was found to true in this investigation as well.
d) The last step is to find the "best fit" of the model to the
experimental data. The question is what is meant by "best fit", and is
usually taken to mean minimization of the deviation of the model from
the experimental data. Several mathematical techniques exist that can be
used to achieve this [165], The advent of the desktop computer has made
these techniques generally available using commercial software.
The thermal reduction performed on the raw Raman spectra signifi
cantly reduced the intensity of the low frequency contribution to the
main peak. After reduction the main peak (450 cm'1) was still asymmet
ric, though, and consequently could not be modelled theoretically
without knowing more about the peak. Three Gaussian peaks was the
minimum number able to give a good fit to this peak. Adding a fourth
peak made no significant improvement in the quality of the fit as
measured by the x2 value. In fact the area of a fourth peak went to zero
196
as the number of iterations of the curvefit algorithm increased,
implying that it was redundant.
The criteria used in this investigation to justify including a
particular Gaussian peak in the curvefitting calculations is the same as
that used by Mysen at al. [162], except that it is additionally speci
fied that each peak fitted must also have a theoretical justification
for its use whenever possible.
As discussed above the number of peaks making up the asymmetric
main Raman peak, (450 cm1) is not known, so there is no theoretical
way of determining the position or intensity of the vibrations causing
W1. Consequently three Gaussian peaks were used to curvefit the main W1
peak, as this was the minimum number required to fit this peak. The D1
(495 cm1), D2 (600 cm'1), W3 TO and LO (at 800 cm1) and the TO and
LO (1050 and 1200 cm'1) peaks were all curvefitted using single Gaussian
peaks, as supported by theory. The SiOH (975 cm'1) was fitted using 2
Gaussian peaks, and the SiOH (3750 cm'1) was fitted using 4 Gaussian
peaks, as supported by theory. The theoretical justification for these
peak assignments is discussed in the literature review.
Certain sharp peaks in Raman spectra are artifacts of the laser
used, and are called plasma lines. They are identified by changing the
excitation wavelength, as the plasma peaks will move by the same amount
as the laser line is changed [187], while the Raman peaks will not move.
No correction was made for the instrument transfer function, J(w),
[154,155], which is not known for the Raman spectrometer used here.
Figure 39(a) shows a typical raw unreduced Raman spectrum from
1001350 cm'1 of a Dynasil sample. Dynasil was run as a reference sample
to confirm the reproducibility and stability of the Raman spectrometer
INTENSITY TOTAL COUNTS
197
100
350 600 850
RAMAN SHIFT TCM
1100
1350
Figure 39. The raw, unreduced Raman spectrum of Dynasil. (a) 1001350
cm'1, (b) 36003800 cm'1. The peak assignments of aSi02 are shown.
INTENSITY [TOTAL COUNTS]
198
RAMAN SHIFT [CM1]
Figure 39continued
INTENSITY TOTAL COUNTS
199
DYNASIL
100
350
600
850
RAMAN SHIFT [CM1]
1 100
350
Figure 40. The thermally reduced Raman spectrum of Dynasil. (a) 1001350
cm"1, (b) 36003800 cm"1. The reduced Raman spectrum, the curvefitted
Gaussian peaks and their peak positions (PP), and the fitted spectrum
calculated from the addition of the curvefitted peaks are shown.
INTENSITY [TOTAL COUNTS]
200
3600 3640 3680 3720 3760 3800
RAMAN SHIFT [CM1]
Figure 40continued
INTENSITY TOTAL COUNTS
201
Figure 41. The raw experimental Raman spectrum of silica gel sample OXA
stabilized at 400C for 400C. (a) 1001350 cm'1, (b) 36003800 cm"1.
INTENSITY [TOTAL COUNTS]
202
RAMAN SHIFT [CM1]
Figure 41continued
INTENSITY TOTAL COUNTS
203
Figure 42. The thermally reduced Raman spectrum of silica gel sample OXA
stabilized at 400C for 24 hrs. (a) 1001350 cm'1, (b) 36003800 cm'1.
The reduced Raman spectrum, the curvefitted Gaussian peaks and the
fitted spectrum resulting from the addition of these peaks are shown.
INTENSITY [TOTAL COUNTS]
204
Figure 42continued
205
with time. The spectrum is identical to other examples of the Raman
spectrum of Dynasil in the literature [5,8789,117], except that this
spectrum has had a linear baseline correction as discussed above. The
Raman spectrum of Dynasil is very similar to the spectra of fully dense
silica gels, except for except small differences in [D^, [D2] and
[SiOH]. Figure 39(b) shows the Raman spectra of the same sample from
36003900 cm'1, with a linear baseline correction subtraction equal to
the intensity of the spectrum at 3900 cm'1. Figure 40 shows the thermal
ly reduced Raman spectrum of the raw (i.e. not thermally reduced) Raman
spectrum of Dynasil from Fig. 39, along with the curvefitted Gaussian
peaks calculated for this spectrum. The large decrease in intensity of
the shoulder below 400 cm'1 and the associated increase in intensity of
the peaks above 400 cm'1 are clearly shown for the thermally reduced
spectra in Fig. 40 in comparison to the raw spectra in Fig. 39.
Figure 41 shows the raw unreduced Raman spectrum, with no baseline
correction, of silica gel sample 0XA heated to 400C for 12 hours. All
the samples were held for 12 hours at each T. The increase in the D1 and
D2 peak intensities and the appearance of the SiOH peaks at 980 and 3750
cm'1 are clearly visible compared to Dynasil (Fig. 39). Figure 42 shows
the baseline corrected, thermally reduced Raman spectrum of the same
sample, along with the curvefitted Gaussian peaks and the envelope
obtained from the addition of all the Gaussian peaks.
These reduced spectra clearly shows the differences between the
Raman spectra of Dynasil (Fig. 40) and of a typical porous silica gel
(Fig. 42). Compared to the reduced Dynasil sample spectrum in Fig. 40,
the D1 (495 cm'1) and D2 (605 cm'1) peaks in the reduced Raman spectrum
of the 400C 0XA sample (Fig. 42) have substantially increased in
206
intensity. The W3 TO (820 cm'1) and LO (846 cm'1) peaks have increased in
frequency and their relative intensity has changed. The SiOH (979 cm'1)
peak is present and very intense due to the large surface area of the
gel. The TO (1050 cm'1) and LO (1176 cm'1) peaks have decreased in
Table 7. Position, height, width as FullWidthHalfMaximum (FWHM), and
area of the Gaussian peaks curvefitted to the Raman spectrum of sample
OXA stabilized at 400C (Fig. 42).
Sample OXA, 400C, rH = 1.2 run.
Peak Position
(cm"1)
Height
FWHM (cm'1)
Area
435
461
172
70448
460
381
548
178606
466
196
76
13130
500
444
35
13890
608
531
40
18994
820
324
100
28675
846
64
24
1387
962
238
104
21870
979
782
30
20648
1050
166
85
12541
1176
122
144
15610
3578
1340
243
234617
3612
810
40
28361
3711
1311
79
91688
3738
2220
29
57190
3746
4822
13
53768
3750
7914
7
50697
INTENSITY TOTAL COUNTS
207
RAMAN SHIFT
CM"1]
Figure 43. The thermally reduced Raman spectra from Fig. 42(a) of sample
OXA stabilized at Tp 400C from a different angle.
INTENSITY TOTAL COUNTS
208
1450
ii
SAMPLE OXA
100
350
600
850
RAMAN SHIRT [CM1]
1100
1350
Figure 44. The thermally reduced Raman spectrum from Fig. 42(a) of
silica gel sample OXA stabilized at 400C, along with the residual
intensity left after the curvefitted spectrum is subtracted from the
experimental spectrum, giving xz = 127,685.
209
frequency. The SiOH (3750 cm'1) peak has increased in intensity, in
direct proportion to the SiOH peak (979 cm'1), and frequency.
Figure 42 is a typical example of the Gaussian peaks produced by
the curvefitting procedure, with a x2 value = 127,685 for this gel. The
curvefitting analysis of the Raman spectrum of a particular sample for a
particular T produces a table of results for that particular spectrum.
Table 7 lists the positions, height, FWHM and areas of the curvefitted
Gaussian peaks, calculated using the criteria specified, for this
sample, OXA at 400C. Figure 43 shows the curvefitted peaks from a
different angle for clarity and for ease of comparison.
Figure 44 shows the reduced spectrum of the 400C OXA sample along
with the residual spectrum left behind when all the curvefitted peaks
are subtracted from the experimental spectrum. This gave a x2 value of
127,685. The closer the residual line is to a straight line the better
the fit and the smaller the x2 value. The Gaussian peaks were fitted
using a LevenburgMarquardt minimum least squres method algorithm
[188]. This algorithm gives a x2 value measuring how good a fit is ob
tained, with smaller values of x2 indicating a better fit. The value of
X2 depends on the intensity of each channel count of the experimental
spectrum, x2 values for different spectrum are not directly comparable
unless the experimental spectrum are normalized to the same value at a
particular wavenumber. The reduced raman spectra were all normalized to
1000 at 455 cm'1 so the quality of the fit for different spectrum could
be compared using X2. For example, the X2 value for the curvefitted
peaks of the Dynasil sample in Fig. 40 is X2 = 29,605, implying a better
fit for Dynasil than for the 400C OXA sample in Fig. 44.
INTENSITY [counts]
210
Figure 45. The evolution of +u
r r
W 1001350 I, (b) 35003800 cÂ£1.
INTENSITY [COUNTS'
211
Figure 45continued
INTENSITY [COUNTS]
212
Figure 46. The evolution of the thermally reduced Raman spectra of
sample OXA, r^ ** 1.2 nm, during densification vo
T inr renown c ~
Increases from
 i_uei.mai.iy reduced Raman spectra of
1.2 nm, during densification via viscous sintering as
i 400 C to 900C. (a) 1001350 cm1, (b) 35003800 cm'1.
INTENSITY [COUNTS
213
Figure 46continued
INTENSITY [COUNTS]
214
figure 47. The evolution of the thermally reduced Raman spectr
sample 2XA, rH w 4.5 nm, during densification via viscous sinti
Tp increases from 400C to 1000C. (a) 1001350 cm'1, (b) 3500
as
cm'1.
INTENSITY [COUNTS]
215
Figure 47continued
INTENSITY [counts]
216
5 7 ~T^lm f thermally reduced R
T L, H 9 during densiffoL d Raman sPecti
" ^00C to 1150C (a) ion VSCUS sint
\a) XU01350 cm'1, (b) 3500
Fp increases from
as
cm'1.
INTENSITY [COUNTS]
217
Figure 48continued
218
Figure 45 is a summary of all the raw experimental Raman spectra
obtained on sample OXA at the T indicated. For clarity each spectra is
offset by a constant amount along the X and Yaxis relative to the
spectrum below it. The change in intensity of the individual peaks can
be seen, showing the relationship between [SiOH] and [D2] Figure 46 is
a summary of the reduced Raman spectra of sample OXA. The increase in
intensity of the reduced spectra compared to the raw spectra as frequen
cy increases can be seen. Figures 47 and 48 are summaries showing the
thermally reduced Raman spectra for samples 2XA and 5XA respectively.
Each spectrum is offset relative to its adjacent spectrum.
The position of one particular peak can be directly compared as a
function of T, Db, etc. The area of a peak at one particular T can not
be directly compared with the area of that peak at another T because
Raman spectral intensities are not directly reproducible. This is
because between runs many variables in a Raman spectrometer can change,
causing the absolute intensity of the scattered light, and therefore the
counts per second, to change. The variables include: Rh of the air,
laser power, laser beam path direction and location, sample position,
sample size, point of impact of laser beam on sample, laser beam
collimation and cross sectional area, sample T increase due to beam
interaction, sample to scatteredlightfocusing lens distance, laser
beam/sample interaction length, diameter and volume, reflectivity of the
sample surface, sample surface roughness, etc.
The most difficult problem encountered was locating the samples in
the same position each time, so the distance from the sample to the
first lens, which effectively governs the sample to detector distance,
varied for each run. The different geometric shape of the samples and
219
the shrinkage of the samples during sintering also changed the
beam/sample interaction volume for every run. Good reproducibility was
obtainable for the same sample if a spectrum was remeasured consecutive
ly. This could not happen in the actual experiments because each sample
had to be removed to allow the next sample to be run and also to undergo
its next heat treatment.
The difficulty of comparing peaks from different sample spectra,
caused by lack of spectrum reproducibility, is solved by comparing the
internal ratios of peak areas for each reduced Raman spectrum. The
internal ratio is the ratio of the area of, for example, the D2 peak,
called [D2], to the area under the whole spectrum, called [Wt] [Wt] is
calculated by adding the areas of all the Gaussian peaks used to
curvefit a Raman spectrum, except for the areas of the 495 cm'1 D1, the
605 cm'1 D2 and the 980 cm'1 SiOH peaks which change during sintering.
The internal ratio of a peak for a specific spectrum can be compared to
the same ratio calculated from the spectrum of the same sample heat
treated to a different T or to another sample. This calculated ratio,
[D2]/[Wt] in this example, is the fractional D2 peak area. When multi
plied by 100, [D2]/[Wt] is equal to the percentage area of the reduced
Raman spectrum represented by this peak. Therefore, a plot of normalized
area, [D2]/[Wt] against T shows the T dependence of the area of the D2
peak as a fraction of the total area of the whole spectrum, while
multiplying the fractional area by 100 gives the percentage area. This
is the case for the plots of all internal peak area ratios. If the Raman
coupling coefficient is linear with concentration then [D2]/[Wt] is
proportional to the concentration of the trisiloxane D2 rings, which
would also be true for all the peaks.
220
The peak positions calculated from the Raman spectra using
curvefitting methods are estimated to have a resolution of 1 cm"1. The
precision of the peak areas, i.e. the area under the curvefitted
Gaussian peaks, is much more difficult to estimate. Any systematic
errors such as inaccuracies in the baseline correction will lead to
errors in the calculated internal peak area ratios. Any errors in the
number and/or type, i.e. Gaussian or Lorentzian, of the functions used
to curvefit a particular peak will also contribute to the cumulative
error of the curvefit data.
The Raman spectra of two examples of each gel type OX, 2X and 5X,
were measured to ensure that the data measured was reproducible and
accurate. The examples were OX and OXA for type OX, examples 2X and 2XA
for type 2X and 2XA and examples 5X and 5XA for type 5X. This means that
6 samples were investigated, and if the results for all six samples were
plotted on each figure, the figures would be very confusing. Consequent
ly the similarity, and therefore the reproducibility, of the results
from the two examples of each gel type will be demonstrated first. One
example, samples OXA, 2XA and 5XA, of each gel type, OX, 2X and 5X, will
be compared in each figure to make them clearer and easier to interpret.
The calculated peak positions and areas for each sample were
combined onto Lotus 123 spreadsheets so that they could be examined as a
function of T, Dg, Db, and Sg. The figures displaying the Raman spectra
curvefitting results were produced from the data on these spreadsheets.
[D2]/[Wt]/Sa (# D2 RINGS/UNIT AREA)
221
SINTERING TEMPERATURE, Tp 1'C]
SAMPLE OX + SAMPLE OXA
Figure 49. This shows that the concentration/unit area of internal pore
surface of the D2 trisiloxane rings, [D2]/[Wt]/Sa, exhibits the same
dependence on Tp for sample OX as for sample OXA within the resolution
of the curvefitting analysis in their respective T ranges.
[D21/[Wt] (** D2 RINGS/UNIT VOLUME)
222
(Thousands)
SINTERING TEMPERATURE, Tp PC]
SAMPLE 2X + SAMPLE 2XA
Figure 50. This shows that the concentration/unit volume of the D2
trisiloxane rings, [D2]/[Wt], exhibits the same dependence on Tp for
sample 2X and sample 2XA within the resolution of the curvefitting
analysis in their respective T ranges.
RATIO OF [D2]/[D 1 ] PEAK AREAS
223
(Thousands)
SINTERING TEMPERATURE, Tp PC]
SAMPLE 5X + SAMPLE 5XA
Figure 51. This shows that the ratio of the concentration/unit volume of
the D2 trisiloxane rings and the D1 tetrasiloxane rings, [D2]/[D.],
exhibits the same dependence on Tp for samples 5X and 5XA within the
resolution of the curvefitting analysis in their respective T ranges.
224
Figures 49, 50 and 51 are examples showing, within the resolution
of the experiments, the similarity of the peak positions and areas
obtained for the two examples of each gel type, OX, 2X and 5X, respec
tively. Sample OX was only measured up to 600C as the T controller
failed during the next heating program, sending a 100% output signal to
the furnace causing an uncontrolled heating rate and loss of the sample.
3.2.8 Curvefitted Raman Peak Positions
Figures 52, 53 and 54 show the T dependency of the peak positions
(PP) of the D1, D2 and W2 peaks, respectively. The behavior of the 495
cm'1 D1 PP depends on [HF] below the T at which densification begins by
viscous sintering, Tdb, but decreases above Tdb (Fig. 52). The 605 cm'1
D2 PP is constant until densification is complete when the remaining
surface D2 rings become bulk D2 rings, so their local environment
changes and their vibrational frequency decreases (Fig. 53). This is
consistent with the assignment of: a) the D2 peak to strained planar
trisiloxane rings, and b) the D1 peak to puckered tetrasiloxane rings in
which the silica tetrahedra are strained in comparison to the average
unstrained silica tetrahedra in fused aSi02, but less strained than the
tetrahedra in trisiloxane rings [5,67]. The magnitude of the strain in
the planar D2 surface rings is so large that variations in their local
environment during sintering have no effect on them and their PP is
constant until the surface rings become bulk rings and they are sur
rounded completely by aSi02. The magnitude of the strain in the puck
ered D1 rings is not as large so the variations in their local environ
ment during sintering does have an effect on them and their PP changes
continuously. The W2 PP (Fig. 54) is reviewed in the discussion section.
D1 RAMAN PEAK POSITION [CM1]
225
(Thousands)
SINTERING TEMPERATURE, Tp fC]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 52. The dependence on the sintering temperature of the D1 tetra
siloxane ring curvefitted Raman peak position (PP) for samples OXA ()
rH 1.2 nm, 2XA (+) rH 4.5 nm and 5XA (0) rH 9.0 nm. The D1 peak
position (PP) of Dynasil (a) is shown for comparison.
D2 RAMAN PEAK POSITION [CM
226
SAMPLE OXA
+ SAMPLE 2XA
0 SAMPLE 5XA
Figure 53. The dependence on the sintering temperature of the D2 trisil
oxane ring curvefitted Raman peak position (PP) for samples OXA (), 2XA
(+) and 5XA (0) The D2 PP of Dynasil (a) is shown for comparison.
(?) RAMAN PEAK POSITION [CM
227
(Thousands)
SINTERING TEMPERATURE, Tp I"C]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 54. The dependence on the sintering temperature Tp of the W2 (?)
curvefitted Raman peak position (PP) for samples OXA (), 2XA (+) and
5XA (0). The Dynasil PP (a) is shown for comparison.
Si OH RAMAN PEAK POSITION [CM
228
(Thousands)
SINTERING TEMPERATURE, Tp I"C]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 55. The dependence on the sintering temperature Tp of the SiOH
curvefitted Raman peak position (PP) for samples OXA (), 2XA (+) and
5XA (0). The Dynasil PP (a) is shown for comparison.
TO RAMAN PEAK POSITION [CM
229
(Thousands)
SINTERING TEMPERATURE, Tp PC]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 56. The dependence on the sintering temperature Tp of the W3 TO
curvefitted Raman peak position (PP) for samples OXA (), 2XA (+) and
5XA (0). The Dynasil PP (a) is shown for comparison.
LO RAMAN PEAK POSITION [CM1]
230
(Thousands)
SINTERING TEMPERATURE, Tp [C]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 57. The dependence on the sintering temperature Tp of the W3 LO
curvefitted Raman peak position (PP) for samples OXA (), 2XA (+) and
5XA (0). The Dynasil PP (a) is shown for comparison.
231
Figure 55 shows the T dependency of the PP of the 980 cm*1 SiOH
peak. The Si OH PP is independent of T until V 0.0 cc/g and the
S p
remaining surface silanols are combined into the silica bulk during pore
closure as densification is completed and their peak frequency becomes
the same as fused aSi02 at 970 cm'1. Similarly to the D2 peak, the
change in PP occurs as the surface Sig0H become bulk Sig0H.
Figures 56 and 57 show the T dependency of the PP of the W3 TO and
W3 LO peaks. W3 TO and W3 LO are so close together that they overlap and
separating their PP accurately as they decrease as Tp increases above
400C is difficult. The overall W3 peak was curvefitted using two
Gaussian peaks. At low Tp, the W3 TO peak had a substantially larger
area than the W3 LO peak. As Tp increased the overall W3 peak shape
changed (Figs. 4548) and decreased in frequency as the W3 TO peak area
decreased and the W3 LO peak area increased until at full density they
were almost equal. As the W3 TO peak is the largest curvefitted W3 peak,
it represents the overall W3 PP trend most accurately, and decreases
smoothly and continuously as Tp increases (Fig. 56). The W3 LO PP does
not decrease until Tp 800C (Fig. 57), when it decreases rapidly as
viscous sintering occurs. It is not clear whether the fact that W3 LO is
constant until viscous sintering starts at 800C is an artifact of the
curvefitting method or an actual physical phenomenon. The separation
between the W, TO and W, LO PP increases as T increases.
3 3 p
Figures 58 and 59 show the T dependency of the PP of the TO and
LO peaks. The LO PP is not influenced by any other peak and
increases as Tp increases above 400C. At low T the TO peak over
laps the 980 cm*1 SiOH peak so the TO PP is influenced by the same W2
peak which causes problems curvefitting the SiOH peak, discussed later.
TO RAMAN PEAK POSITION [CM
(Thousands)
232
(Thousands)
SINTERING TEMPERATURE, Tp [*C]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 58. The dependence on the sintering temperature Tp of the TO
curvefitted Raman peak position (PP) for samples OXA (), 2XA (+) and
5XA (0). The Dynasil PP (a) is shown for comparison.
LO RAMAN PEAK POSITION [CM1]
(Thousands )
233
(Thousands)
SINTERING TEMPERATURE, Tp PC]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 59. The dependence on the sintering temperature Tp of the LO
curvefitted Raman peak position (PP) for samples OXA (), 2XA (+) and
5XA (0). The Dynasil PP (a) is shown for comparison.
SiO H RAMAN PEAK POSITION [CM
(Thousands)
234
(Thousands)
SINTERING TEMPERATURE, Tp PC]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 60. The dependence on the sintering temperature Tp of the SiOH
curvefitted Raman peak position (PP) for samples OXA (), 2XA (+) and
5XA (0). The Dynasil PP (a) is shown for comparison.
235
At high Tp during viscous sintering the TO PP increases, but again it
is unclear whether the fact that the TO PP decreases in sample 5XA as
Tp increases up to 800C is an artifact of the curvefitting method
involving W2 or an actual physical phenomenon. As both the TO and
LO PP are larger in sample 5XA than in sample OXA, it is probable that
as the TO and LO PP are related to d(SiO) there are differences in
the structure of these gels, which are related to the differences in
their starting sol composition.
Figure 60 shows the T dependency of the PP of the isolated 3750
cm'1 SigOH peak, exhibiting the same dependence on T as the 980 cm'1
Sis0H peak in Fig. 55.
3.2.9 Curvefitted Raman Peak Areas
Figure 61 shows the T dependency of the normalized internal ratio
of the combined area of the 3 Gaussian peaks used to curvefit the W1
peak, divided by the total integrated area of the Raman spectrum (except
for the D1, D2 and SiOH peaks), [W1]/[Wt]. This is proportional to the
concentration/unit volume of the structural units causing the W1 peak.
Figure 62 shows the same data for D1 tetrasiloxane rings, i.e. [D1 ]/[]
as a function of Tp. The concentration of the D1 rings is roughly con
stant for type 2X and 5X gels, but goes through a maximum for the
microporous type OX gels. Examination of the D1 peaks in the Raman
spectra in Figs. 46, 47 and 48 also shows this difference between gels.
[Wl]/[Wt] AS A FRACTION OF TOTAL AREA
236
(Thousands)
SINTERING TEMPERATURE, Tp CCI
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 61. The dependence on the sintering temperature Tp of the area of
the W1 curvefitted Raman peak as a fraction of the total Raman spectrum
area for samples OXA (), 2XA (+) and 5XA (0). The Dynasil peak area (a)
is shown for comparison.
[D1 ]/[Wt] ( D1 RINGS/UNIT VOLUME)
237
(Thousands)
SINTERING TEMPERATURE, Tp CC]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 62. The dependence on the sintering temperature Tp of the area of
the D1 tetrasiloxane ring curvefitted Raman peak as a fraction of the
total Raman spectrum area for samples OXA (), 2XA (+) and 5XA (0) The
Dynasil peak area (a) is shown for comparison.
[D1 ]/[Wt]/Sa (DI RINGS/UNIT AREA)
238
0.00018
0.00017
0.00016
0.00015 
0.00014 
0.00013 
0.00012
0.00011
0.00010
0.00009
0.00008
0.00007 H
0.00006
0.00005 
0.00004
0.00003 
0.00002 
0.00001 
0.00000
0.400
SAMPLE OXA
0.600 0.800
(Thousands)
SINTERING TEMPERATURE, Tp PC]
+ SAMPLE 2XA
1.000
0 SAMPLE 5XA
1.200
Figure 63. The dependence on the sintering temperature Tp of the concen
tration/unit area of the internal pore surface of the D1 tetrasiloxane
ring, (D1]/[Wt]/Sa, for samples OXA (), 2XA (+) and 5XA (0).
[D21/[WtÂ¡ (# D2 RINGS/UNIT VOLUME)
239
(Thousands)
SINTERING TEMPERATURE, Tp PC]
SAMPLE OXA + SAMPLE 2XA o SAMPLE 5XA
Figure 64. The dependence on the sintering temperature of the area of
the D2 trisiloxane ring curvefitted Raman peak as a fraction of the
total Raman spectrum area, (a) For samples OXA (), 2XA (+) and 5XA (0).
The Dynasil peak area (a) is shown for comparison, (b) For samples OX
(), OXA (+), 2X (O), 2XA (a), 5X (x) and 5XA (v). Within the resolution
of the curvefitting analysis the peak areas are the same for the two
samples examined for each type of gel within the T range of each sample.
[D2]/[Wt] (# D2 RINGS/UNIT VOLUME)
240
(Thousands)
SINTERING TEMPERATURE, Tp ["Cl
OX + 2XA 0 2X A 2XA X 5X V 5XA
Figure 64continued
[D2]/[Wt] (** D2 RINGS/UNIT VOLUME)
241
BULK DENSITY, Db [g/cc]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 65. The dependence on the bulk density Db (g/cc) of the area of
the D2 tetrasiloxane ring curvefitted Raman peak as a fraction of the
total Raman spectrum area for samples OXA (), 2XA (+) and 5XA (0). The
Dynasil peak area (a) is shown for comparison.
[D2]/[Wt]/Sa (= D2 RINGS/UNIT AREA)
242
(Thousands)
SINTERING TEMPERATURE, Tp CC]
SAMPLE OXA + SAMPLE 2XA o SAMPLE 5XA
Figure 66. The dependence on the sintering temperature Tp of the concen
tration/unit area of the internal pore surface of the D2 trisiloxane
ring, [D2]/[Wt]/Sg, for samples OXA (), 2XA (+) and 5XA (0).
243
Figure 63 shows the T dependence of the D1 concentration/surface
area ([D2]/Sg), i.e. the number of 4membered silicate rings per unit
area of internal pore surface s the normalized D1 concentration divided
by the surface area, [D1]/[Wt]/Sa, units of #/m2 or #/nm2 The [D^/Sg of
type 2X and 5X gels is roughly constant, similarly to [D1]/[Wt], while
it increases slightly as T increases for the type OX gel. One possible
explanation is that the radius of curvature of type OX gels is so small
that D1 ring formation is energetically more favorable than for type 2X
and 5X gels.
