Kinetics of Formation of Monodisperse Colloidal Silica Particles

Under certain circumstances, monodisperse sols can be formed (Stöber and Fink, 1968). The hydrolysis of alkoxysilanes occurs by nucleophilic mechanis...
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Ind. Eng. Chem. Res. 1996, 35, 4487-4493

4487

Kinetics of Formation of Monodisperse Colloidal Silica Particles through the Hydrolysis and Condensation of Tetraethylorthosilicate Sheng-Li Chen* Department of Chemical Engineering, University of Petroleum, Dongying, Shandong 257062, People’s Republic of China

Peng Dong, Guang-Hua Yang, and Jiu-Jin Yang National Laboratory of Heavy Oil Research, University of Petroleum, Changping, Beijing 102200, People’s Republic of China

Kinetic studies of the hydrolysis and condensation of tetraethylorthosilicate (TEOS) during the formation of uniform silica particles were performed through determining concentrations of TEOS and silicic acid by means of gas chromatography and a conductometer, respectively. It was shown that both hydrolysis of TEOS and condensation of Si(OH)4 are first order with TEOS and Si(OH)4, respectively, and the relationships of the hydrolysis and condensation rate constants with reaction condition variables, such as temperature, NH3 concentration, and H2O concentration, were determined. In addition, the particle growth rate was investigated with relation to the hydrolysis and condensation kinetics. Experiments showed that, during most of the reaction, the amount of formed particles is less than that of consumed TEOS, indicating that reaction intermediates exist during the process of silica formation. In the early stages of the Sto¨ber process, the reaction intermediates include silicic acid and subparticles, while in the case of seed growth experiments without the formation of new particles or after the early stages of Sto¨ber process, the reaction intermediates primarily consist of silicic acid and the growth rate of silica equals the rate of silicic acid condensation. Introduction Monodisperse colloidal particles, uniform in size, shape, and composition, have wide application not only in the field of physical chemistry dealing with dynamic behavior and stability of particulate systems (Wiese et al., 1970), but also in industries including catalysts (Badly et al., 1989), chromatography (Unger, 1986), ceramics (Sacks et al., 1984), pigments, pharmacy, photographic emulsions, etc. (Overbeek, 1982). Monosize silica particles can be prepared by hydrolysis and condensation of alkoxysilanes in a mixture of alcohol, water, and ammonia. Three reactions are generally used to describe the hydrolysis and condensation of alkoxysilanes (Artaki et al., 1985; Brinker et al., 1990):

by a hydroxyl group, the electron density of silicon is reduced, accelerating the hydrolysis rate of other alkoxide groups (inductive factors) (Schmidt et al., 1984; Matsuyama et al., 1991). As a result, it was generally accepted that, under the conditions required for the formation of monosize silica ([NH3] g 0.5 M, [H2O] . [TEOS]), the first alkoxide group hydrolysis is the limited step in alkoxysilane hydrolysis. Once an alkoxide group is hydrolyzed, the others will be hydrolyzed rapidly, followed by the condensation of Si(OH)4, resulting in the formation of monosize silica spheres (Matsoukas et al., 1989; Bogush et al., 1991). Therefore, the chemical reactions describing the hydrolysis and condensation of alkoxysilanes, invoking the formation of monosize silica, can be briefly written as follows:

Si(OR)4 + 4H2O ) Si(OH)4 + 4ROH

(4)

≡SisOR + HOsSi≡ ) ≡SisOsSi≡ + ROH (2)

nSi(OH)4 ) nSiO2 + 2nH2O

(5)

≡SisOH + HOsSi≡ ) ≡SisOsSi≡ + H2O (3)

To date, some work has been done on the kinetics of hydrolysis of TEOS during the formation of monosize silica particles. Methods used to determine the concentration of TEOS by previous authors are mainly 29Si NMR (Bogush et al., 1991; Bailey et al., 1992), 13C NMR (Van Blaaderen et al., 1992), and Raman spectroscopy (Harris et al., 1990; Matsokas et al., 1988). In order to study the TEOS hydrolysis kinetics, Byers (1987) used gas chromatography for determining the concentration of ethanol produced by TEOS hydrolysis when the reaction proceeded in other alcohol than ethanol. Most authors only studied the kinetics of TEOS hydrolysis at several reaction conditions, and what is more, there is great difference among kinetics constants obtained by different authors (see Table 1). The reasons for the great difference in kinetics constants obtained by different authors are not clear;

