J. Phys. Chem. 1996, 100, 12517-12531
12517
Acidic Sol-Gel Polymerization of TEOS: Effect of Solution Composition on Cyclization and Bimolecular Condensation Rates Li Voon Ng and Alon V. McCormick* Chemical Engineering and Materials Science Department, UniVersity of Minnesota, Minneapolis, Minnesota 55455 ReceiVed: January 5, 1996; In Final Form: May 9, 1996X
For batch sol-gel polymerization of TEOS in acidic ethanol solutions, we report kinetic trends over a wide range of initial solution compositions that yield homogeneous gels. We find in these systems the prevalence of extensive nonrandom cyclization over a wide composition range. We unambiguously monitor the formation of various well-defined silicate oligomers early in the reaction to quantify the competing processes of cyclization and bimolecular condensation. We introduce a new kinetic model that is substantially modified from previously used random branching models in order to account for cyclization reactions. As do previous models, this model allows first-shell substitution effects on condensation rate constants, but it does not rely on mean field site kinetics. The dimerization rate constant varies strongly with pH in a manner consistent with a reaction mechanism involving ionized intermediates. It also decreases mildly with the water concentration experienced during reaction. Higher condensation rate constants vary among each other and with pH in a manner consistent with the expected ionization behavior. The cyclization rate constants are comparable in magnitude to the dimerization rate constant. Near the expected isoelectric point of the end-group, cyclization is favored over end-group/end-group bimolecular condensations. At higher pH though, bimolecular reactions are favored and there is no longer a negative first-shell-substitution effect. Dilution with ethanol increases the cyclization rate constants and tends to lower bimolecular rate constants. These results suggest a correlation between the compositions that favor homogeneous gelation and those that exhibit selective cyclization early in the reaction.
Introduction Random branching theory (RBT) has been successfully used to model many organic condensation polymerization processes and is in some cases consistent with inorganic sol-gel polymerization.1-3 The primary assumptions in this theory are twofold. The first assumption is that all functional groups are equally likely to undergo reactive encounters, i.e., mean field functional group kinetics. Rate constants, though, may be modified for sites with different local structure (e.g., random branching with unequal reactivity due to first-shell substitution effects1, 4). The second assumption is that no intramolecular (cyclization) reactions take place. This is usually acceptable because random cyclization only mildly affects the overall rate and conversion. Sol-gel reactions, however, can exhibit selective, nonrandom, cyclization. Small rings of three and four silicon tetrahedra are commonly observed by 29Si NMR,5-12 Raman spectroscopy,13,14 photoacoustic infrared spectroscopy,15 and gas chromatography16-18 in concentrations much higher than can be accounted for by random cyclization. Using GC-MS techniques, Wheeler17 has separated and identified various cyclic and bicyclic oligomers, up to hexamers, in some tetraethoxysilane (TEOS), tetramethoxysilane (TMOS), methyl(trimethoxy)silane, and methyl(triethoxy)silane systems. The presence of larger rings (generally difficult to distinguish from linear sites with 29Si NMR) and of heterocyclic species (some of which are evident in aqueous silicate systems) has also been conjectured.8,19 Cyclization is more favorable for TEOS than for TMOS,8 and it evidently becomes more favorable at low waterto-silicon ratio (between 1 and 2) and pH ( 2 is sufficient for hydrolysis to eventually reach completion, since this is the ratio required by stoichiometry to achieve complete conversion to silica:
Si(OEt)4 + 2H2O f SiO2 + 4EtOH Even as researchers have come to recognize that complete hydrolysis is exceptional, it is still generally assumed that the average degree of hydrolysis increases uniformly with W/Si. Our 29Si NMR results (Figure 8) show that, contrary to this expectation, hydrolysis is still far from complete even when W/Si ) 4. Instead, the average degree of hydrolysis on the monomer at W/Si ) 4 is close to that at W/Si ) 2. Hydrolysis is close to completion only when W/Si g 8. We will consider W/Si effects on the condensation rate constants due either to solvent composition or to the degree of hydrolysis.
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Figure 7. Demonstration that the average degree of hydrolysis for i siloxy-substituted silicon sites, 〈j〉i, generally becomes constant before significant changes in the concentration of (i + 1) siloxy-substituted silicon sites, [Qi+1]. Compositions, [TEOS]/[EtOH]/[H2O]/pHCl, are shown in the graphs. 〈j〉0 and 〈j〉1 are represented by × and O, respectively. pHCl has an insignificant effect. Part A shows water-poor systems (only 〈j〉0 reported since only dimerization occurs), and part B shows water-rich systems.
