Effect of formamide additive on the chemistry of silica sol-gels II. Gel structure

Journal of Non-Crystalline Solids 105 (1988) 223-231 North-Holland, Amsterdam

223

EFFECT OF F O R M A M I D E ADDITIVE O N THE C H E M I S T R Y OF SILICA S O L - G E L S II. Gel structure G. O R C E L 1 a n d L.L. H E N C H Advanced Materials Research Center, 1 Progress Boulevard #14, A lachua, FL 32615, USA

I. A R T A K I a n d J. J O N A S School of Chemical Sciences, Department of Chemistry, University of Illinois, Urbana, IL 61801, USA

T.W. Z E R D A Department of Physics, Texas Christian University, Fort Worth, TX 76129, USA

Received 6 July 1987 Revised manuscript received 16 May 1988

In the present work we studied the influence of formamide on the structural and textural characteristics of tetramethoxysilane-derived silica gels by Raman spectroscopy, small angle X-ray scattering, Mo acidic test, and N 2 adsorption-desorption isotherms. It was shown that sols are made of primary particles of about 20 ,~ in diameter. These primary structural units agglomerate in secondary particles of about 60 ,~ in diameter. Gelation occurs when the secondary structural units agglomerate with each other and form a three-dimensional network throughout the sample. The evolution of the relative Raman intensity of the Si-O-Si peak at 830 cm 1 confirms that polycondensation still takes place after gelation, until a reduced time (reaction time/gelation time) t / t o of about 2, after which no significant variation of the Raman intensity is observed. The structural and textural characteristics were found to be dependent on the concentration of formamide. The particle size, pore volume, and average pore radius increase when the concentration of formamide increases. These results are in very good agreement with previous work which showed that formamide decreases the hydrolysis rate but increases the polycondensation rate of tetramethoxysilane.

1. Introduction T h e process of gel f o r m a t i o n starting with liquid sols p r o d u c e d f r o m silicon alkoxides has b e e n u n d e r s t u d y for s o m e time [1-5]. These gels, after aging a n d drying, are fired to p r o d u c e glasses of e x t r e m e l y high q u a l i t y [6]. A m a j o r c o n c e r n in the p r o d u c t i o n of these m o n o l i t h i c d r i e d gels is the p r e v e n t i o n of cracks d u r i n g aging a n d drying. As the solvent escapes f r o m within the gel or as the p o r e size changes d u r i n g these processes, stresses are i n t r o d u c e d i n t o the silica n e t w o r k which m a y cause fracturing. R e c e n t l y [7-10], studies have

1 Current address: Spectran Corp., 50 Hall Road, Sturbridge, MA 01566, USA. 0022-3093/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

b e e n m a d e r e g a r d i n g d r y i n g c o n t r o l chemical a d ditives ( D C C A s ) which have been f o u n d to r e d u c e cracking. T h e d y n a m i c effects of the f o r m a m i d e D C C A on the f o r m a t i o n of the d r i e d gels will be a n a l y z e d in this s t u d y b y c o m p a r i s o n with a s t a n d a r d s o l - g e l system. Previously, v a r i o u s techniques have b e e n applied to the analysis of s o l - g e l systems including light scattering [11], I R [12], N M R [13-15], small angle X - r a y s c a t t e r i n g ( S A X S ) [16-18] a n d the m o l y b d e n u m acidic test [19,20]. However, s e l d o m have different a n a l y t i c a l m e t h o d s b e e n a p p l i e d to the s a m e s o l - g e l system. T h e p r e s e n t s t u d y unites the results r e g a r d i n g the p o l y c o n d e n s a t i o n step of g e l a t i o n a c q u i r e d b y M o acidic test, SAXS, p o r e size analysis, a n d R a m a n scattering. This l a t t e r m e t h o d was r e c e n t l y used [21] to s t u d y the dy-