≡SisOR + H2O ) ≡SisOH + ROH

(1)

where R is an alkyl group, CxH2x+1. Because water and alkoxysilanes are immiscible, a mutual solvent such as alcohol is normally used as a homogenizing agent. Base or acid should be used as catalyst for the hydrolysis and condensation. Gels are usually formed under acidic conditions, whereas sols are generally prepared under basic conditions. Under certain circumstances, monodisperse sols can be formed (Sto¨ber and Fink, 1968). The hydrolysis of alkoxysilanes occurs by nucleophilic mechanism. Under basic conditions, water dissociates to produce nucleophilic hydroxyl anions (OH-) in a rapid first step, and then the hydroxyl anion attacks the silicon atom. When an alkoxide group (OR) is replaced * To whom correspondence should be addressed.

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4488 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 Table 1. Comparison of TEOS Hydrolysis Rate Constants Obtained by Previous Authors (in Ethanol Solutions) method to determine [TEOS] Raman spectrum 29Si NMR 29Si NMR 13C NMR a

ratio of rate constantsa

rate constants, min-1 Kh* ) 0.0025[H2O]1.5[NH3]0.5 Kh ) 4.9 × 10-3 at [NH3] ) 1.0 M, [H2O] ) 1.0 M Kh ) 8.4 × 10-3 at [NH3] ) 1.0 M, [H2O] ) 3.8 M Kh ) 6.1 × 10-3 at [NH3] ) 0.668 M, [H2O] ) 1.8 M (in propanol)

1 1.96 0.454

reference Harris et al., 1990 Bailey et al., 1992 Bogush et al., 1991 Van Blaaderen et al., 1992

The ratio of rate constants to that reported by Harris et al. (1990) at the same [NH3] and [H2O] conditions (Kh/Kh*).

perhaps it is due to the uncertainties incident to those methods used to measure TEOS concentration. It takes 8-10 min for us to perform one [TEOS] measurement using 29Si NMR or 13C NMR. As a result, if concentrations of NH3 and H2O were higher, invoking the reaction to proceed rapidly, large errors in TEOS concentration measurement would occur, or even it would be impossible to carry out the measurement. The errors in [TEOS] measurement by Raman spectroscopy are also large due to the lower [TEOS], lower Raman response, and interference produced by Rayleigh scattering of silica particles. Under basic conditions, silicic acid is unstable and its concentration is low, so it is difficilt to determine the silicic acid concentration. Therefore, only two papers have been reported dealing with silicic acid condensation until now (Bogush et al., 1991; Harris et al., 1990), and the results were inconsistent with each other. Bogush and Zukoski’s (1991) experiments showed that the condensation of silicic acid proceeded independently of the growing silica particles, but Harris’s (1990) research suggested that the condensation rate of silicic acid was proportional to the surface of the growing particles. To date, only two articles have dealt with the relation of silica growth rate to the TEOS hydrolysis rate. Bogush et al. (1991) and Matsoukas et al. (1988) reported that the growth rate of silica was equal to the TEOS hydrolysis rate with the concentration of hydrolyzed species in solution being negligible. Except for this, no other investigation has been made on the growth rate. We investigated the kinetics of formation of monosize silica particles through measuring TEOS concentration by gas chromatography (GC), which is much more precise in TEOS concentration measurement than NMR and Raman spectroscopy, and monitoring the variation of silicic acid concentration and particle diameter by use of a conductometer and transmission electron microscope (TEM), respectively. The relationships of kinetics constants with reaction variables were determined, and the relation between the silica particle growth rate and the hydrolysis and condensation kinetics was investigated as well. Experimental Section Chemical Reagents. The following chemical reagents were used in the experiments: Tetraethylorthosilicate (TEOS) (reagent grade), dehydrated ethanol (analytical purity), ammonium hydroxide (guarantee grade), redistilled water, phenyl bromide (analytical purity), and heptane (analytical purity). TEOS and dehydrated ethanol were distilled before use, and the others were used as received. The concentration of NH3 in ammonium hydroxide was determined by titration. Procedures of Experiments. Ethanol containing correct amounts of water and ammonia was measured