Above Tdb during viscous sintering the fraction of bulk D1 rings
increases compared to the fraction of surface D1 rings until eventually
all the D1 rings in the gel are bulk D1 rings and Sg = 0.0 m2/g. As Fig.
62 shows, the D1 peak is finite and still present when Sa = 0.0 m2/g at
full density, so [D.,]/[Wt]/Sa becomes infinite, which obviously cannot
be shown in Fig. 63.
Figure 64(a) shows the T dependence of the normalized D2 concen
tration, [D2]/[Wt] exhibiting the expected maximum in D2 concentration.
Figure 64(b) shows the same data for all 6 gel samples, confirming the
reproducibility of the variation with T of the D2 peak area for the
different gel types. Figure 65 shows the variation of [D2]/[Wt] with Db,
demonstrating that the maximum [D2] concentration is reached as Tp
increases with little or no increase in Db.
Figure 66 shows that the D2 concentration/Sg, = [D2]/[Wt]/Sg,
increases continuously as Tp increases in all the gels. If [D2]/Sg
increases continually as Tp increases, surface D2 ring formation by
condensation polymerization of adjacent Sig0H must occur continuously as
Tp increases. In other words increasing Tp does not in itself destroy D2
244
rings, as might be expected due to their large intrinsic strain and
apparent metastability. Increasing Tp actually increases the concen
tration/m2 of the surface D2 rings on the remaining pore surface. It is
the structural rearrangement occurring during viscous sintering leading
to the loss of internal pore surface area which causes the decrease in
the total concentration/m3 of surface D2 rings (i.e. [D2]/[Wt]). There
fore the decrease in overall D2 trisiloxane ring concentration observed
in Figs. 64 and 65 occurs because the Sg of the gels decreases as
viscous sintering occurs. During the bond breakage and reformation that
occurs during viscous sintering, the metastable D2 trisiloxane rings are
replaced by more stable, larger silicate rings until at full densificat
ion the D2 concentration, [D2] is very similar to that for a fused
aSi02 sample with the same Tf. The fact that fused aSi02 and dense
gels do have the same [D2] means that because the =Si0Sis bridging 0
bonds in the bulk, as opposed to the surface, of the silica particles in
a gel are not broken during densification, yet =Si0Si= in 90% of the
D2 rings are broken, 90% of the D2 rings have to be in the part of the
gel where =Si0Si= are broken, i.e. on the internal pore surface, as
expected [5].
Figure 67 shows the expected [189] decrease in the 970 cm"1 SiOH
peak area, [Sig0H]/[Wt] as Tp increases. The overall [Sis0H] decreases
as Tp increases and is larger in type OX and 2X gels because they have a
larger Sg. Figure 68 shows that [Sig0H]/Sa = [Sis0H]/[Wt]/Sa also de
creases as Tp increases. The decrease in [Sig0H]/Sa (#/nmz) as Tp
increases has been observed on fused aSi02 by a number of investigators
[Si OHl/[lVt] ( SiOH/UNIT VOLUME)
245
0 SAMPLE OXA
(Thousands)
SINTERING TEMPERATURE, Tp [*C]
+ SAMPLE 2XA 0 SAMPLE 5XA
Figure 67. The dependence on the sintering temperature Tp of the area of
the 980 cm'1 SiOH curvefitted Raman peak as a fraction of the total
Raman spectrum area for samples OXA (), 2XA (+) and 5XA (0). The
Dynasil peak area (a) is shown for comparison.
[Si OHJ/[Wt]/Sa (** Si OH/UNIT AREA)
246
(Thousands)
SINTERING TEMPERATURE, Tp PC]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 68. The dependence on the sintering temperature of the concentra
tion/unit area of the internal pore surface of the 980 cm"1 surface
silanols, [SiOH]/[Wt]/Sa, for samples OXA () 2XA (+) and 5XA (0).
([W3 TO] + [W3 LO])/[Wt] AS A FRACTION
247
(Thousands)
SINTERING TEMPERATURE, Tp [C]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 69. The dependence on the sintering temperature Tp of the area of
the W3 (TO and LO) curvefitted Raman peak as a fraction of the total
Raman spectrum area for samples OXA (), 2XA (+) and 5XA (0) The
Dynasil peak area (a) is shown for comparison.
(!Â¥4 TO] + [T4 LO])/[Wt] AS A FRACTION
248
(Thousands)
SINTERING TEMPERATURE, Tp PC]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 70. The dependence on the sintering temperature Tp of the area of
the (TO and LO) curvefitted Raman peak as a fraction of the total
Raman spectrum area for samples OXA (), 2XA (+) and 5XA (0). The
Dynasil peak area (a) is shown for comparison.
[SiO Hl/[Wt] O SiOH/UNIT VOLUME)
249
(Thousands)
SINTERING TEMPERATURE, Tp PCI
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 71. The dependence on the sintering temperature Tp of the area of
the 3750 cm"1 SiOH curvefitted Raman peak as a fraction of the total
Raman spectrum area for samples OXA (), 2XA (+) and 5XA (0). The
Dynasil peak area (a) is shown for comparison.
(vaav xiMn/Hos **) ots]
250
(Thousands)
SINTERING TEMPERATURE, Tp [*C]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 72. The dependence on the sintering temperature of the concentra
tion/unit area of the internal pore surface of the 3750 cm'1 surface
silanols, [SiOH]/[Wt]/Sa, for samples OXA () 2XA (+) and 5XA (0) .
[SiO HJ (3750 CMl)/[SiOH] (960
251
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 73. The dependence on the sintering temperature T of the ratio
of areas of the 3750 cm'1 SiOH peak and the 980 cm'1 SiOH peak,
[SiOH]/[SiOH], for samples OXA (), 2XA (+) and 5XA (0).
252
[5,18990], The increase in [D2]/[Wt]/Sa with T in Fig. 66 is directly
related to the associated decrease in [SiOH]/Sg s [SiOH]/[Wt]/Sg in
Fig. 68 via the formation of surface D2 rings during the condensation
polymerization reaction. Figure 68 shows that [Si0H]/Sg is smaller in
type OX gels than in type 2X and 5X gels. This is related to the very
small radius of curvature of the type OX gels, which also caused [D^/Sg
to increase in type OX gels but remain constant in type 2X and 5X gels
as Tp increased (Fig. 63).
Figures 69 and 70 show the T dependency of [W3]/[Wt] and [WJ/[Wt]
respectively. [W3]/[Wt] is the combined area of the W3 TO and W3 LO peaks
and [W^]/[Wt] is the combined area of the TO and W^. TO peaks. These
peaks are influenced during curvefitting by the problems associated with
the change in the intensity and position of the W2 peak.
Figures 71 shows the T dependency of the normalized area of the
3750 cm'1 Sis0H peak, [Sis0H]/[Wt] Figure 72 shows the T dependency of
[Si0H]/Sg = [SiOH]t/[Wt]/Sg. The 3750 cm'1 SiOH peak shows the same T
dependency in Figs. 71 and 72 as the 980 cm'1 SiOH peak in Fig. 67 and
68. Figure 73 shows the ratio of the 3750 cm'1 [SiOH] peak area to the
970 cm'1 SiOH peak area. This ratio is constant and =1113 for all
the gels within the resolution of the curvefitting analysis, which means
that the Gaussian peaks used to curvefit the two different Sig0H peaks
are selfconsistent.
253
3.3 Discussion
3.3.1 Comparison of the Values of the Structural Density Calculated
from Isothermal N= Sorption and from 1L0 Pvcnometrv
The structural density Dg of metal alkoxide derived silica gels
has been measured by many investigators (Figs. 218) [719,2830,179
180,182,183]. The dependence of Dg on processing variables has never
been systematically investigated. The Dg of silica gels is an area of
controversy because Dg values as large as 2.38 g/cc have been published
[28,29], which is larger than the Dg of fused aSi02 (for a cylindrical
sample of Dynasil, a Type III aSi02, He pycnometry gave Dg = 2.203
0.0025 g/cc). This was discussed in the literature review. These values
have never been reproduced using different techniques on the same gels,
so in this investigation three different techniques were used to measure
Dg of alkoxidederived silica gels as a function of Tp and Db to avert
any questions concerning the credibility of the data. These measurements
are summarized in Figs..3032 and 34.
Figure 30(a) shows the Tp dependency of Dg measured by N2 sorp
tion, which is a noisy plot. The Dg versus Dfa plot in Fig. 30(b) is much
smoother even though the thermal history, T(t), and Tp of the individual
type OX samples are very different. Dg is dependent on the T(t) of each
sample, which obviously includes both T and t. This dependency is
accounted for by plotting Dg versus a property of the gel which is also
dependent on the sample's T(t). Db fulfills this requirement.
The Ds versus Tp plot in Fig. 31(a) for the H20 pycnometry data is
also noisy. There is a wide range of Dg values for each holding Tp due
to the dependency of Dg on each sample's T(t), as demonstrated quantita
tively in Fig. 29. This means that Dg is dependent on T but different
254
T(t) cause different stages of Dg development to be reached for the same
final T Since Db also depends on T(t), a chaotic Dg dependency on Tp
(Fig. 31(a)) is smoother when plotted against Db (Fig 31(b)).
Figure 32(a) compares Dg of monolithic type OX gels calculated
from: a) Db and Vp (measured by isothermal N2 sorption) and b) the
skeletal volume measured by H20 pycnometry. Both data sets show a
similar shape, but for a given Db the magnitude of Dg is different.
There are several possible reasons why Ds depends on the experimental
technique used to measure it. These reasons are discussed below.
3.3.2 The Dependence of the Magnitude of Vp on the Experimental
Techniques Used to Measure Vp
The Dg of type OX silica gels measured by both these techniques
goes through a maximum value, called Dsmax, at the temperature Tsmax. The
difference between Dsmax values measured by N2 adsorption and H20 pycnom
etry is 8.41.8%. The pore volume Vp of a gel can be measured by H20
adsorption as well as N2 adsorption. Vp measured by H20 adsorption
equals the weight of H20 adsorbed into the gel pores divided by the dry
weight of the gel and the density of the adsorbed H20. Based on a
comparison of ten measurements of the magnitude of Vp measured for the
same silica gels by N2 adsorption and H20 adsorption, Vp measured by N2
adsorption is 1.115 (a10 = 0.0352) times larger than Vp measured by H20
adsorption. This is equivalent to a difference of 11.53.5%.
For isothermal N2 sorption, Dg is calculated from Vp and Db using
equation (43). For H20 pycnometry, Dg is calculated from the molar
volume of the silica gel skeleton. For a fixed Dfa, the molar volume is
inversely related to Vp. Therefore, the 8.41.8% difference observed in
the magnitude of Dsmax could be due to the 11.53.5% difference in the Vp
255
measured by the N2 adsorption and H20 pycnometry. Dgmax would differ by
11.53.5% if the differences were due to the Vp measurement differences
alone. The question is whether the difference between 8.41.8% and
11.53.5% is significant, and if so what causes the difference.
The most probable cause of changes in Dg after removal from the
sintering furnace is interactions of the gels with H20. Adsorbed H20
reacts with the surface structure [5,31,35], This influences both the
surface silicate ring structure and V(0). The H20 pycnometry samples
have been saturated with H20, so all the surface area has been exposed
to H20 molecules. The weight used in the Dg measurement is that of the
dry sample immediately after removal from the furnace at 200C. Conse
quently the measured weight, and calculated molar volume and Vp are not
for identical structural states of the sample.
The skeletal volume (which is equivalent to the molar volume)
measured by the H20 pycnometry is representative of the rehydrated
structure rather than the metastable dehydrated structure stabilized at
Tp of that sample. This means that Dg is calculated from the weight of
the metastable dehydrated structure and the skeletal volume of the
rehydrated structure.
The adsorption of H20 should reduce Dg slightly by increasing the
surface [OH] concentration during rehydrolysis of the strained D2
trisiloxane surface rings. Analysis of the Raman spectra in Chapter 4
shows that the absorption of H20 into the pores of gels causes a slight
increase in the molar volume of the gel, so Dg decreases. The Raman
spectra of gels saturated with absorbed water also show that the D2 peak
has decreased in size and that the main W1 450 cm'1 peak and the D1 605
cm'1 peak have become more overlapped (Fig. 87). This suggests that
256
after water adsorption the structure has reverted to the structure found
in gels stabilized at lower Tp, which have a smaller Dg, because the
same details are seen in the Raman spectra of low Tp gels (Figs. 4548).
These observations suggest that the adsorption of H20 should
decrease Dg. Therefore the actual Dg values measured by H20 pycnometry
are smaller than the De of the"metastable dehydrated structure would be
^ X
if they could be measured, due to the hydration effects discussed above.
The N2 sorption Dg samples were not stored in a vacuum so they
also adsorbed H20 into their pores before the degassing treatment
required for pore volume measurement. This means that these samples have
also been rehydrated, and the skeletal volume measured is that of the
relaxed hydrated structure. Degassing the samples before N2 adsorption
removes all adsorbed liquids from the pores, but does not return the
surface structure to the original structure obtained at the Tp. The Dg
values measured by N2 sorption are therefore for rehydrated structures,
similar to the H20 pycnometry data, except that the sample weight of the
N2 sorption samples is also that of the rehydrated sample.
Six silica gels were weighed immediately after removal from a
furnace after sintering at Tp between 600 and 900C. Their pores were
then saturated with H20 for 3 days before drying overnight at 180C and
reweighing. Comparison showed that on average their dry weight had
increased by a factor of 1.01427 0.00137. Therefore the Dg of the
rehydrated gels calculated from N2 sorption data using the weight of
metastable dehydrated gels would be 1.40.13% less than the Dg of the
rehydrated gels calculated from N2 sorption data using the weight of
rehydrated gels due to the difference in weight caused by rehydration.
Consequently, as the H20 pycnometry sample Dg were calculated from the
257
weight of the metastable dehydrated structure and the skeletal volume of
the rehydrated structure while the N2 sorption sample Dg were calculated
from the weight and the pore volume of the rehydrated structure, the
8.4% difference in Dgmax for these two techniques would decrease to 8.4 
1.4 = 7.0% when comparing Dg calculated from the weight of the metast
able dehydrated structure and the volume of the rehydrated structure.
When the weight of a gel increases due to rehydration the skeletal
volume also increases, and Dg calculated from these values will include
this. In general, compared to Dg calculated from the weight and volume
of the metastable dehydrated gel, Dg calculated from the dehydrated
weight and the rehydrated volume will be smaller. Dg calculated from the
rehydrated weight and the rehydrated volume will be even smaller due to:
a) including the low density [OH] phase and its influence on the molar
volume of silica, and b) the other factors discussed above. Therefore
the above calculations show that the difference in calculated from
N2 sorption and H20 pycnometry is > 7.0% and this difference cannot just
be explained by differences in the physical state of the gels. Both H20
pycnometry and N2 sorption measure the Dg of rehydrated type OX gels, so
the differences in Dg measured by these two techniques must be due
mainly to the difference in the magnitudes of Vp measured by the two
techniques because the difference between 8.41.8% and 11.53.5% is not
statistically significant.
The difference in Vp measured by the two experimental techniques
is due to a number of effects. These include: a) the mass and surface
fractal nature of porous xerogels, b) the effect of the very small
radius of curvature of the pores on the density and packing factor of
the adsorbate, c) any physical or chemical interactions between the
258
adsorbate and the pore surface, and d) the socalled annulus volume
between the pore surface and the center of mass of the adsorbed mole
cules at the interface.
Fractal properties of silica gels. The mass and surface fractal
nature of these gels means that the magnitude of Vp and Sg, respective
ly, depends on the yardstick used. This is the diameter of the molecule
used to measure them. The surface fractal dimension of microporous gels
2.98, which means that the surface fills space [5,1912]. The packing
factor of the different molecules influences the pore volume. So does
the surface chemistry if it influences the packing structure, or local
ordering near the surface, of the condensed probing molecules. The
magnitude of all these factors will vary with the radius of curvature of
the pore.
Only type OX gels were characterized by all 3 Dg measurement
techniques. The maximum structural density value, Dgmax, of type OX gels
is different for each measurement technique. It is also larger than the
density of fused aSi02, 2.20 g/cc, for all three measurements. For type
OX gels, Dgmax occurs at similar values of Db, in the range 1.251.4 g/cc
(Figs. 3034). From N2 sorption, Dgmax = 2.450.03 g/cc, from H20 pycnom
etry, Dgmax = 2.260.01 g/cc and from helium pycnometry, Dgmax
2.3000.005 g/cc. The N2 sorption values are so large that if they did
not show the same dependency on Db as the data obtained by H20 pycnome
try and helium pycnometry, they would be questionable.
Dsmax shuld increase as the diameter of the probing molecules
decreases because the pore volume measured increases as the molecules
decrease in size, so the skeletal volume decreases for the same sample
259
weight. This implies that the diameter of the molecules and atoms
increase such that N2 < He < H20.
The actual radii of atoms and molecules depends on their state and
environment. For instance, helium is always used in preference to N2 in
gas pycnometry because although they both exhibit ideal gas behavior
near ambient pressures at room Tp the inertness and smaller size of the
helium atom enables it to penetrate even the smallest pores [2]. Yet the
Vp of a porous silica gel measured by liquid N2 in isothermal N2 adsorp
tion at 197C is larger than Vp measured by gaseous helium in helium
pycnometry at 25C. The effective radius of the N2 molecule as a liquid
appears to be smaller than the effective radius of a helium atom as a
gas, contradicting a previous report [2].
The covalent radius of helium is 0.93 [193], of N2 is 1.20 and
of H20 is 1.48 [194,p.571], while the Van der Waals radii of helium is
1.20 , of N2 is 1.50 and of H20 is 1.30 . The BET crosssectional
areas of adsorbed N2 and H20 (on nonpolar solids) are 16.2 2 and 10.8
2 [2], giving a radii of 2.01 for an adsorbed N2 molecule and a radii
of 1.64 for an adsorbed H20 molecule. As Vp measured by liquid N2
during N2 adsorption at 197C is always larger than Vp measured by H20
adsorption at 25C, the effective radius of N2 molecule as a liquid
appears to be smaller then the effective radius of a H20 molecule as a
liquid, also contradicting a previous report [2]. There is therefore no
obvious correlation between Vp measured by absorbed helium, N2 and H20
molecules and their radii.
The packing factor. The effective radius, or yardstick, of the
molecules and atom used to measure Dg is therefore difficult to ascer
260
tain. Not only do they vary as described above, but tbeir packing
efficiency will also depend on the extent of their interaction with the
surface. For instance because of the Hbonding tendency of H20, the
adsorption of H20 is sensitive to the degree of polarity of the adsor
bent surface. The BET monolayer capacity of H20 adsorbed on silica
calculated from the H20 isotherm is roughly equal to [OH] of the surface
[195]. The packing factor of the 2dimensional monolayer will depend on
[OH], so the BET crosssectional area of H20 on silica is determined by
its surface structure and composition.
Gregg and Sing [195] give a value of 20 2 for H20 adsorbed on
silica, compared to a value of 10.8 2 on nonpolar surfaces. This will
have a knockon effect into the adjacent layers, which means that the
bulk packing factor of H20 directly adjacent to the surface monolayer in
the pores in silica gel also depends on the surface [SiOH]. The effect
will decrease with distance from the surface, but explains why Vp of the
pores in silica gels measured by H20 adsorption is smaller than Vp
measured by N2 sorption, despite H20 having a smaller molecular radius
than N2 calculated from the BET crosssectional area on nonpolar
solids.
The annulus volume. The density of liquids in these pores will
depend on the size of the pore. For pores only a few molecules in
diameter there are restrictions on how many molecules can fit in the
pore. Only 9 layers of gas can condense in pores both 9.1 molecules in
diameter and 9.9 molecules in diameter, but 10 layers can condense in a
pore 10.1 molecular diameters across. If a different diameter molecule
is used, then these condition change. The empty volume not occupied by
261
the adsorbed molecules is called the annulus volume. Estimating the size
of the annulus volume is not possible because the exact shape of the
pores in these fractal materials is not known. Both the connectivity and
shape of the pores in silica gels will affect their measured V but
quantifying these effects is very difficult.
The density of adsorbed condensed liquids. It could also be argued
that the values used for the density of the N2 and H20 adsorbed in the
micropores of the gels, which is used for the calculation of Dg from the
N2 sorption and H20 pycnometry measurements, are wrong. These incorrect
values might be producing the large Dg values seen. The value used to
calculate Dg from H20 pycnometry was the value of bulk H20 at 24 C =
0.9973 g/cc. Etzler et al. [196] has shown that the density of H20
adsorbed in micropores is likely to be smaller, rather than larger, than
the value of bulk free H20 at the same T. Etzler et al. give a value of
what they call the pore density of H20 of 0.966 g/cc at 25C. If the
density of liquids in micropores is actually lower than for bulk
liquids, but the bulk H20 density value is still used to calculate the
pore volume (as is done in this investigation), then the pore volume
measured will be too low. This means that the skeletal volume measured
will be too large. If the skeletal volume is too large, then the correct
calculation of Dg should use a smaller skeletal volume value. Then the
calculated Dg values should be even larger than they are already. For
example, using a H20 density value of 0.966 g/cc instead of 0.9973 gives
a maximum Dg value of 2.341 g/cc instead of 2.267 g/cc. Similar argu
ments can also be used to increase the Dg for both the N2 sorption and
helium pycnometry measurements, so the differences in Dgmax would still
262
exist. All these factors can contribute to the different pore volumes
measured using different molecules in very small pores.
3.3.3 Helium Pvcnometrv
The differences in the helium pycnometry Dg and D values of the
type OX gels in Fig. 34 compared to the N2 adsorption and H20 pycnometry
values (Figs. 3032) are also related to the diameter of the molecules.
The gels used during helium pycnometry remained dehydrated as they were
not exposed to H20 at any stage during measurement, so Dg is larger than
if the gels had been exposed to H20. As the gels measured in the helium
pycnometer were fine powders, their viscosity at a specific Tp is higher
than for a monolithic gel and they retain porosity to higher T.
Figure 34(a) shows that at 200C the magnitude of the Dg of each
gel increases as [HF] increases, i.e. 5X > 2X > OX, in the order of
decreasing Sg and increasing rH. Dg increases to a maximum value, Dgmax,
as Tp increases. The standard deviation, a8, of each Dg value measured
by helium pycnometry is < 0.004 g/cc. The Tgmax at which Dgmax is
reached also increases as [HF] increases, i.e. 5X > 2X > OX. Dg then
decreases to a stable value of 2.212.23 g/cc when densification is
complete. The type 5X gel, with a larger rH and smaller Sg, reaches its
Dgmax value at the highest Tgmax and stays constant at Dgmax to the highest
T
smax
The type 5X gel densifies at the highest T This is expected, and
is related to the structure and texture of the gel. In viscous sintering
the strain, e, associated with densification is proportional to the
total interfacial (or surface) energy (= Sg7gv, where 7gv is the solid
vapor surface energy, which is directly proportional to the surface
263
tension), and inversely proportional to the viscosity, t], and the radius
of curvature, rH, of the surface, so e a Sg7sv/r?rH [5] At a particular
Tp type 5X gels have smaller Sfl, larger rH and larger rj, so they start
to sinter viscously at the highest Tp and complete densification at the
highest Tp. In contrast, within the resolution of the He pycnometer,
Dsmax aPPears to be independent of [HF] Dgmax is very similar for each
gel type, between 2.302.31 g/cc, so Dsmax does not correlate with any of
the physical properties of the gels which do change with [HF].
Dg stayed constant (within the resolution of the helium pycnome
ter) after viscous sintering had finished and the gels were fully dense.
The silica gel powders have fully densified with no closed porosity. If
there was any closed pores the powdered gels would have expanded, or
foamed, as Tp was increased, so Dg would decrease as the gels expanded.
After reaching full density Dg stayed constant when heated for a further
100C, so no foaming can have occurred and the gels contained no
residual closed pores.
In contrast, a monolithic type OX silica gel with rH 1.2 nm
foams at 850C when sintered in the humid Florida air. This is because
the [SiOH] content of monolithic gels is higher than a powdered sample,
for a given T, so the associated rÂ¡ is lower. Powdered samples also have
a decreased diffusion distance through the tortuous connected porosity
which the condensed H20 molecules have to travel before they can escape
from the gel. The same decrease in [SiOH] of powdered gels compared to
monolithic silica gels, for a given T, causes rÂ¡ of the powder and the
associated Tp required for full densification to increase.
In summary, the thermal dependency of the structural density of
alkoxide derived silica gels shown in Figs. 30, 31, 32 and 34 is
BULK AND STRUCTURAL DENSITY [g/cc]
264
0.200 0.400 0.600 0.800 1.000 1.200
(Thousands)
SINTERING TEMPERATURE, Tp [*C]
Figure 74. The dependence on the sintering temperature Tp (C) of the
structural density Dg [g/cc] () of a powdered type OX silica gel,
measured using He pycnometry, and the bulk density Dfa [g/cc] of mono
lithic silica gels [169] sintered in humid Florida air (+) and sintered
in a dehydrating atmosphere of flowing CC14 () .
265
believable. The magnitude of Dg depends on the structure and texture of
the gels, the thermal history characterized by Dfa and the experimental
technique used to measure Dg. Figure 74 shows Dg measured by helium
pycnometry for type OX, 2X and 5X gels and Db for type OX gels [169] in
humid air and in a dehydrating atmosphere. The influence of rH, Sg and
[SiOH] on Dg and Dfa can be seen clearly in Figs. 34 and 74.
3.3.4 Comparison to Earlier Work
Earlier data, discussed in the literature review, shows that the
magnitude of Dg of a gel initially depends on whether it is a xerogel
(Figs. 2124, 28), dried at 1 atmosphere, or an aerogel (Figures 26 and
27), dried hypercritically. Dg. The magnitude of Dg also depends on T ,
the pH of the gel [17] and the initial concentration of the silica
precursor in the sol [17]. For neutral or high pH xerogels (Figs. 2224)
and for aerogels (Figs. 26 and 27), Dg initially increases as Tp in
creases above 200C, and the maximum D0 value, Dmv, is reached when
densification is complete. In comparison, in acid catalyzed xerogels Dg
decreases below Domav after T increases above T until viscous sinte
smax p smax
ring is completed. The magnitude of Dcm.v and Dc above Tcm=v are indepen
olllaA o oIIkjA
dent of the magnitude of Sg. The Tp dependency of the Dg of the acid
catalyzed, low pH silica xerogels shown in Figs. 3032 and 34 confirms
the data from the literature for similar gels shown in Figs. 21 and 28.
3.3.5 Reason for the Similarity of for Type OX. 2X and 5X Gels
The helium pycnometry Dg measurements gave very similar values for
the maximum structural density, Dsmax, of type OX, 2X and 5X silica gels.
The Dsmax was 2.302.32 g/cc for these gels (Fig. 34) despite their very
266
different textural properties (Tables 4 and 6). Since Dgmax is approxima
tely constant while rH (= 20,000Vp/Sa) changes by a factor of 9.0/1.2
7.5 as [HF] increases from OX to 5X, it appears that the magnitude of
Dsmax fr t*16136 gels is independent of the textural or physical proper
ties of the gel which change with [HF] i.e. V Sg and rH. The magni
tude of V Sa and rH of a particular gel depends on d^ [5,191], i.e.
their magnitude depends on the experimental technique used to measure
them. The magnitude of Dgmax of a particular gel is also dependent on the
experimental technique used to measure Dgmax, due to the fractal nature
of the gel and the scale of its pore morphology. Since Dg(nax is constant
while rH increases significantly, it is possible that the fractal dimen
sions df of these HF catalyzed gels are very similar, i.e. df does not
change as [HF] increases. The df of a silica gel depends on all the
processing variables [4,5,197,198], so comparing values of df of gels
prepared in different ways is difficult. As a first approximation,
Winter et al. [198] found that when 1.25 x 10'^ M NaF was added to a
neutral, R = 4, TMOS silica gel, df stayed constant and = 2.2, while the
radius of gyration Rg increased from 100 to 150 . This is consistent
with type OX, 2X and 5X gels because rH oc Rg, and rH increases as [HF]
increases in these gels, while it supports the hypothesis that df
remains constant as [HF] increases.