224

G. Orcel et aL / Chemistry of silica sol-gels H

namics of the sol-to-gel transition of a simple silica gel and to follow the further evolution of the S i - O - S i network. Raman spectroscopy is well suited for studying these systems since no special sample preparation techniques are required to protect the integrity of the sample. Alterations in the polymerization process caused by the DCCA may thus easily be probed. From light scattering theory, the Raman intensity is known to be proportional to the number density of vibrators (bonds) in the scattering volume, N. Unfortunately, quantitative information regarding the various perturbations on this proportionality is not available so only qualitative trends in N may be derived from the spectra. The same bonds ( C H 3 - O - S i , C H 3 - O H , Si-O-Si, etc.) will be observed in both systems (with and without DCCA); any qualitative differences between growth and decay rates, peak heights or shapes will thus be explained as effects of the additive. The reaction of silica colloids with molybdic acid had been used for a long time to characterize soluble silicates [22-24]. In an acidic medium, the SiO 2 particles dissolve and form monosilicic acid Si(OH)4. The reaction between Si(OH)4 and molybdic acid produces a yellow complex [25]. The development of the color of the solution can be recorded as a function of time and gives information on the depolymerization rate of the silica particles. Furthermore, the rate constant of the depolymerization reaction can be related to the particle size of the colloids [22]. We applied the same procedure to the study of silica sols prepared in an organic solvent. The purpose of this experiment was to estimate the size of the silica particles and to correlate these results with the Raman data. The formation of SiO 2 gel from silicon alkoxide occurs through hydrolysis and polycondensation reactions. The structural units which developed prior to gelation are polymer-like. They can be studied by SAXS and meaningful results are obtained when the "particles" can be well represented by a radius of gyration. Dilution experiments showed that the Guinier approximation is valid for these systems [16,26]. Solid samples can be studied by SAXS as well, provided they are thin enough and the coefficient

of transmission is not too low. An analysis of the scattering curves in the Porod and Guinier regimes allows the computation of the electronic radius of gyration and the fractal dimension [26]. The last quantity indicates a possible structure for the "particles" and suggests a potential growth mechanism. Additional information on the gel network structure can be obtained using gas adsorptiondesorption isotherms. Nitrogen is the usual adsorbate and by applying the BET theory the surface area, pore volume and average pore radius can be obtained [27]. In addition, in the range of very small particle size with which we are concerned, the pore diameter and the particle diameter are of the same order of magnitude [28].

2. Experimental The two types of silica sols were prepared by dropwise addition of a water-methanol mixture to the initiating silicon alkoxide reagent (Si(OCH3)4, tetramethoxysilane = TMOS) which had been previously mixed either with the DCCA (solution I) or with an equivalent amount of methanol (Type II solution, no DCCA). A final concentration of 1.6 molar silicon was employed with a 10 : 1 mole ratio of water to silicon. The experiments were all carried out at room temperature, (21 + 1)o C. The Raman spectrometer has been described in detail elsewhere [29]. An argon ion laser (SpectraPhysics 165), operating near 0.5 W at 488 nm, was used as the excitation source. A 1.2 cm -1 slit width was employed with a 4 cm-1 step interval. Since no depolarized component for the SiO 2 network modes was detected in trial runs, the laser was set to vertical polarization and no analyzer was used. The samples were placed in sealed glass containers which functioned throughout the experiments as the Raman cuvettes. Once sealed, the sample spectra were run periodically until well after gelation when aging and drying were performed. The spectral profile was recorded digitally on floppy disks and later transferred to a VAX-11 computer for processing via RADAP, a general data analysis program written for this lab. The molybdic acid test was carried out as described by Iler [2]. First a solution of (NH4)6Mo 7

G. Orcel et a L / Chemistry of sifica sol-gels II

O244H20 was prepared. The pH was adjusted with concentrated ammonia. The concentrations in the mixture were: 0.57 M in Mo4z- and 1.18 N in N H ~ . The reagent was prepared by diluting the previous solution with 1.5 M sulfuric acid. The final mixture was 0.07 M in MoO 2 - , 0.15 N in NH~- and 0.38 N in SO2 - . The pH was around 1.2. An aliquot of the silica sol was added to the reagent. The reacting mixture to be analyzed contained 2.4 mg of SiO 2. The evolution of the color with time was monitored by measuring the absorbance of the solution at 400 nm with an HP 4850 A diode array spectrophotometer. For the SAXS experiments we used the facilities of the National Center for Small Angle Scattering Studies at Oak Ridge National Laboratory. The sample-detector distance was 2.13 m and the transmission coefficient of the samples about 30%. A more detailed description can be found in ref. [16]. The samples for the N 2 adsorption-desorption study were allowed to age at room temperature for 24 h. They were dried at 200 ° C for one day and outgassed at 300 ° C for 4 h. The analyses were performed on a fully automated QuantachromeAutosorb 6, and lasted about 15 h. 3. Discussion