Figure 1. Gas chromatogram of the extract (without phenyl bromide in this sample). The sample was at 4 min after the reaction started under the condition of [NH3] ) 2 M, [H2O] ) 6 M, [TEOS] ) 0.212 M, and T ) 25 °C. A 30 m long and 0.25 mm i.d. fused silica capillary column coated with poly(methylphenylvinylsiloxane) was employed using flame ionization detection and helium as carrier gas (20 cm/s). The column oven temperature was programmed as follows: 50 °C for 1 min and then temperature increase at 10 °C/min until 300 °C.

into a reactor which was kept at a desired temperature. Agitation was achieved by using a magnetic stirrer (>150 rpm). A separate volume of ethanol containing a desired amount of TEOS was measured into a container which was kept at the same temperature as the reactor. To initiate the reaction, the TEOS-containing ethanol was either injected or quickly poured into the reactor. Samples of the reaction mixture were taken from the reactor to monitor the concentration of TEOS and the size of the growing particles. The conductance of the reaction solution was measured by a continuousreadout conductometer. GC Analysis of TEOS. Gas chromatography (GC), developed by Zhao and Dong (1992), was used to measure the concentration of TEOS in reaction solution. This method is precise and quick without the shortcomings that NMR and Raman spectroscopy have in the determination of TEOS concentration. Some improvements were made on the GC method, and the detailed procedures are described below. First, a sample of reaction solution was taken from the reactor and was put into a heptane-water extraction mixture (C7:H2O ) 1:1 v/v; reaction solution: extraction mixture ) 1:4 v/v) in a small extraction tube. Then the extraction tube was shaken vigorously, making the sample contact with the C7-H2O mixture thoroughly. The TEOS was quickly extracted into C7 phase, and the extraction tube was immediately placed

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4489

Figure 2. Mass spectra: (A) mass spectrum of peak B in the gas chromatogram; (B) standard mass spectrum of TEOS.

into dry ice to freeze the water phase. In this way, the reaction was quenched. The whole process was finished in 2-3 s. After that, the extract (the C7 phase) was poured out on top of the iced-water phase, and finally, the amount of TEOS in the extract was analyzed by means of GC. A certain amount of acetic acid was added to the extraction mixture according to the ammonia content in the reaction solution, so that the NH3 was just neutralized by acetic acid, servicing to quench the reaction. Experiments showed that the concentration of TEOS in the extract did not change with time even in more than 10 h, so the quenching was successful. As an internal standard substance for quantitative analysis, phenyl bromide was added to the reaction solution. The gas chromatogram of the extract is shown in Figure 1, to illustrate the separation of TEOS and other partially hydrolyzed and condensed silicon-containing species. There were two peaks in the above gas chromatogram, and the qualitative analysis of GC peaks was performed

with a SSQ-710 mass spectrometer and pure substance retention time. It was ascertained that peak A was the solvents (including heptane and ethanol) and peak B was TEOS. Shown in Figure 2 is the standard mass spectrum of TEOS and the mass spectrum of peak B. It is evident that the mass spectrum of peak B is identical to the standard mass spectrum, indicating that peak B does not involve other species than TEOS. Other species (SixOy(OR)z(OH)4x-2y-z) were not present in the extract in a detectable amount. This result is consistent with that found by Bogush et al. (1991). Monitoring of Unstable Silicic Acid. Because of the low dielectric constants of the ethanol solution, ammonia is present primarily as unprotonated NH3. If the ammonia deprotonated a silicic acid group, the net number of ionized species would increase and would be reflected as an increase in solution conductivity. As a consequence, conductivity increase can be associated with the formation of hydrolyzed TEOS and decreases

4490 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 Table 2. Experimental Conditions and Resultsa no.