so the rate constant ki,m represents functional group (not silicon site) reactivity. The averaged value of 〈j〉i that should be used in eq 9 is shown in Table 1 for each system. Although all reactions are of course reversible in principle, no appreciable depolymerization of ethoxy silicates occurs at low conversion, so eq 9 neglects depolymerization. We will be able to check the success of this assumption by the quality of fit over the conversions examined. Equation 9 can be used when no cycles are present, so we apply it to systems showing only dimers. The curve fits of eq 9 for dimerization are shown in Figure 9. Figure 10 shows that k00 depends mainly on initial HCl concentration, decreasing with pHCl up through pHCl ) 4.0. It increases mildly with W/Si (whether via (w/a)e or 〈j〉i) until W/Si approaches 1. The rate constants are listed in Table 1. Note that eq 9 is written assuming water-producing condensation and neglecting alcohol-producing condensation. This has been supported for TEOS systems.22 It is unlikely that the change in k00 caused by changing W/Si could be explained by any change in role of alcohol-producing condensation which, if anything, would produce an opposite trend.
Figure 8. Statistically averaged degree of hydrolysis ((a) 〈j〉0, (b) 〈j〉1, and (c) 〈j〉2) as a function of W/Si. Detailed correspondence with composition is shown in Table 1.
Under conditions of hydrolysis equilibria, Sanchez30 showed that a random branching model can be represented by the reactions of lumped silicon sites as defined by eq 8 f-1
d[Qi]/dt )
∑ {ki-1,m〈j〉m[Qm]〈j〉i-1[Qi-1] -
m)0
ki,m〈j〉m[Qm]〈j〉i[Qi]} (9) where f ) 4 for a four-functional silicon. Equation 9 is written
3. Competing Bimolecular and Cyclization Reaction Rates. Polymer growth can occur only through bimolecular condensation, which requires the diffusion of two molecules toward each other before reaction can take place. Cyclization is unimolecular and does not contribute to polymer growth. It requires no molecular diffusion but probably requires favorable molecular configuration. Solvation can affect the local configuration and reconfiguration mobility of a molecule and so can affect cyclization. Solvation may even create an effective shield around the molecule, discouraging branching. Moreover, the diffusion dependence should make the bimolecular reaction rate more sensitive to reactant concentration. In this section eq 9 is not appropriate, and we develop a model that should reveal these competitions between cyclization and bimolecular condensation. Condensation Rate Equation with Cyclization. To model the competition of cyclization versus bimolecular reactions, we adopt a molecular kinetic model rather than a site kinetic model. The goal of the model is 3-fold: (1) to see if the cyclization scheme can match the data, (2) to see if the rate constants follow reasonable trends, and (3) to see whether these trends can help
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J. Phys. Chem., Vol. 100, No. 30, 1996 12525
Figure 9. Curve fits with the dimerization rate equation (eq 9) for water-starved systems. Compositions, [TEOS]/[EtOH]/[H2O]/pHCl, are shown in the graphs. Symbols b and O represent [Q0] and [Q1], respectively. Curves represent optimal solutions of eq 9. Note that time scales change from figure to figure.
rationalize the prevalence of cyclization. In a polymerization reaction, molecular kinetic modeling is usually laborious or impossible since the number of distinct molecules ordinarily grows huge for any significant conversion. Thanks in part to preferred cyclization, though, at conversions up to 40% the number of distinct molecules in the TEOS systems remains
sufficiently small that a molecular kinetic model is tractable. NMR indicates that only linear chains and small rings are present since no Q3 sites are detected. Growth may occur only by monomer/end-group or end-group/end-group condensation. Moreover, the low Q2-to-Q1 ratio suggests that few chains larger than pentamers are present. Thus, early in the reaction, 29Si
12526 J. Phys. Chem., Vol. 100, No. 30, 1996
Ng and McCormick
polymerization can be characterized following the molecular reaction scheme kL
1L1
kL
1L2
kL
1L3
kL
1L4
kL
2L2
kL
2L3
(1) L1 + L1 98 L2 (2) L1 + L2 98 L3 (3) L1 + L3 98 L4 (4) L1 + L4 98 L5 (5) L2 + L2 98 L4
Figure 10. Apparent dimerization rate constant from eq 9 as a function of pHCl for water-starved systems. [TEOS]init ) 2.86 M at different W/Si values: (b) 0.5, (9) 0.6, ([) 0.7, (2) 0.8, (1) 0.9, and (+ 0) 1. W/Si ) 0.5 at different [TEOS]init values: (×) 2.45, (.) 3.44 M. The + is for [TEOS]init ) 2.82 and W/Si ) 0.8. Lines are drawn to connect points from systems with similar initial TEOS, ethanol, and water concentrations.