3.1. Raman spectroscopy The sol which contained several different chemical species (CH3OH, H 2 0 , HCONH2, TMOS, and the various S i - O - S i polymers) generated a spectrum consisting of the superimposed peaks for each constituent. In the spectrum presented in fig. 1, all of these peaks are seen except those due to TMOS since the hydrolysis was completed. The peaks of a typical formamide containing gel are identified in fig. 1. In order to compare the various spectra taken over several days and involving different solutions, some type of internal calibration was required. A constituent with an invarient concentration provides the best source of calibration. Since the formamide is neither created or consumed in the gelation process, the DCCA peaks provided an excellent choice. Obviously, however, this does not

225

o methanol ° formamide c, ~Si-O- Si~-

o

I

J

i

I

I000

i

i

i

i

I

J

I

i

2000 FREQUENCY

I 3000

J

I

I

I 4000

(cm")

Fig. 1. Typical Raman spectrum of a silica sol.

facilitate comparison between Type I and Type II solutions. As any further additives may only complicate the spectrum, the only viable alternative was the methanol C - O stretching mode at 1100 cm-1. Unfortunately, the methanol concentration changes due to hydrolysis. However, this problem is alleviated after approximately 0.7 t c when both Raman and N M R results indicate near-completion of hydrolysis [13]. After approximately 6 t G, some methanol appeared outside the gel, either as a pool atop of it or between the gel and the walls of the container. The data presented after this period therefore have this additional error, but as no major changes in the spectra occurred, the effect on the calibration is minimal. The experiments were performed using polarized incident laser light and a 90 ° observation scattering geometry with no analyzer. Raman theory [30] for molecular liquids and gases predicts for this setup that the band intensity is proportional to the incident light intensity I 0 and the number of molecules N in the scattering volume: I(1,) - 16~r41'4 I ~ 0 N(~ 45ct245 + 7Y2 )'

(1)

where a and y denote the isotropic and anisotropic parts respectively of the polarizability tensor (get/63,) for a given vibration of frequency p. The TMOS or methanol band intensities are thus proportional to the number of these molecules in solution. Assuming no change in geometry or laser

G. Orcel et aL / Chemistry of silica sol-gels H

226

power during an experiment, the decrease in time of the TMOS peak will reflect the rate of hydrolysis. Equation (1) fails to describe the silica gel peak intensities. Since gels lack translational symmetry, the system behaves not like a crystal but rather like a very large molecule. For disordered polymers, the Raman band intensities can be written

o o

~-

o

200

l

I(.)=:t-

) g(.) .

o

9

E

:= o

I00

~:

as

o

o methanol forrnamide

2

(2)

The transition polarizabilities ( S a / S Q ) may change with frequency, and could be affected by interchain interactions depending upon the polymer configuration. The Raman peaks at 340 c m and 830 cm -1 are quite broad implying a wide distribution of angles between S i - O - S i bonds and also various force constants, both leading to a spread of ( S a / S Q ) values. The density function of vibrational state g(v) may be found from lattice dynamics calculations. Usually satisfactory results are obtained when the frequencies of the calculated g(v) function coincide with the observed bands. When disordered polymers are involved, and exact comparison between the Raman intensities and the theoretical results cannot, in principle, be carried out. Therefore, we limit our discussion to a first order approximation by assuming the intensities of the 830 and 340 cm-1 peaks depend on the number of S i - O - S i bonds in the'sample without specifying the actual dependence. In fig. 2, the S i - O - S i stretching vibration band at 830 cm -1 is seen to grow continuously with time. A similar increase in the 340 cm-1 band is also observed, although this band has not been analyzed to the same extent since its lower intensity made it more difficult to detect. From general silica polymerization theory, SiO 2 particles are known to grow in size even after they bond together to form a network which expands throughout the sample. The increasing Raman intensity therefore is obviously linked directly to the particle size although as stated above the specific relationship between relative Raman intensity and number of S i - O - S i bonds in the particles cannot at present be specified.

or -0

,

l 2

F i g . 2. T i m e d e p e n d e n c e

,

I i I ~ 4 6 Reduced Time (T/TG)

I 8

of the 830 cm -x Si-O-Si

i I0

band.