T, °C

[TEOS]0, M

[H2O], M

[NH3], M

L, µm

tm, min

Kh, min-1

Kc, min-1

CN25-605 CN25-101 CN25-152 CN20-1005 CN20-151 CN20-62 CN35-1505 CN35-102 CN35-61 CN25-61

25 25 25 20 20 20 35 35 35 25

0.214 0.212 0.212 0.212 0.212 0.212 0.212 0.213 0.212 0.211

5.87 9.89 14.9 9.88 15.0 6.0 14.9 9.92 5.98 6.04

0.498 0.997 2.00 0.50 1.00 2.00 0.494 1.99 0.996 1.03

0.461 0.615 0.477 0.481 0.446 0.733 0.369 0.689 0.496 1.10

17.5 5.3 1.8 11.0 4.0 7.0 4.0 2.0 6.5 9.0

0.0134 0.0531 0.170 0.021 0.0754 0.045 0.0605 0.142 0.0372 0.0297

0.152 0.560 1.30 0.244 0.59 0.33 0.656 1.22 0.404 0.279

a CN25-61, seed growth experiment with the seed average diameter being 0.573 µm and relative standard deviation 2.8%, and no new particles formed during the growth. The number density of seeds is 1.01 × 1010/cm3. L, final average particles diameter; tm, time maximum conductivity occurs; Kh, TEOS hydrolysis rate constants; Kc, silicic acid condensation rate constant.

in conductivity with the formation of siloxane bonds and the loss of the protonated NH4+ as shown below:

≡SiOH + NH3 ) ≡SiO- + NH4+

(6)

≡SiO- + HOSi≡ + NH4+ ) ≡SisOsSi≡ + NH3 + H2O (7) Therefore, the unstable silicic acid can be monitored by measuring the conductivity of reaction solution as used by Bogush et al. (1991). The Peak Method, a method for determining reaction kinetics of unstable intermediates developed by Chen (1996), was used to find out condensation kinetics from the conductivity variation during the course of reaction. Monitoring of Growing Silica Particles. Small volumes of the reaction suspension were dropped onto a Formvar coated copper electron microscope grid which was placed on filter paper to quickly remove the liquid. A Phillips-400 transmission electron microscope was used to measure the average particle size and the standard deviation of particle size distribution. Results and Discussion Kinetics of TEOS Hydrolysis and Silicic Acid Condensation. A. Hydrolysis and Condensation Kinetics Constants. Experiments were carried out by independently varying the temperature (T), [H2O], and [NH3]. Every reaction variable was assigned three different values. Experimental conditions are presented in Table 2. The hydrolysis of TEOS was found to be first order with respect to TEOS, being consistent with previous works. Shown in Figure 3 are changes in ln([TEOS]0/ [TEOS]) over the course of reaction; the slopes of the linear line ln([TEOS]0/[TEOS]) ∼ t are the first-order rate constants of TEOS hydrolysis (Kh). Obviously, the curve of ln([TEOS]0/[TEOS]) ∼ t is an excellent linear line with a linear correlation coefficient greater than 0.999. Because the sampling time is short (2-3 s) and the precision of quantitative analysis of GC is high, the Kh is precise. The silicic acid condensation was also found to be first order with respect to silicic acid; the first order-rate constants of TEOS hydrolysis and silicic acid condensation are also reported in Table 2. Assume Kh and Kc are functions of T, [H2O], and [NH3] as follows:

( )

K ) K0 exp -

Ea [H2O]R[NH3]β RT

Figure 3. Linear curve of ln([TEOS]0/[TEOS]) ∼ t.

From the data in Table 2, constants K0, Ea, R, and β in the above equation were found out by the Marquardt (1963) regression method, and the empirically found rate constants are as follows:

( )

Kh ) 74.36 exp -

Ea [H2O]1.267[NH3]0.971 RT

(8)

Ea ) 25.2 kJ/mol

( )

Kc ) 19408 exp -

Ea [H2O]1.196[NH3]0.7854 RT

(9)

Ea ) 33.2 kJ/mol The calculation errors of eqs 8 and 9 are 2.1% and 4.0%, respectively. B. Simulation of Conductance of Reaction Solution and Molal Conductivity of Ammonium Silicate. By the use of the relationship between molal conductivity (Λ) and concentration (C) (Fuoss and Onsager, 1957),

Λ ) Λ0 - SxC + AC ln C + BC

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Figure 4. Conductance in experiment CN25-101 and CN20-62 solutions (cell constant of the electrode 1.07 cm-1). Figure 6. Simulation of results of growing seed diameter of experiment CN25-61.