(6) L2 + L3 98 L5 kR
3
(7) L3 98 R3 kR
4
(8) L4 98 R4 The symbols Li and Ri represent chains and rings, respectively of i monomeric units. The rate constant kLiLm characterizes a bimolecular reaction between chains of lengths i and m, while kRi characterizes a cyclization reaction to form an i-membered ring. The units of the rate constants are in terms of moles of molecules. If we assume mean field molecular reaction rates, the corresponding rate equations describing molecular concentrations are
d[L1]/dt ) -2kL1L1[L1]2 - kL1L2[L1][L2] - kL1L3[L1][L3] kL1L4[L1][L4]
d[L1]/dt ) -k00〈j〉02[L1]2 - 2k01〈j〉0〈j〉1[L1][L2] 2k01〈j〉0〈j〉1[L1][L3] - 2k01〈j〉0〈j〉1[L1][L4] d[L2]/dt ) +(1/2)k00〈j〉02[L1]2 - 2k01〈j〉0〈j〉1[L1][L2] 4k11〈j〉12[L2]2 - 2k11〈j〉12[L2][L3] d[L3]/dt ) +2k01〈j〉0〈j〉1[L1][L2] - 2k01〈j〉0〈j〉1[L1][L3] 2k11〈j〉12[L2][L3] - kσ3〈j〉12[L3] d[L4]/dt ) +2k01〈j〉0〈j〉1[L1][L3] - 2k01〈j〉0〈j〉1[L1][L4] + 2k11〈j〉12[L2]2 - kσ4〈j〉12[L4] d[L5]/dt ) +2k01〈j〉0〈j〉1[L1][L4] + 2k11〈j〉12[L2][L3]
d[L2]/dt ) +kL1L1[L1]2 - kL1L2[L1][L2] - 2kL2L2[L2]2 kL2L3[L2][L3]
d[R3]/dt ) kσ3〈j〉12[L3]
d[L3]/dt ) +kL1L2[L1][L2] - kL1L3[L1][L3] - kL2L3[L2][L3] -
d[R4]/dt ) kσ4〈j〉12[L4]
(11)
kR3[L3] d[L4]/dt ) +kL1L3[L1][L3] - kL1L4[L1][L4] + kL2L2[L2] 2
kR4[L4] d[L5]/dt ) +kL1L4[L1][L4] + kL2L3[L2][L3] d[R3]/dt ) kR3[L3] d[R4]/dt ) kR4[L4]
(10)
The parameters of these equations can be related to the parameters of the site balance of eq 9 as follows. We assume that the molecular rate constant depends on the number of functional groups on the appropriate Si site(s), which is given by the measured average degree of hydrolysis at that site. We assume all sites of the same connectivity i have the same 〈j〉i, e.g., 〈j〉1 represents the degree of hydrolysis of the end-groups equally well for a dimer as for a trimer. We assume that functional group reactivity is influenced only by FSSE, e.g., k01 represents the functional group rate constant equally well for functional groups involved in molecular reaction L1 + L2 f L3 as for functional groups involved in molecular reaction L1 + L3 f L4. The resulting substitution gives
As in eq 9, the functional group rate constant kim for a bimolecular reaction has units of functional group concentration ((mole silanol)/(liter solution))-1‚h-1. The power of 2 on 〈j〉1 in the cyclization terms appears because the probability that a chain undergoes cyclization depends on the probability that both ends are hydrolyzed. A factor of 1/2 is associated with kii to prevent overcounting two indistinguishable reactions, thus satisfying the consistency requirement that the total concentration of monomeric units is conserved with time.1 Note that eq 11 assumes neither mean field site reaction kinetics nor mean field functional group reaction kinetics. A straightforward example illustrating the importance of this treatment is that, by eq 11, cyclization cannot take place until L3 or L4 are present. By contrast, eq 9 fails to account for this obvious requirement. The silicon site distribution can be calculated from the molecular concentrations and compared to the 29Si NMR results in a least squares optimization program29 to obtain the rate constants. We have found that inclusion of chains larger than L5 does not improve the solution significantly and decreases the robustness of the solution. However, L5 must be included. Figure 11 shows the curve fits of the silicon site concentrations 3R 4R [Q0], [Q1], [Qnr 2 ], [Q2 ], and [Q2 ], where the superscript nr represents disubstituted silicon sitesthat are not part of threeor four-membered rings. For some cases, the algorithm is unable to converge on k11 as a consequence of the low
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J. Phys. Chem., Vol. 100, No. 30, 1996 12527
Figure 11. Curve fits of bimolecular and cyclization reaction using the molecular kinetic model (eq 11). Compositions, [TEOS]/[EtOH]/[H2O]/ 3R 4R pHCl, are shown in the graphs. Symbol representation is b [Q0], 9 [Q1], [ [Qnr 2 ], 2 [Q2 ], and × [Q2 ]. Curves are optimal solutions of eq 11. 3R 4R 4R [Q4R ] is generally close to [Q ], so [Q ] is distinguished by the dashed line. [Q ] is absent in compositions 2.86/5.28/2.86/3.4, 1.63/9.82/3.27/3.1, 2 2 2 2 1.43/9.84/5.72/3.0,3.4, and 1.43/8.08/11.45/3.0. The poor fit for composition 1.43/8.08/11.45/3.0 is due to high W/Si and high pHCl.
concentration of Q2, but an upper limit for k11 can still be estimated. Similarly, for cases where no rings are observed, an upper limit for the apparent cyclization rate constant is also estimated. These upper limits will be represented in the following figures by open symbols.