The dependence of Raman intensity on particle size is not due to a pure scattering phenomenon but rather to the fact that the vibrators, S i - O - S i bonds, are organized in macromolecules. Since all the sols have a similar p H [13], we assume that the architecture of the three-dimensional network is the same for all the samples [17]. However, it should be noted that condensation of internal silanols induces an increase of the Raman intensity of the bands at 340 and 830 cm -1, which is not accompanied by an increase of the particle size. As shown in fig. 2, higher intensities are obtained when formamide is present in the sol (solution I). The curves representing the variation of relative Raman intensity with reduced time, can be divided into two parts: (1) From t / t G = 0 to 2, which corresponds to a rapid increase of the intensity; (2) for t / t G > 2, which corresponds to a plateau. The slope of the first part of the curve increases with the concentration of formamide. This indicates that S i - O - S i bonds are formed more rapidly when the silicate solution contains formamide. This result is in very good agreement with the values of gelation times as well as polycondensation rate constants observed for the same solutions [13]. At the gelation point ( t / t G = 1) the relative Raman intensity of solution I is about twice that of solution II (table 1). If the assumption that the Raman intensity is related to particle size is correct, then these results indicate that larger particles are achieved at the time of gelation for the formamide containing solution.

G. Orcel et al. / Chemistry of silica sol-gels H Table 1 Variation of sol characteristics as a function of the reduced time ( t / t G ) Reduced time: P~ (%) Pn (%)

Ix/I n kll/k I

0.5

0.6

0.7

0.8

0.9

1.0

25 35 46 61 71 72 81 87 90 92 1.45 1.48 1.48 1.52 1.62 1.67 1.38 1 . 4 1 1 . 4 1 1.48 1.55 1.58

After a reduced time of about t / t o = 2 no major variation of the relative Raman intensity is observed. This means that the number of new S i - O - S i bonds created is very small, or that the depolymerization rate is similar to the polymerization rate. The relative Raman intensities for the different gels are reported in table 1 as a function of reduced time. If we assume that the particle size increases with Raman intensity, then the preceding results suggest that solution I has larger particles than solution II. Furthermore, solution I relative Raman intensity has a maximum intensity at t > 2t~ which is only about 25% larger than the relative Raman intensity for solution II compared to a ratio of 1.7 for the relative Raman intensities of the same samples at the gelation point. This indicates that solution II, which does not contain any formamide DCCA, undergoes polycondensation after gelation to an extent greater than solution I. After gelation, an increase in particle size can be achieved only by condensation of the different hydroxyl groups located on the surface of the particles. Since gels derived from solution II have smaller particles they present a larger specific surface area, and thus should have a higher content of surface silanols [2]. Furthermore, formamide easily forms hydrogen bonds with the surface silanols [20], thus slowing polycondensation reactions in gels derived from solution I. 3.2. Mo test

Under specific conditions, silicic acids can react with molybdic acid to produce /3 silico-

227

molybdic acid [25]. The overall reaction can be written as follows: Si(OH)4 + 12MOO42- + 20H + --* SiMO1202o + 12H20. (3) Depending on the p H and on the different concentrations, this complex is stable and allows the measurement of absorbance without any need for correction of the fading of the color [31]. The absorbance is proportional to the concentration of the yellow complex. An early study by Coudurier et al. [25] demonstrated that silicate oligomers depolymerize into monomers according to a firstorder reaction. By reacting solutions of monosilicic, disilicic and polysilicic acids with Mo reagent, the order of the depolymerization reaction as well as the rate constant could be determined. Three depolymerization rate constants were identified, depending on the nature of the species which react: monosilicic acid disilicic acid polysilicic acid

~1 )

k2 ) k3)

complex/3,

(4)

complex/3,

(5)

monosilicic acid,

(6)

with k I - 2 min -1, k 2 - 1 min -1 and k 3 0.2 min -1. The rate constants k~ and k 2 a r e dependent upon the concentration of molybdic acid. On the other hand, the rate constant for depolymerization, reaction (6), k 3, is independent of the concentration of Mo reagent and much smaller than the rate constants corresponding to reactions (4) and (5). Consequently, the concentration (C) of silica remaining at the instant t, obeys the following relationship: -

log C o / C = - log P + kt,

(7)

where Co is the total concentration of silica, P the fraction of silica not depolymerized, and k the rate constant of the depolymerization reaction of the higher-ordered silica polymers. A typical plot according to eq. (7) is shown in fig. 3. The extrapolation of the linear portion to the time t = 0 allows the determination of P , whereas the slope of the same straight line gives k. By extracting samples from the batch at different reaction times and determining P and k, it is possible to follow the gelation process.

