• TABLE OF CONTENTS
HIDE
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Key to symbols
 Abstract
 Introduction
 A chronological literature review...
 Structural and textural analysis...
 Structural analysis of porous silica...
 Dielectric relaxation analysis...
 Dielectric relaxation analysis...
 Structural analysis of water adsorbed...
 Near-infrared spectroscopy of water...
 Discussion on the behavior of water...
 Appendix
 Reference
 Biographical sketch
 Copyright














Title: Porous silica gel monoliths
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
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Permanent Link: http://ufdc.ufl.edu/UF00090185/00001
 Material Information
Title: Porous silica gel monoliths
Series Title: Porous silica gel monoliths
Physical Description: Book
Creator: Wallace, Stephen,
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Bibliographic ID: UF00090185
Volume ID: VID00001
Source Institution: University of Florida
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Resource Identifier: alephbibnum - 001683431
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Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
        Page v
        Page vi
        Page vii
    List of Tables
        Page viii
        Page ix
    List of Figures
        Page x
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    Key to symbols
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    Abstract
        Page xxxiv
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    Introduction
        Page 1
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    A chronological literature review of the structure and the vibrational spectroscopy of amorphous silica
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    Structural and textural analysis of porous silica gels during sintering
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    Structural analysis of porous silica gels during the absorption of water into the gel's micropores
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    Dielectric relaxation analysis of water removal from a type ox silica gel monolith
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    Dielectric relaxation analysis (DRS) of water absorbed in monolithic porous silica gels
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    Structural analysis of water adsorbed in the pores of alkoxide derived silica gel monoliths
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    Near-infrared spectroscopy of water adsorption in a silica gel monolith
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    Discussion on the behavior of water adsorbed into porous silica gels
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    Appendix
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    Reference
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    Biographical sketch
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    Copyright
        Copyright
Full Text











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, thought-provoking 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 a-Silica . . . . 6
2.1.2 Structural Models of a-Silica . . . . 7
2.1.3 TEM Studies of a-Silica Structure . . .. 18
2.1.4 Molecular Dynamic Simulations of
the Structure of a-Silica ......... 19
2.1.5 Molecular Orbital (MO) Calculations of
the Structure of a-Silica ......... 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 a-Silica . 44

2.4 Raman Spectroscopy of a-Silica . . ... ..... 68

2.5 The Density, Spectroscopy and Structure of
Pressure Compacted a-Silica . . . ... ..... 81

iii









2.6 Raman Spectroscopy of Neutron Irradiated a-Silica . .


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(Si-O) 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 a-SiO2 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 Sen-Thorpe Central Force Function Analysis Of
the Raman Spectra . .. . . . . 404
4.4.10 The effect of H20 absorption on the main 430
cm-1 W1 Raman Peak . . . . . . .. 406

4.5 Conclusions . . . . .. . . . . . 407

4.6 A Summary of the Structure and Texture of Alkoxide Derived
Silica Gels During Sintering and Water Adsorption . 410










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 NEAR-INFRARED 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 a-SiO2 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 Full-Width-Half-Maximum (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 metal-alkoxide
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 a-Si02 [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 metal-alkoxide
derived silica gels and of water absorbed into their pores. .464

13. NIR Transmission Peaks of H20 Molecules H-bonded 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 a-SiO2 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 silicon-oxygen bond length, d(Si-O), the O-Si-O bond
angle, 9, and the tetrahedral angles, 6 and A, which define
the angular orientation of the tetrahedra about their
bridging Si-0 bonds. After [56]. . . . . . . ... 15

3. The Si-0 bond length as a function of -Sec(B) for the silica
polymorphs low tridymite, low quartz, and coesite. The
d(Si-O) 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(Si-O) in coesite (upper
curves in (a) and (b)) with those calculated for the bridging
d(Si-O) in a disilicate molecule, H6Si207 (lower curves in (a)
and (b)). d(Si-O) 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(Si-O) 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 a-quartz.
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









cm-1, where E = 0 cm-1. Stokes Raman-shifted frequencies (E-e)
are positive wavenumber values, and anti-Stokes Raman-shifted
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 short-lived (10-14
sec) electronic "virtual state", which decays with the
release of a photon. When the final vibrational state of the
molecule is higher than that of the initial state, the
released photon energy is E-e, and Stokes-Raman scattering
has occurred. When the final state is lower, the released
photon has energy E+e, and anti-Stokes 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 a-SiO2.
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 a-SiO2. The bond-bending axis is parallel to the
bisector of the Si-O-Si 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 Si-O-Si plane, and is assigned to
the W4 peak at 1060 cm-1 and 1200 cm"1. The bond rocking
direction is orthogonal to the other axes and is normal to
the Si-O-Si plane. After [85]. . . . . . . . .