The kinetic equations are

d[TEOS] ) -Kh[TEOS] dt

(10)

d[Si(OH)4] ) Kh[TEOS] - Kc[Si(OH)4] dt

(11)

[TEOS]0 dLt3 d[SiO2] ) 3 ) Kc[Si(OH)4] dt L∞ - L03 dt

(12)

From eqs 10-12, we have

Figure 5. Molal conductivity (Λ) of ammonium silicate in EtOHH2O-NH3 solutions.

the conductances of experiments CN25-101 and CN2062 were calculated with the kinetics obtained in this work, and the results are shown in Figure 4. The molal conductivity was obtained during the conductance simulation and presented in Figure 5. Figure 4 indicates that the conductance variations measured in experiments are identical to that calculated from the kinetic model. The molal conductivity (Λ) is not constant but decreases with the increase of C. Λ in ethanol solution containing 9.89 M H2O and 0.997 M NH3 is greater than that in ethanol solution containing 6.0 M H2O and 2 M NH3 (see Figure 5). The above behavior of molal conductivity of ammonium silicate is consistent with that of inorganic salts in alcohol (Zhang, 1994). Growth Rate of Monosize Silica Particles. A. Growth Kinetics of Monodisperse Silica in Seed Growth Experiment. Suppose the reaction intermediates in solution are primarily made up of silicic acid, with other silicic acid condensed species can be ignored. The whole process could be presented as follows: Kh

Kc

TEOS 98 Si(OH)4 98 SiO2 particles Because the equilibrium concentration of Si(OH)4 in alcohol solutions is very low (∼10-4 M) (Bogush, 1991), in comparison with the concentration of Si(OH)4 in the reaction solution (∼10-2 M), the condensation of Si(OH)4 is approximated as an irreversible reaction.

{ [

L(t) ) L03 + 1 -

Kc exp(-Kht) + Kc - Kh

]

Kh exp(-Kct) (L∞3 - L03) Kc - Kh

}

1/3

(13)

where L0 is the initial seed diameter, L∞ the final particle seed diameter, and Lt the diameter of growing seed at t minutes after the reaction. The comparison between growing seed diameter determined by TEM and that calculated by eq 13 is shown in Figure 6. The fact that the growing seed diameter calculated by eq 13 is identical to that determined by experiment indicates eq 13 can well describe the variation of diameter with time. In order to investigate and clearly present the changes of various kinds of species in reaction solution, all species are represented in one figure and in the same unit (mole number of silicon in 1 L of reaction solution).

[Si(OH)4] ) [TEOS]0

Kh [exp(-Kht) Kc - Kh exp(-Kct)] (14)

The concentration of consumed TEOS([TEOS]R) is

[TEOS]R ) [TEOS]0{1 - exp(-Kht)}

(15)

The concentration of produced solid silicon dioxide can be described as

[SiO2] ) [TEOS]0

Lt3 - L03 L∞3 - L03

(16)

4492 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996

Figure 7. Variation of various species in CN25-61 reaction solution.

Figure 8. Simulation results of growing particles diameter of experiment CN20-62.

Reaction intermediates (M), involving silicic acid and its condensation species, are the consumed TEOS minus produced solid silicon dioxides:

[M] ) [TEOS]R - [SiO2]

(17)

The variation of [Si(OH)4], [TEOS]R, [SiO2], and [M] during the course of reaction is shown in Figure 7. The following conclusions could be drawn from Figure 7: (a) During most of the reaction, the amount of produced solids SiO2 is less than that of consumed TEOS, and the amount of intermediates can not be ignored. This result is inconsistent with the Bogush et al. (1991) and Matsoukas (1988) statement that the concentration of hydrolyzed species can be ignored. (b) The intermediates primarily consist of silicic acid, and the amount of silicic acid condensation species contributed to intermediates is much less than that of silicic acid. The growth rate of silica equals the rate of silicic acid condensation. Growth Kinetics of Monodisperse Silica in the Sto1 ber Process. In the Sto¨ber process, all silica particles are formed spontaneously in situ in a short time, followed by self-sharpening growth. All equations in the above section are applicable, providing L0 is equal to zero.