There are several possible explanations of why Dgmax is constant
for type OX, 2X and 5X silica gels:
Inaccuracy of experimental techniques. The Dg measurements could
all be inaccurate and give the same Dgmax values by chance. This has been
discounted in the discussion above.
267
The particles in the gel might be large enough for their structure
to be unaffected by further increase in r The particles in these gels
might be large enough to be representative of an equivalent bulk gel
structure. In other words the gel particles would be large enough that
any increase in particle size that might occur as [HF] increases does
not affect the average structure of the silica particles. This means
that the smallest particle size in the OX type gel is so large that it
contains enough tetrahedra for the ring size distribution statistics in
the gel particle to be unaffected by the increase in the number of
tetrahedra caused by the increase in particle size. The number of
tetrahedra would already be a statistically significant basis set large
enough to represent the bulk structure of the gel, and increasing the
number of tetrahedra in the basis set would not significantly change the
ring statistics or the structure of the gel.
The average ring size distribution of fused aSi02 is not known
with certainty. Analysis of a threebody potential MD model of the
structure of fused aSi02 produces 3, 4, 5, 6, 7 and 8membered rings in
the approximate ratio 1:4:8:8:4:1 [199]. Assuming that no tetrahedra are
shared, 143 tetrahedra are required to form this many rings. Of course
some tetrahedra are shared by different rings, so the actual number of
tetrahedra required is smaller. The number of tetrahedra required to be
in the sample set before an increase in its magnitude causes less than a
specified change, for instance 0.5%, in the average d(SiO), 6 and ring
statistics, is unknown. Put another way, how large does a gel particle
have to be before any further increase in size causes no further change
in its average structural parameters?
268
This is a very difficult question to answer, especially since Dgmax
is larger than 2.20 g/cc so the gel structure is more compact than fused
aSi02. When the gel is heated above Tgmax, Dg decreases towards 2.20
g/cc, so the structure of the gels at Dgmax is metastable. This means
that any discussion about the influence of particle size on Dgmax con
cerns the influence of particle size on a metastable compact structure.
The radius of a SiO4' tetrahedra is d(SiO) + radius of 0 atom =
1.62 + radius of 0 atom. The radius of 0 depends on its bonding. Si02
is about 50% ionic and 50% covalent, so (ionic radii + covalent radii)/2
(1.35 + 0.74)/2 = 1.05 . The Van de Waals radius calculated for 0
from molecular crystals 1.40 . The ionic radius of Si4+ is 0.42 , so
the ionic radius of 02' is d(SiO) 0.42 1.62 0.42 = 1.20 ,
assuming the ions just touch [194]. The variation in 0 radius from 1.05
to 1.40 means that it is not clear which radius should be used in
silica. This is not surprising as molecular orbitals do not have sharply
defined edges.
Therefore the radius of the tetrahedra is 1.63 + 1.40 = 3.03 .
The effective volume of a tetrahedra, though, is not the volume of a
sphere of radius 3.03 because the corner 0 atoms are shared by adja
cent tetrahedra. Rather, the radius of a sphere describing the volume
occupied by a tetrahedra is equal to d(SiO) = 1.62 . The volume of a
sphere of radius = 1.62 is 17.8 3, and of a cube 3.24 high is 34.0
3. The effective volume of SiO4 tetrahedra in fused aSi02 might lie
somewhere between these values.
The molecular weight of Si02 is 60 g, and Dg 2.20 g/cc, so 1
mole of silica occupies 60/2.20 = 27.27 cm3. NA = 6.023 x 1023 mole
cules/mole, so one silica tetrahedra occupies 27.27/6.023 x 1023 =4.52
269
x 10'23 cm3 = 45.2 3. Therefore the effective volume is larger than the
volume calculated from the geometric shape of a silica tetrahedra.
TEM analysis of colloidal particles led to an empirical relation
ship between the average pore radius, rp, of colloidal particles and the
radius of the largest sphere that could fit in the pores created by
these colloidal particles. From this data, rH = 12 gives an average
particle diameter of about 100120 = rp 5060 for colloidal
spheres with random close packing [5,p.269].
Orcel found, from molybdic acid analysis of silica sols, a primary
particle radius 20 , containing 33510/45 745 tetrahedra [4,182].
These primary particles agglomerate to form dense secondary particles.
These dense secondary particles are the particles in the gel which have
an average particle radius rp. Their packing geometry governs the pore
structure. Orcel measured the Guinier electronic radius of gyration of
the secondary particles using SAXS [4,182], He found that for a range of
silica gels rp 60 s 120 diameter, similar to rp measured above
from the empirical relationship.
Topological analysis of the ring statistics in a 20 X 20 X 35 =
14000 3 MD fused aSi02 unit cell showed that this unit cell contained
a statistical distribution of the silicate rings similar to that
expected in silica [200]. This MD unit cell contained 1080 atoms = 360
SiO^' tetrahedra, made up of 360 Si and 720 0. Therefore it is possible
that as few as 360 tetrahedra are required for the sample set to be
statistically similar to silica. As there are 360 tetrahedra in the unit
cell, the tetrahedral volume = 14000/360 = 38.9 3, similar to the
effective volume of a tetrahedra. This MD unit cell is equivalent to a
sphere of radius = 15 . A planar 6 membered siloxane ring is about 12
270
across, and a trisiloxane ring is about 7 across [201], In a fused
aSi02 matrix, rings containing 4 or more tetrahedra are puckered so the
diameter of the 6 membered ring will be smaller than 12 in a silica
matrix and would fit in a sphere 30 in diameter.
A 120 diameter particle contains 905000/45 20,000 tetrahedra
and 60,000 atoms. The OX gel particles size measured by this analysis
65 times larger than the MD unit cell. Swiler [200] found a statistical
ring size distribution in this relatively small MD unit cell, so the
particles in OX gels should be large enough to contain a distribution of
silicate rings unaffected by any further increase in particle size.
This also depends on whether the Sg to volume ratio of the parti
cles is small enough that the surface structure does not affect the bulk
structure. The surface area to volume ratio affects the ring size
distribution statistics and the NBO/BO ratio.
If Sg 750 m*/g and Vp 0.45 cc/g, rH 1.2 nm based on a
continuous cylinder model. The theoretical rp of colloidal spherical
particles (i.e. not surface fractals) is given by the equation rp =
3/(Sa x Dg) For Sg = 750 mz/g, rp = 1.8 nm. This calculation does not
include the area lost due to particle to particle contact, or the neck
size. In the extreme where the neck size is the same size as the
particles, the particles become a continuous cylinder which has the same
shape and size as the cylindrical pore model, so rp = 1.2 nm. Therefore
the average rp for colloidal particles lies somewhere between these two
extremes.
For a gram of material with Sg = 750 m2/g, rp is 12 to 18 , yet
experimental measurements infer rp 60 for type OX gels [4,182]. This
apparent contradiction is explained by the mass and surface fractal
271
properties of these silica gels which allows particles to possess larger
Sg than if they were dense Euclidian particles. Even though the parti
cles are quite large compared to the pores, the silica gel can still be
described as an interfacial material. The interfacial nature is charac
terized by the surface fractal property of the gels. This allows the
gels to have a larger rp than allowed for a specific Sg for colloidal
gels by having a "space filling fractal surface" [5]. The relationship
between Sa, V rH, rp, Cn, Db, Dg and [HF] is influenced by df and dg.
The experimentally determined rp values are supported by the above argu
ments, and might be large enough for the particle structure to be
unaffected by further increase in rp because the particle structure is
already representative of a bulk structure.
The influence of HF on rp. Another possible explanation of why
Dsmax doesn't change as the hydrofluoric acid concentration, [HF],
increases is that rp could be constant as [HF] increases. In other words
the addition of HF to OX gels does not cause rp to increase any further.
Instead, a decrease in the coordination number of the particle, Cn,
would cause the Db decrease observed. The exact influence of [HF] on r ,
Cn and the packing factor is not known from experiments.
Any differences between the three gel types must be due to the
increase in HF concentration in the starting sol for each gel because,
as discussed in the experimental procedures section, the composition of
all the silica gels were identical except for [HF]. The reference
concentration was called IX, so the 5X gel contained five times the HF
concentration of the IX sol, 2X contained two times the HF concentra
tion, and OX contained zero times the HF concentration of the IX sol
272
i.e. none. Otherwise the gels were all aged, dried and heat treated in
identical ways. The addition of HF to the sol led to an increase in Vp
and rh, and a decrease in Dfa and Sg (Fig. 33).
When rp is calculated from rH, its magnitude depends on Cn. The
magnitude of the change of rp with [HF] then depends on whether the Dfa
decrease and rH increase seen as [HF] increases is due to an increase in
rp or to a decrease in Cn, or a combination of both. For a given rH/rp
ratio, the magnitude of Dfa depends on Cn. Therefore for a constant Cn, Db
will also be constant if rp increases as [HF] increases. In reality an
increase in [HF] causes rH to increase and Db to decrease, so Cn must
decrease if rp increases or stays constant. Therefore it is possible for
rp to stay constant.
The gel structure would change due to changes in the hydrolysis
and condensation rate constants and associated reduction in gelation
time as [HF] increases. The gel structure could change to look more like
Fig. 2 of Schaefer et al. [202] as [HF] increases, which shows the
suggested structure for silica aerogels which have a low Cn, small rp
and Db, but a large rH. This is likely to happen because the concentra
tion of silica in the starting sol is constant. As R = 16 the volume of
H20 in the sol is also constant, so large particles can not be formed to
produce Vp = 1.0 cc/g and Sg = 300 M2/g as Db would be larger then the
actual experimental values. To give the correct, smaller Dfa values the
structure must become more open, so Cn decreases as [HF] increases.
The addition of F ions accelerates the gelation process. F'
causes the condensation process to proceed via the formation of higher
branched polymers without the participation of the dimers or the trimers
in the polymerization process. This leads to the formation of a loose
273
and relatively open silica network with larger pores [203]. The consen
sus opinion is that the increase in rH caused by the addition of HF is
due more to a decrease in the Cn and the packing factor than to an
increase in r [204]. It is reasonable then that C decreases as r
increases as [HF] increase, rather than Cn staying constant as rp
increases.
A value of rp 60 for rH = 1.2 nm implies that the particles in
gels might be random close packed. They could be more loosely packed,
i.e. Cn smaller, based on Db values, but not close packed. rp can be
directly calculated from Dfa and Cn, but only for a monosized particle
distribution. Pore size distributions calculated from isothermal N2
sorption spectra show that the width of the pore size distribution in
gels increases as the [HF] increases [183,184]. A wider pore size
distribution implies a wider particle size distribution. A wider
particle size distribution allows more efficient packing, so for a given
average particle size Dfa will increase as the width of the particle size
distribution increases. Therefore as Db decreases rapidly as [HF]
increases, despite the pore size distribution increasing in width, it is
even more likely that the coordination number, Cn, of the gel particles
is decreasing as [HF] is increasing, even if rp is increasing.
German et al. [205] plotted the dependence of relative density on
Cn for monosized particles. At a relative density = 0.5, s Db = 1.1 g/cc
for fused aSi02, Cn 4 for random packing. For a distribution of
particle sizes Cn would be larger. The increase in Cn depends on the
width of the distribution. Therefore Cn is between 4 and a maximum of 8,
the value for random close packing.
274
Vasconcelos [183] calculated the genus and relative genus (which
are oc the Cn and the relative Cn) for OX, 2X and 5X gel types as a
function of T, ,but he did not calculate rp. He showed that the genus,
and therefore Cn, decreases as [HF] increases. He also showed that as Tp
increases, Cn decreases for OX gels, but increases up to 800C for 2X
and 5X before decreasing to zero as sintering occurs, mimicking the Dg
[T] behavior. The inference for silica gels is that Cp increases as Tp
initially increases, but increasing [HF] lowers Cn, as proposed above.
This means that the increase in rH seen as [HF] increases is caused by a
relatively large decrease in the Cn of the gel particles and a relative
ly small increase in their rp, as opposed to just an increase in rp.
In summary then, it is possible that as [HF] in these silica gels
increases, rp increases only slightly, while Cn decreases enough to
produce the observed decrease in Db, so the gel particles are already so
large in the HF free type OX silica gels, that the increase in rp caused
by the addition of HF does not change the average bulk structure of the
gels. Therefore Dgmax should not, and does not, change as [HF] increases.
3.3.6 The Raman Spectra of the Silica Gels
Curvefitting the W1. and Si0H Raman peaks. Three Gaussian
peaks were needed to curvefit the main Raman peak, W1, at 450 cm'1.
Figure 42(a) shows these three peaks for the 400C OXA gel at 435, 460
and 466 cm'1 (Table 7). These peaks have the medium, largest and small
est areas respectively. Figure 40(a) shows these three peaks for
Dynasil, where the three peaks exist at 417, 402 and 464 cm'1 respectiv
ely. The Raman spectrum of Dynasil is very similar to the spectrum of
dense silica gels. There are slight differences in the intensity of the
275
D1, D2 and SiOH peaks due to variations in and [OH], No conclusions
can be reached from changes in the shape, area and position of the three
W1 Gaussian peaks during densification. There is no experimental or
theoretical justification for 3 peaks, 3 is just the minimum number of
Gaussian peaks required to give a reasonable fit to the W1 peak.
During sintering the largest W1 curvefitting peak, 460 cm"1,
decreases in size as Db increases (Fig. 40 compared to Fig. 42). This
peak decreases because the main W1 peak, on its high wavenumber side,
and the SiOH peak (980 cm'1) decrease in intensity. This is accompanied
by a general broad decrease in intensity of the Raman spectrum between
500 and 1100 cm"1 as Tp increases. The VDOS of the structure responsible
for the Raman spectrum and the residual fluorescence background not
removed by the baseline correction both cause this decrease.
The decrease in the area of the dominant W1 curvefitting peak at
460 cm"1, for the reasons mentioned above, could be the cause of the
decrease in the area of the W1 peak visible in Fig. 61 above 800 C. As
the W1 peak area values plotted in Fig. 61 are the combined areas of the
three Gaussian peaks, it is not clear if the decrease in W1 peak area
above 800C is real or an artifact of the curvefitting technique.
To curvefit the 7001100 cm"1 region correctly, two Gaussian peaks
were required for the 979 cm"1 SiOH peak below 600700C. The highest
frequency peak is a narrow, intense, peak attributed to isolated Sig0H.
It is visible at 979 cm"1 in the 400C 0XA sample in Figs. 42(a) and 55.
The lowest frequency peak is a smaller peak at low T. It is visible at
962 cm"1 in the 400C 0XA sample in Figs. 42(a) and 54.
At low Tp the peak at 962 cm"1 is caused by the Si0 symmetrical
stretching vibration of Hbonded surface Sig0H groups. The Hbonding
276
reduces the Si0 bond strength by redistributing the charge. d(SiO)
increases and the stretching vibration frequency decreases. Some SigOH
groups are Hbonded to physisorbed H20 molecules. Their heats of adsorp
tion are higher than normal due to the very small radius of curvature,
so they stay adsorbed until relatively high T. The remaining SigOH
groups are Hbonded to adjacent SigOH groups close enough to form
Hbonds. The symmetrical stretching vibration of SiOR groups also makes
a contribution to the low Tp 962 cm'1 peak. [SigOH] decreases (Figs.
678) as Tp increases and the remaining physisorbed H20 is driven off.
The intensity of the 962 cm'1 peak decreases until at 500600C there
are only isolated SigOH left.
The curvefitting method used involved the successive fitting of
the Raman spectrum of a silica gel sample sintered to progressively
higher Tp. The output peak positions, heights and widths from the last
spectrum are used as the input for the next spectrum curvefitting
calculation. As Tp increases the intensity and width of the large 460
cm'1 Gaussian peak decreases in all six gel samples, while the 962 cm'1
peak only decreases in intensity and width up to 600700C. Above
600700C the small remaining fluorescence contribution to the back
ground disappears and the 962 cm'1 Gaussian peak shifts to 807 cm'1 in
Figs. 40(a) and 54. This Gaussian peak also increases in intensity and
width, concomitant with the decrease in the 460 cm"1 peak, as it shifts.
Therefore the increase in intensity of this Gaussian peak above 700C as
it shifts to lower frequencies is one of the reasons for the decrease in
intensity of the 460 cm'1 peak. As the former shifts to 807 cm'1 in Figs.
40(a) and 54, it accounts for more and more of the intensity of the
600900 cm'1 region at the expense of the latter.
277
When only isolated Sig0H groups remained, the 962 cm'1 peak was
still needed to obtain a good fit to the reduced spectrum, but it had
shifted to 807 cm'1 as shown in Fig. 54. It is visible at 807 cm"1 in
Fig. 40(a) as the broad peak below W3 (800 cm'1) in the Dynasil spec
trum. This single peak is the minimum number of additional peaks
required, besides the peaks assigned to the vibrational modes Wj TO, W3
LO, SiOH and TO, to curvefit the 7001100 cm'1 region above 600
700C. An additional peak does not produce a significant decrease in the
value of x2
Seifert et al. [163] also curvefitted the 7001350 cm'1 region of
the thermally reduced Raman spectra of fused aSi02. They used two
Gaussian peaks at 732 and 881 cm'1 to replace the one at 807 cm'1 used in
this investigation. In a later paper Mysen et al. [164] curvefitted the
larger 3001500 cm'1 region. They appear to have performed a larger
baseline correction, so the intensity in the 6001000 cm1 region was
significantly reduced compared to [163]. Consequently Mysen et al. [164]
only needed one Gaussian peak at 896 cm'1 to curvefit this region. Even
with such a large baseline correction, though, Mysen et al. [164] still
needed a peak to curvefit the spectrum.
Seifert et al. [133] curvefitted the reduced spectrum of aSi02
A
compacted via compression. They needed a Gaussian peak at 890 cm'1 in
every spectra to obtain a satisfactory fit to the W3 and W^ peaks.
The broad 807 cm"1 peak required to curvefit the silica gels in
this investigation therefore concurs with the results of Mysen et al.
[164] and Seifert et al. [133], There might be a vibrational mode in
this frequency range, but it would only be present in low concentra
278
tions. The Raman peak it produces is not very intense and is obscured by
other more intense peaks, i.e. the W3 peak at 800 cm'1.
Structural assignment of the curvefitted W2 peak. This broad peak
only appears when curvefitting fused aSi02 and silica gels. It could be
just a baseline correction. It could be real and due to a vibrational
mode of the structure but be invisible at low Tp due to the problems of
curvefitting overlapping peaks.
Several investigators have found peaks in this area. Lucovsky [98]
discussed a peak in the 900950 cm'1 range. He did not show a spectra or
discuss the shape or intensity of the peak. He assigned it to a non
bridging 0 atom, C.,'. McMillan [69] also discussed a peak seen at 910
cm*1 in wet and dry fused aSi02 samples which did not scale with any
defect peaks. He said it occurs in the region commonly assigned to the
symmetric Si0 stretching vibration of a =Si0' or =Si=0 group.
Galeener [92] assigned the outofphase stretching of an isolated
silica tetrahedron to around 990 cm'1. He associated this mode with the
stretchingtype motion which occurs at the theoretical W2 band edge. He
explained that this theoretical mode had a low Raman intensity due to
its asymmetrical vibration and a small Raman coupling coefficient. The
broad 807 cm'1 peak in Fig. 40(a) the 896 cm'1 peak found by Mysen et
al. [164] and the peak in the 900950 cm"1 range discussed by Lucovsky
[98] and McMillan [69] could be this theoretical W2 mode [92].
Since Lucovsky [99] and McMillan [69] do not actually show any
Raman spectra containing the peak they discuss, neither the intensity or
position of this peak are clear. It could be the Si0 stretching
vibration of bulk SiOH groups imbedded in fused aSi02 (970 cm'1). As
279
the frequency of this peak is slightly above the 900950 cm'1 region,
this is unlikely.
3.3.7 Separation of the Condensation and Viscous Sintering Processes
Plotting the properties of silica gels as a function of their bulk
density, Db, (Figs. 34(b) and 65) supports the conclusion reached by
Krol et al. [247] that there are two distinct processes occurring in
silica gels during densification. These are the completion of the
condensation reaction, which occurs at lower Tp, and pore closure during
viscous sintering, which occurs at higher T As Tp increases the
condensation reaction is completed with little or no change in Dfa while
both Dg and [D2] increase significantly up to their maximum values. This
is also the Tp range in which most of the weight loss occurs (Fig. 38).
Above D the rate of weight loss and [D,] both decrease as D. starts
to increase until Vp = 0.0 cc/g. The completion of the condensation
polymerization reaction and the start of viscous sintering process can
overlap. The degree of overlap depends on many variables, including the
heating rate and the texture and structure of the silica gel. A small
change in [OH] and the NBO/BO ratio [5] has a large effect on the
viscosity i of a gel and the temperature Tdb at which viscous sintering
starts. Therefore whatever controls the condensation rate controls Tdb
and the degree of overlap of the condensation reaction and pore closure.
When HF is added to a silica sol, the condensation polymerization
rate increases, leading to a smaller [OH] concentration and surface area
and a larger average pore radius. This increases Tdb. This is shown in
Figs. 35 and 36, where Db and Sg stay constant to higher Tp as [HF] in
creases in samples OX, 0XA, 2X, 2XA, 5X and 5XA. At a particular T, [OH]
280
is decreased by sintering in an atmosphere free of H20, which also
increases Tdb. This can also be seen in Figs. 35 and 36, where Db and Sg
stay constant to higher Tp in samples 2XA and 5XA, sintered in dry
helium, compared to samples 5X and 5XA, sintered in humid Florida air.
The control of [OH] Sg and rH by [HF] and of [OH] by sintering
atmosphere have the same influence on the shape of graphs plotted
against Db. Increasing [HF] and decreasing [OH] both cause: a) Db to
change less before the dependent property, such as Dg, [D2] Sg or a
Raman peak position or area, reaches its minimum or maximum, b) Tdb to
increase, and c) the degree of overlap of the completion of the conden
sation polymerization reaction and the start of viscous sintering to de
crease. Increasing [HF] and decreasing [OH] causes the condensation
reaction to go to completion at the lowest Tp possible, which causes the
viscosity to increase more quickly so the gel has to be heated to a
higher Tp before the viscosity at which viscous sintering can occur is
reached. In other words a smaller [OH] increases rÂ¡ for a particular Tp
so sintering starts at a higher Tdb. The magnitude of this effect
depends on the heating rate [5].
In Fig 32(a) Db does increase slightly while Dg increases to Dsmgx.
These gel samples were fully hydroxylated so the viscosity was low
relative to the helium pycnometry samples and viscous sintering occurred
at the lowest Tdb possible. In Fig. 34(b) Dg increases to Dgmgx with
little or no increase in Db because the condensation reaction was
completed at the lowest possible Tp with no loss of pore volume. The
increase in Db seen during the condensation phase is smaller the larger
the [HF] concentration and the drier the sintering atmosphere, i.e., Db
stays constant to higher Tp as [HF] increases and the viscosity increas
281
es. This has the effect of moving the Tdb of the viscous sintering
region to a higher starting T. Therefore increasing [HF] and the
viscosity have the same effect on the dependence of Dg on Db. This is
because increasing [HF] causes the structure to look more like a high pH
catalyzed gel, i.e. more colloidal in appearance with a lower [SiOH].
Dg decreases above Tg[nax as viscous sintering starts causing pore
closure and Db increases until densification is completed. Dg and Db
have the same value if there are no closed pores in the dense silica
gel. Krol et al. conclusion [247] is also supported by the relationship
between Dg and Sa which exhibits the same type of behavior as Fig 34(b) .
3.3.8 Thermal Dependency of D., Trisiloxane Ring Concentration
Figure 65 shows the dependency of the D2 trisiloxane ring concen
tration, [D2], on Db, while Figure 54 shows the Tp dependency of [D2] for
these silica gels. Generally, as the D2 rings form on the pore surface,
the OX type gel, with the largest Sa, would be expected to have the
largest [D2] and the 5X type gel the smallest [D2]. As Tp increases, [D2]
increases faster in the order OX > 2X > 5X, so [D2] increases fastest in
the gel with the smallest rH. The maximum [D2] is very similar in the 2X
and 5X type gels, yet their Sg are different. The sharp radius of curva
ture that causes D2 rings to form more easily at low Tp might also
prevent as many D2 rings forming per nm2 at higher T.
Figure. 65 shows that for all three gel types [D2] increases until
Tdbi when Db starts to increase. As Tp increases further, Db increases
and Sg decreases as viscous sintering starts, while the D2 surface
concentration, [D2]/[Wt]/Sfl) increases continuously (Fig. 66). Therefore
the increase in [D2] stops, not due to the completion of any particular
282
mechanism, but because D2 rings are lost faster as Sg decreases than
they can be replaced by new [D2] ring formation. This also explains why
2X and 5X type gels have similar maximum [D2]. The 5X type gel retains
Sg to a higher Tp at a higher [D2] surface concentration, while the 2X
type gel loses Sg at a lower T, preventing [D2] from increasing as far
as it could if it retained Sg.
3.3.9 Comparison of Dvnasil and Dense Silica Gels
Table 8 shows that dense silica gels have smaller [D2]/[Wt] larger
[SiOH]/[Wt] and larger 0 values than the Dynasil sample, all of which
should cause smaller Dg values than for Dynasil (which is a commercial
dense Type III asilica with Dg = 2.2030.025 g/cc measured using the He
pycnometer). Yet the fully dense gels have larger Dg values than
Dynasil. Some residual metastable high density silica gel structure
might still be present in the dense gels causing this anomaly. Heating
these gels to above Tg would cause these structural properties to
approach those of Dynasil.
Table 8. A comparison of the properties of densified metalalkoxide
derived silica gels and Dynasil.
Sample type
OXA
2XA
5XA
Dynasil
Ds (g/cc) from
He pycnometry
2.230
2.230
2.219
2.203
[D2]/[Wt]
0.0068
0.0089
0.0148
0.0174
[SiOH]/[Wt]
0.0120
0.0002
0.00018
0.0008
6* ()
134.0
134.0
133.6
133.1
Calculated from the gel's Raman spectra using SenThorpe theory [91].
283
3.3.10 Relationship Between the W, and Raman Peak Positions and D_
Above Dsmax, when the structure of the silica gels is identical in
composition to fused aSi02, the observed decrease in Dg can be intu
itively and empirically related to changes in the Raman peak positions
[70], as discussed in the following section.
3.3.11 Molecular Orbital Explanation of the Dependence of dCSiO') on 9
First, the empirical observation that d(SiO) decreases as 6
increases can be explained using molecular orbital theory. As Dg de
creases towards the equilibrium density of fused aSi02 = 2.20 g/cc, the
molar volume Vm increases. For a 1% increase in 6, d(SiO) decreases by
0.0774% [74], so the molar volume of aSi02 is determined by 6 and not
d(SiO). Therefore the =Si0Si= bridging bond angle, 9, increases (to
the average value of fused aSi02, 6 144, when Vp = 0.0 cc/g) as Vm
increases [41] and the associated bond strain decreases. The overlap
between the 0 p7T orbital containing the lone pair electron and (the
originally empty) Si dir orbitals increases as the 7T bonding increases,
so the delocalization of the 7r electrons increases. This causes the
covalent nature of the bond to increase.
The covalency of the Si0 bond determines its directionality,
which is described by the directionality ratio r Ka/Kg. Increasing the
k bond causes r to increase as the related ionic nature decreases. The
Si0 bond strength is characterized by the force function Kg (N/m). The
force function is equal to the slope of the bond's potential energy
well. As the (dp)7r orbital overlap increases, the BornMayer potential
well deepens and Kg increases. Kg is inversely proportional to the cube
root of the bond length, so d(SiO) a Kg3, as described by the Badger
284
Bauer equation [206,p.243]. Therefore as 8 increases, Kg increases and
d(SiO) decreases [70].