9. Schematic of the normal modes of vibration in a-silica. (a)
The out-of-phase (high-frequency) and in-phase (low-


. 46









frequency) vibrations of two coupled Si-0 stretching motions,
where only Si-0 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 a-silica. 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 [112-3]. . . . .. . . . 66

11. The Raman spectrum of fused a-silica 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 a-silica
densified via irradiation with neutrons to the indicated flux
densities. After [100] . . . . . . . . . .75

13. Planar Si-0 rings of order n = 2, 3, 4 and 5, with Si-O-Si
angles 6 given for 0 = 109.50, the tetrahedral value [67]. . 76

14. The dependence of the energy of an =Si-0-Sis 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 a-silica 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(Si-O) 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 a-silica
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 a-silica. 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) 100-1350
cm'1. (b) 3600-3800 cm'1. The peak assignments of a-SiO2 are
shown. . . . . . . . . . . . . .. 197

40. The thermally reduced Raman spectrum of Dynasil. (a) 100-1350
cm-1. (b) 3600-3800 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) 100-1350 cm-1. (b) 3600-
3800 cm"1 . . . . . . . . . . . . 201

42. The thermally reduced Raman spectrum of silica gel sample OXA
stabilized at 400C for 24 hrs. (a) 100-1350 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) 100-1350 cm"1, (b)
3500-3800 cm-1. . . . . . . . . . . .. 210

46. The evolution of the thermally reduced Raman spectra of
sample OXA, rH = 1.2 nm, during densification via viscous
sintering as T increases from 400C to 900C. (a) 100-1350
cm-1, (b) 3500-3800 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) 100-1350
cm-1, (b) 3500-3800 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) 100-1350
cm-1, (b) 3500-3800 cm-1. . . . . . . . . . .

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 Si-OH
(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 SiO-H
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 Si-OH 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, [Si-OH]/[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 SiO-H 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, [SiO-H]/[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 cm-1 SiO-H peak and the 980 cm" Si-OH peak,
[SiO-H]/[Si-OH], 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 Si-0
bond length, d(Si-O) (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(Si-O) 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 a-silica
with increasing fictive temperature [100], and for pressure
compacted fused a-silica [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 a-silica with increasing fictive temperature
[100], and for pressure compacted fused a-silica [133]. . 324

85. The extrapolated dependence on the hydroxyl concentration,
[OH] (Wt %), of the structural density of Amersil [210], a
Type II a-silica, and of Suprasil [211], a Type IV a-silica. 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 (100-1350 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 Si-O 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 Si-O 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(Si-O), for samples #124, #136, #127, #141 and #139. .. 362

95. The natural log of the D2 trisiloxane curvefitted Raman peak
area, In [D2]/[Wt], plotted against the natural log of the
time of absorption, In t (mins), for samples #136, #127, #141
and #139 . . . .. . ... . . . . . . 380

96. The dependence on the water content, W (g/g), of the area, as
a fraction of the total Raman spectrum area, of the 605 cm-1
D2 trisiloxane and the 980 cm-1 Si-OH 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 #10-A 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 #10-A for a water content W -
0.467 g/g. . . . . . . . . ... .. . .417

99. The Cole-Cole 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 #10-A at W = 0.467 g/g. The angle of
suppression, a, of the semi-circular plot of relaxation RI
below the x-axis 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 #10-A, 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 #10-A, 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 #10-A 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 #10-A 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 #10-A 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 #10-A),
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 2-dimensional 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 H-bonds. The values
of the critical statistical thicknesses are indicated. =
permanent bonds, - = transitionary H-bonds. . . . ... 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 Cole-Cole plots radss]

a = Ks Born nearest-neighbor bond-stretching central force function
[N/m]

ab Bond polarizability = am/coordination of atom

am Molecular polarizability

9 Born near-neighbor bond-bending non-central force [N/m]

ILV Liquid-vapor 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 10-12 F/m

1L Viscosity of a liquid [Pa.s]

6 Contact angle in the Laplace-Young equation []

6 Intertetrahedral sSi-0-SiE bridging 0 bond angle [*], i.e.
the average bridging O bond angle representing the V(6)
associated with a-SiO2, 6 =
Oc Critical bridging oxygen bond angle []

Oe Equilibrium bridging oxygen bond angle [] 144-148

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 [m-1] = 19436 cm-1 a 514.5 nm

p Scattered phonon wavenumber [m''] = vt-UR s 19336-15436 cm-1

VR Raman frequency wavenumber [m"1] a 100-4000 cm-1

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 O-Si-O angle [*], s= <0-Si-0

w Radial frequency [rad/s] = 2rf = 1/r


xxV









WD

WL

WP

WR

A

a-silica

a0

Aiso

AS

B(f)

c

Cb

Cn

CPMASS NMR

CRN

D

d(O-H)

d(O..0)

d(Si..Si)

d(Si-O)

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

Cross-sectional area [m2]

Amorphous silica = a-SiO2

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]

Oxygen-Hydrogen (O-H) bond length [nm]

Oxygen to first 0 neighbor distance [nm]

Silicon to first Si neighbor distance [nm]