[

L(t) ) 1 -

Kc exp(-Kht) + Kc - Kh Kh exp(-Kct) Kc - Kh [SiO2] ) [TEOS]0 (Lt/L∞)3

]

1/3

L∞ (18)

Figure 9. Changes of various species in CN20-62 reaction solution.

the condensation reaction gets faster and faster (Schmidt et al., 1984; Klempere et al., 1988a,b). As a consequence, the concentration of soluble condensed species is much smaller than [Si(OH)4]. Hence, the condensed species, which appear in the initial period of the Sto¨ber process, are mainly (colloid unstable) subparticles as called by Philipse (1988) and Bogush et al. (1991). The change of reaction intermediate concentration is consistent with the mechanism of monosize silica formation, proposed by Chen (1994). The mechanism will be discussed in detail in other papers.

(19)

The comparison between growing particle diameter determined by TEM and that calculated by eq 18 is shown in Figure 8. Shown in Figure 9 are the changes in [Si(OH)4], [TEOS]R, [SiO2], and [M] during the course of the Sto¨ber process. We could conclude from Figure 9 that, at the initial stages of reaction, the intermediates involve not only silicic acid but also condensed species, whereas after that the intermediates are primarily made up of silicic acid. Under basic conditions, as condensation proceeds, the electronic density of silicon atoms decreases; therefore

Conclusions 1. The TEOS concentration in reaction solution to prepare monodisperse silica could be measured quickly and accurately through extracting the reaction solution by C7-H2O mixture and analyzing the TEOS concentration in the extract with GC. 2. Both hydrolysis of TEOS and condensation of silicic acid are first order with respect to TEOS and silicic acid, respectively. Relationships of the hydrolysis rate constant (Kh) and condensation rate constant (Kc) with reaction condition variables were empirically found to be

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4493

Kh ) 74.36 exp(-Ea/RT)[H2O]1.267[NH3]0.971 Ea ) 25.2 kJ/mol Kc ) 19408 exp(-Ea/RT)[H2O]1.196[NH3]0.7854 Ea ) 33.2 kJ/mol 3. The fact that, during the most of the reaction, the amount of formed silica is less than that of consumed TEOS indicates reaction intermediates exist during the process of silica formation. In the initial stages of the Sto¨ber process, the reaction intermediates include silicic acid and colloid-unstable subparticles, while in the case of seed growth experiments without the formation of new particles or after the initial stages of the Sto¨ber process, the reaction intermediates primarily consist of silicic acid and the growth rate of silica equals the rate of silicic acid condensation. Acknowledgment Financial support was granted by the China National Natural Science Foundation. Literature Cited Artaki, F.; Bradley, M.; Zerda, T. W.; et al. NMR and Raman study of the hydrolysis reaction in sol-gel process. J. Phys. Chem. 1985, 89, 4399-4404. Badly, R. D.; Ford, W. T. Silica-bound sulfonic acid catalysts. J. Org. Chem. 1989, 54, 5437-5443. Bailey, J. K.; Mecartney, M. L. Formation of colloidal silica particles from alkoxides. Colloids Surf. 1992, 63, 151-161. Bogush, G. H.; Zukoski IV, C. F. Studies of the kinetics of the precipitation of uniform silica particles through the hydrolysis and condensation of silicon alkoxides. J. Colloid Interface Sci. 1991, 142 (1), 1-18. Brinker, C. J., Scherer, G. W., Eds. Sol-Gel Science; Academic Press: San Diego, 1990; p 108. Byers, C. H.; Harris, M. T.; Williams, D. G. Controlled microcrystalline growth studies by dynamic laser-light-scattering methods. Ind. Eng. Chem. Res. 1987, 26, 1916-1923. Chen, S.-L. The mechanism and kinetics of formation of monodisperse silica particles through the hydrolysis and condensation of tetraethylortho-silicate. Ph.D. Thesis, University of Petroleum (China), 1994. Chen, S.-L.; Dong, P.; et al. A method for determining reaction kinetics of unstable intermediates formed in series reactions. Proceedings of the 1996 Asian-Pacific Chemical Reaction Engineering Forum, June 26-28, 1996, Beijing, China; pp 555560. Fuoss, R. M.; Onsager, L. Conductance of unassociated electrolytes. J. Phys. Chem. 1957, 61, 668-682. Harris, M. T.; Brunson, R. R.; Byers, C. H. The base-catalyzed hydrolysis and condensation reaction of dilute and concentration TEOS solutions. J. Non-Cryst. Solids 1990, 121, 397-403.