228

G. Orcel et al. / Chemistry of silica sol-gels H 0,6-

3.25 hours 0.5-

oD A

0.41

0 ~o 0.35.25 hours

°=

•J

0.2-

0.1 0.0 500

I 0'00

1500

TIME (min)

Fig. 3. Typical absorption curve of a sol analyzed with the Mo acidic test. The time dependences of P and k are represented in table 1 for the different samples. When formamide is present in the sol, lower values for k and P are observed than for the sample without formamide. These results were expected considering previous 295i N M R experiments [13] which showed that solution I contains less higher polymeric species that solution II and that the hydrolysis rate is larger when no formamide is present (table 2). The shape and size of polymeric structural units are determined by the relative values of the rate constants for hydrolysis and polycondensation reactions (kH and k c respectively). Fast hydrolysis and slow condensation favor formation of linear Table 2 Chemical characteristics of the different solutions kla (103 1/mol.h) Solution I Solution II

2 12

kc (l/mol.h)

HP (% Si)

> 32 29

42 100

polymers. On the other hand, slow hydrolysis and fast condensation result in larger, bulkier, and more ramified polymers [17]. As illustrated by the values of k H and k c reported in table 2, larger particles are anticipated for solution I, which implies a lower value for the depolymerization rate constant: k I < kll. Since the p H of the sol is well above 2 but still acidic and is not significantly displaced by addition of formamide to the solvent, we can assume that the silica particles in the sol have the same shape, irrespective of the experimental conditions, and are spherical in nature. As shown by the R a m a n data, larger particles are produced when formamide is added to the sol. Then, P and 1 / k should increase with the concentration of formamide. Since the particle size increases with time, P and 1 / k should also increase with time. In an attempt to correlate k with the diameter, d, of the silica particle in the solution, Iler [22] showed that

(8)

log d = a + b log k,

where a and b are constants and depend on the experimental conditions of the test. Since the sol is extremely diluted for the Mo dissolution analysis, as a first approximation we consider that the constants have the same values as those determined for silica colloids: a = - 0 . 2 5 0 and b = - 0 . 2 8 7 [22]. This allows us to estimate the particle diameter (PD) of the silica particles in the sol at the different steps of the sol-gel process. The results are given in table 3 and it is possible to conclude that the particles are about 20 A in diameter at the gelation point and larger particles are formed when formamide is present in the solution.

Table 3 Structural and textural properties of the gels Property Solution I (with DCCA) Solution II (no DCCA)

PD a) (A)

PR (A)

PV (cm3/g)

SA (m2/g)

D1 (A)

D2 (,~)

FD

24

30

1.19

784

59

24

2.29

20

12

0.356

607

58

20

2.25

a) Nomenclature: PD, particle diameter (Mo test); PR, pore radius; PV, pore volume; SA, specific surface area; D1, Guinier radius at gelation point; D2, Guinier radius on film heated at 200 o C; FD; fractal dimension at gelation point.

G. Orcel et al. / Chemistry of silica sol-gels H

3.3. S A X S

Small-angle X-ray scattering is a powerful technique which has been recently used for the characterization of the sol-gel process [16-18, 32-34]. By analyzing the scattering curves using Guinier's approximation, it is possible to obtain the value of the electronic radius of gyration of the particles comprising the sol and gel [35]. This type of analysis was performed on solutions I and II as well as on films derived from the same solutions and heat treated at 200 °C for 1 h. The results are presented in table 3. Near the gelation point the sols are formed of particles of about 60 ,~ in diameter compared to scattering units of about 20 A in diameter for the films. Dilution experiments showed that the radius of gyration measured in the sols does not vary with the quantity of solvent [16,36]. This result indicates that, first, the Guinier approximation is valid for these systems, and second that the polymer is relatively rigid [26]. These measurements are in very good agreement with the values obtained by the Mo acidic test. These results suggest that the gel structure is formed of different units. We have proposed [10,16,36] that primary particles of about 20 ,~ in diameter agglomerate in secondary particles of about 60 A in diameter (fig. 4). Based on geometric considerations, these secondary particles contain at most 13 primary particles. Gelation occurs