Silicon-Oxygen (Si-O) bond length [nm]

A tetrasiloxane ring, whose oxygen breathing mode causes
the peak at 495 cm'1 in the Raman spectrum of a-silica

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 cm-1 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 s-character

Tortuosity factor in the Carmen-Kozeny equation

xxvii









Fused a-Si02 Type I, II, III or IV non-porous 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 10-34 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 10-23 J/K

k Reaction rate [Mole-1min-]

k Wavevector = 22/A [m-1]

k' = k[H20]0 Reaction rate for a pseudo-first-order rate law [min"1]

K* E Complex dielectric constant = KI + iK2 = Re(K) + Im(K)

Ka = g The 0-Si-O bond-bending non-central force function [N/m =
1000 dyn/cm]

Kc Equilibrium constant = [products]/[reactants]

Kn Knudsen number = A/rH

Ko-H The O-H bond-stretching force function [N/m]


xxviii









Ks = a The Si-O bond-stretching central force function [N/m] =
W2 (l/Msi + 1/Mo)

Kg The Si-O-Si bond-bending non-central-force-function [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 dm-1]

M Atomic mass

MASS NMR Magic Angle Sample Spinning NMR

MD Molecular Dynamics

MO Molecular Orbital

n Refractive index

n(wR) Bose-Einstein thermal phonon population factor =
[(exp((h/2~)2rcvR)/kT)-l]-1 = 3.0063 for vR 104 cm-1

NA Avagadro's number = 6.023 x 1023 atoms/mole

NBO/BO Ratio of non-bridging oxygen (i.e. SiOH) to bridging oxygen
(i.e. Si-O-Si) 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

Si-OH


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 = n-1

Surface area [m2/g] of a porous material calculated from
the N2 sorption isotherm using BET theory

Small Angle Neutron Scattering

Small Angle X-ray 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 Si-O stretching vibration of an SiOH group at 970 cm-



The O-H stretching vibration of an SiOH group at 3750 cm-


SiO-H









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

Half-life [mins] = ln2/k for a first-order 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. peak-to-peak 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 Ds-1

Volume fraction of pores = (l-p)

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 cm-1 Si-OH, the 495 cm-1 D1 and the 605 cm'1 D2 peaks

Main a-silica Raman peak at 450 cm'"

Theoretical a-silica Raman peak in 800-950 cm-1 region

Symmetric Si-0 stretch (SS) peaks at 792, 828 cm'1 in the
Raman spectrum of a-silica

Asymmetric Si-O stretch (AS) peaks at 1066, 1196 cm-1 in
the Raman spectrum of a-silica

Raman peak of Si-OH stretch vibration at 970 cm-'

Raman peak of SiO-H stretch vibration at 3750 cm'1

Wide angle neutron scattering

Wide angle X-ray 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 a-SiO2 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 == n-m'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 central-force-function 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 [7-19] have recently published data showing values

of the skeletal density, Ds, of metal-alkoxide-derived silica gels

during sintering which are greater than that of fused a-silica. The

skeletal density, Ds, of fused a-silica 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 a-silica

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 a-silica 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 [21-37] 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 3-membered 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 a-silica 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 a-Silica

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] = 30-100 ppm and [Na] = 4 ppm). These include Infrasil,

IR-Vitreosil, 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 H2-02 flame, [OH] = 150-400

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 02-H2 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 volume-T 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 a-Silica

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 X-rays [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 a-Silica
S// Infrasil (I) Fa. Heraeus
SHerasil (He) Fa. Heraeus
Vitreosil (JR) Fa. Thermal-Syndicate
>_ Homosil (H) Fa. Heraeus
S2.2030 -Ultrasil (U) Fa. Heraeus
Z
IL
SpH
-J

m 2.2020 SpV
S



2.2010 TYPE ITTIV a-Silica
Suprasil (S) Fa. Heraeus
Spectrosil (SpV) Fa. Thermal-Syndicate
Spectrosil (SpH) Fa. Thermal-Syndicate
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 a-SiO2 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 X-ray 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 S-shaped liquidus curve. It

was brought to a thermodynamical-statistical 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 x-ray 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 Si-0 distance d(Si-O) = 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

Si-O-Si 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 a-Si02. Good agreement with the measured pair function

distribution curve was obtained by assuming a random orientation of the

dihedral angle, 6, about the Si-0 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 Si-O-Si

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 a-SiO2.