Walrafen et al. [134] explain the increase in d(SiO) (and 6) as 9
decreases in terms of steric considerations. As 8 decreases, the two
tetrahedra connected by the bridging 0 bond come into contact and the
repulsion between them increases because SiO^" tetrahedra are incom
pressible in compression. The repulsion is counteracted by the increase
in d(SiO) and the counter rotation of the tetrahedra around the Si0
bonds of the nonlinear SiOSi bond. As 8 increases, d(SiO) decreases
and the 1060 and 1190 cm"1 Si0 asymmetric stretching (AS) vibration
peaks increases in frequency. This occurs because as 8 increases and
d(SiO) decreases, the Si0 stretching Born potential energy well, E =
f(d(Si0)}, narrows (Fig. 5). E is the potential energy. The central
force function, Kg a dE/d[d(Si0)], increases so the AS peak increas
es as Dg decreases, which is shown experimentally in Figs. 32, 58 and
59. This is in agreement with molecular orbital theory, which explains
the increase in Kg as an increase in the covalency of the bond.
If the covalency increases as Dg increases, the directionality
ratio r * Ka/Kg must increase. This is seen by Revesz [70] for silica
polymorphs above 2.33 g/cc. As Kg and r increase as Dg decreases, KQ
must increase more than Kg for a given increase in r. Therefore the
OSiO Born potential well, E = must narrow more quickly than the
Si0 stretching Born potential energy well as d(SiO) decreases.
As 8 increases the W3 800 cm"1 Si0 symmetric stretching (SS)
vibration peak, which involves a =Si0Sis bending vibration occurring
at right angles to the AS vibration, decreases in frequency. As 8
increases and d(SiO) and Dg decrease, the SiOSi Born potential energy
285
well, E = f{0}, broadens (Fig. 5), so the SiOSi noncentral force
function, Kr = dE/d0, decreases and the frequency of the W3 SS peak de
creases. This is shown experimentally in Figs. 32, 56 and 57.
As Tp increases above Tsmax, Dg of type OX, 2X and 5X silica gels
decreases below so Vm increases. As V increases, 6 increases. The
smax m m
empirical inverse relationship between 9 and d(SiO) (equation 2)
implies that as 9 (and r) increase, d(SiO) decreases and Kg increase.
Therefore the frequency of the W4 LO Si0 stretch vibration increases,
the associated wavelength decreases, and the wavenumber increases, i.e.
W4 LO should increase as Dg decreases, which is exactly what is seen
experimentally (Fig. 59). In contrast, Kg decreases as 8 increases so W3
TO should decrease above Tgmax, which is seen in Fig. 56.
Walrafen et al. [134] supports this interpretation of the depen
dence of the Raman peak positions of fused aSi02 on its average struc
tural properties, d(SiO), 8 and 8.
In the crystalline polymorphs of silica the IR 1100 cm'1 Si0
stretching vibration peak decreases 29 cm'1, from 1106 to 1077 cm'1, as
Dg increases 0.6 g/cc, from 2.27 to 2.87 g/cc [70]. In the 0XA silica
gel sample the equivalent W. LO Raman peak increases by 9 cm'1 from
about 1188 to 1197 cm'1 as Dg decreases from 2.30 to 2.23 g/cc. As Dg
decreases, 9 increases, d(SiO) increases and the LO vibrational
frequency increases, so the same mechanism appears to cause the peak
to decrease in both crystalline and gel silica.
As the size of cyclosiloxane rings increases the number of silica
tetrahedra in a ring increases and 8 increases. The frequency of the
Raman active oxygen ring breathing mode associated with these rings
decreases as 6 increases, so D2 = 605 cm'1 and D1 = 495 cm1. As 8
286
increases the BornMayer potential governing the frequency of the oxygen
ring breathing mode should broaden. The force function would decrease
and the mode frequency decrease. Figure 52 shows that D1 increases in
frequency below 700C, then decreases during viscous sintering. The D1
peak shift could be due to changes in the main 410 cm'1 peak, or related
to changes in the vibrational environment of these tetrasiloxane rings.
Figure 53 shows that the more strained trisiloxane D2 rings are almost
independent of Tp until the gels are fully dense and only bulk D2
trisiloxane rings remain.
The relationship of the dihedral angles, 6 and A, to 0 and d(SiO)
has not been calculated from MO theory. Walrafen asserts from analysis
of Raman spectra that the dihedral angles and d(SiO) decrease as 6
increases [134].
3.3.12 Theoretical Relative D_ Calculation
Raman spectra can also be used to probe the =Si0Sin structure of
aSi02. Information about the changes occurring during sintering can be
obtained by quantifying the W3 and peak position dependence on T. The
W3 and Raman peak positions have been related to the =Si0Sis silica
gel structure which cause these Raman peaks by the SenThorpe central
force function theory [912]. This theory is reviewed in the literature
review section on modelling the vibrational behavior of aSi02. The
absolute 9 values calculated from this theory are about 10% too small.
Therefore the absolute values cannot be used for comparison to experi
mentally determined 0 values, but the relative changes in 9 can be
compared using the absolute changes in 6 in degrees or using the percent
relative change in in %. The relative Dg of the silica phase giving a
287
value of 9 can be calculated from 9 using a simple model discussed
below. This calculated relative Dg can be used for comparison.
Calculation of 9 from W, and W^. Equations (9) and (10) were
developed from the SenThorpe theory. They describe the dependence of W3
and W4 on two unknown variables, Kg and 9, and the atomic masses of Si
and 0. These two equations contain two unknowns. Both unknowns can be
alternatively eliminated via substitution of a peak position for an
unknown variable. This produces equations (11) and (12). Galeener [92]
showed that the baremodes of W3 and lie nearer the L0 rather than
the TO modes in fused aSi02 so he used the W3 L0 and L0 peak posi
tions to calculate 9 and Kg.
The curvefitted W3 TO peak is much larger that the W3 L0 peak and
the baseline correction influences the size and position of the curvefi
tted W3 L0 peak much more then the W3 TO peak. Therefore the W3 TO peak
position is a more reliable indicator of the movement of the W3 peak
position during densification. In addition the W3 TO and L0 are only 40
cm'1 apart and they both decrease by 30 cm'1 during sintering, so the W3
TO peak was used instead of the W3 L0 peak in equations (11) and (12).
The W4 TO peak lies on the shoulder of the SiOH peak, so its peak
position is influenced by the size of the 980 cm'1 peak. The magnitude
of the influence is unknown. The LO peak is isolated from any other
peaks, so the LO is the best peak to use even if the baremode
does not lie near the LO peak.
For the Dynasil sample, using equations (11) and (12) and the
peak positions from Fig. 40 yields 9 = 133.1 and Kg = 553.2 N/m.
Substitution of the W3 TO peak positions from Fig. 56 and the LO peak
288
positions from Fig. 59 into equations (11) and (12) yields the variation
with Tp of 9 (Fig. 75) and Kg, respectively, for samples OXA, 2XA and
5XA gels. At 400C, Kg is 553.6, 554.8 and 556.1 N/m respectively. The
curvefitting peak position resolution is 1 cm'1 so Kg has a resolution
of 1.07 N/m. As Tp increases Kg decreases to 553.3 N/m for OX gels,
552.3 N/m for 2X gels and 552.7 N/m for 5X gels when they are fully
dense. An increase in Kg causes a decrease in d(SiO) so 9 should
increase as Tp increases, as seen in Fig. 75. The largest Kg decrease of
3.4 N/m = 0.62% occurs in the 5X gels. The observed decrease in Kg is
statistically significant but small, which correlates with the small
percentage decrease in d(SiO) observed in Fig. 76, where d(SiO) is
calculated from 9 using equation (2). The Dg oc 1/molar volume oc
l/d(Si..Si)3 a 1/03 oc d(SiO)3 a Kg9, so Dg oc Kg9. Therefore, since Dg
changes by 510%, only a small change in Kg was expected, and only a
small decrease in Kg was found.
D increases to Dom,v during densification. The T ov at which Demav
S SiTlaX w oillaA oIIIOa
is reached varies, but doesn't occur until 600C. If Dg variation with
Tp depended on the molar volume of the silica component of the gel, i.e.
if Dg was controlled by the density of the silica component of the gel,
as opposed to [OH] and [OR] then 9 would be expected to go through a
minimum at T,.
smax
Figure 75 shows the Tp dependence of 9 calculated from equation
(12). 9 has a resolution of 0.25. Within this resolution, 9 is at a
minimum at 400 for type OX, 2X and 5X gels, while Tgmax > 600C. At Tp =
400C, 9 is 127.5, 128.5 and 130 for type OX, 2X and 5X gels respec
tively.
Si O Si BRIDGING O ANGLE, THETA f]
289
(Thousands)
SINTERING TEMPERATURE, Tp CC]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 75. The dependence on the sintering temperature Tp of the bridg
ing oxygen bond angle, 8 () calculated from the W3 TO and the W4 LO
Raman peak positions using equation (11), for samples OXA (), 2XA (+)
and 5XA ().
Si O BOND LENGTH, d(Si O) [A]
290
(Thousands)
SINTERING TEMPERATURE, Tp PC]
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 76. The dependence on the sintering temperature Tp of the Si0
bond length, d(SiO) (), calculated from 6 in Fig. 75 using equation
(2), for samples OXA (), 2XA (+) and 5XA ().
291
In type OX gels 0 increases continuously as Tp increases above 400C to
0 = 134 at full density. In type 2X gels, 0 stays constant until 600C
and then increases to 134 at full density. In type 5X gels, 0 stays
constant until 700C and then increases to 133.6 at full density. This
compares with 133.1 for Dynasil. The largest increase in 0 = 6.5 =
5.1% occurs in the OX gels. 0 does not go through a minimum that
correlates with Tgmax, which is discussed later. Comparison of Fig. 75
with Fig. 34 shows that 0 does not correlate with D below T but does
correlate with Dg above Tgmax during viscous sintering.
Calculation of d(SiO') from 0 using an empirical relationship.
Equation (2) relates d(SiO) to 0 in silicates. Figure 76 shows the Tp
dependence of d(SiO) calculated from 0 using equation (2). d(SiO) has
a resolution of 0.00044 . At 400C, d(SiO) is 1.6377 , 1.6351 and
1.6319 for type OX, 2X and 5X gels respectively. After densification,
d(SiO) decreases to the same value, within the resolution of the
calculation, for all the gels = 1.624 . The largest decrease in d(SiO)
= 0.0135 s 0.83% occurs in the type OX gels.
Calculation of d(Si..Si) from 0 and d(SiO'). The density of the
silica phase causing the Raman spectra of the silica gels is determined
by its molar volume. The molar volume is proportional to the average
separation of the Si atoms in the middle of each silica tetrahedra,
which is the d(Si..Si) distance. d(Si..Si) is determined by 0 and
d(SiO) of the =Si0Si= connecting bridging bonds, and are related by
the equation d(Si..Si) = 2d(Si0)Sin(0/2).
292
Calculation of Relative from d(Si..Si). Amorphous silica is
isotropic so the molar volume is proportional to (Si..Si)3. The calcu
lated relative Dg of the silica structure causing the Raman spectra of
the silica gels equals its mass divided by its volume, so Dg a
l/[d(Si..Si)]3 a l/(2d(SiO)Sin(0/2))3. The dependence of d(SiO) on 9
is known (Fig. 76), so the relative Dg can be calculated from 9.
9 is calculated from the W3 and W4 peaks which are caused by
vibrational modes of the bridging 0 bonds, sSi0Si=. As Tp increases,
[SiOH] decreases as sSi0Si= are formed by the condensation reaction
which causes the weight decrease in the first place, so [=Si0Si=]
increases concomitantly. Therefore the weight of the structure causing
the Raman peaks from which 9 is calculated is constant or increasing,
i.e. not decreasing, as Tp increases, but if sSiOSis increase in
concentration then their relative mass is increasing, but the volume
increases in direct proportion to the increase in mass, so Dg is still
governed by 9 and d(SiO) .
The loss of the NBO bonds during weight loss might cause 9 to
decrease via trisiloxane ring formation, but above 400C the calculated
9 increases continuously (Fig. 75) and the calculated relative Dg
decreases continuously (Fig. 77) while the weight, which might be
causing 9 to decrease by this hypothesis, is decreasing (Fig. 38).
Therefore the weight loss does not appear to be related to 9. The weight
loss is related to Dg increase below Tgmax, via the loss of a low density
phase which does not affect 9.
CALCULATED RELATIVE STRUCTURAL DENSITY
293
SAMPLE OXA + SAMPLE 2XA 0 SAMPLE 5XA
Figure 77. The dependence on the sintering temperature Tp of the calcu
lated relative structural density, which is calculated from 8 and
d(SiO) as discussed in the text, for samples OXA (), 2XA (+) and 5XA
()
RELATIVE STRUCTURAL DENSITY
294
0.300 0.500 0.700 0.900 1.100
(Thousands)
SINTERING TEMPERATURE, Tp [C]
Figure 78. The dependence on the sintering temperature Tp, for samples
OXA (), 2XA (+) and 5XA () of the calculated relative structural
density (from Fig.77) and the experimental relative structural density,
calculated from experimental Dg data in Fig. 34 by assuming that at Tp =
400C the experimental Dg is equivalent to an experimental relative Dg
value of 1.
295
Figure 77 shows the Tp dependence of the relative Dg of the gels
calculated assuming Dg oc l/[d(Si..Si)]3. The relative Dg is calculated
relative to the fully dense silica gels, which have a relative Dg = 1 =
2.20 g/cc. At 400C, the relative Dg is 1.054 s 2.32 g/cc for type OX
gels, 1.046 = 2.30 g/cc for type 2X gels and 1.030 = 2.266 g/cc for type
5X gels.
Figure 78 shows the relative Dg calculated from 9 (called the
calculated relative Dg) compared to the experimental relative Dg calcu
lated from the experimental helium pycnometry (called the experimental
relative Dg) data in Fig. 34. The experimental relative Dg = (Dg at
Tp)/(Dg at 400C), so at Tp = 400C the experimental relative Dg = 1.00.
Tp = 400 is used as the reference Tp because the He pycnometry Dg are =
2.222 g/cc for type OX, 2X and 5X gels at 400C. Given the simplicity of
the model used to calculate the relative Dg from 9, the similarity of
the magnitude of the maximum values of the experimental and calculated
relative Dgmax is encouraging.
Below Tgmax, the calculated and experimental relative Dg have very
different Tp dependencies in Fig. 78. Therefore the calculated relative
Dg does not correlate with the experimental Dg below Tgmax. SenThorpe
model calculations show that 9 is at a minimum value (Fig. 75) and the
calculated relative Dg (Fig. 78) is at a maximum value by Tp = 400C
while the experimental Dg of the gels is still increasing, so another
mechanism apart from 9 decrease must also be causing experimental Dg
increase below Tgmax. This is expected because the Raman spectra from
which the relative Dg is calculated only characterizes the relatively
dense sSi0Si= silica structure, whereas the experimental Dg includes
both this relatively dense phase and the relatively low density low
296
density SiOH and SiOH phases. The other mechanism causing Dg increase
below Tsmax therefore involves the loss of SiOH and SiOR groups.
Above 700C the Tp dependencies of the calculated and experimental
relative Dg are not identical but do show similar trends. For each gel
type the calculated and experimental Dg reach full density at the same
Tp. For type OX gels, they both decrease from 1.32 at 700 at the same
rate to 1.0 at 900C during viscous sintering. For type 2X gels, the
calculated relative Dg decreases from 1.035 at 700C to 1.0 at 1000C
while the experimental relative Dg increases from 1.036 at 700C to
1.043 at 800C, before decreasing to 1.003 at 1000C during viscous
sintering. For type 5X gels, the calculated relative Dg decreases from
1.032 at 700C to 1.0 at 1120 while the experimental relative Dg
increases from 1.035 at 700C to 1.041 at 800C, before decreasing to
0.998 at 1120C during viscous sintering. Therefore the calculated and
experimental relative Dg decrease at similar rates above Tdb during
viscous sintering. Below T^ additional mechanisms, including the loss
of the low density phase, cause the differences observed between the
calculated and experimental relative Dg. These mechanisms are different
from the mechanism causing the changes observed in the calculated
relative D0 below T
s smax
3.3.13 29Si MASS NMR of Gels
Raman spectroscopy characterizes the vibrational modes of the
bridging oxygen bond, sSi0Si=, and its dependence on the bridging 0
bond angle, 6. 29Si solid state MASS NMR [35] experiments also charac
terize the bridging 0 bonds and its dependence on 9. Quantitative data
exists for the environmental dependence of the Si peak position on 9
297
[5]. The 9 of gels can be calculated from the Q4 peak position of their
MASS NMR spectra using the empirical relationship Q4 [ppm] = 0.58895 
23.2, R2 = 0.982 [5]. Using this equation and MASS NMR spectra, Brinker
et al. [5] showed that in A2 gel samples, Q4 sites have the same average
bridging oxygen bond angle, 6 = 149 s 111 ppm, at 200C and at 1100C
when the gel is fully dense.
The MASS NMR spectrum of the 600C A2 gel shows a broad peak with
a maximum at 107 ppm = 142. Brinker found that statistically accept
able curvefitting of this spectrum using the accepted peak positions of
91 and 101 ppm for Q2 and Q3 sites required a Q4 peak at 105 ppm =
139 [35]. This is equivalent to a change in 6 for the Q4 site, A9, from
149 to 139 which = 10 = 7.2%. Brinker did not analyze the corre
sponding Raman spectra using the SenThorpe central force theory to
calculate 9 from the positions of the W3 TO and LO peaks. These Raman
9 values could have been compared to his MASS NMR 9 values.
MASS NMR spectroscopic analysis was performed on type OX gel
samples heat treated to 180C and 810C. Within the resolution of the
NMR instrument the Q2 and Q3 Si site peaks positions did not change,
while their intensity decreased, confirming Brinker et al.'s observa
tions [35]. For a 180C type OX gel, rH 1.2 nm, MASS NMR spectroscopy
shows a Q4 peak at 111.0 ppm = 148.8, while at 810C Q4 = 107.2 ppm =
142.4. The decrease in 9 is A9 = 6.4 s 4.5% for type OX gels, while
A9 = 10 s 7.2% for Brinker's A2 samples.
There are several possible explanations for this difference in the
minimum value of 9, i.e. a shift in Q4 to 105 ppm at 600C for the A2
gel versus a slightly smaller shift to 107.2 ppm at 810C for the OX
gel. Since the 810C OX gel has been sintered to a higher Tp, Db is
298
larger so 0 has been through the minimum in 6 at a slightly lower Tp and
by 810C has started to increase as viscous sintering occurs. The
differences in the structure and texture of the gels are also involved.
Type OX gels are made from TMOS using a large R = 16 ratio, while
Brinker's A2 gels are made from TEOS, using a two stage hydrolysis gels
with a small R = 4 ratio. This influences many properties. The differ
ence in 6 is also caused by the curvefitting method used by Brinker. The
810C type OX peak position = 107.2 ppm is very similar to the
position of the peak maximum of the experimental MASS NMR spectra found
by Brinker for the 600C A2 sample, but he curvefitted this spectra to
give a smaller 0 value = 105 ppm = 139.
Vega et al. [177] showed, using MASS NMR, that during drying the
average 9 of a silica gel decreased by 5, from 150.8 to 145.7 for the
particular gels they examined. This equates to an increase in the
relative Dg of 3.0% calculated using the model relating 0 to d(Si...Si).
Figure 79 is a compilation of all the values of 0 calculated from
the MASS NMR, Raman and IR spectra discussed above [5,177,207]. The 0
values calculated from the Raman spectra of the type OX gels (+) have
been shifted, by adding 13, to allow them to be compared to the other
data. This shift is justified by assuming that the relative change in 0
calculated from Raman spectra is correct, but that the absolute magni
tude is too low because of the difficulty of precisely modelling the CRN
structure of aSi02. Figure 79 shows that initially after casting and
ageing the average 0 is larger in silica gels than the average 0 in
fused aSi02, then decreases during drying at 180C to a value similar
to fused aSi02. After drying, as Tp increases 0 continues to decrease
down to a minimum value at T av. When T increases above T 0
smax p smax
Si BRIDGING O ANGLE, THETA [*]
299
0.000 0.200 0.400 0.600 0.800 1.000
(Thousands)
SINTERING TEMPERATURE, Tp [C]
NMR [138] A NMR [187] X IR [266]
Figure 79. The dependence on the sintering temperature Tp of the bridg
ing oxygen bond angle, 6 [], calculated from the MASS NMR spectra of a
silica gel () [177], the MASS NMR spectra of an A2 gel (a) [5], the
peak positions of the IR spectra of a type OX gel (X) [207], the W3 TO
and W, LO Raman peak positions of sample OXA (+), and the MASS NMR of a
type OX gel (0)
300
increases during viscous sintering until, at full density when Vp = 0.0
cc/g, 6 has the same equilibrium value as fused aSi02.
3.3.14 Comparison of 6 Calculated from MASS NMR and Raman Spectra
Brinker shows 6 that increases from 139 at 600C to 149 at
1100C during densification, A$ = +10 s +7.25% [5]. The value for 6
that would be seen if the MASS NMR spectrum of a fully dense type OX gel
was measured would be similar to the dry OX gel, i.e. 148.8. There
fore 6 would increase from 142.4 to 148.8, Ad 6.4 s 4.5%, during
densification. Application of the SenThorpe central force model to the
Raman spectra of type OX gels shows that 6 changes from 128.6 at Tsmax,
Db = 1.257 g/cc, to 134 at 900C, Db = 2.20 g/cc, so A6 = +5.4 s 4.2%
and that the analyses of the MASS NMR and Raman spectra show the same
direction and size of change in 6 during the viscous sintering of type
OX gels above Tcm.v.
smax
The 4.2% increase in 6 of OX gels above T calculated from the
smax
Raman spectra equates to a 4.5% decrease in the relative Dg, calculated
using the model connecting 6 to d(Si..Si). This compares to an actual
decrease in Dg above Tgmax of 3.0% measured by He pycnometry, 2.7% by H20
pycnometry and 9.1% by N2 sorption. Calculating the relative Dg from the
MASS NMR 6 data yields a decrease in the calculated relative Dg of 4.1%
for type OX gels, and 6.8% for Brinker's A2 gels.
As explained above, the value of 6 calculated from the MASS NMR of
the 810C OX gel is not the minimum value of 6 seen in type OX gels
during sintering. Therefore the decrease in relative Dg in OX gels is
actually larger than 4.1%. How much larger is unknown, but the magni
tudes of the relative Dg decrease above Tgmax in type OX gels calculated
301
from Raman and MASS NMR spectra are similar. They are also smaller than
in A2 gels because the magnitude of the relative Dg of type OX and A2
gels depends on the structure of the gel, and these gels have different
structures. Dgmax of A2 is slightly larger than Dgmax type OX gel and 6 of
A2 at Tgmax is slightly smaller than 6 at Tgmax of type OX gels, so the
calculated relative Dg for A2 at Tg[nax should be larger than for type OX
gels. The calculated relative Dgmax for A2 is 1.073, so this prediction
is correct.
3.3.15 Explanation of the Increase of D_ to D at T
S SmaX SilloX
There are several possible mechanisms which could contribute to
the experimental increase in Dg to a maximum, Dgmax, during the initial
stages of densification. They include: a) weight loss of [OH] and [OR]
groups, b) structural relaxation via loss of excess free volume, c) D2
trisiloxane ring formation during condensation of adjacent surface SiOH
groups close enough to react, d) decrease in the NBO/BO ratio via the
formation of bridging SiOSi bonds, both bulk and surface, due to
completion of the condensation reactions, e) structural relaxation and
skeletal densification [5], and f) The presence of a metastable high
density silica structure in the gels which is present after drying but
before the gel is heated above 180C.
Brinker et al. [5] say that only condensation in the bulk silica
gel can cause Dg to increase, and that acid catalyzed gels possess
significant quantities of internal SiOH groups. The width of the SiOH
peak in the Raman spectra of silica gels could be due to internal bulk
SiOH as well as Hbonded surface SiOH. Internal condensation in the bulk
of the gel particles could be causing Dg increase without forming D2
302
rings, because Raman spectra show that most of the D2 rings form on the
internal pore surface and disappear during densification. Central force
model analysis of Raman spectra shows that 6 is a minimum by 400C, yet
weight loss is still occurring. Weight loss is due entirely to H20 loss
above 400C [5], so condensation is still occurring. We need to know
what are the relative contributions of each mechanism to the increase in
D to D at T measured in these acidcatalyzed silica gels,
s smax smax J
Weight loss. Figure 38 shows the TGA spectra of the type OX, 2X
and 5X gels, demonstrating that the overall weight loss decreases as
[HF] increases. Both [OH] and [OR] groups are lost by thermal oxidation
and condensation of SiOH forced into contact during viscous flow. It is
possible that the increase in Dg is due directly to the loss of the low
density fraction measured in the TGA spectra.
A OX gel losses 4.1% of its weight between 200700C (Fig. 38),
where 700C is the T, T mv, at which D reaches its maximum value, Dom=v.
SlTiaX S SnlaA
The 4.1% weight loss represents this low density fraction. It consists
mostly of surface OH groups with some bulk OH groups. The remainder is
made up of surface and bulk OR groups. If you assume that the density of
the fraction lost during heating is 1.0 g/cc, then the density of a
model containing 4.1% of the fraction with Dg = 1.0 g/cc and 95.9% of
the silica phase with Dg Dgmax at 700C = 2.30 g/cc, is (0.041+0.959)/
{(0.041/1.0)+(0.959)/2.3)) 2.184 g/cc. This is 5.06% smaller than
smax' This compares with a measured He pycnometry Dg value for type OX
gel at 200 C = 2.093 g/cc, which is 9.0% smaller than Dgmax.
Alternatively if the fraction lost during heating was the direct
cause of the 2.093 g/cc value, it would have to have a Dg = 0.041 /
303
[{(0.041+0.959) / 2.093) (0.959/2.30)] =0.67 g/cc. The type 2X gel
loses 3.35% (Fig. 38) of its weight between 200800C while Dg = 2.1344
g/cc at 200C and Dg(nax = 2.317 g/cc at 800C. For the Dg of the model to
equal the measured Dg at 200C, the fraction lost during heating would
have to have Dg = 0.65 g/cc. The type 5X gel loses 2.6% (Fig. 38) of its
weight between 200800C while Dg = 2.1647 g/cc at 200C, and Dgmax =
2.310 g/cc at 800C. So for the Dc of the model to equal the measured D0
s s
at 200C, the fraction lost during heating would have to have Dg = 0.64
g/cc. The Dg of the low density fraction calculated by this model for
type OX, 2X and 5X gels are surprisingly similar, 0.67, 0.65 and 0.64
g/cc, respectively.
The similarity infers that a correlation exists between weight
loss and Dg increase as Tp increases. The same mechanism might be
responsible for Dg increase in each gel and whatever constitutes the low
density fraction would be involved in this mechanism. These gels are
acid catalyzed gels with a large R ratio, so the low density fraction
consists mostly of surface silanol groups [5]. The gels turn brown in
the 200400C Tp range due to carbon formation during oxidation of the
OR groups, so the concentration of organic groups, [OR], is significant.
[OR] would have to be measured to find the exact concentration. Brinker
et al. [5,p.555] shows that sample A5 is the same as samples A2 and A3
except that R = 15.3, similar to the R = 16 used in type OX gels. A5
contains 0.01 OR/Si, 0.42 OH/Si and 1.79 bridging 0/Si, so [OR] is 2.3%
of [OH]. Type OX gels are likely to have a similar [OR]/[OH] ratio.
