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.