The truly characteristic part of the electromagnetic spectrum is the

far-infrared 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 a-quartz and used the valence-bond force

field approximation, giving d(Si-O) w 0.16 nm and 0 1500. They

obtained force constant values of Ks w 480 N/m (Si-0 stretching), Ka

35 N/m (O-Si-O bending) and KBg 5 N/m (Si-O-Si bending). Although the

selection rules were not adhered to, 15 predicted frequencies were

within the ranges of the spectra of fused a-SiO2 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 a-SiO2 which was

developed to investigate the vibrational spectroscopy of a-Si02. They

applied an energy minimization technique with a Keating force-field to

obtain equilibrium atomic coordinates from the original model and

concluded that the Bell-Dean random structure is an acceptable descrip-

tion of a-SiO2. The relaxed structure gave approximately the correct

values for the density, enthalpy of crystallization and the X-ray 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 force-field function is also required, as

well as better information on the bond-angle 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 a-Si02,

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 Porai-Koshits 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 non-coalescing 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 a-SiO2 the number of structural constraints

exceeds the number of degrees of freedom, means that a-SiO2 must have a

granular structure. He gave a broad review [52] of the spectroscopic

properties of a-SiO2 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 a-Si02 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 a-SiO2. 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 9-cristobalite microcryst-

als, the Raman spectrum of a-SiO2 should resemble 9-cristobalite, 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 a-SiO2 with

radically different medium-range structures. They compared the RDF and

the neutron and X-ray structure factors computed from each model with







14

experimental data. Despite the differences in medium-range 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 a-Si02, 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 a-SiO2 for the

four ranges of order, namely short- (SRO), intermediate- (IRO, or

medium), long- (LRO) and global-range 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(Si-O) ; 0.161 nm, and each

0 atom bridges between 2 Si atoms. There is a small spread in d(Si-O), a

small spread in the O-Si-O angles, 0, (spread w 0.75*), and a large

spread in 0. Bell and Dean's ball and stick model [49-51] 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(Si-O), the O-Si-O bond angle, b, and the tetrahe-
dral angles, 6 and A, which define the angular orientation of the
tetrahedra about their bridging Si-O 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 Zachariasen-Warren model [40,41] for a-SiO2.

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 a-SiO2 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(Si-O) 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 Porai-Koshits [LPK] micro-

crystalline model [57], which consists of microcrystallites of cristoba-

lite, with connective Si-0 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 a-SiO2 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 a-SiO2. Structural parameters are not uncorrelated; d(Si-O) and

0 are known from chemical theory to be correlated. Furthermore 6 must be

correlated with d(Si-O), 0, 0 and other values of 6 in order for the

ring of bonds to close on themselves. Significant numbers of regular

rings (planar 3-fold and puckered 4-fold) are believed to exist in

a-Si02, 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 3-membered rings a network of

corner sharing tetrahedra could accommodate, such that the networks

should be strain free besides the 3-membered 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 3-membered 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 3-membered 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 a-SiO2.



2.1.3 TEM Studies of a-Silica Structure

Gaskell and Mistry [62] produced high resolution TEM micrographs

of small a-SiO2 particles about 15 nm in diameter. Micrographs of solu-

tion-precipitated a-SiO2 had a more regular, ordered appearance than

those of a flame hydrolyzed a-Si02. 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 a-Si02

using dark field TEM images. Bright spots observed in the dark-field

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 a-Silica

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 a-Si02. 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 a-SiO2 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 3-body interaction term

to a modified ionic pair potential to simulate the directionally

dependent bonding in a-SiO2. 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 X-ray and

neutron scattering data on a-SiO2. Ring size distribution measurements

of the 648 atom a-Si02 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 a-Si02 by

applying a uniaxial strain throughout an MD cell. They used a 2-body

Born-Mayer-Huggins potential because a 3-body potential provided no

improvement in the behavior they investigated. The fracture stress of

the MD a-Si02 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 a-SiO2 failed by

extension of the Si-O bonds while 0 did not have time to increase.



2.1.5 Molecular Orbital (MO) Calculations of the Structure of a-Silica

O'Keeffe and Gibbs [66] used MO theory to model defects in a-SiO2.

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

Si-O single bonds, so Si=O bonds can be ruled out as a major defect in

a-Si02. The strain energy in 2-membered 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 a-Si02 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 bond-breaking, by H20

molecules. Molecular Orbital calculations suggested that bond angle

deformation (i.e. strain) is most effective in increasing the chemical

activity of the Si-O-Si bond. Strain transforms an inert Si-O 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 Si-O bond.







21

The strain-free bonding configuration corresponded [67] to the

minimum energy value where d(Si-O) = 0.163 nm, the 0-Si-O 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 Si-0

bond energy of 100 kcal/mole. Increasing or decreasing d(Si-O) by 0.01

nm required 330 kcal/mole. Changing b by 10* required %25 kcal/mole.

Strained surface defects in dehydroxylated a-SiO2 exhibited en-

hanced reactivity compared to unstrained defects in two respects [68].

First, the strained defects acted as strong acid-base 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 Si-0 bond in the strained defects were more susceptible to

reactions with adsorbed chemicals, which resulted in bond rupture.

McMillan [69] did a series of ab-initio MO calculations to obtain

nonempirical force fields for silicate molecules. He obtained values of

around Ks = 600 Nm"1 for Si-0 stretching, K. = 40-50 Nm"1 for 0-Si-O

bending, and Kg = 17 Nm-1 for Si-O-Si 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 a-SiO2. 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 Si-0 bond which are related to the magnitude

of the r bonding between Si and 0. The Si-0 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 Lorenz-Lorentz equation:



R = (n2-l/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 cm-1 peak shifts from 1106 to 1077 cm1.