Structural relaxation. Brinker et al. [5] divides shrinkage in
gels into 3 regions. Region I, where weight loss occurs with little
304
shrinkage. Region II, where both shrinkage and weight loss are large,
though the shrinkage is less than in region II. Region III, where
shrinkage occurs via viscous flow with little weight loss which commenc
es near Tg for the corresponding fused aSi02 composition.
The relative magnitudes of the shrinkage and weight loss in the
different regions and the Tp ranges in which they occur depend on the
structure of the gel. The structure of a gel is determined by the
composition of the sol from which it is made. For type OX gels region I
occurs below 200C. Region II occurs between 200C and the Tp at which
densification is completed. Region III occurs between 800C and Tp at
which densification is completed, so it overlaps with region II (Figs.
35, 38). Region III depends on rH, [OH], rÂ¡ and Sg, so regions II and III
are more clearly separated for type 2X and 5X gels.
Brinker et al. [5] explain gel shrinkage in region II. It is due
to a) the continuation of the condensation reaction associated with
weight loss, and b) the increase in Dg by structural relaxation causing
the loss of excess free volume with no associated weight loss. Structur
al relaxation will be most important for acidcatalyzed systems prepared
with low R values. Condensation occurs irreversibly under these condi
tions, freezing in a metastable structure far from equilibrium. This
contains relatively large concentrations of organic groups due to
incomplete hydrolysis and reesterification [5],
Both these factors promote a more open structure containing more
excess free volume. Therefore the large R ratio in type OX gels will
promote complete hydrolysis and less excess free volume, so less
structural relaxation can occur. Brinker et al. [5,104,2830] have
performed detailed investigations of the structural evolution of some
305
acid catalyzed silica gels. Specifically they examined sample A2, which
is a xerogel prepared by the twostep acid catalyzed hydrolysis of TEOS
in an ethanol solvent, with R = 5.1 and pH 0.8 measured using a
nonaqueous pH electrode near the gel point [5,p.555]. The mass fractal
dimension, df, is 1.9 for sample A2 [197].
Type OX gels, prepared by a one step acid catalyzed hydrolysis of
TMOS with no solvent, using R 16, gives pH = 0.96 one hour after
adding the TMOS to the acidified H20, measured using an aqueous pH
electrode. The addition of HF to a type OX composition to make type 2X
and 5X gels gives similar pH values, e.g., pH = 1.02 for a 2X gel.
Increasing pH and R gives a denser, more colloidal structure, leading to
an increase in df [197]. The value of df for type OX gels is unknown,
but Schaefer et al. [197] found that df is 2.11 for sample A3. A3 is
similar to A2 except that R is 12 for A3 and 5.1 for A2 [5],
The conditions under which A2 and OX gels are made are different,
which causes differences in the structures of the dried gels. These
differences involve, for type OX, a higher percentage completion of the
hydrolysis and condensation reactions leading to a more crosslinked,
denser structure with less excess free volume and a higher df than A2.
This causes Dg of type OX gels at 200C to be larger than for hi, 2.094
g/cc versus 1.7 g/cc [5].
The exact differences in structure are difficult to quantify, but
Brinker states [5,2829,32] that sample A2 gives a measurable DSC
exothermic peak of 4.7 cal/g (19.7 J/g) between 400700C [35]. This is
assigned to structural relaxation. A type OX gel does not show a DSC
peak above 300C, so the ratio of the number of nonbridging 0 atoms to
the number of bridging 0 atoms (NBO/BO) must be significantly smaller in
306
OX gels than in A2 (NBO/BO is a measure of the percentage completion of
the condensation reaction). This causes a denser structure with less
excess free volume and a larger Dg at 200C in type OX gels than in this
A2 gel.
Brinker et al. calculated the Dg of A2 (Fig. 21) from Vp (measured
by N2 sorption) and Db. They obtained values of Dg 1.76 g/cc at 200C
and DclTiav 2.35 g/cc at T = 700C [5]. For type OX gels the same
technique gives Dg = 2.22 g/cc at 200C and Dgmax = 2.43 g/cc, while
helium pycnometry gives Dg = 2.092 g/cc at 200C and Dgmax = 2.299 g/cc
at T 700C. The difference in Domav at 700C can be explained by the
different techniques used to measure Dg. A2 has a smaller Dg at 200C
and a larger increase in Dg between 200600C so the mechanisms contrib
uting to the increase in Dg in A2 gels must make a smaller contribution
in type OX gels. The exothermic structural relaxation DSC peak measured
for A2 was 23 J/g. This is a large DSC peak so a peak of this size can
be measured accurately and easily. As no DSC peak is visible for type OX
gels in the same Tp range, the excess free volume must be significantly
smaller in OX gels than in A2. The small Dg at 200C for the A2 gel is
therefore related to its large excess free volume compared to OX type
gels, as well as the SiOH and SiOR concentrations.
The A2 gels might have another mechanism causing the small Dg at
200C and the large increase in Dg by 700C but from the experimental
evidence it is more likely that the same mechanisms are occurring in A2
and type OX gels. The magnitude of the excess free volume associated
with the DSC exotherm is much larger in A2 gels than in type OX gels,
due to the more open structure of the A2 gels. The decreases of this
excess free volume during structural relaxation, combined with the
307
decrease in [SiOH] and [SiOR] contributes to the larger increase in Dg
observed in A2 between 200700C than in type OX gels.
At 200C the Dg of type 5X is > Dg of type 2X gels which is > Dg
of type OX gels, so the excess free volume of these HF catalyzed gels is
even smaller than OX. Their Sg, and therefore their bulk [Sig0H] ,
decrease in the reverse order to Dg above, which also contributes to the
observed differences in Dg at 200C. The same mechanisms produce the
increase in Dg below Tgmax in these gels as in the A2 gel and the type OX
gels, i.e. the loss of a low density phase and excess free volume. The
decrease in the excess free volume of the type 2X and 5X gels occurs
because the F ions from HF acts like a base catalyst.
Cyclic trisiloxane ring formation. The shrinkage in region II
involves both structural relaxation and condensation. The condensation
reaction produces trisiloxane rings on the internal pore surface of
gels. As discussed in the literature review, Raman spectroscopy reveals
the existence of the formation of D2 trisiloxane rings in silica gels
above 200C. Brinker suggested that the formation of D2 rings could be
the cause of the increase of Dg above 2.20 g/cc, due to their compact
nature [31].
The relationship between fP2l and SiOHI. The curvefitted Raman
peak areas are proportional to the concentration/g of gel, i.e. the mass
concentration (#/g). For example, [D2]/[Wt] (Fig. 64) gives the # D2
rings/g. This is related to the concentration/unit surface area, # D2
rings/m2, by Sg (m2/g), i.e. (# D2 rings/g)/(m2/g) # D2 rings/m2.
308
The D2 mass concentration, [D2]/[Wt] (Fig. 64), does not correlate
with [SiOH]/[Wt] (980 cm'1, Fig. 67) or [SiOH]/[Wt] (3750 cm'1, Fig.
71) as Tp increases because Sg is decreasing (Fig. 36), so the mass D2
concentration does not correlate with the mass SiOH concentration. On
the other hand, the D2 concentration/m2 [D2]/[Wt]/Sg, (Fig. 66) does
correlate with the Sis0H concentration/m2, i.e. both [Si0H]/[Wt]/Sg
(980 cm'1, Fig. 68) and [SiOH]/[Wt]/Sa (3750 cm'1, Fig 72), as Tp
increases, so [D2]/Sg increases as [Si0H]/Sa decreases. Stoichiometri
cally, 2 SiOH groups disappear during the formation of one D2 ring, so
[SiOH] should decrease twice as fast as [D2] increases. Calculation of
concentration from a Raman peak area requires knowing the coupling
coefficient Cb. If D2 and SiOH have similar Cb values, then
[SiOH]/[Wt]/Sg should decrease twice as fast as [D2]/[Wt]/Sa increases as
Tp increases. Examination of Figs. 66, 68 and 72 shows that the relative
decrease in [Si0H]/[Wt]/Sg is roughly twice as large as the increase in
[D2]/[Wt] as expected [5].
Possibility of D, formation occurring by 400C. Roughly 50% of the
surface Sig0H groups in aSi02 are lost between 100400C [189190].
The surface [Sig0H] on a fully hydroxylated fused aSi02 surface is
about 4.9 OH /nm2 Not all the Si3 atoms in a D2 ring have to be Sig0H
groups. A minimum of 2 Si3 atoms per D2 ring have to have been Sig0H
groups during the ring formation because they take part in the condensa
tion reaction forming the ring. Therefore Brinker et al.'s [5,p.647]
estimate that a maximum of 4.5 Sig atoms/nm2 are involved in D2 rings is
approximately equal to 2 D2 rings/nm2 in an A2 gel dehydroxylated in a
hard vacuum at 600C. As discussed in the section on water absorption
309
(Chapter 4), this is about twice as large as [D2]/Sa in a type OX gel,
so [D2]/Sg 1 D2/nm2 As two SigOH groups react to form a D2 ring, then
2 x 1 2 SisOH groups/nm2 are required to form [D2] in a type OX gel.
Sample OXA reaches its maximum [D2] by 400C. Approximately 50% of the
surface OH groups are left on aSi02 by 400C [189], i.e. 4.9 [0H]/nm2
x 0.5 2.45 [OH]/nm2, so 2.45 [0H]/nm2 have disappeared due to conden
sation reactions. This decrease is large enough to cause D2 ring forma
tion by 400C, and supports the experimental observation that all the D2
rings form in the 100400C region in type OX gels, i.e. by Tp = 400C.
Is the Increase in D_ up to T due to FD.,1 increase T311? The D2
peak areas of type OX, 2X and 5X silica gels have been quantified by
curvefitting their Raman spectra (Figs. 6466). Dg of type OX gels has
been measured by three different techniques (Fig. 32(b)). Dg of OX, 2X
and 5X gels has been measured using He pycnometry (Fig. 34).
The shape and magnitude of the D versus T plot for silica gels
s p
depends on many variables. These include the experimental Dg measurement
technique, the size of the gel and its structure and texture as repre
sented by rÂ¡, [OH], rp, rh, etc. The D2 versus Tp plot for Brinker's A2
sample in Fig. 21 [28,29] shows that Dsmax 2.35 g/cc at 700C when
measured by N2 sorption. In comparison the N2 sorption Dsmax of OX gels
is 2.42 g/cc. The Raman spectra of an A2 gel at 680C in Brinker et al.
[31] show that [D2]/[Wt] in A2 gels is significantly larger than in type
OX gels at 600C (Fig. 64). A2 and type OX gels have measurable differ
ences in structure (due to the way they were made), so the size and
magnitude of the Dg versus Tp plot depends on the way the gels are made.
310
Comparison of Figs. 32(b) and 64 shows that for type OX gels
[D2]/[Wt] and Dg do not show the same Tp dependency up Tgmax. Fig. 80
summarizes these data for type OX gels. It shows the linear regressions
of the three experimental Dg data sets (plotted as a percentage change
relative to Dg = 2.20 g/cc) compared to [D2] (plotted as a percentage of
[Wt]). [D2] is constant at 5.7% between 400800C while Dg goes through
a maximum. [D2] = 0 in gels at 200C [5], so [D2] increases to its
maximum in OX gels between 200 and 400 C, while Dg increases to Dgmax
between 200C and 600C. Therefore the dependence on Tp of [D2] in type
OX gels does not correlate with the Tp dependence of Dg up to Tgmax.
In Figure 80 all the curves decrease to 0% by 800C except for
the linear regression of the change in the He pycnometry Dg, which
finished sintering at a higher Tp. This is because the latter was
measured on a powder while the former were measured on monolithic gels,
and the powder densified at a higher Tp because it had a lower [SiOH] .
Comparison of Figs. 34(a) and 64 shows that [D2] and Dg are also
not related up to Tgmax in the type 2X and 5X gels. Fig. 81 summarizes
this data. It shows the He pycnometry Dg values from Fig. 34(b) as a
percentage change relative to 2.22 g/cc compared to [D2] as a percentage
of [Wt] Between 400C and 700C the Dg versus Tp behavior is very
similar for these gels, while the thermal dependence of [D2] is very
different for each gel. At 400C, [D2] is 5.6% for OX gels, 3.4% for 2X
gels and 1.6% for 5X gels, while Dg is 2.20 g/cc for all three gels.
Therefore [D2] does not control the Tp dependence of Dg of the type 2X
and 5X gels below T either.
& smax
CHANOE RELATIVE TO FULLY DENSE SAMPLE
311
0.200 0.400 0.600 0.800 1.000
(Thousands)
SINTERING TEMPERATURE, Tp [*C]
Figure 80. The dependence, on the sintering temperature Tp for type OX
gels, of the experimental relative structural densities (calculated from
Fig. 32(b) and represented by the best fit linear regressions) {Dg 
1/((1/Db)V ) [] water pycnometry [ + ], He pycnometry [0]); the calcu
lated relative structural density (a) from Fig. 77; and the D2 trisilox
ane Raman peak area, [D2]/[Wt] as a percentage of the total Raman
spectrum area (X), calculated from Fig. 64.
CHANGE RELATIVE TO VALUE AT T = 4QCTC
312
(Thousands)
SINTERING TEMPERATURE, Tp fCJ
Figure 81. The dependence on the sintering temperature Tp of the experi
mentally determined relative structural density measured using He
pycnometry (calculated from Fig. 34(a) assuming a relative Dg = 1.00 at
Tp = 400C) and the D2 trisiloxane Raman peak area, [D2]/[Wt], as a per
centage of the total Raman spectrum area (calculated from Fig. 64), for
samples OXA, 2XA and 5XA.
313
In addition, [D2] of type OX gels increases rapidly up to Tp =
400C then stays constant between 400800C at [D2] 5.6%, yet type OX
gels show the largest increase in Dg between 400 and 800C, from 2.224
g/cc to 2.30 g/cc. In contrast, for sample 5XA, [D2] increases from
1.63% to 4.70% while Dg increases from 2.22 to 2.31 g/cc between 400C
and 800C, so for the same increase in Dg very different changes in [D2]
occur. Yet again, D2 formation cannot be the mechanism causing Dg
increase up to T
r smax
Above Tsmax, [D2] is correlated with Dg during viscous sintering.
In other words [D2] and Dg decrease at the same rate due to hS0Sh
bond breakage and reformation during pore closure when rÂ¡ is low enough.
This is responsible for the decrease in both Dg and [D2] above Tgmax.
This mechanism is different from the one causing Dg increase below Tsmax,
which in turn must be different from the one causing [D2] increase.
Comparison of the Tp dependencies of fDJ and the calculated
relative D. Figure 82 shows the Tp dependence of the calculated rela
tive Dg and [D2] (plotted as a percentage as of [Wt]) for each gel type.
Below T the relative Dc calculated from 6 does not correlate with
srnax s
[D2]. In the viscous sintering region above Tgmax they decrease at the
same relative rates, just like the experimental Dg and [D2] .
CHANGE RELATIVE TO FULLY DENSE SAMPLE
314
(Thousands)
SINTERING TEMPERATURE, Tp PC]
Figure 82. The dependence on the sintering temperature Tp of the calcu
lated relative structural density (from Fig. 77), and the D2 trisiloxane
Raman peak area, [D2]/[Wt] as a percentage of the total Raman spectrum
area and calculated from Fig. 64, for samples OXA, 2XA and 5XA.
315
3.3.16 Possible Structural Mechanisms of D_ Increase Below T...
s smax
When the molar volume of aSi02 is increased or decreased by
different techniques, i.e. compression, thermal expansion, etc., in each
case different mechanisms can be responsible for the volume change. For
example, the polymorphs of crystalline silica have different Dg, and the
Dg of type OX silica gels decreases during viscous sintering above Tg(I)ax.
Different mechanisms cause the changes in Dg seen in these two cases.
For the same change in the W4 PP, the Dg change seen in the crystalline
polymorphs of silica [70] is about 2.6 times larger than that seen in
the viscous sintering stage of type OX gels, so different mechanisms
must be responsible for the Dg changes observed.
Different methods of changing the molar volume of Si02 having
different mechanisms is also seen in quartz [208]. For example, differ
ent mechanisms are responsible for the molar volume changes associated
with thermal expansion and with pressure compaction. For a given ADS, 6
changes less and the tetrahedral tilt angle changes less during pressure
compaction than for the same ADg during thermal expansion. During
compaction, the rate of change of 6 is constant as the molar volume
decreases while tetrahedral distortion becomes more important and the
dihedral angle increases more slowly [208]. During thermal expansion the
rate of 6 increase is constant but increases more rapidly than during
pressure compaction for a given ADg, while the dihedral angle decreases
more rapidly as the molar volume increases and tetrahedral distortion
does not occur. For a given molar volume change, 6 changes 2.5 times
more during thermal expansion than during compaction.
Three methods of changing the density of aSi02 are discussed in
the literature review. These are: a) compressive force, b) fast neutron
316
irradiation and c) fictive temperature Tf variation. Other methods of
changing the density of aSi02 include thermal expansion [209], 7
irradiation [80], [OH] variation [209], thermal history [209], different
methods of manufacture [38], thin films versus bulk [141], etc.
The increase in Dg below Tgmax in gels might be caused by one of
the mechanisms causing the increase in Dg in fused aSi02 by a) b) or
c) above. The changes in [D2] and 6 for a specific increase in Dg in
fused aSi02 compacted by these three mechanisms can be compared with
the changes in [D2] and 6 in gels for the same increase in Dg to give
insight into the mechanism causing the Dg increase in gels.
Influence of Tf on D_ and FD^ 1 /fWt 1 in fused aSiO.. Galeener et
al. [56,100,113] investigated the relationship between [D2] and Dg in
fused aSi02 as a function of T# and neutron irradiation flux. They heat
treated samples of Suprasil W, a Type IV aSi02, to different Tf,
quenched them, measured the Raman spectra of each Tf sample, and then
calculated [D2] and the PP in each spectrum. Figure 12(a) shows [D2]
versus Df, where Df is Dg at Tf.
It is not stated in Fig. 12 or in the text in Galeener et al.
[56,100,113] whether the fractional area under the 606 cm'1 line is a
percentage of the main Raman peak at 450 cm'1, [D2]/[W1], or a percentage
of the entire spectra, [D2]/[Wt] The difference between these two
different ratios is 200 % in Mikkelson et al. [100], while the same
ratios only show a difference of 3050% for type OX gels, depending on
Tp. The magnitude of the difference depends on the size of the D2 peak.
Therefore it is important to know which area is presented in Fig. 12 so
that it can be accurately compared to gels. For one sample, Tf = 1050C,
317
a value of 3% is quoted for [D2]/[W1 ] and 1% for [D2]/[Wt] in Mikkelson
et al. [100], Based on this information Fig. 12 must be showing
[D2]/[Wt] since at Tf 1050C the fractional area 1.4% in Fig. 12(a).
Fig. 12 shows how much of the Dg increase in gels might be direct
ly attributed to the increase in [D2] Galeener's compilation of Tf and
neutron irradiation density dependence on [D2]/[Wt] in Fig. 12(b) shows
that an increase in Dg from 2.20 to 2.25 g/cc caused [D2]/[Wt] to
increase from 0.009 = 0.9 % to 0.204 s 20.4 %. Dg increases by 0.05 g/cc
as [D2]/[Wt] increases by 19.5 %, equivalent to 0.00256 g/cc per 1.0 %
increase in [D2]/[Wt] The linear regression equation which gives the
best fit to Fig. 12 is [D2]/[Wt] 3.902 x Df 8.57537, R2 0.99883,
where Df is Dg at Tf.
Mikkelson et al. [100] measured [D2]/[Wt] using French curves to
draw in the W1 shoulder under D2. For a specific peak, the peak area is
smaller measured using a French curve correction of the peak shoulder
than using Gaussian function curvefitting, so for a specific Tf the D2
peak area measured by curvefitting would be slightly larger, so for a
particular Dg, [D2]/[Wt] should actually be larger than in Fig. 12. The
exact increase in area would depend on the original D2 peak area.
Galeener did not experimentally determine Dg of the Type IV
Suprasil samples, but measured Dg from Bruckner' data [38] on the
dependence of Dg on Tf for different types of fused aSi02 (Fig. 1).
Examination of Fig. 1 shows that Mikkelson et al. [100] used the data
for the dependence on Tf of a Type II aSi02 in Fig. 12(a). But Suprasil
is a Type IV fused aSi02, which for a particular Tf has a smaller Dg
than a Type II fused aSi02 (Fig. 1). Figure 12 [100] shows that
[D2]/[Wt] 0.03 and Dg = 2.2054 g/cc for T^ = 1450C. Figure 1 shows
318
that for Tf 1450C, Ds = 2.2054 g/cc is for Type II, and Dg 2.20275
g/cc for Type IV, so [D2]/[Wt] 0.03 is actually associated with Dg =
2.20275 g/cc. Replotting Fig. 12 using the Type IV Dg values from
Bruckner [38] shows that for a particular Dg, yet again [D2]/[Wt] should
actually be larger than in Fig. 12. This means that as Tf increases the
increase in Dg associated with [D2] formation in the fused aSi02 sample
is smaller than shown in Fig. 12.
Mikkelson et al. [100] also measured [D2]/[Wt] from the Raman
spectra of neutron irradiated fused aSi02 samples made by Bates et al.
[119] who measured their Dg. Galeener compared this data to his data
for Tf aSi02 in Fig. 12(b). The [D2] of irradiated aSi02 and aSi02
with different Tf have a similar dependence on Dg, even though the
compaction mechanisms appear to be very different.
Figure 10 shows the dependence of the Raman PP of Suprasil as a
function of Tf. The W3 and W4 peaks can be used to calculate 6 and the
associated relative Dg using the SenThorpe theory [91].
Comparison of irradiated aSi02 with silica gel. The Raman spectra
of neutron irradiated fused aSi02 with Dg = 2.25 g/cc [119] can be
compared with the spectra of a OX gel with a similar D In the irradi
ated fused aSi02 the D2 peak appears to be broader and more intense and
have a larger area, while the D1 peak is similar in intensity. The main
W1 peak increases in frequency and narrows. In the irradiated aSi02
sample [SiOH] is too small to cause a peak. The W3 and peaks in the
Raman spectra of irradiated aSi02 move in the directions expected for
Dg increase [119]. At Dg = 2.204 g/cc, 0 is 133.7, giving a relative Dg
 1.00. At Dg = 2.252 g/cc, ADg = 0.048 g/cc, 6 is 129.5, A6 = 4.3,
319
giving a calculated relative Dg = 1.0342, an increase of 3.42%. There
fore a 1% increase in the relative Dg, calculated from 9, compares to an
actual increase in the experimental Dg of 0.0140 g/cc h 1.40%. In
comparison, for a fully dense type OX gel, Dg = 2.23 g/cc (Fig. 34) and
9 = 134.0 (Fig. 75) giving a calculated relative Dg = 1.00, and at
Tsmax Ds 230 S/cc ADs 07 S/cc = 32%* 6 128.6, A9 5.4,
giving a calculated relative Dg = 1.045, an increase of 4.5%. Therefore
a 1% increase in calculated relative Dg compares to an actual increase
in the experimental Dg of 0.0156 g/cc = 1.56%, so the relationship
between the W3 and peak positions (from which 9 is calculated) and Dg
is similar in type OX gels and irradiated fused aSi02
Influence of pressure compaction on D. and D.J Seifert et al.
[133] investigated the relationship between [D2] and Dg in fused aSi02
compressed in a solid medium, high pressure compaction apparatus. They
measured Dg, the Raman spectrum and the PP in each spectrum (Fig. 1 of
Seifert et al. [133] and Table 1 of Seifert et al. [133]). During
compaction Seifert et al. [133] found that [D2] was roughly constant as
Dg increased (Fig. 83) 9 and the calculated relative Dg can be deter
mined from the W3 and peak positions using the SenThorpe theory.
Comparison of the influence of rD=1 variation on in asilica
compacted using different compaction mechanisms. Figure 83 shows the
dependence of [D2]/[Wt] on Dg in aSi02 samples which has had their molar
volume changed by three different mechanisms. The [D2]/[Wt] of the type
OX gels in Fig. 83 are the curvefitted peak areas (Fig. 64). They have
been extrapolated from Tp = 400C down to 200C, where [D2]/[Wt] = 0 and
[D2]/[Wt] AS 96 OF TOTAL SPECTRUM AREA
320
EXPERIMENTAL STRUCTURAL DENSITY [g/cc]
Ds from He PYCNOM.
Figure 83. The dependence on their experimental Dg [g/cc] of the D2
trisiloxane Raman peak area, [D2]/[Wt] (as a percentage of the total
area of their respective Raman spectrum) for silica gel sample OXA (),
for fused aSi02 with increasing fictive temperature, Tf, [100], (repre
sented by the best fit linear regression), and for pressure compacted
fused asilica [133] (also represented by the linear regression).
321
Dg 2.092 g/cc. For fused aSi02 compacted using a compressive force
[133], the linear regression (R2 = 0.62) fitted to the measured
[D2]/[Wt] values (Fig. 83) shows that [D2]/[Wt] is roughly constant as Dg
increases. For fused aSi02 with different Tf, the linear regression (R2
= 0.96) fitted to the [D2]/[Wt] values in Fig. 12 is shown in Fig. 83.
[D2]/[Wt] increases very quickly as Dg increases in comparison to type
OX gels. Overall, for a specified increase in Dg, [D2]/[Wt] increases by
very different amounts in each system so different mechanisms must be
causing the increases in Ds, and increases in [D2]/[Wt] can not be
causing the increases in Dg.
Table 9 summarizes the Dg changes in type OX gels above and below
Tsmax an<* the associated changes in [D2]/[Wt] Table 9 shows the calcu
lated equivalent changes in Dg in pressure compacted fused aSi02 [133]
and fused aSi02 with different Tf [100] caused by the changes in the
magnitude of [D2]/[Wt] measured in type OX gels during sintering.
[D2]/[Wt] increases by 0.057 below Tgmax and decreases by 0.050 above
T _v in type OX gels. Below T ,v an increase in [D5]/[Wt] of 0.057 is
associated with an increase in Dg 0.21 g/cc (He pycnometry) in type OX
gels, which equates to an increase in = 2.2120 2.1975 = 0.0145 g/cc
in fused aSi02 with different Tf. In pressure compacted aSi02 the
increase in [D2]/[Wt] as Dg increases is so small that the increase in Dg
for an increase in [D2]/[Wt] of 0.057 can not be calculated. Above Tgmax
a decrease in [D2]/[Wt] of 0.050 is associated with a decrease of Dg =
0.070 g/cc (He pycnometry) in type OX gels, which equated to a decrease
in Dg 2.2120 2.1993 = 0.0127 g/cc in fused aSi02 with different Tf.
The mechanism causing [D2]/[Wt] to increase in fused aSi02 as Tf
increases is roughly an order of magnitude too small to directly cause
322
Table 9. Summary of a) Dg changes measured in type OX silica gels in
particular Tp ranges and the Db and [D2]/[Wt] change occurring in the
same Tp ranges, and b) the Dg change caused by a change in the [D2]/[Wt]
of the same magnitude as measured in the type OX gels in (i) Suprasil
with different Tf [100] > and (ii) pressure compacted fused aSi02 [133],
Type OX silica gels
Temperature
interval
200+500C
500*800C
800 CDense
Dg [g/cc] from
He pycnometry
2.09 2.30
(+10.0%)
2.30
2.30 2.23
(3.14%)
Dg [g/cc] from
H20 pycnometry
2.16 2.255
(+4.4%)
2.255
2.255 2.21
(2.04%)
Ds [g/cc]
(N2 sorption)
2.225 2.42
(+8.76%)
2.42
2.42 2.22
(9.0%)
Db [g/cc]
1.15
(+0.0%)
1.15 1.5
(+23.3%)
1.5  2.23
(+48.7%)
[D2]/[Wt]
0.0 0.057
0.057
0.057 0.007
Fused aSi02 with different Tf [100]
2.1975 2.2120
(+0.66%)
_
2.2120 f 2.1993
(0.58%)
Compacted fused asilica [133]
Dg is constant**
2.204 2.204
2.204
2.204 2.204
Calculated for a change in [D2]/[Wt] of the magnitude seen in OX gels,
calculated for a change in [D2]/[Wt] of the magnitude seen in OX gels,
showing no statistically significant changes because [D2] is constant
during compaction.
the measured increase in Dg in these silica gels. This infers that D2
rings formed via the SiOSi bond breakage and reformation which occurs
as Tf increases can only make a small contribution to the increase in Dg
below Tgmax in silica gels. This does not mean that D2 ring formation via
a condensation reaction in gels, as opposed to bond breakage and
reformation during Tf increase, cannot make a larger indirect contribu
tion to Dg increase via, for example, a large effective interaction
323
volume which could cause 6 in silicate rings adjacent to the D2 rings to
decrease, thus increasing Dg.