Klemperer, W. G.; Mainz, V. V.; Ramamurthi, S. D.; Rosenberg, F. S. Molecular growth pathways in silica sol-gel polymerization. Better Ceramics through Chemistry 3; Materials Research Society Symposium Proceedings 121; Elsevier: New York, 1988a; pp 1-14. Klemperer, W. G.; Mainz, V. V.; Ramamurthi, S. D.; Rosenberg, F. S. Structural characterization of polysilicate intermediates formed during sol-gel polymerization. Better Ceramics through Chemistry 3; Materials Research Society Symposium Proceedings 121; Elsevier: New York, 1988b; pp 15-24. Marquardt, D. W. An algorithm for least-squares estimation of nonlinear parameter. SIAM J. Appl. Math. 1963, 11 (2), 431441. Matsoukas, T.; Gulair, E. Dynamics of growth of silica particles from ammonia-catalyzed hydrolysis of tetraethylorthosilicate. J. Colloid Interface Sci. 1988, 124 (1), 252-261. Matsoukas, T.; Gulari, E. Monomer addition growth with a slow initiation step: a growth model for silica particles from alkoxides. J. Colloid Interface Sci. 1989, 132 (1), 13-21. Matsuyama, I.; Satoh, S.; et al. Raman and GC-MS study of the initial stage of the hydrolysis of tetramethoxysilane in acid and base catalyzed sol-gel process. J. Non-Cryst. Solids 1991, 135 (1), 22-28. Overbeek, J. Th. G. Monodisperse colloidal systems, fascinating and useful. Adv. Colloid Interface Sci. 1982, 15, 251-277. Philipse, A. P. Quantitative aspects of the growth of (charged) silica spheres. Colloid Polym. 1988, 266, 1174-1180. Sacks, M. D.; Tseng, T.-Y. Preparation of silica glass from model powder compacts. J. Am. Ceram. Soc. 1984, 67, 526-532, 532537. Schmidt, H.; Scholze, H.; Kaiser, A. Principles of hydrolysis and condensation reaction of alkoxysilanes. J. Non-Cryst. Solids 1984, 63, 1-11. Sto¨ber, W.; Fink, A. Controlled growth of monodisperse silica spheres in the micro size range. J. Colloid Interface Sci. 1968, 26, 62-69. Unger, K. K.; Jilge, G.; et al. Evaluation of advanced silica packing for the seperation of biopolymers by high-performance liquid chromatography. J. Chromatogr. 1986, 359, 61-72. Van Blaaderen, A.; Van Geest, J.; Vrij, A. Monodisperse colliodal silica spheres from tetraalkoxysilanes: Particle formation and growth mechanism. J. Colloid Interface Sci. 1992, 154 (2), 481501. Wiese, G. R.; Healy, T. W. Effect of particle size on colloid stability. Trans. Faraday Soc. 1970, 66, 490-499. Zhang, S.-J. The thermodynamic properties and transport properties for electrolyte solutions. Ph.D. Thesis, Zhejiang University, 1994. Zhao, R. Y.; Dong, P. Studies on the kinetics of hydrolysis of tetraethylorthosilicate in the formation of monodisperse silica particles. Wuli Huaxue Xuebao 1995, 11 (7), 612-616 (in Chinese).

Received for review April 10, 1996 Revised manuscript received August 1, 1996 Accepted August 5, 1996X IE9602217

X Abstract published in Advance ACS Abstracts, October 15, 1996.