The bond strength also decreases, the average 0 decreases from 146.8 to

139*, the d(Si-O) 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 Si-0 bond increases concomi-

tantly [70]. The increase in density can be attributed to decreasing

dr-pr 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 Si-0 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 Si-0. 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(Si-O)

decrease as the Si-0 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 Si-0 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 dr-pr type for Si

is well established, especially in bonds to 0 [70-73]. Overlap between

filled 0 pr and Si dr orbitals increases as 0 increases.

Hill and Gibbs [74] examined the interdependence between tetrahe-

dral d(Si-O) 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(Si-O)

correlates linearly with -sec8 over the entire range of observed angles

(137-180*). Shorter bonds involve wider angles, so that


d(Si-O) = -0.068 secO + 1.526, R2 = 0.74









for d(Si-O) = 0.1585 0.1623 nm.

The variance in d(Si-O) is small compared to d(Si...Si), so the

Si...Si separation involved in a Si-O-Si linkage can be approximated by

the linear equation



log d(Si...Si) = log 2d(Si-0) + 0.81 log sin(0/2). (3)



Log 2d(Si-0) is the intercept = 0.503. It has been proposed [74] that

Si...Si controls the lower limit of 0 at a value = 0.30-0.31 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 "hard-sphere" nonbonded

radius for silicon may not be realized in solids.

The d(Si-O) bond length also depends weakly on the d(Si...Si)

separation distance. As the Si atoms approach each other as 0 decreases,

d(Si-O) increases slightly.



d(Si-O) = -0.121 d(Si...Si) + 1.982 (4)



for d(Si...Si) = 0.3 0.32 nm.

Newton and Gibbs [75] used ab-initio MO theory to calculate

energy-optimized d(Si-O) 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

(d-p) i-bonding involving all 5 of the 3d atomic orbitals of Si and the

lone-pair atomic orbitals of the 0. There was a build-up 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 ab-initio calculations of bonding in

silicates. He showed that the disiloxy (Si-O-Si) group is very similar

in silicates, a-Si02 and the gas phase molecule disiloxane with d(Si-O)

= 0.162 0.165 nm and 0 = 140 150*. d(Si-O) shortened nonlinearly

when plotted against 0, but linearly when plotted against either the

hybridization index of the bridging 0 atom, A2 = -l/cos
fraction s-character, 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(Si-O) plotted against 0, on which is superim-

posed the experimental bond length and angle data for the a-SiO2 polym-

orphs [76]. The data follow the general contour of the surface, but the

observed d(Si-O) 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 Si-O bond length as a function of -Sec(0) for the silica
polymorphs low tridymite, low quartz, and coesite. The d(Si-O) 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(Si-O) in coesite (upper
curves in (a) and (b)) with those calculated for the bridging d(Si-O) in
a disilicate molecule, H6Si207 (lower curves in (a) and (b)). d(Si-O)
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(Si-O) 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 a-quartz. 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 a-Si02 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 [72-3] investigated the bond structure of the

Si-O bond and favored the (d-p)r bonding model, discussed by Revesz

[70], for the Si-O bond in silicates. This involves the atomic d-orbit-

als of Si and the p-orbitals of 0 in Si04 tetrahedra, with the possibil-

ity of an admixture of s and p character in the d-orbitals as well as

significant overlap with the three Si d-orbitals and/or the Si

a -orbitals. Janes and Oldfield [73] examined the question, given the

existence of (d-p) r-bonding, to what extent is the effect significant;

i.e. does the correlation between d(Si-O) and 0 originate from changes

in (d-p) r-bonding? Molecular Orbital calculations showed the possibili-

ty of (d-p) i-bonding but implied only minor structural significance, so

the (d-p) w-bonding effect facilitated charge transfer, but it was

insensitive to variations in d(Si-O) or 0.

Devine et al. [77-80] concluded from Magic Angle Sample Spinning

Nuclear Magnetic Resonance (MASS NMR) data of compacted a-SiO2, 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) = 13-16 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 0-60 KJ/mol, or 0-5000

cm-1. This is equivalent to a temperature (kT) of 0-6000 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, 3N-6. 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 Raman-shifted frequencies
(E-e) are positive wavenumber values, and anti-Stokes Raman-shifted
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
short-lived (10-14 sec) electronic "virtual state", which decays with
the release of a photon. When the final vibrational state of the
molecule is higher than that of the initial state, the released photon
energy is E-e, and Stokes-Raman scattering has occurred. When the final
state is lower, the released photon has energy E+e, and anti-Stokes
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 Anti-Stokes

E +e

Li
U


0



(c)


T
E

i


Anti-Stokes
Raman


Raleigh


E-e
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- 0-0- 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 3N-3. N is the number of atoms

in the primitive unit cell. These 3N-3 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 3N-3 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 time-dependent 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

time-independent perturbation followed by a time-dependent 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 time-dependent 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 time-dependent 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 time-dependent 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 a-SiO2. 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 a-Si02 are discussed in the next section.