The dependence of [D2]/[Wt] on Dg (Figs. 34 and 64) for type 2X
and 5X gels is slightly different from type OX gels, but still very
different from the dependence on [D2]/[Wt] of the Dg of compacted fused
aSi02 and of fused aSi02 with different Tf.
The decrease in D above T as D. increases is due to viscous
s smax b
sintering as rÂ¡ decreases far enough for metastable structures to relax
and form thermodynamically more stable structures via =Si0Sis bond
breakage and reformation.
The effect of 6 variation on D_ during different densification
mechanisms. The relative Dg of compacted fused aSi02 can be calculated
from 6 (which is calculated from the W3 TO and LO Raman PP) in just
the same way as was done for silica gels. The relative Dg is calculated
from 0 which is calculated from the Raman spectra, so the calculated
relative Dg characterizes the aSi02 structure probed by the Raman spec
tra. Figure 84 shows the dependence on the experimental relative Dg of
the calculated relative Dg for the type OX, 2X and 5X silica gels,
compacted fused aSi02 [133] (represented by a best fit linear regres
sion) and fused aSi02 with different Tf [100] (also represented by a
best fit linear regression). The calculated relative Dg of the silica
gels is plotted so that the calculated relative Dg of the fully densif
ied gel is 1.0. The calculated relative Dg of the pressure compacted
fused aSi02 is calculated from the PP of the Raman spectra measured by
Siefert et al. [133] and is plotted so that the calculated relative Dg
of the fused aSi02 sample before compaction is 1.0. The calculated
CALCULATED RELATIVE STRUCTURAL DENSITY
324
Figure 84. The dependence on their experimental relative Dg (calculated
assuming Dg = 2.20 g/cc = 1.0) of the calculated relative Dg (calculated
from the W3 TO and W4 LO Raman peak positions using the SenThorpe
theory [91]) for silica gel samples OXA (), 2XA (+) and 5XA (0); for
fused asilica with increasing fictive temperature, Tf, [100] (repre
sented by the best fit linear regression); and for pressure compacted
fused asilica [133] (represented by the best fit linear regression).
325
relative Dg of the fused aSi02 with different Tf is plotted so that the
calculated relative Dg of the sample with = 900 C is 1.0. The arrows
on the plots of the calculated relative Dg of the silica gels indicate
their direction of change occurring during the increase in Tp. While Tp
increases to Tsmax, the calculated relative Dg stays roughly constant
while the experimental relative Dg increases to Dsmax because the in
crease in the experimental relative Dg is due to the loss of the weight
loss observed in the TGA spectra, which did not effect 0. Then, as Tp
increases above T m,w) the decrease in the calculated relative D is
roughly proportional to the decrease in the experimental relative Dg
(giving a slope of 1), as 6 increases. Figure 84 therefore shows that
for a specified increase in the experimental relative Dg, the calculated
relative Dg increases by very different amounts in each system.
For a given increase in Dg, the increases in [D2]/[Wt] and the
calculated relative Dg in fused aSi02 with different Tf are much larger
than the increases in silica gels during densification, which in turn
are much larger than the increases in pressure compacted fused aSi02.
Therefore for a specified increase in Dg, the increase in [D2]/[Wt] and
the calculated relative Dg of both compacted fused aSi02 and fused
aSi02 with different Tf is very different compared to both silica gels
and to themselves. This means that different mechanisms are causing Dg
and [D2]/[Wt] to increase in both these systems and in silica gels.
The increase in [D2]/[Wt] and the decrease in 0 in pressure com
pacted fused aSi02 [133] are much smaller than in aSi02 gels for a
specific increase in Dg, so the mechanism causing the increase in Dg
cannot be the same. 0 increases by only a small amount during pressure
compaction, so the dihedral angle, S, must be changing to allow more
326
efficient packing of tetrahedra in rings as Dg increases. Changes in the
dihedral angle, 6, do not affect the W3 and peaks in the Raman spec
trum of aSi02, so changes in S cannot be quantified by the SenThorpe
central force function theory. Changes in the dihedral angle do influ
ence the W1 main raman peak. Walrafen et al. [129] showed that the W1
peak narrows during pressure compaction, so the dihedral angle changes.
Bond breakage could be involved in the pressure compaction
process. If bonds broke and reformed with no change in 9 or ring
statistics, no volume change would occur unless more efficient packing
of the tetrahedra occurred with no change in 9. For bond breakage to
contribute to the increase in D$, a decrease in the molar volume must
occur, so the ring statistics must shift to a smaller average ring size.
This would cause a decrease in the average 9 value and in the width of
the 9 distribution. The bridging 0 bond angle, 9, calculated from the
TO and LO Raman peaks, increases only slightly during the pressure
compaction of fused aSi02 [133], as shown by the small increase in the
calculated relative structural density in Fig. 84, so the contribution
of bond breakage to the increase in the experimental Dg is small.
The increase in [D2]/[Wt] and the decrease in 6 (which equates to
an increase in the calculated relative Dg) in fused aSi02 with differ
ent Tf [100,113] are much larger than in aSi02 gels for a specific
increase in Dg so the mechanisms causing the increase in Dg cannot be
the same. The increase in [D2]/[Wt] and the decrease in 9 are so large
that bond breakage causing a decrease in the average ring size must be
the mechanism of Dg increase as Tf increases. The dihedral angle change
is small in comparison. A large Tf involves more thermal energy so bonds
break more frequently and can form less stable structures than at lower
327
Tf which are more compact and are locked in during quenching from Tf.
In silica gels, since the increase in calculated relative Dg
caused by the decrease in 0 is large enough to account for the decrease
in Ds observed above Tsmax, the increase in 0 via bond breakage must be
the dominant mechanism during viscous sintering. Bond breakage causes an
increase in the average ring size and a decrease in [D2]/[Wt] while the
contribution of the dihedral angle is relatively small.
When 0 is obtained from the MASS NMR spectra of gels, it is
calculated from the position of the peak of a broad Q4 band using a
regression equation derived from the relationship between the position
of the narrow Q4 peaks observed in the crystalline polymorphs of silica
and the 0 of each polymorph. The 0 values measured here, by Vega et al.
[177] and by Brinker et al. [35] from MASS NMR spectra thus actually
only give an average 0 value of the broad 0 distribution, V(0) which
occurs in aSi02. Therefore an average 0 of the gel is decreasing as Tp
increases from 200C to Tsmax in Fig 79. (V(0) can be extracted from both
MASS NMR spectra [178] and WAXS spectra [41].) Aujla et al. [178] shows
that D2 ring formation affects the width, shape and position of V(0).
This leads to the difficult problem of how to compare size distributions
with different heights and widths using just a single number such as 0.
Since the initial [D2]/[Wt] is small, not all the Q4 Si atoms can
be associated with the D2 rings. Therefore an overlapping bimodal 0
distribution is initially formed as [D2] increases, centered around 0
137 for the D2 rings [5,p.577] and 0 = 148 for the remaining rings.
These are so close together that two distinct peaks cannot be seen.
After [D2]/[Wt] reaches maximum intensity, there are two different
Q4 sites. These are Q4 Si contained in D2 rings and Q4 Si contained in
328
fourmembered and higherorder rings. Brinker et al. [5,p.578,p.647]
estimates that 2030 % of the Si atoms in a gel can be incorporated into
D2 rings. Neither the 600C A2 or the 810C OX gel contain a peak
with a chemical shift equivalent to = 148, the angle associated with
unstrained silicate rings containing 4 tetrahedra or more. In order for
the Q4 Si sites to produce the peaks = 142.4 and = 139 seen in the
600C A2 and 810C OX gel MASS NMR spectra respectively, several situa
tions can be proposed. The most likely is that the larger siloxane rings
are distorted so that their average 8 has decreased and all the siloxane
rings combine to give the Q4 peak measured.
Exactly what causes the larger siloxane rings to distort is
unknown. The silicons contained in 4membered and higherorder rings
might be affected more in gels by their nearest D2 rings then in fused
aSi02, so the 8 associated with these silicons is reduced to 139 .
It is possible that D2 formation in gels has a larger influence on 8,
and therefore Dg, than in fused aSi02. In other words for a specified
increase in [D2]/[Wt] the increase in Dg seen in fused aSi02 [100] might
be smaller than in silica gels, so the effect of [D2]/[Wt] on Dg is
larger in gels than in fused aSi02 [100]. This means that D2 rings
might have a larger interaction volume in gels than in fused aSi02.
[D2]/[Wt] and Dg do not correlate below Tgmax due to the compli
cating factors discussed earlier, but they do correlate above Tgmax when
the concentration of impurities is very low in comparison (Figs. 80 and
81) so [D2]/[Wt] and the Dg of pure silica gel can be compared. Since
[ D2 ] / [Wt ] and Dg do correlate above Tgmax, a large D2 interaction volume
would help explain the Tp dependence of the Dg of the gels above Tsmax.
329
Interaction volume of D, rings. As shown above, the formation of
D2 rings from larger rings by bond breakage cannot by itself cause the
changes observed in Dg below Tgmax, but the indirect effect of the
formation of the strained D2 rings on the structure of the gel skeleton
itself might explain why Dg increases above 2.20 g/cc, due to a large
effective interaction volume of the D2 rings on the aSi02 matrix.
The D2 rings form on the surface of the internal pores in the
gels, so a large effective interaction volume (i.e. radius of influence
on the structure) would be a surface effect. The effective depth of
surface effects depends on the specific case, and can vary a lot
depending on the effect you are looking at. This case would involve the
atomic structure described by d(SiO), 9 and ring size distributions.
What is the interaction volume of D2 rings for Suprasil compared
to gels and why should it be any different in gels versus bulk aSi02? A
possible explanation is the effect of the H+ point charges removed
during sintering. The presence of H+ in the gel structure (in the form
of OH groups) causes charge redistribution in the chains terminated by
OH groups, which might cause the structure to expand when present on the
large surface area in gels. Then during D2 formation, two H+ are lost in
each H20 molecule formed during ring formation, which might cause more
contraction to occur in gels during D2 formation than seen in D2 forma
tion by bond breakage in fused aSi02, so Dg would increase more in gels
in comparison. Another difference is that D2 is on the surface in gels
but in the bulk matrix in dense aSi02. Fused aSi02 has bulk D2 rings
in a rigid matrix, while in gels about 90% of the total [D2] consist of
D2 rings on the less rigid 2dimensional internal pore surface.
The effect of protons on aSi02 can be investigated using MO
330
theory. West [93] removed a proton from MO hydroxylated D1 and D2 rings
and showed that significant changes occurred in bond lengths and angles.
Unfortunately it is not possible to define a volume for a single D1 or
D2 ring so it was impossible to say whether the removal of a proton from
these siloxane rings caused an overall increase or decrease in the
volume, and therefore Dg, of each ring.
The formation of surface D2 trisiloxane rings in gels by conden
sation reactions could also produce a compressive force on the surface,
which could compact the aSi02 structure. Thus, the very large Sa/Vm
ratio in gels would then have an influence on Dg, and an even larger
influence on ADg/AT.
3,3.17 MASS NMR Versus Raman Spectra Between Tp 200 and 400C Above
Tsmax all the organic impurities and adsorbed H20 in silica gel have
been removed. Surface OH groups are the only impurities in the silica
gel structure, so the Raman spectra characterize the entire gel struc
ture because [OH] is so small. At lower Tp impurities constitute up to
6% of the gel and do not contribute to the vibrational modes character
ized by a Raman spectrum. For instance, the impurities do not contribute
to the W3 and W^ peaks caused by the SiOSi structural component, the
SenThorpe central force theory only applies to the pure silica struc
ture, and any impurities present must be taken into account.
29Si MASS NMR of silica gels characterizes the local environment
of 29Si atoms. The peak position of the Q4 Si atom in MASS NMR spectra
has been strongly correlated with 6 [5] Raman spectroscopy character
izes the vibrational modes of the sSiOSis bridging oxygen. The W3 and
peak positions have also been strongly correlated with 6 [91,92,134,
331
141]. Both spectroscopic techniques characterize the silica component of
the gels. Peak positions in the both MASS NMR and Raman spectra depend
on the average angle of the bridging 0 bond, not with any angle associ
ated with nonbridging 0 bonds. Therefore 29Si MASS NMR and SenThorpe
central force theory analysis of Raman spectra both yield values of 9
for just the =Si0Si= silica structure.
Application of the SenThorpe central force model to the Raman
spectra of type OX gels shows that 9 increases from 127.4 at 400C to
131 at 800C, so A9 = +3.6 = +2.83% (Fig. 75). The MASS NMR analysis
of type OX gels shows that 9 decreases from 148.8 at 180C, to 142.4
at 810C, so A9 = 6.4 = 4.5%. A minimum 9 value might already have
been reached by 400C as Tp increases, in which case MASS NMR would also
show an increase from a minimum at 400 as Tp increases. Brinker et al.
[5] showed that 9 of sample A2 decreased from 149 to 139 between 200
and 600C, which is a lower Tp than 800C. Both techniques show 9
increases above 800C. Analysis of the Raman spectra shows that 6 does
not change between 400C and 600C, so it is possible that MASS NMR
analysis of a 400C gel would also give a value of 6 as small as that
for the 600C gels. The decrease in 9 would then occur by 400C.
The Raman spectra of type OX, 2X and 5X gels could not be measured
below 400C because the wavelength of the laser was too short to prevent
sample fluorescence, but MASS NMR and Raman spectroscopy yield 9 from
the same structure so one could predict that the Raman spectra of a gel
below 400C would reflect the changes in 9 measured by MASS NMR. The W3
PP would increase in frequency and the W4 PP would decrease in frequen
cy. Brinker [5,Fig.48,p.583] measured the Tp dependence of the IR W4
peak of a multicomponent borosilicate gel. W4 was constant from 25C to
332
400C, before increasing as in Fig. 59. Perry et al. [207,Fig. 2]
measured the Tp dependence of the IR of a Type VI, acid catalyzed,
pure silica xerogel made by Geltech Inc (1 Progress Blvd, Alachua, FI.
32615). was also constant from 180C to 400C before increasing as in
Fig. 59. This data suggests that: a) a multicomponent glass or gel can
be related to 8 using the SenThorpe theory [91] in the same way as a
single component glass or gel, and b) below Tp 400C, 8 calculated
from MASS NMR spectra increases while 6 calculated from Raman spectra is
constant. Therefore MASS NMR and Raman spectra analysis of gels yield
contradictory results below Tp 400C.
The MASS NMR data therefore suggests that 8 increases from a
minimum 139 at 400C to 149 at 200C, while the Raman spectra
suggest that 8 remains constant at a minimum as Tp decreases from 400C
to 25C and a high density metastable phase is present in the gels after
drying. The reason for these contradictions are unknown, but might be
related to the different structures of the A2 and type OX gels at low Tp
caused by the different compositions of their starting sols.
For example, analysis of the IR PP of two sets of TEOS xerogels
made with R = 1 and R = 20 show different Tp dependencies [5,p.582]. At
R = 1, increases from 1080 cm'1 at 200C to 1105 cm'1 at 800C,
whereas at R = 20, W4 increases from 1080 cm'1 at 200C to only 1085 cm'1
at 800C and does not increase further until the gel densities by
viscous sintering above 800C. Therefore, as R increases the smaller 8
associated with smaller PP are retained to higher T as are the
larger calculated relative Dg associated with smaller 8, everything else
being equal.
333
3.3.18 The Magnitude of
The Dgmax values measured by the different experimental techniques
are all greater than 2.20 g/cc. The magnitude of these values is
supported by spectroscopic evidence and is not an artifact of the
measurement technique. Both Raman and MASS NMR spectra show peak
positions associated with a silica phase having a density greater than
fused silica. The peak positions are interpreted to mean that the
magnitude of 9 in gels decreases below the value of 9 measured in fused
aSi02.
It is possible that Dgmax might be larger than 2.20 g/cc in the
silica gels because the particles compromising the structure of the gels
are so small that the techniques used to measure Dg will always give
values larger than 2.20 g/cc. In other words it could be an artifact of
the small scale of the gel particles, and even fused aSi02 ground to an
average particle diameter of 20 nm might have Dg > 2.20 g/cc. This could
be tested by measuring the MASS NMR and Raman spectra of fused aSi02
ground to a finer and finer powder, while simultaneously measuring Dg
using pycnometry.
This would mean that as the silica gel particles are the same size
until viscous sintering is finished, they possess Dg equal to Dgmax even
at 200C and the observed Dg increase does not involve 6 decrease. This
supports the IR and Raman spectra showing that the W3 and Raman peak
positions are constant between 200C and Tgmax, but contradicts the MASS
NMR results which show that 6 of silica gels at 200C is the same as
fused aSi02 which infers that the structure of silica gel is not a
dense metastable structure at 200C.
334
A dense metastable structure might have been caused by capillary
stress during drying, possibly via an influence on the primary particles
formed in the sol, and extrapolation of the Raman spectra would support
this. But Vega et al.'s [177] MASS NMR investigation of a drying gel
shows that 8 decreases from 150 to 145 during drying as the H20 is
removed. The dry gel value, 145, is near Brinker's MASS NMR value of
148 of a dry gel. These similar data infer that the structure of the
silica phase at 200C is not a high density metastable phase and the Dg
of the silica gel particles increases from 200 up to Tgmax, so Dgmax
cannot be > 2.20 g/cc just because of the small size of the gel parti
cles. Yet again, the MASS NMR and Raman spectra contradict each other
below T .
smax
3.3.19 Dependence of of Fused aSiO.. on fOH1
Shackelford et al. [210] measured the influence of [OH] on the Dg
of a Type II Amersil sample, Tf = 1100C. As [OH] increased from 0.0 to
0.10 wt%, Ds decreased from 2.20246 g/cc to 2.20164 g/cc. Bruckner [211]
measured the influence of [OH] on the Dg of a Type IV Suprasil sample,
Tf = 1300C. When [OH] increased from 0.024 to 0.132 wt%, Dg decreased
from 2.20379 g/cc to 2.20180 g/cc. Figure 85 shows the linear regres
sions of these experimental data extrapolated to [OH] 6 wt%. Based on
these extrapolated regressions, the addition of 6 wt% OH to Amersil
would cause Dg to decrease from 2.203 g/cc to 2.152 g/cc. This is a
decrease of 0.051 g/cc s 2.32% = 0.386% per 1% [OH] increase. The
addition of 6 wt% OH to Suprasil would cause Dg to decrease from 2.204
g/cc to 2.099 g/cc. This is a decrease of 0.104 g/cc = 4.72% = 0.786%
per 1% [OH] increase.
STRUCTURAL DENSITY [g/cc]
335
HYDROXYL CONCENTRATION [OH] (Wtt)
Figure 85. The extrapolated dependence on the hydroxyl concentration,
[OH] (Wt %) of the structural density of Amersil [210], a Type II a
silica, and of Suprasil [211], a Type IV asilica.
336
The model used to calculate the density of the phase lost from
gels in a TGA spectra can be applied to these fused aSi02 samples. The
density of the 6 wt% OH phase causing Dg to decrease in Amersil from
2.203 g/cc to 2.152 g/cc is 1.58 g/cc. Dg decreases in Suprasil from
2.204 g/cc to 2.099 g/cc, so the density of the 6 wt% OH phase is 1.20
g/cc. This compares with a density of 0.65 g/cc for the phase lost from
gels in a TGA spectra, calculated assuming that Dg of the residual pure
silica phase remained constant and = Dgmax. The density of the OH phase
in fused aSi02 is about twice the calculated density of the low density
phase in gel, 0.640.67 g/cc
If these phases actually had the same density, the assumptions
used to calculate the density of the low density phase in gels are
wrong. Half the density increase observed in silica gels up to Tgmax
would then actually be due to an increase in Dg of the pure silica
phase. This would imply that 8 does decrease between 200C and 400C as
Dg increases, agreeing with the analysis of the MASS NMR experimental
data and contradicting the SenThorpe [91] analysis of the Raman spectra
between 25 C and 400C.
3.4 Conclusions
The addition of HF to a type OX acidcatalyzed silica gel causes
Vp and rH to increase and Sg and Db to decrease (Fig. 33). The F' anion
acts as a base catalyst and has a similar effect on the texture as the
addition of a base catalyst, for example NH^OH or NaOH.
The structural density Dg of a metal alkoxide derived silica gel
is dependent on its thermal history T(t). Three independent experimental
337
techniques were used to show that: a) the structural density Dg of a
silica gel is dependent on its thermal history (Fig. 30, 31, 32 and 34),
b) the maximum structural density Dgmax is significantly larger than the
Dg of fused aSi02, 2.20 g/cc, c) the magnitude of Dgmax depends on the
technique used to measure it because of the fractal nature of silica
gels, i.e. it depends on the size of the molecule of the technique used
measure Dg, d) Dgmax occurs at Db = 1.25 1.4 g/cc in type OX gels, e)
the temperature at which Dsmax occurs, Tsmax, increases as rH increases
and as the size of the gel decreases, and f) from N2 sorption, Dsmax =
2.450.03 g/cc, from H20 pycnometry, Dgmax = 2.260.01 g/cc and from He
pycnometry, Dgmax = 2.3000.005 g/cc.
The silica gel samples whose Dg were measured using N2 sorption
and water pycnometry had all absorbed water into their pores, so their
internal pore surfaces were rehydroxylated. The value of Dgmax in these
gels were still significantly larger than 2.20 g/cc, so the structure of
these silica gels at Tgmax is not metastable but in thermodynamic equi
librium. If the structure of the gels at Tsmax was metastable, when water
was absorbed into their pores, Dg would decrease until Dg < 2.20 g/cc.
The difference in the magnitude of Dgmax measured by these two
techniques is not due to the physical state of the gels, for instance
[SigOH], but is due to the difference in the magnitude of Vp measured by
N2 sorption and H2 pycnometry. The fractal properties of these gels
determines the dependence of the magnitude of their Sg and Vp on the
size of the gas molecule used to measure them. The rH and surface
chemistry of the pores will also effect Vp through their influence on
packing factor and [Sig0H]. For instance, Vp measured by water absorp
tion at 25C is smaller than Vp measured by N2 sorption at 197C,
338
despite H20 having a smaller molecular radius than N2 when calculated
from the BET crosssectional area on nonpolar solids. There is no
obvious correlation between Vp measured by absorbed helium, N2 and H20
molecules and their radii.
The addition of HF to type OX gels causes the changes in texture
shown in Fig. 33, which in turn are responsible for the increases in
Tsmax seen in Fig. 34 as rH increases from 1.2 nm to 9.0 nm. In contrast,
the Dsmax measured by He pycnometry is independent of [HF].
Dsmax = 2.3000.005 g/cc when measured by helium pycnometry for
type OX, 2X and 5X gels, despite their large differences in texture and
structure. The magnitude of Dgmax for these gels is therefore independent
of the textural or physical properties of the gel which change with
[HF], i.e. Vp, Sg and rH> This appears to be because the gel particles
(which make up the gel matrix containing the porosity) in type OX gels
are large enough for their structure to be unaffected by the small
increase in rp which occurs as [HF] increases. Thus, the magnitude of
the bulk structural changes causing the changes in Dg during Tp increase
would be the same for all the gels. The decrease in Db of the dry gels
(Tp = 180C) seen as [HF] increases (Fig. 33) is not caused by this
small increase in rp, but is due to a decrease in the Cn of the gel
particles which is large enough to cause the observed increase in V .
This decrease in Cn as [HF] increases is large relative to the increase
in rp caused by [HF] increase.
The experimentally observed dependency of Dg on Tp involves two
stages. The first stage occurs as Tp increases above 200C up to about
Tg[nax (which can be similar to Tdb in some gels) and involves the comple
tion of the condensation polymerization reaction. In this Tp range, Dg
339
increases to Dsmax, [D2] increases to its maximum concentration, and most
of the observed weight loss occurs while Db stays constant or only
increases slightly in comparison to the relatively large increase in Dg
and [D2]. The second stage occurs as Tp increases from Tgmax up to the Tp
at which densification is completed. In this Tp range, densification
occurs via viscous sintering, and the rate of weight loss and [D2] both
decrease as Db increases until Vp = 0 cc/g. The upper Tp range of the
first stage and the lower Tp range of the second stage can overlap. The
size of the overlap depends on the heating rate and the texture and
structure of the silica gel.
Raman Spectroscopy allows the molecular and vibrational structure
of silica gels to be nondestructively monitored and characterized during
densification. Curvefitting of thermally reduced experimental Raman
spectra of silica gels allows the areas and positions of Raman peaks to
be accurately measured. The curvefitting data agrees with the literature
assignments of the D1 peak to puckered tetrasiloxane rings and the D2
peak to strained, planar trisiloxane surface rings. It shows that the
concentration/unit area of internal pore surface of the surface trisilo
xane D2 rings increases continuously as Tp increases. Therefore D2 rings
are continuously formed via condensation polymerization of adjacent
surface silanols on the internal pore surface as Tp increases.
The bulk D2 concentration, [D2]/[Wt] does not correlate with Dg
below but it does correlate with D above D so different
smax1 s smax9
mechanisms must be responsible for Dg change above and below Tgmax.
The causes of the increase in D below D include: a) the loss
of a low density phase composed of SiOH and SiOR groups. If this causes
the increase in D to D then the density of this phase = 0.64 0.67
b blllOA *
340
g/cc in type OX, 2X and 5X gels, b) structural relaxation via loss of
excess free volume. In comparison to Brinker et al.'s A2 silica gel [5],
type OX gels have a much smaller excess free volume, so at 200C the Dg
of type OX gels is much larger than A2 and the loss of excess free
volume does not contribute significantly to the increase in Dg as Tp
increases to Tgmax, whereas it does make a significant contribution to
the increase in the D of A2 as T increases to Tm (Fig. 21) .
The decrease in the bulk D2 concentration, [D2]/[Wt] seen above
Tdb in Figs. 64 and 65 is due to the structural rearrangement occurring
during viscous sintering, as bond restructuring occurs while the surface
area decreases, allowing the metastable surface structure of porous gels
to relax to a more stable bulk configuration which is identical to the
structure of fused asilica with the same T^. This also explains why 2X
and 5X type gels have similar maximum [D2]. The 5X type gel retains Sg
to a higher Tp at a higher [D2] surface concentration, while the 2X type
gel loses Sg at a lower T preventing [D2] from increasing as far as it
could if it retained Sg. The increase in [D2]/[Wt]/Sg (Fig. 66) is
directly related to the decrease in [Sig0H]/[Wt]/Sg (Figs. 68 and 72).
The concentration/unit area of internal pore surface of D2 rings
correlates well with the concentration/unit area of internal pore
surface of Sig0H, so [Sig0H]/[Wt]/Sg decreases about twice as fast as
[D2]/[Wt]/Sa increases during sintering.
DgmgX f silica gels measured by water pycnometry is representative
of gels which have been exposed to water so the surface D2 rings have
been rehydroxylated, and yet D still goes through a maximum and D >
2.20 g/cc. This is evidence that the D2 rings are not solely responsible
for the magnitude of Dg. During sintering, changes in the bridging
341
oxygen angle 9 in these silica gels (which are calculated from their
Raman spectra using the SenThorpe theory [91]) occur in the bulk of the
gel, where they are not influenced by adsorbed water.