229

when the secondary particles are linked to each other forming a three-dimensional network all across the sample. This description of the structure of the sol and gel, which has recently been proposed [10,16,36], is confirmed by another X-ray diffraction study by Himmel et al. [37]. They showed that gels manufactured from hydrolysis and polycondensation of TEOS by a small amount of acidic water are made of primary particles of about 10 A in diameter which associate in secondary chain-like clusters. The size of these clusters can be approximated to 60 A in diameter, which is the average diameter of the pores. Also, TEM experiments on silica particles prepared by the so-called Sti3ber process [38] demonstrate that nucleation and growth occur by a coagulative mechanism, which supports the description of the gel structure given above. The analysis of the diffraction curves in the Porod region leads to the computation of the fractal dimension (FD). This quantity is dependent on the shape and geometry of the diffraction centers and also indicates a possible growth mechanism. In table 3 we report the values of the fractal dimension of the sols near the gelation point. These values suggest a percolation cluster (PC) or a diffusion-limited aggregation (DLA) mechanism. Particles grow by addition of small polymeric units to randomly added sites on a nucleus (PC) or through a random walk to a seed cluster (DLA) [26]. This description is in good agreement with the observation of a structure composed of agglomeration of units of different sizes: secondary particles made of several primary particles, which in turn agglomerate to form a gel. 3.4 N 2 isotherms

The N 2 isotherms analyzed with the BET theory, allow the determination of the pore volume and specific surface area. It is also possible to compute the average pore radius (PR) by assuming a cylindrical shape for the pores [27]. PR can then be deduced from the specific surface area (SA) and the pore volume (PV) according to the following relationship: Fig. 4. Schematic representation of primary and secondary particles in a gel.

PR = 2PV/SA.

(9)

230

G. Orcel et aL / Chemistry of silica sol-gels H 100

....-

.......,

..-

80 A

60 .J

0 40

..•...."

"

20 0.00

i

0.20

0.40

0.60

0.80

1.00

P/Po

Fig. 5. Typical N 2 adsorption-desorption isotherms of a gel.

For our samples this assumption was verified by the shape of the isotherms (fig. 5). The results are given in table 3 for both types of samples. F r o m these data, if we assume that the pore diameter is of the same order of magnitude as the particle size, we can deduce that the particle size of a gel prepared with formamide is larger than the one prepared without formamide. Furthermore, these values confirm the order of magnitude of the size of the gel particles as determined by SAXS and Mo acidic test. Great care should be taken when analyzing these data since the sample preparation involves heat treatment (300 ° C in our case). During outgassing the samples shrink. Shrinkage is accompanied by an increase of connectivity, and a decrease of the average pore size as well as pore volume. The amount of shrinkage is a function of the concentration of formamide. Since the gels prepared with procedure I shrink less than those prepared with procedure II, the formamide-containing gels are expected to present a higher pore volume as well as a larger average pore radius.

4. Conclusion The molybdenum acid dissolution test, R a m a n spectroscopy, small angle X-ray scattering and nitrogen adsorption-desorption isotherms have been used to characterize the structure and texture of gels prepared with and without formamide

DCCA. There is good agreement between the results from these different techniques. It was suggested that the structure of the gels is made of primary particles of about 20 ~, in diameter, which agglomerate in larger particles of about 60 ~, in diameter. The growth of the particles can be described by a diffusion-limited aggregation or percolation cluster mechanism. The R a m a n scattering experiment confirmed that polycondensation still takes place after gelation has occurred, up to 2 times t r . The formamide-containing sol (solution I) has a relative R a m a n intensity larger by 70% than solution II at the gelation point. However, the difference is only 25% at a reduced time of 2. Even though the N 2 adsorption-desorption isotherms cannot be used to assess gel particle size directly, they give valuable information on the texture of the gels. It was shown that formamide produces larger particles and also increases the pore diameter and pore volume. The authors gratefully acknowledge the financial support of A F O S R contract No. F496520-C0072 and No. 81-0010, the assistance of Dr. M. Bradley and R. J.S. Lin ( O R N L ) for the collection of the R a m a n and SAXS data respectively, and Dr. D.R. Ulrich for his continued encouragement to pursue interinstitutional research.

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