44

2.3 Modelling the Vibrational Behavior of a-Silica

Wadia and Balloomal [46] developed a model explaining the Raman

and IR spectra of a-SiO2 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 wave-like form

for the normal modes of vibration.

Bell and Dean [49] took a third approach to determining the

vibrational behavior of a-SiO2. They used a physical ball and stick

model of a giant inorganic molecule complying with short range structur-

al data obtained from X-ray and neutron scattering experiments on







45

a-SiO2. They calculated the normal mode frequencies and atomic ampli-

tudes of vibration of the model using a central Si-0 force constant Ks =

400 N m'1 (1 N m'1 = 1000 dynes/cm). The ratio of the non-central O-Si-O

force constant Ka to the Ks was taken as 3/17 w 0.176. They obtained

frequency distribution histograms for a-SiO2 which were similar to

experimental Raman spectra, possessing all the main structural peaks.

With the surface non-bridging bonds fixed, they obtained peaks at 400,

500 (shoulder), 750 and 1050 cm'1. This compared with their observed

experimental peaks at 500, 600, 800 and 1100 cm-1.

Detailed analysis of selected normal modes by Bell and Dean [49]

showed that the 1050 cm-1 band in the calculated spectrum was associated

with an asymmetric bond stretching vibration where bridging oxygen atoms

moved parallel to the Si...Si line joining their immediate Si neighbor

(Fig. 8). The modes in the 500 cm-1 (shoulder) and 800 cm'1 regions were

associated with bond bending vibrations in which 0 atoms moved along the

bisectors of the Si-O-Si angles (Fig. 8). In the 400 cm-1 peak the modes

were associated with the bond-rocking motion of bridging oxygens

vibrating perpendicular to the Si-O-Si 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 a-SiO2 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 a-SiO2.
The axes point along the direction in which the bridging 0 atom moves in
the bond bending, stretching and out-of-plane rocking normal modes.
These normal modes correspond to peaks in the Raman spectra of a-SiO2.
The bond-bending axis is parallel to the bisector of the Si-O-Si 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 Si-O-Si 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 Si-O-Si
plane, i.e. out-of-plane. After [85].






47

a-SiO2 (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 long-range 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 energy-loss 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 a-SiO2 by determining the poles in K2 and Im(-l/K*)

and comparing their positions with those of the observed Raman spectra.

Kramers-Kronig 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 TO-LO

pairs at 455 and 495 cm-1, 800 and 820 cm-1, and 1065 and 1200 cm-1. 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 cm-1 peak was wrong [87], as

was [5] Walrafen's [88,89] assignment to mSi+ and mSi-O0 defect centers.

Wong and Angell [90] reviewed the early literature of the paracry-

stalline models for the vibrational spectroscopy of a-SiO2. They pointed

out that the abnormal excess heat capacity of a-Si02 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 ball-and-stick 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 a-SiO2

[49-51]. This approach reproduced the broad density of states, implying

that a-Si02 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

a-Si02 consists of a random 3-dimensional 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 a-Si02, as does the

magnitude of the bridging 0 bond, 0. 0 determines whether the material

possesses narrow molecular modes or broader solid-state band-like 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 a-Si02. They used just the nearest-neighbor

central Born-force, Ks, between Si atoms bonded to 0 atoms, which

allowed them to study the transition from molecular to solid-state

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 a-Si02, effec-

tive coupling among the tetrahedra leads to solid-state modes, rather

than molecular modes. Therefore the vibrational characteristics of

a-Si02 are determined more by 0 than by the Si04 tetrahedra. Inclusion

of a small non-central force does not modify these results, because the

near-neighbor non-central 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 a-SiO2



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 highest-frequency bands in the vibrational

density of states (VDOS) of a-SiO2. 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), out-of-

plane motion of the Si-0-Si bridging bonds, w3 (= W3) to the bond

bending (B), or symmetric stretch (SS), motion of the Si-O-Si bridging

bonds, and w- (m W4) to the bond stretching (S), or antisymmetric

stretch (AS), motion of the Si-O-Si bridging bonds [94] (Fig. 8). In Sen

and Thorpe's model [91] the bond rocking (R) motion perpendicular to the

plane of the Si-O-Si 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 vibrational-band limits calculated for the central-force 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 O-Si-O angles 0 = cos1'(-1/3) = 109.5* and

common Si-O-Si angles 0. The dihedral angle, 6, was allowed to have any

value. The bonds possessed the types of vibrations known to exist in the

a-Si02 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 a-Si02, 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 Si-0 bond-stretching constant,







52

Ks, and the Si-O-Si 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 = (W32-W42) (32+w42)-1 (+4M0/3Msi). (12)



Substitution of the W3 and W4 peak positions of a-SiO2 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 Sen-Thorpe theory was realistic and could be used to analyze

the structure of a-SiO2.