Above D decreases as the molar volume V increases due to
smax s m
the increase in the =Si0Si= bridging bond angle 6. As Dg decreases and
9 increases, the W3 SS Raman peak decreases and the W^ AS Raman peak
increases as expected from the SenThorpe centralforce function theory
[91]. The experimental and calculated relative Dg correlate above Tgmax,
so the decrease in D above Tm, is due to the increase in 9.
s smax
The increase in 0 which causes the decrease in D above T,w as D.
s smax b
increases is due to viscous sintering. As Tp increases, rj decreases far
enough for metastable structures to relax and form thermodynamically
more stable structures via the sSiOSis bond breakage and reformation
which occurs during viscous sintering. During this process [D2] decreas
es to its equilibrium concentration and V(9) shifts to its equilibrium
distribution.
During pressure compaction of fused aSi02, [D2] and 9 hardly
change at all while the dihedral angle distribution changes to allow
more efficient packing of silica tetrahedra as Dg increases.
When Tf increases in fused aSi02, the increase in [D2]/[Wt] and
the decrease in 9 are so large that bond breakage causing a decrease in
the average ring size must be the mechanism of Dg increase. The dihedral
angle change is small in comparison.
In silica gels the maximum D value, D is larger than the D
of fused aSi02, 2.20 g/cc, because its the 9 in silica gels is smaller
than the 9 in fused aSi02. The calculated relative Dg increase caused
by the decrease in 9 is large enough to account for Dg decrease seen
342
above Tgmax, so the increase in 9 via bond breakage is the dominant
mechanism during viscous sintering. Bond breakage causes an increase in
the average ring size and a decrease in [D2] while the dihedral angle
contributions is relatively small.
Since [D2]/[Wt] and Ds do correlate above Tsmax, a large interac
tion volume of D2 rings in gels compared to D2 rings in fused aSi02
would help explain the Tp dependence of the Dg of silica gels. This
could be due to the loss of the point charges which occurs during D2
formation via condensation polymerization of adjacent Si2OH, i.e. the
protons (H+ ions) lost from the SigOH groups on the internal pore
surface in the water molecule formed by the condensation reaction.
Application of the SenThorpe centralforce function theory [91]
to the Raman spectra shows that 9 increased continuously above Tp
400C and the relative Dg calculated from 9 decreased continuously above
Tp 400C. In contrast, calculation of 9 from the Q^* peak position in
29Si MASS NMR spectra of silica gels showed that initially 9 decreased
as T increased to T a. Therefore, for T < T v, it is not clear
p smax p smax
whether the value of 9 of the bulk silica skeleton is already smaller
than that found in fused aSi02, as inferred by the W3 TO and LO
Raman peak positions, or if 9 decreases to a smaller value, as inferred
by the MASS NMR peak position. For Tp > Tsmax, both Raman spectroscopy
and MASS NMR show that 9 increases to the same equilibrium value as
found in fused aSi02, in agreement with the experimental Dg data.
CHAPTER 4
STRUCTURAL ANALYSIS OF POROUS SILICA GELS DURING THE
ABSORPTION OF WATER INTO THE GEL'S MICROPORES
4.1 Introduction
The medium range order of fused aSi02 is defined by the distribu
tion of silicate rings which exist in the structure. The ring size
distribution contains an average of 5 to 6 silica tetrahedra, SiO^",
per ring, with a minimum of 3 and a maximum of about 8 or 9 tetrahedra.
There might also be some twomembered silicate rings, called disiloxane
rings, but their concentration is very small if they are present at all
[175]. Silicate rings containing 4 or more tetrahedra are not planar
rings but are puckered because that is their energetically most favor
able configuration. In the disordered topology which exists in aSi02,
steric and bonding requirements favor nonplanar, puckered configurations
for rings containing > 4 silica tetrahedra. This allows 6, S and d(SiO)
to approach their equilibrium values. The equilibrium angle, #e, of the
bridging oxygen bond connecting the tetrahedra in rings containing > 4
tetrahedra is therefore between 144148 [5,41].
The D2 trisiloxane rings are planar with 6 = 137 [5,p.577] so
they are strained in comparison to larger unstrained rings. Therefore
their bridging oxygen bonds are strained, causing the Si3 atoms to
become more acidic and the 0 atoms to become more basic [175] This
makes them more susceptible than unstrained rings to bond breakage by
rehydroxylation (as opposed to hydroxylation, because they have already
343
344
been dehydroxylated) via dissociative chemisorption of adsorbed H20
molecules [175]. Fused aSi02 contains 12% D2 rings, depending on Tf
[100], assuming a coupling constant or scattering crosssection 1. In
fused aSi02 the D2 rings are in the bulk structure, so they are inac
cessible to physisorbed H20 molecules. Therefore the adsorption of H20
onto the external surface of a fused aSi02 sample has an insignificant
effect on the intensity of the 605 cm'1 D2 peak in its Raman spectrum.
The rehydrolysis of a dehydroxylated fused aSi02 surface is a two
step process involving adsorption of H20 molecules onto the surface
(physisorption) followed by rehydroxylation via a dissociative bond
breaking reaction (chemisorption). The physisorption of a H20 molecule
occurs via Hbonding to, preferentially, a surface Sig0H or, alterna
tively, an acidic Si3 atom contained in a strained D2 ring if [Sig0H] is
small [175] For fused aSi02 which has no internal porosity, physisorp
tion is the ratedetermining step above about 450C where [Sig0H] is
relatively small and the surface is hydrophobic. The surface becomes
more hydrophobic as [Sig0H] decreases. Below about 450C [Sig0H] is
large enough that the physisorption step is facile because the surface
is hydrophilic in comparison to the surface heated to T > 450C [1,175],
On an aSi02 surface dehydroxylated by heating to a high enough T
the kinetics of the physisorption process is determined by the extent of
strain of the =Si0Si= bond, i.e. the size of 6 or, more specifically,
(66e) which is the size of its deviation from its equilibrium value.
The size of 6$e for a specific silicate ring is determined by the
number of tetrahedra in the ring [5]. The rehydration kinetics of an
aSi02 surface dehydrated above 450C is therefore initially determined
by the reaction kinetics of the rehydrolysis of D2 rings [5,p.654]. The
345
rehydrolysis of D., rings occurs via the dissociative chemisorption of
physisorbed H20 molecules. This involves the exothermic reaction [5]
sSi30Si3= + H20 = 2=Si3OH (44)
where Si3 is a Si atom in a D2 trisiloxane ring. This rehydrolysis
reaction also occurs during aSi02 dissolution, and is the reverse of
the condensation polymerization reaction which occurs between adjacent
SiOH groups. Both dissolution and condensation are discussed in detail
by Her [1] and Brinker et al. [5], Their rates and reaction mechanisms
are catalyzed by F' ions, as well as by H+ and OH' ions, i. e. they are
both pH dependent. The influence of [F] [H+] [OH'] and pH on the
reaction rate and reaction mechanism of the rehydrolysis of D2 rings is
not discussed by Brinker et al. [5]. Like dissolution and condensation,
the rate of D2 rehydrolysis is dependent on T.
D2 rehydrolysis can only happen after a H20 molecule has been
physisorbed onto a strained Si3 atom, which is a Lewis acid since it
possesses an unoccupied d orbital that is available as an electron
acceptor. The rate of physisorption is controlled by the molecular
basicity of the adsorbate molecule (H20 in this case) and the degree of
strain of the surface silicate rings, which increases the acidity and
accessibility of the Si3 atoms. The basicity of the bridging 0 (which
can function as a Lewis base (electron donor) or a Bronsted base (proton
acceptor) due to its lone pair of electrons in the strained rings
appears to be less important in governing the reactivity of the rings
[175]. The reaction kinetics of the rehydrolysis of D2 rings is there
fore determined by the ratelimiting H20 physisorption step [5,p.651],
346
because the subsequent dissociative chemisorption step is very rapid.
Subsequent H20 adsorption occurs on the SigOH formed by the rehydration
of the trisiloxane rings. The rehydrolysis of the remaining surface
occurs adjacent to areas of initially rehydrated surface and its
rehydrolysis kinetics is determined by the hydrolysis rate of the
remaining unstrained fourmembered and larger silicate rings, which is
much slower than that of the D2 rings [1,33,175]. Therefore the [D2]
concentration determines the initial rehydration kinetics of a dehy
drated aSi02 surface.
During the densification of monolithic silica xerogels via viscous
sintering, the dehydroxylation of the internal pore surface leads to the
formation of D2 rings on this surface via condensation polymerization of
adjacent SigOH groups. Up to 25% of the surface can be covered by
trisiloxane rings at the maximum [D2] concentration, with the remainder
covered by larger silicate rings and SigOH [175] The actual surface
concentration of each component depends on the thermal history and pore
texture of the gel. The maximum [D2] occurs between 400C and 1000C,
depending on the pore texture (Fig. 64).
One of the unique, and potentially most useful, results of the
development of large monolithic silica xerogels is the Type VI porous
stabilized silica gel, available in a range of geometric shapes and
sizes. No other material combines a pure aSi02 matrix, with all its
unique properties, with porosity tailored to a desired combination of
Sa, Vp and rH. This material is made by stabilizing at a Tp high enough
to complete the condensation polymerization reaction in the aSi02
structure while driving the viscous sintering process far enough to give
the desired porosity texture and morphology. Type VI porous aSi02 can
347
then be used as a host matrix for guest materials, including laser dyes,
nonlinearoptical materials, wavelength shifters, scintillation
detectors, etc. The kinetics and energetics of the surface chemistry of
the pores will govern the aSi02 host matrix/guest material interac
tions This includes the kinetics of the impregnation process, the
chemical behavior of the guest, the long term stability of the guest,
etc. The pore surface contains large concentrations of strained D2
rings, which will influence the physical chemistry of the surface. The
object of this study is to gain insight into the rate of reaction of the
surface D2 rings with bulk H20 and H20 vapor, and how large an influence
H20 has on the surface chemistry. This is important for both the initial
introduction of a material into the Type VI gelsilica host matrix and
the long term stability of the matrix/guest interface.
The concentration, [D2]/[Wt] of the surface D2 trisiloxane rings
in the pores of monolithic Type VI silica gels dehydroxylated at
different Tp was measured as a function of time t and H20 content, W,
using Raman spectroscopy. The specific objectives of this study were:
a) To quantify the stability of surface D2 rings in Type VI porous
silica gel, made from type OX gels, with respect to adsorbed H20. This
includes calculation of the equilibrium constant Kc and the reaction
rate k for surface D2 rehydrolysis, b) To investigate the influence of
the processing temperature Tp on the stability of trisiloxane rings
w.r.t. adsorbed H20. If the rehydrolysis is an activated process, Tp
should not affect the reaction rate k, but the influence of Tp on the
matrix in which the D2 rings are embedded, i.e. on iÂ¡, Ds, etc. might
affect k, and c) To measure the increase in [SigOH] caused by surface
rehydrolysis during H20 absorption into silica gels.
348
4.2 Experimental Procedure
The Raman spectrometer that was used to characterize the structure
of silica gel during densification was also used to probe the structural
changes occurring during H20 absorption. Four cylindrical samples of
type OX silica gel, sample numbers #124, #136, #127 and #141, with rH =
1.2 nm, diameter 1.0 cm and height 4.0 cm were examined. Sample #136
was dehydroxylated at 600C, #124 and #127 at 650C, and #141 at 800C,
giving the Db listed in Table 10. After stabilization, the samples were
furnace cooled to 150C, removed, their volume and dry weight (at W 
0.0 g/g) measured and calculated. Deionized H.,0, pH 5.6, was
adsorbed at 25C via the vapor phase, as opposed to the liquid phase, to
avoid possible fragmentation of the samples due to the very large
capillary stresses generated by absorption of liquid H20 in the micropo
res in these silica gels. Each gel was placed in a resealable container,
with a deionized H20 reservoir giving an Rh = 100% atmosphere, identical
to that described in the H20 pycnometry experimental procedure in
Chapter 1. The container had about 100 cm3 of free volume above the H20
reservoir so its atmosphere saturated very quickly compared to the time
required to fill the pores in the gel.
After time t the cylinder of silica gel was removed from the Rh =
100% atmosphere, weighed and transferred to the Raman spectrometer. The
laser beam was focussed so that it passed through the length of the
cylinder 1 mm below the surface of the cylindrical gel nearest the
collecting lens of the spectrometer. This distance was chosen as a
balance between: a) the need to keep the attenuation of the Raman signal
as small as possible, and b) keeping the laser beam from touching the
gel surface due to the optical distortion caused by the deformation of
349
the viscoelastic gel during sintering. No attempt was made to have the
same side of a gel facing the monochromator while measuring different
Raman spectra, so different portions of a gel, all 1 mm below the
surface, were probed each time.
The Raman spectra were recorded from 1001400 cm"1 and from 3000
4000 cm"1 in the same fashion as described in the silica gel densificat
ion experimental procedure section (Chapter 1). The laser did not cause
any H20 to evaporate or boil off the sample. If it had, the sample would
have lost weight during the time required to record the spectra and
turned white due to light scattering. The gel did not lose weight or
turn opaque in the 30 mins required to obtain a spectra, so the T
increase caused by the laser was not large enough to affect W.
As soon as a spectrum was measured the gel was returned to the Rh
 100% atmosphere and allowed to continue adsorbing H20 as fast as
possible from the Rh = 100% air. For samples #136, #127 and #141, Raman
spectra were recorded periodically, and W measured, until the pores were
fully saturated with H20 and no further change was seen in the Raman
spectra. The gels were then heated at 190C for 24 hrs to remove all the
absorbed H20 and their Raman spectra recorded.
Sample #124 was dealt with differently. After the Raman spectrum
was measured at W = 0.0 g/g, H20 was adsorbed until W = 0.0284 g/g at t
= 66 hrs. #124 was then allowed to adsorb a small amount of H20 before
sealing in a dry airtight container. Its Raman spectrum was next
measured at t = 1800 hrs (75 days) and W = 0.0731 g/g, t = 1805 hrs and
W * 0.0857 g/g, and t = 1821 hrs and W = 0.0876 g/g, where [D2]/[Wt] was
found to = 0.0386 in each case.
350
Sample #139 was a type 2X silica gel, rH 4.5 nm, with a diameter
0.53 cm, height 1.25 cm, which was stabilized at 900C and charac
terized in the same way as samples #136, #127 and #141.
The Raman spectra were baseline corrected, thermally reduced and
curvefitted using Gaussian functions as described in Chapter 1.
4.3 Results
Table 10 lists some physical properties of these cylindrical gels.
Figure 86 shows the rate of H20 absorption of each sample normalized to
the dry sample mass to give the H20 content W as a function of time t.
Samples #136, #127, #141 and #139 were allowed to adsorb H20 as fast as
possible and exhibit a tn dependency on time t before reaching their
maximum absorbed H20 content Wmax. For five type OX gels, including
samples #136, #127 and #141, n 0.697 (ct5 = 0.045), so W a t070. The
type 2X gel, #139, has a similar time dependency, n = 0.667, and adsorbs
H20 most quickly. Simplistically, the relative rates of H20 absorption
into the gels can be explained in terms of their permeability D. The
gels which absorb H20 most quickly have the largest permeability. D does
not vary by more than 2.5 from #141 to #139, i.e. at t = 60 hrs, W =
0.24 g/g for #141 while W = 0.60 g/g for #139. For the type OX samples
#136, #127 and #141, rH remains constant during sintering (Fig. 37)
while Vp decreases, so D decreases as Tp increases. Consequently the
type OX gels absorb H20 most quickly in the order #136 > #127 > #141 in
Fig. 59. Sample #124 was sealed until t 1821 hrs, when W = 0.0876 g/g,
to investigate the long term effects of H20 absorption.
Figure 87 shows the Raman spectra of sample #127 for values of W
from 0.0 g/g to Wmax = 0.329 g/g, as well as after removing the adsorbed
WATER CONTENT, W [g WATER/g GEL]
351
0 20 40 60 80 100 120
TIME, t [HRS1
Figure 86. The rate of absorption of water vapor from a reservoir of
deionized water into the pores of type OX gel samples #124, #141, #127,
#136, with rH 1.2 nm, and type 2X gel sample #139, with rH 4.5 nm.
352
Table 10. Properties of the cylindrical silica gel samples used for H20
absorption studies.
Sample
I.D.
Pore
Radius rH
[nm]
Stabilization
Temperature
td rc]
Bulk
Density
Db [g/cc]
Pore
Volume V
[cc/g]
W
max
t g/cc]
#124
1.2
650
1.29
0.341

#136
1.2
600
1.22
0.383
0.381
#127
1.2
650
1.27
0.352
0.329
#141
1.2
800
1.48
0.241
0.254
#139
4.5
900
0.90
0.675
0.600
H20 by reheating at 190C so that W decreased to 0.0167 g/g. As W in
creases the 460 cm'1 W1 peak and the 498 cm'1 D1 peak overlap until, at
Wmaxi W1 no longer has a visible separate peak. Curvefitting shows that
the D1 peak area, [D1]/[Wt], is constant but its peak position (PP)
decreases slightly from 499 to 497 cm"1. The area of the asymmetric W1
peak cannot be measured (due to the problem of separating the baseline
and the Rayleigh elastic scattering peak from the W1 peak area) but its
PP increases as W increases. The increase in the frequency of the W1 PP
is the cause of its overlap with the D1 peak. The 609 cm'1 D2 PP decreas
es in frequency to 604 cm"1 while its area decreases in intensity to the
level seen in dense aSi02. The W3 TO PP decreases in frequency from 814
cm'1 to 802 cm'1. The LO PP also decreases from 1186 cm'1 to 1180 cm"1,
unlike the changes during densification of silica gels when W3 and
shift in opposite directions, but similar to the effect of applying a
tensile stress to fused aSi02 [132]. The 980 cm'1 Sig0H peak increases
in area but does not shift in frequency. A new peak appears at 915 cm'1
as W increases which is attributed to the S++0H vibration of geminal
surface silanol groups [=Si(<*0H)2] formed during rehydroxylation [25].
COUNTS [ARBTRARY UNITS]
353
RAMAN SHIFT [CM 1 ]
Figure 87. The evolution of the Raman spectrum (1001350 cm'1) of sample
#127, stabilized at Tp = 650C (Db 1.28 g/cc, rH 1.2 nm) as the
water content W increases from 0.0 g H20/g gel to W = = 0.329 g/g,
and then as the gel is then redried by reheating at Tp = 190C.
354
Several changes occur to the Raman spectra of a silica gel when it
is heated to 190C to remove the adsorbed H20. The 915 cm"1 peak de
creases in intensity until an individual peak is no longer visible, but
the 980 cm"1 SiOH peak shows a shoulder on its low frequency side so a
small 915 cm"1 peak is still present on the low frequency shoulder of
the 980 cm"1 peak. The W3 and peaks return to their original peak
positions, while the D2 peak moves back about half of the original
distance that it moved at W The D2 peak area increases slightly as
surface condensation forms new D2 rings, and it would continue to in
crease if Tp was increased. The 460 cm"1 W1 peak does not return to its
original peak position, but close examination of the 190C spectra shows
that the W1 peak position has decreased slightly in frequency. If Tp was
increased, W1 would also decrease back to 460 cm"1.
Figure 88 shows the internally normalized D2 peak area [D2]/[Wt]
as a function of time. For samples #136, #127, #141 and #139, [D2]/[Wt]
decreases most rapidly in roughly the same order that W increases in
Fig. 86. #124 decreases to [D2]/[Wt] = 0.0386 at W = 0.0731 g/g after t
= 1800 hrs. Combining Figs. 86 and 88 allows [D2]/[Wt] to be plotted as
a function of W in Figure 89, where [D2]/[Wt] shows a roughly linear
dependency on W, so [D2]/[Wt] shows a better correlation with W in Fig.
89 than it does with t in Fig. 88. #124 also shows a roughly linear
dependency on W in Fig. 89 like samples #136, #127, #141 and #139.
After the pores are saturated with H20, the residual normalized
[D2] concentration, [D2]/[Wt] 0.015, is similar for all the gels. This
concentration is similar to the [D2] value seen in fully densified gels
and fused aSi02, so the D2 rings left after complete rehydrolysis and
densification must be rings formed in the bulk silica matrix via
!D2]/[Wt], (** D2 RINGS/UNIT VOLUME)
355
TIME, t [HRS]
#124 + #136 0 #127 A #141 X #139
Figure 88. The dependence, on time t (hrs) for which the gels were
exposed to an Rh = 100% atmosphere, of the area of the D2 trisiloxane
curvefitted Raman peak, as a fraction of the total spectrum area, for
samples #124, #136, #127, #141 and #139, and for a B2 gel [5],
[D2]/[Wt], (** D2 RINGS/UNIT VOLUME)
356
WATER CONTENT, W [g WATER/g GEL]
#124 + #136 O #127 A #141 X #139
Figure 89. The dependence on the water content W of the area of the D2
trisiloxane curvefitted Raman peak, as a fraction of the total Raman
spectrum area, for samples #124, #136, #127, #141 and #139.
357
condensation of internal hydroxyls. [D2]/[Wt] 0.015 is probably the D2
ring concentration required topologically for the packing factor
dictated by a bulk density of 2.2 g/cc, given the bonding requirements
of silica tetrahedra in aSi02.
The SenThorpe centralforce function theory can be applied to
these Raman spectra in the same way as it was used to analyze the Raman
spectra of silica gels during densification (Chapter 3). The W3 TO and
LO peaks are used for the same reasons, though in this case they both
decreased in frequency as W increases. Figures 90 and 91 show the
dependency of Kg on t and W respectively. Figures 92 and 93 show the
dependency of ( on t and W. In contrast to the densification of silica
gels where Kg decreases slightly and 6 increases significantly, when H20
is adsorbed into their pores Kg decreases significantly while 6 increas
es only slightly. The decrease in Kg is a W, so Kg decreases more in
#139 because it adsorbs more H20 than the other gels. Since the decrease
in [D2]/[Wt] is also a W, it is likely that Kg and [D2] are directly
related. The decrease in Kg is due to the redistribution of charge that
occurs when H20 molecules are adsorbed on the pore surface.
Figure 94 shows the dependency of the calculated relative Dg
(calculated from d(SiO) and & using the same model discussed in Chapter
3) on W. The absorption of H20 into the pores of a silica gel causes it
to expand. This has been observed in a dilatometer for the absorption of
H20 from humid air into the pores of a gel. The normalized expansion
decreases as the Tp of a gel increases [184]. The data in Fig. 94 is
noisy but its overall trend agrees with this experimental observation.
It shows that the calculated relative De decreases as W increases and
9
the rate of decrease decreases as T increases.
Si O FORCE FUNCTION, Ks [N/m]
358
TIME, t [HRS]
#124 + #136 0 #127 A #141 X #139
Figure 90. The dependence on time t (hrs) of the Si0 force function, Kg
(N/m), calculated from the W3 TO and W4 LO Raman peaks using equation
(11), for samples #124, #136, #127, #141 and #139.
Si O FORCE FUNCTION, Ks [N/m]
359
WATER CONTENT, W [g WATER/g GEL]
#124 + #136 0 #127 A #141 X #139
Figure 91. The dependence on the water content W (g/g) of the Si0 force
function, Kg (N/m), calculated from the W3 TO and LO Raman peaks
using equation (11), for samples #124, #136, #127, #141 and #139.
Si BRIDGING O ANGLE, THETA [']
360
#124
TIME, t [HRS]
#136 0 #127 A #141
#139
Figure 92. The dependence on time t (hrs) of the bridging oxygen bond, 0
(), calculated from the W3 TO and LO Raman peaks using equation
(12), for samples #124, #136, #127, #141 and #139.
Si O Si BRIDGING O ANGLE, THETA [*]
361
WATER CONTENT, W [g WATER/g GEL]
#124 + #136 0 #127 A #141 X #139
Figure 93. The dependence on the water content, W (g/g), of the bridging
oxygen bond, 6 (), calculated from the W3 TO and LO Raman peaks
using equation (12), for samples #124, #136, #127, #141 and #139.
CALCULATED RELATIVE STRUCTURAL DENSITY
362
WATER CONTENT, W [g WATER/g GEL]
0 #124 + #136 0 #127 A #141 X #139
Figure 94. The dependence on the water content, W (g/g), of the calcu
lated relative structural density, determined from 9 and d(SiO), for
samples #124, #136, #127, #141 and #139.
363
The absorption of H20 into porous Vycor [212] also causes expan
sion [1]. This has been explained by H20 adsorption on the pore surface
forming [SigOH] during surface rehydrolysis which generates a surface
charge on the large internal Sfl of Vycor. The neighboring surface
charges repel each other and the skeletal volume swells, which would
explain the observed expansion of silica gels during H20 absorption.
4,4 Discussion
The time dependency of the rehydrolysis of [D2] rings by H20
adsorbed from the vapor phase depends on the relative rates of: a) the
movement of the H20 molecules from outside the gel through the pores to
the D2 rings, i.e. the H20 absorption step, and b) the D2 rehydrolysis
via dissociative chemisorption of physisorbed H20 molecules. The rate of
rehydrolysis of D2 rings is actually determined by the rate of H20
physisorption, i.e. the H20 adsorption step, which is slower than the
actual dissociative chemisorption reaction [175]. The rate determining
step depends on which of these processes, water absorption or water
adsorption, occurs most quickly.
4.4,1 The Movement of H..0 Molecules Through Pores
The absorption of H20 into the pores of a monolithic silica gel,
which involve the transport of H20 molecules from atmosphere outside the
gel to the internal porosity, is a more complex process than it might at
first appear. If an initially dry gel is placed in a closed container
with a H20 reservoir, after the lid is closed Rh increases to 100% at a
rate determined by T and the volume of the closed container. As the
internal volume of the container is about 100 cm3, the air saturates
364
quickly relative to the 23 days required to saturate the pores in the
gel. The gel becomes surrounded by a relative vapor pressure, P/Pq, = 1
and a concentration gradient is set up with P/PQ 1 at the surface of
the gel and P/PQ = 0 inside the pores of the gel. Under the influence of
the chemical potential gradient caused by the concentration gradient,
H20 molecules diffuse into the pores. Ideally the rate of diffusion of
the H20 molecules into the pores would be described by the solution of
Fick's second law of diffusion applicable to a cylindrical symmetry for
these boundary conditions. Unfortunately, we are dealing with the
diffusion of polar molecules into micropores which have a chemically
reactive surface containing significant concentrations of SigOH and D2
rings, which are capable of physisorbing H20 molecules. This means that
the possibility also exists for Knudsen diffusion, surface diffusion,
physisorption, chemisorption, condensation of H20 molecules in pores,
Fickian diffusion and convection of the liquid H20 formed during conden
sation, and the movement of condensed H20 under the influence of capil
lary stress to all occur, in addition to the Fickian diffusion of H20
vapor driven by the chemical potential created by the H20 concentration
gradient.
Knudsen diffusion Knudsen diffusion occurs when the meanfreepath
of a molecule is greater than the diameter of the pore in which the
molecule is diffusing, so moleculepore wall interactions are dominant,
i.e. when the Knudsen number Kn = A/2rH is greater than 1, where A =
mean free path of the molecules. Knudsen diffusion occurs when the pore
diameter is so small that the gas molecules hit the pore surface more
often than they hit each other, and is not the same as surface diffusion
365
which involves the movement of molecules physisiorbed to the pore
surface. In chemical potential controlled Fickian (viscous) diffusion,
i.e. a concentration gradient with no geometrical constraints, molecule
molecule interaction is the rate limiting process and the concentration
gradient at any time is described by Fick's diffusion laws [194].