The splitting of the highest-frequency mode W4 into a well-sepa-

rated transverse-optical longitudinal-optical (TO-LO) pair is not

accounted for by this theory. The position of the so called bare-mode,

whose frequency is split by Coulomb interactions into the TO-LO 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 X-ray

diffraction value of 144* [41]. Galeener [92] obtained values of Ks z

444-569 N/m and 0 126-130.

The calculated wavenumber of the lowest-frequency 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

low-frequency 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 [96-97] 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 in-phase stretching

associated with bending-type motion at W1. It is reduced for the out-of-

phase stretching associated with the stretching-type 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 a-SiO2. 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 cm-1. He

derived an expression relating the full-width-half-maximum (FWHM) of the

Raman peaks to the FWHM of 0, i.e AO. The X-ray 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 in-phase 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 a-SiO2 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 Si-O-Si

angle, the bending (B) motion [92]. Galeener preferred to call this the

symmetric-stretch (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 ESi-O-Si= 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 asymmetric-stretch (AS) motion (Fig .9(a)).

Lucovsky [98] presented evidence for the existence of a Raman

active peak in the 900-950 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

Out-of-Phase
High Frequency,
(a) Bending or
Asymmetric
Stretching (AS)


W4 LO


1190 cm-1


Si Si

In-Phase
Low Frequency,
Bending or
Symmetric
Stretching (SS)

W1


450 cm-1


9 P

---Si Si ---0
/
/ \
O 0
Silicon "Cage" Motion,
Involving some SS of the O Atom


W3 TO

790 cm-1


W3 LO

810 cm-1


Figure 9. Schematic of the normal modes of vibration in a-silica. (a)
The out-of-phase (high-frequency) and in-phase (low-frequency) vibra-
tions of two coupled Si-O stretching motions, where only Si-O 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].


W4TO


1060 cmT1







56

charge state of -1) though he did not actually show a Raman spectra

showing this peak. Lucovsky assigned the 605 cm-1 peak to three-coordi-

nated oxygen atoms (C3), describing the peak as an intrinsic defect in

terms of the valence-alternation-pair model. Galeener [67,100-103] and

Brinker et al. [5] have since shown that this assignment is wrong.

Bell [50] showed that the fit between experimental ball-and-stick

model and theoretical Raman curves for a-SiO2 improved after further

refinement of the CRN model. The theory predicted the 1200 cm"1 peak and

slightly exaggerated the size of the 800 cm"1 peak due to too small a

cluster size. It did not predict the correct behavior of the 600 and 495

cm-1 peaks due to lack of some unspecified symmetry in the 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 a-SiO2 glasses, and their interpretation

in terms of structural models. He pointed out that the first successful

Raman spectra of a-SiO2 was obtained by Gross et al. [104] in 1929.

McMillan [94] summarized his knowledge of the a-Si02 Raman peaks.

These were: a) Two weak, depolarized bands depolarizationn ratio p

0.75) near 1060 and 1200 cm-1, b) A strong band at 430 cm"1 which is

highly polarized and also asymmetric, partly due to thermal effects and

partly due to weak bands near 270 and 380 cm'1 which correspond to

maxima in the depolarized spectrum, c) Two weak sharp polarizable peaks

near 500 and 600 cm"1 of controversial origin, attributed to broken

Si-O-Si bonds, or to small siloxane rings. McMillan [94] dismissed







57

Phillips [52] assignment involving double-bonded Si=O linkages as not

being supported by ab-initio 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 Si-O stretching vibrations within the framework structure, or

to the TO and LO vibrational components, separated in frequency by the

electrostatic field in the glass. The 430 cm-1 peak was assigned to the

symmetric motion of the bridging oxygen in the plane bisecting the

Si-O-Si 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 a-SiO2 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 a-SiO2 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 a-SiO2

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 a-SiO2. 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 a-Si02 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 Si-O stretching force

constant, Ks, with values varying from 300 to 700 Nm"1. Gibbs et al.

[105] carried out an ab-initio molecular orbital (MO) calculation for

the SiOH4 molecule, giving Ks = 665 Nm-1. This is consistent with most of

the calculations which have reproduced the high-frequency region of the

vibrational spectrum, associated with the Si-0 stretching motions.

Inclusion of the nearest-neighbor 0...0 interaction, which changes

during Si-O stretching, might lead to slightly lower values.

Most MO calculations have also considered the 0-Si-O and Si-O-Si

bending forces, Ka and Kg respectively. The estimated K, value has

ranged from 20 to 70 Nm-1, expressed as (l/d(Si-0)2)(dE/d(d(Si-O)2)},

where d(Si-O) is the Si-0 bond length and E is the theoretically

determined energy [94]. Kg has been estimated at 2-20 Nm-1. Gibbs et al.