Mass flow through a pipe (i.e. pore) can be: a) viscous flow (i.e.
laminar), when Kn 1 and the mass velocity adjacent to the pore
surface is zero, b) slip flow, when 1 > K > 0.01, or c) Knudsen flow
(i.e. molecular), when Kn 1 and the mass velocity adjacent to the
surface is > zero. As the molecules in a liquid are in contact, A is
molecular diameter, which 0.25 nm for H20. For a type OX gel, Kn =
0.25/2 x 1.2 0.1, so the transport of condensed H20 through the gel
pores occurs as slip flow. For H20 vapor, A 70 nm [194] so Kn = 70/2
x 1.2 30 and Knudsen flow dominates. The effect this will have depends
on whether the H20 moleculepore wall interactions slow down or speed up
the rate of movement of H20 molecules through pores compared to mole
culemolecule interactions, both of which are possible depending on the
specific conditions, including the value of Kn [213].
Surface diffusion The surface diffusion of physisorbed H20 mole
cules depends on the surface diffusion coefficient, which in turn
depends on the jump frequency of the molecules between adjacent adsorp
tion sites, the energy barrier between adsorption sites (i.e. the
activation energy, AE) the sticking coefficient of the adsorbed H20
molecules and the concentration of available adsorption sites. The
movement of adsorbed H20 molecules is an activated process so the jump
frequency would be dependent on the adsorbed H20 concentration, AE and
366
T. The HjO molecules are Hbonded to SigOH groups, so the jump frequency
also depends on the strength of the Hbond, which is determined by the
acidity of the SigOH group, pKg, and the water content, W. The
concentration of available adsorption sites decreases as the concentra
tion of physisorbed H20 molecules increases, but increases as [SigOH]
increases via surface D2 ring rehydrolysis. This is a complex process,
so quantifying the surface diffusion coefficient, and its contribution
to the movement of H20 molecules through the pores, would be difficult.
Phvsisorption. i.e. adsorption Physisorption has the effect of
adding a sink term to Fick's laws. H20 molecules physisorb on [SigOH]
groups and strained Si3 sites, as described in the introduction, and
also on H20 molecules already physisorbed. The removal of H20 molecules
from the pore atmosphere via physisorption decreases the concentration
of H20 molecules in the pore atmosphere. Therefore P/Pq and the local
H20 concentration gradient for a particular time t will change, probably
by decreasing, from that predicted by Fick's diffusion laws, so the rate
of movement of H20 molecules through pores will decrease.
H20 molecules adsorbed onto the reactive, curved, fractal surface
which exists on the internal pores of acid catalyzed gels are very
tightly bound in comparison to those adsorbed on a flat fused aSi02
surface. Their sticking coefficient is higher and their jump frequency
is lower. The thickness, t, of the adsorbed water layer is proportional
to the relative pressure P/PQ, ignoring chemisorption effects, and can
reach up to 1.5 nm [190] on a flat surface exposed to water vapor. As
this adsorbed layer is bound so tightly in silica gel pores, it is
possible [181] that the pore radius of pores through which H20 molecules
367
are moving is reduced by the thickness, t, of the adsorbed H20 layer, or
an amount f(t) a t, and that an effective pore radius = rH f(t) should
be used in the Laplace, CarmenKozeny and Kelvin equations.
Chemisorption Chemisorption, and the associated loss of H20 mole
cules via D2 rehydrolysis, occurs when H20 molecules are physisorbed on
Si3, as discussed in the introduction. The rate of rehydrolysis, after a
H20 molecule has already been physisorbed, depends on the reaction rate
constant k, while the equilibrium concentration of the products, 2Sig0H,
and reactants, D2 and H20, depends on the equilibrium constant Kc.
Chemisorption will have no direct effect on the rate of H20 molecule
movement through pores in the vapor phase because it can only occur
after physisorption has already occurred, i.e. H20 molecules have
already been adsorbed. It will affect surface diffusion as discussed
above. Chemisorption will have an indirect effect on vapor phase and
adsorbed surface H20 diffusion because D2 rehydrolysis should create
more SigOH groups on which more H20 molecules can physisorb.
Condensation and transport of absorbed H,0 into porous silica gels
After a H20 molecule has diffused into the gel, physisorption of the H,0
molecules onto the internal pore surface leads to the formation of a
monolayer of adsorbed H20. The adsorbed monolayer has the same shape as
the pore surface, so the vapor pressure of the adsorbed H20 is described
by the Kelvin equation [194,214]. If the pores are cylindrical in nature
then the surface is concave and has a negative radius of curvature, so
the vapor pressure (P) of a H20 monolayer adsorbed on the curved pore
surface is decreased relative to the vapor pressure (PQ) of a H20
368
monolayer adsorbed on a flat surface. The decrease in vapor pressure
caused by the sharp negative radius of curvature of cylindrical micropo
res leads to condensation of H20 onto the adsorbed monolayer when the
vapor pressure of the H20 in the pores is greater than the vapor press
ure associated with the curved pore surface. For H20 at 25C, P/PQ 
0.35 for rH 1.0 nm, 0.59 for 2.0 nm and 0.77 for 4.0 mu. Therefore
in a Rh = 100% atmosphere, equivalent to P/P0 = 1.0, condensation would
occur in the pores in a type OX silica gel as soon as a monolayer is
formed if they all had negative radii of curvature (concave).
The first H20 vapor molecules to diffuse into the pores will
physisorb on the surface of the pores nearest to the gel surface so any
H20 which condenses should also condense in the pores nearest the
surface. The negative radius of curvature of the pore surface induces a
pressure drop across the vaporH20 meniscus of the condensed absorbed
H20 called the capillary stress, AP, which is described by the Laplace
Young equation, AP = 2qLVr'1cosi [194,214]. qLV (N/m) = liquidvapor
surface tension, r (m) = radius of curvature and cos = the cosine of
the wetting angle 6 (). AP is due to the pressure difference across the
meniscus. This causes a pressure gradient whose magnitude, for a given
r, depends on cos6. For the adsorption of H20 on aSi02, if 6 = 0 H20
wets an aSi02 surface and AP is positive, while if 6 = 180, H20 beads
on an aSi02 surface and AP is negative.
Therefore, if the internal surface of a capillary tube of fused
aSi02 is fully hydrated, then the surface is hydrophilic and H20 will
wet the surface, so cos6 = 1, AP is positive and H20 can be absorbed
into the capillary tube. On the other hand, if the fused aSi02 capil
lary tube is heated to a sufficiently high T, the internal surface of
369
the capillary is dehydroxylated, the surface becomes hydrophobic and H20
will not wet the surface but beads, so cos# = 0, AP is negative and H20
can not be absorbed into the capillary tube unless an external force
large enough to overcome AP is applied.
In this study though, even though the gels had been dehydroxylated
at T ranging from 600900C, H20 is absorbed into all the gels with a
t07 time dependency to saturate the pores in about 60 hours (Fig. 86).
So, even though the silica gels had been dehydroxylated at T high enough
to make a fused aSi02 surface hydrophobic, H20 is still absorbed into
the silica gel pores. Therefore, as H20 is absorbed, AP is positive, H20
is wetting the silica gel pore surfaces and the pore surfaces which have
been dehydroxylated at 600900C are hydrophilic so the surface chemis
try of the internal pore surface of a metal alkoxide derived silica gel
is different from a flat fused aSi02 surface. As discussed above, this
is due to the formation of strained D2 rings in the pores. The Lewis
acidity of the Si3 atoms, which governs the ease with which a H20 mole
cule can be adsorbed, is enhanced by strain in the rings enabling them
to accept the lone pair of electrons of the 0 in H20 molecules [175].
The basicity of the bridging 0 atoms might also be expected to
govern the ease of adsorption on strained silicate rings, but Bunker and
Brinker [175,215] showed that this is less important than the acidity of
the strained rings and the molecular basicity of the adsorbate.
Thus, when H20 molecules diffuse into the pores of a silica gel
they adsorb on the pore surface until a monolayer is formed and conden
sation can occur in concave pores. The capillary stress caused by the
pressure drop across the meniscus will tend to pull the condensed H20
further into the pores, as is seen when a gel is immersed directly into
370
H20 or the tip of a capillary tube is placed in H20. The condensed H20
can only be pulled into the pore until a 2nd meniscus is formed by the
movement of the condensed absorbed H.,0 below the external surface of the
gel, which will create an equal and opposite AP balancing the force of
the initial meniscus, which has moved down the pore. This will prevent
further movement of the condensed H20 into the pore until enough addi
tional H20 has condensed to remove the 2nd surface meniscus, creating a
force imbalance forcing the H20 further into the pores. This cycle will
repeats until eventually the pores are totally filled with H20.
The volumetric rate of flow of H20 through a porous body is
measured by the flux, J (m3/m2 of porous body/time = m/s), which is
governed by the Darcy equation [216], J = DAPl/tjl, where D = the
permeability (m2), APL = the pressure gradient in the liquid (Pa), and
r]L = viscosity of H20 (Pa.s). Positive flux moves in the direction of
increasingly negative pressure, so the flow is towards regions of
greater tension in the liquid. The rate of absorption of condensed H20
into a silica gel will therefore depend on D, APL and r?L. In a silica
gel these parameters are all strongly dependent on rH.
The permeability D of silica gels Scherer et al. [216] measured
the permeability D of two silica gels, gel A and a B2 gel, by measuring
the flux of pore liquor through ascast gels as a function of APL. Gel A
was an acidcatalyzed TEOS silica gel with R 16, Sg 550 m2/g, rH
1.25 nm, Vp 0.344 cc/g and (assuming Dg 2.2 g/cc) Db 1.25 g/cc, so
rH is very similar to a type OX gel, while Sa and Vp are smaller. The B2
gel is the same twostep acidbase catalyzed B2 gel discussed by Brinker
et al. [33,175] except that rH = 2.8 nm in Scherer et al. [216]. Scherer
371
et al. [216] found that D 15 nm2 for the B2 gel and D 1 nm2 for gel
A, so D increased by a factor of 15 while rH2 only increased by a factor
of 2.242 =5.02, so the increase in rH does not account for all of the
increase in D. The order of magnitude difference in the values of D in
gels A and B2 was attributed to a much larger width of the pore size
distribution in the B2 gel than in gel A [216], Much of the pore volume
(25%) in the B2 gel is due to pores with rH > 5 nm, and 10% of Vp is
in pores with rH > 10 nm, so the largest pores carry most of the flow.
Type OX gels should have a similar permeability to gel A, D 1 nm2 ,
because they have similar rH.
The permeability D of a porous material can be calculated from the
CarmanKozeny equation [5,216], D = (1p) (Vp/Sg)2/(fsft) = vv3/5(pSgDg)2
VvrH2/20, where Vy = VpDb (1p) = volume fraction of pores, Vp = pore
volume, Db = bulk density, p = Db/Dg = volume fraction of solid, Dg =
skeletal density, rH = 2Vp/Sg = average cylindrical pore radius, Sg =
surface area, fg and ft are factors intended to account for the noncir
cular crosssection and nonlinear path (tortuosity) of the pores in a
real material, and the factor 5 represents an empirical approximation of
the factors fg and ft, i.e. fgft 5. Adler showed that the CarmanKozeny
equation was particularly well suited to the calculation of the perme
ability of fractal networks [216,217]. Scherer et al. [216] used this
equation to calculate D from the texture of the gels. After allowing for
the changes in rH and Sg that occur during drying, they obtained D
0.31.0 nm2 for gel A which compares well with the value derived from
the Darcy equation. The value of D calculated for the B2 gel from the
CarmanKozeny equation was much smaller than the value calculated from
the Darcy equation, which was attributed to the broad pore size distri
372
bution in the B2 gel (see Fig. 3 of Scherer et al. [216]). The Carmen
Kozeny gives a similar value of D, compared to the experimentally
determined value of D, for gel A, which has a relatively narrow pore
size distribution. It gives a much smaller value of D, compared to the
experimentally determined value of D, for a B2 gel, which has a rela
tively broad pore size distribution. This infers that the CarmanKozeny
equation is only applicable to porous bodies which contain relatively
narrow pore size distributions.
The permeability in fractal materials is therefore a rH2, every
thing else being constant, with the added condition that the experimen
tally determined D will increase significantly compared to the Carman
Kozeny D as the width of the pore size distribution dVp/drH increases
[216] due to the rH2 dependency of D. Using the textural values in Table
4, the CarmanKozeny equation gives values of D equal to: D 0.036 nm2
for type OX gels, 0.21 nm2 for IX gels, 0.675 nm2for 2X gels, 1.97 nm2
for 4X gels and D = 2.96 nm2 for type 5X gels. Based on these calcula
tions, D increases by a factor of 2.96 nm2/0.036 nm2 = 82 while rH
increases by a factor of 9 nm/1.2 nm 7.5, so rH2 =56.25. The width of
dVp/drH increases significantly from type OX gels to type 5X gels, so D
should actually increase by a factor significantly larger than 82 for
these gels.
The connectivity of the porosity of gels [183], which is related
to the coordination number of the nodes of the interconnected pores,
might also have a strong influence on their permeability to both H20 and
H20 vapor. The connectivity of interconnected pores is accounted for by
the tortuosity factor ft in the CarmanKozeny equation.
373
The pressure gradient in the H..0 in the pores. APL As discussed
above the magnitude of the pressure gradient in the Darcy equation is
determined by the Laplace equation, so APL is oc rH'1. The actual shape,
curvature and size of real pores is not represented by rH, so determin
ing the correct magnitude of APL is difficult.
The viscosity of the H..0 in the pores. nL The viscosity of H20, r?L,
in confined spaces is controversial [5,218220]. Horn [218] say that rÂ¡L
is constant down to rH = 2 nm. Conversely, Clifford [219] and Etzler et
al. [220] review a large body of work and show that as rH decreases
below about 0.5 /zm, r?L oc rH'1 and that rjL in pores with rH 1 nm is 220
times as large as r]L of bulk H20. This is the accepted behavior [204] .
Simplistically then, assuming r?L a rH'1, because D oc rH2 and APL oc
rH"1, J = DAPl/7l oc rH2rH'1/rH1 a rH2 The volumetric flow of H20 through a
gel should therefore increase as rH increases, all other factors being
equal. H20 should be absorbed into a type 5X gel, rH = 9.0 nm, signif
icantly faster than a type 2X gel, rH = 4.5 nm, which should absorb bulk
H20 significantly faster than a type OX gel, rH = 1.2 nm.
The rate of mass transport of bulk H20 (as opposed to H20 vapor)
through a porous silica gel is determined by Darcy's equation, rather
than Fick's law, because the effect of APL is greater than the H20
concentration gradient. Conversely the rate of mass transport of H20
vapor through the atmosphere in the pores of a silica gel is determined
by Fick's law because there is no pressure gradient, so the H20 vapor
concentration gradient has a larger effect.
Fig. 86 shows that when exposed to an Rh = 100% atmosphere samples
#136, #127 and #141 (type OX gels) have similar H20 absorption rates and
374
saturate in about 60 hrs. Since these gels were stabilized at Tp varying
from 600 to 800C yet they all saturate in 60 hrs, they must absorb H20
at the same rate through individual pores, but they have different
numbers of pores, i.e. V so W is different. This means that T is
r p max p
not directly responsible for determining the rate of absorption of H20
into these acidcatalyzed, high R ratio, TMOS silica gels.
The type OX gels and the type 2X gel, #139, also show similar
rates of H20 absorption from a H20 saturated atmosphere, i.e. #139
saturates in about the same time while absorbing H20 2.5 times faster.
Yet type 2X gels have a calculated permeability D about 0.675/0.0362
20 times larger than type OX gels, so type 2X gels might be expected to
absorb H20 about 20 times quicker than type OX gels, which is not the
case. As discussed by Scherer et al. [216], the calculated D for B2 gels
is significantly smaller than the experimentally determined D, due to
the large spread or width in the pore size distribution, dVp/drH. The
actual D of type 2X gels should therefore be even larger than the
calculated D, and type 2X gels would absorb water > 20 times quicker
than type OX gels if the transport of water condensed in the pores
determined the rate of increase of W absorbed from an Rr = 100% atmo
sphere The type 2X gels only absorb water 2.5 times more quickly than
type OX gels, which means that transport of condensed H20 does not
contribute significantly to the rate of H20 vapor absorption into gels
pores. This infers that the mass transport of condensed H20 through gel
pores is not the rate determining step of H20 vapor absorption and that
the factors discussed above must also be taken into consideration. The
actual rate determining step is unknown, but probably involves the rate
of diffusion of water vapor through the pores. It is possible that the
375
mass and/or surface fractal dimensions of the gels, df and dg, might
also affect the H20 vapor absorption rate.
4,4.2 Water Vapor Absorption
As discussed in the introduction, the dehydrated pore surface is
very reactive. Physisorption and dissociative chemisorption of the H20
molecules occurs, which makes the actual absorption and condensation
processes more complex than the simplistic situation discussed above.
The pore surface dehydrated at high T has a small [SigOH] and a large
[D2] so the formation of an adsorbed monolayer of H20 is more complex
than on a completely hydrated hydrophilic surface. It is well known that
for a nonpolar adsorbate the shape of the plot of the statistical
thickness of the adsorbed layer of the adsorbate on a nonporous non
polar adsorbent as a function of relative pressure P/PQ (called the
tplot [190]) is independent of the composition of the adsorbent, as
long as no condensation or chemisorption occurs [190], During the
adsorption of H20 on aSi02, though, H20 is a polar molecule which will
physisorb on Sig0H but not on the unstrained Si atoms found on the
surface of dehydrated fused aSi02, which has a very low concentration
of strained Si3 atoms. Therefore the shape of the H20/aSi02 tplot, and
consequently the associated H20 sorption isotherm, is dependent on
[SigOH]. Its shape is dependent in a complex way on both [Sig0H] and the
pore morphology and texture [221], In comparison the adsorption of a
nonpolar molecule such as N2 is not affected by [Sig0H] of a dehydrated
aSi02 surface. This means that Sg calculated from the H20 adsorption
isotherm at 25C using the BET theory [2] is significantly less than Sg
calculated from the N2 sorption isotherm [221].
376
The shape of the sorption isotherm of H20 into a silica gel, which
involves absorption, adsorption and condensation, therefore depends on
both [SigOH] and rH, while the total volume of H20 adsorbed, W is oc
V As [SigOH] decreases, for a low value of P/PQ it becomes more diffi
cult to adsorb H20 molecules so the volume of H20 adsorbed and therefore
the fraction of the surface covered by H20 molecules at P/PQ, decreases
in comparison to a fully hydrated aSi02 surface. On the other hand, as
P/P0 increases, the driving force for condensation to occur in a small
pore, as described by the Kelvin equation, increases, but condensation
is prevented from happening until a monolayer is formed on the surface.
The shape of the adsorption isotherm is therefore governed by the
opposing driving forces of the degree of hydrophobicity of the surface
and condensation in the pores. In addition, because an aSi02 surface
becomes more hydrophobic as [SigOH] decreases, more chemisorption can
occur, so W decreases and [SigOH] increases as the adsorbed H20 dissoci
ates (at a rate governed by k and Kc) Therefore the deviation of the
desorption arm of the isotherm at P/PQ = 0 from the original starting
point on the isotherm increases, as does the size of the hysteresis loop
in the sorption isotherm [221],
When a type OX gel is immersed in liquid H20, H20 diffuses simul
taneously into all the pores intersecting the outside surface of the
gel. This traps air remaining in the pores inside the advancing H20
front. The trapped air forms a bubble which is compressed by the H20
driven into the gel by AP until AP is balanced by the pressure of the
compressed air. The pressure can be very large, depending on rH, and can
causes brittle failure as the pressure exceeds the gel's yield stress.
377
HjO vapor adsorbed from an Rh = 100% atmosphere might be also
expected to condense in the pores intersecting the outside surface of
the gel, trapping the air in the internal pores. When H20 is diffused
into a type OX gel from the vapor phase, though, a trapped air bubble is
never seen. For condensation to occur in a pore, the pore must have a
negative radius of curvature, i.e. concave like a cylinder. In reality
though a gel contains both convex, concave and saddleshaped pore
surface. The porosity is only modelled as a concave cylindrical pore to
calculate rH. H20 vapor will only condense in the concave pores, so air
can escape from internal pores via pores in which H20 has not condensed
and which are connected to the gel's external surface.
Absorption of H20 into the pores of gels can involve all these
complex and interdependent effects. The relative contribution of each
process depends on the conditions of the system, which change as W
increases. This means that the W a t07 time dependence shown during the
absorption of H20 into #127 is not just due to simple Fickian diffusion,
but is due to contributions from some or all of these mechanisms.
4.4.3 D, Rehvdrolvsis Rate Analysis in type OX gels
When the Raman spectra are measured, the laser beam is a finite
distance below the external surface of the gel. It takes time for the
H20 to diffuse to the place in the gel probed by the laser beam. Based
on the discussion above, it is not clear whether H20 will advance into a
gel through the pores in a planar or rough front, whether it will occur
in the vapor or liquid phase, or even if surface diffusion of physisor
bed H20 molecules will dominate. It is even possible that the H20 will
advance in a form similar to the fractal front seen when liquid H20 is
378
adsorbed into porous compacts of fine powders [222,223], where the
roughness or width of the advancing front is inversely oc its velocity.
As no bubble is formed, though, when H20 is adsorbed into gels
from the vapor phase, it seems unlikely that a contiguous liquid front
will be formed, for the reasons discussed earlier. Therefore H20 vapor
can move through pores which are unrestricted by condensed H20. The rate
of HgO vapor movement is different from the volumetric flow rate of
condensed H20, so as the diffusing front moves into the gel it will
advance at different rates in different places on the microscopic level
and will broaden as it advances.
The concentration of H20 in the interaction volume of the gel
probed by the laser, i.e. the H20 content W, will therefore be changing
with time in an unknown manner, though it is reasonable to assume that W
in the laser interaction volume oc the bulk W. Initially there will be an
induction period, which is the time required for the adsorbed H20 to
travel to the laser beam/sample interaction volume, during which W = 0.0
g/g and [D2]/[Wt] stays constant and 0.06. Once H20 reaches the
interaction volume, i.e. after the induction time, the W in the laser
interaction volume should show a time dependency similar to the bulk W.
After the induction period, the dependency of [D2]/[Wt] on t and W
will determine whether the movement of H20 molecules through the pores
to the D2 rings or D2 rehydrolysis is rate determining in these gels. As
the H20 continues to move into the gel, W in the interaction volume will
increase. Based on the arguments presented above, is unlikely to reach
Hnax (which will occur when all the pores are saturated) immediately
after the induction period. The pores are so small though (1 nm),
compared to the laser beam size (1 mm), that the Raman spectra measured
379
from the laser beam are representative of the average conditions of the
gel at that particular time, which depends on the W of the interaction
volume. As the H20 continues to diffuse into the gel, W in the interac
tion volume will continue to increase until it reaches
After the induction time, if the movement of H20 through the pores
is the rate determining step and the D2 rehydrolysis rate is signifi
cantly faster, then the D2 concentration, [D2]/[Wt], would show a
similar dependence on time as the H20 content. A diffusion rate usually
measures distance as a function of time. Obviously [D2]/[Wt] is not a
distance, but under these conditions it would be a the movement of the
H20 into the gel. The overall W shows a smooth (as opposed to discontin
uous) t07 increase with time in Fig. 86, so the increase of W in the
interaction volume and the movement of the H20 molecules into the gel
are likely to show the same t0,7 time dependence. Since the D2 rehydroly
sis would happen significantly more quickly in comparison, [D2]/[Wt]
would be a W, which is a t0,7. Therefore if [D2]/[Wt] is also a t07, H20
absorption must be the rate determining step, although as [D2]/[Wt]
decreases during H20 absorption while W increases during H20 absorption,
[D2]/[Wt] should actually be a t"07 if H20 absorption is the rate deter
mining step.
The time dependency of the rehydrolysis reaction can be obtained
from [D2] = At*n, where A is a constant. If the reaction is time depen
dent, plotting In [D2]/[Wt] against In t will give a straight line with
a slope = n. Replotting Fig. 88 in this form for samples #136, #127,
#141 and #139 gives Fig. 95. After an induction time of 1020 hrs, all
the gels show a roughly linear behavior. Linear regression of this
linear section, after the induction time, gives n = 0.62 for #137,
D2 PEAK AREA, In [D2]/[Wt]
380
In TIME, In t [mins]
+ #136 0 #127 A #141 X #139
Figure 95. The natural log of the D2 trisiloxane curvefitted Raman peak
area, In [D2]/[Wt] plotted against the natural log of the time of
absorption, In t (mins), for samples #136, #127, #141 and #139.
381
Rz =0.995, and n = 0.61 for #136, Rz =0.939. Therefore [D2]
tD2]0t"06, where [D2]Q = [D2] at t = 0 hrs. This is slightly slower than
the expected t0*7 time dependence. The minus sign in t'0*6 occurs because
[D2]/[Wt] decreases as W increases. Therefore [D2] = [D2]0t'*6, so the
rate of absorption of H20 into the pores determines the shape of Fig. 88
and the rate of D2 rehydrolysis is much faster than the rate of water
adsorption in these gels. The decrease from n=0.7 to n = 0.6 in the
time dependency, which means that the rehydrolysis reaction takes
slightly longer than water vapor absorption, occurs because the D2
rehydrolysis rate is large enough compared to H20 absorption rate to
require this extra amount of time for rehydrolysis to occur.
If the rate of D2 ring rehydrolysis in type OX gels is determined
by the rate of H20 absorption then [D2]/[Wt] plotted against W should be
roughly linear because it removes the t'06 time dependence of the rate
of H20 absorption. Figure 89 shows that all five samples do exhibit a
roughly linear dependency. The least squares correlation coefficient is
Rz = 0.990 for #136 and Rz = 0.954 for #127. Sample #124 also shows a
linear dependency on W compared to the other samples when time is
removed as a variable, except its slope is steeper. Therefore the rate
of rehydrolysis of D2 surface trisiloxane rings in type OX and 2X silica
gel monoliths is determined by the rate of absorption of H20.
In Fig. 89, the type OX gels have different Tp and show the same
dependence on W, but because the D2 rehydrolysis rate is determined by
the H20 vapor absorption rate, k can not be measured so it is not
possible to reach any definitive conclusions on the influence of Tp on
the D2 rehydrolysis rate. Sample #139, rH = 4.5 nm, also shows a linear
dependency on W, but for the same reason it is not possible to reach any
382
definitive conclusions on the influence of rH on the D2 rehydrolysis
rate.
After #124 was allowed to equilibrate at W 0.0731 g/g for 1800
hrs, [D2]/[Wt] decreased to a value slightly below that for the other
samples (Fig. 89). This could be because a) the adsorbed H20 molecules
cannot reach some of the D2 rings in the other samples so quickly
because they are more inaccessible, and/or b) the rate of H20 absorption
is just fast enough such that equation (44) can never quite reach
equilibrium in the other samples during the absorption stage, but #124
can reach equilibrium for W = 0.0731 g/g after 1800 hrs.
4.4.4 The P2 Rehvdrolvsis Equilibrium Constant K_ for type OX gels
The equilibrium constant Kc of equation (44) at 25C is
Kc [hS3OH]V[D2][H20], (45)
assuming that the activity coefficients of each constituent (which in
reality depend on rH and their local environments) is 1. Kc can be
calculated from the equilibrated data of sample #124 in Fig. 89 if the
concentrations of the reactants and products can be converted to the
same units. This, of course, presumes that an equilibrium constant Kc
can be calculated for the D2 rehydrolysis reaction, which is a heteroge
neous, solid state reaction occurring on the internal surface of
micropores, 2.4 nm in diameter, of a material which is both a surface
and a mass fractal. Assuming that the data on sample #124 is in equilib
rium, Kc can in principle be calculated from equation (45).
383
There are a number of problems. These include:
a) D2 rehydrolysis involves breaking a trisiloxane ring to form a
trisiloxane chain, which equation (44) infers creates two SijOH groups
for each D2 ring, so [SijOH] 2([D2]Q[D2]t), where [D2]Q = [D2] at t = 0
hrs and [D2]t = [D2] at time t for t > 0 hrs. Therefore Kc = 