[105] calculated a similar value of 100 Nm"1 for K and 8-18 Nm-1 (as a

function of the 6) for Kg for H6Si207 [94].

Revesz [70] discussed the directionality ratio, r, of silica

polymorphs and a-silica. The directionality ratio r is a dimensionless

ratio originally mentioned by Phillips [106,p.337], defined as the ratio

of the next-nearest-neighbor bond-bending noncentral (directed) force,

1, to the nearest-neighbor 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 a-SiO2.







60

Phillips [106] discussed r for binary crystals of formula ANB8-N,

for which a = Ks is the bond-stretching force function of the AB bond.

There should be both A-B-A and B-A-B bond-bending noncentral force

functions in ANB8N, i.e. Ka and K but Phillips does not distinguish

between them. The A-B-A bond-bending force function Kg determines the

resistance to rotation of A around B, while the B-A-B bond-bending 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 a-silica. 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 a-SiO2 the 0-Si-O bond-bending force, Ka, is larger than the

Si-O-Si bond-bending 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

O-Si-O bond angle 0 = 109.5* is very rigid, while the Si-O-Si bond

angle, 0, is much more flexible, so Ka > Kg. The Si-0 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 Si-O bond stretching force constant, is the largest and

consequently the dominant force function, so it is used in all vibra-

tional models [45,91-2,107,108]. Some models also include a bond-bending

force-function 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 a-Si02 using a Bethe lattice and quote

a value for 6 of 78 N/m. They define 9 as the non-central force con-

stant, so must be the 0-Si-O bond-bending 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

Si-O-Si bending vibrations [70]. He gave a value for a-SiO2 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 Si-O-Si bending force function. On the other

hand this value is very similar to the expected value of the O-Si-O

bending force function Ka. According to Sen and Thorpe [91], Ka/Ks 5 0.2

for AX2 glasses, where Ka is the O-Si-O 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 a-SiO2. Revesz gives a value for

a-cristobalite of r = 0.199 calculated from values given by Rey [109].

Examination of [109] shows that Rey gives values for the O-Si-O bending

force constant, not the Si-O-Si 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 corner-sharing each oxygen between two Si04 units. Sen

and Thorpe [91] found that the vibrations derived from Si-0 stretching

in a-silica depend on 0 between the tetrahedra. As this angle is larger

than 112* in a-SiO2 (1440, in fact [41]) the stretching modes of adja-

cent tetrahedra become coupled. This causes the high-frequency bands

(1060 cm-1 and 1200 cm"1) of modes where the coupled Si-0 stretches are

out of phase, giving the resultant oxygen motion parallel to the Si...Si

line (Fig. 9(a)). A low-frequency set of modes (the 450 cm'1 W, peak)

where adjacent Si-0 stretching is in phase give the resultant oxygen

motion in the plane bisecting the Si-O-Si bond (Fig. 9(a)), which agrees

with Galeener et al. [42,55,88,92]. This model does not predict the 800

cm-1 Raman peak, which must involve other considerations. Bell and Dean

[51] did reproduce this peak, involving predominantly Si motion (consis-

tent with the isotopic substitution experiments of Galeener and Geiss-

berger [110]), as a silicon cage motion shown in Fig. 9(b).

Barrio and Galeener [107,108] tried another approach to modeling

the vibrational behavior of a-SiO2. 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 bond-length 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 a-SiO2. 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 "near-perfect" [107] agreement with the vibrational density of states

(VDOS) produced by the large-cluster 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 cm-1 because of neglected Coulomb

forces. The 495 and 606 cm'1 peaks are not reproduced because they arise

from defects in the structure not modeled by the Bethe lattice.

The Born noncentral force Ka is a two-body force which can accu-

rately simulate the more accurately simulate the more realistic Keating

three-body 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 a-SiO2. 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 a-Si02 structure consisted of clusters having







64

the internal topology of cristobalite, a cubic structure with density 5%

greater than a-SiO2. 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)2-Si=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 cm-1).

This is refuted by Galeener and Wright [43]. Phillips [54] attributed

the D2 peak to a ring mode associated with intercluster cross-linking.

Galeener [103,112] reviewed the Raman and ESR spectroscopic

evidence for the structure of a-SiO2. 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 = SiO-H vibration,

and W5 = 970 cm-1 s Si-OH 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 a-SiO2, 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 a-SiO2

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 a-SiO2 shows no detectable

ESR signals, so ESR signals are seen only after the sample is subject to

various kinds of radiation, including Cu Ka X-rays. The most important

of these signals is the E' line whose origin is the spin of an electron

in the unbonded sp3 of a 3-bonded 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 non-bridging oxygen defects discussed earlier concern-

ing Raman defects.

McMillan [69] summarized the vibrational studies of a-Si02. He

discussed a defect peak seen at 910 cm-1 in wet and dry a-Si02 samples

which does not scale with any other defect peaks. This band occurred in

the region commonly assigned to the symmetric Si-O stretching vibration

of an =Si-0', or sSi=O group.




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