4. Rate Constant Results. As shown in Figure 12, the dimerization rate constant, k00 , is a strong function of solution pH, decreasing monotonically toward a minimum near pHCl ) 4.0.74 This trend agrees with that reported by Fyfe and Aroca31 and with that found for water-starved systems (Figure
12528 J. Phys. Chem., Vol. 100, No. 30, 1996 10). Again, k00 is a weak function of W/Si (via (w/a)e or 〈j〉i). However, at a given pHCl, k00 tends to decrease with increasing equilibrium water-to-ethanol molar ratio, (w/a)e (or 〈j〉i). These trends are also shown by the monomer/end-group condensation rate constant, k01. There is no obvious correlation between the end-group/endgroup rate constant, k11, and pHCl. However, since the kinetic trajectories, and consequently the polymer growth pattern, are determined by the relative reaction rates, we examine the rate constant ratio k11/k00 in Figure 13. k11/k00 shows a minimum near pHCl ) 2.5. On the other hand, k01/k00 remains near unity, increasing only when k11/k00 rises above unity (near pHCl ) 3.5). This pattern is consistent with that reported by Sanchez30 and Pouxviel22 for pHCl between 2.6 and 3.3. However, far above the apparent isoelectric point, k11 g k00, meaning negative FSSE is not universal. This is easily overlooked because 4R Q3R 2 and Q2 have usually been inappropriately lumped into all Q2, and a broad range of pH has not been examined. Note that at the composition where k11 g k00, ring formation is also suppressed (see Figure 3). The apparent cyclization rate constants kσ3 and kσ4, shown in Figure 14, decrease monotonically as pHCl rises toward 4.0, and they decrease with (w/a)e. Nevertheless, Figure 15 shows that kσ3 and kσ4 generally stay close in magnitude to k00. An exception is seen at pHCl g 3.0 at either high or low (w/a)e. At these compositions, cyclization is suppressed (see Figure 3). For high (w/a)e (0.5), the formation of both three- and fourmembered rings is suppressed. 5. Influence of Solution pH on FSSE Rate Constants. For the hydrolysis and condensation of alkyl(trialkoxy)silanes in aqueous solution, Pohl and Osterholtz56 observed a minimum in dimerization rate constant at pD 4.5. To explain these results, they proposed a condensation reaction mechanism that is both acid and base catalyzed. Iler54 has also proposed that the polymerization of silicic acid involves ionized intermediates to explain the minimum gelation rate at the isoelectric point of silica, near pH 2. The acid and base ionization equilibria (with constants Ka and Kb, respectively) on an i connected silanol can be represented by Ka
(a) Qi-OH + H3O+ 798 Qi-OH2+ + H2O
Ng and McCormick
Figure 12. Bimolecular condensation rate constants from eq 11 for water-rich systems. (a) The dimerization rate constant, k00, decreases monotonically toward a minimum near pHCl ) 4.0. It also decreases with (w/a)e. (b) The monomer/end-group condensation rate constant, k01, exhibits similar trends as k00. (c) The end-group/end-group rate constant, k11, while decreasing slightly with pHCl, is very small for pHCl between 2.5 and 3.0. Compositions, [TEOS]/[EtOH]/[H2O]/pHCl, with similar TEOS concentration and W/Si are represented by the same symbols: (9) 2.86/5.28/2.86/3.0,3.4, ([) 2.02/8.11/4.04/2.5, (×) 1.87/ 7.56/7.54/2.2, (2) 1.63/9.82/3.27/2.6,3.1, (1) 1.43/10.71/2.86/3.0,3.4, (b) 1.43/9.84/5.72/3.0,3.4, and (+ 0) 1.43/8.08/11.45/3.0. Open symbols represent upper limits only. Lines are drawn to connect points from systems with similar initial TEOS, ethanol, and water concentrations
Kb
(b) Qi-OH + OH- 798 Qi-O- + H2O Several reports indicate that the ionization equilibria are shifted by substitution on the silicon sites. For instance, polysilicic acid has been observed to be a stronger Bro¨nsted acid than the monomeric silicic acid.54 The isoelectric point for polysilicic acid is thus expected to be lower, (between 1.5 and 2) than that for the monomeric silicic acid (between 2 and 3). Similar arguments have been made for the acid- and basecatalyzed polymerization of alkoxysilanes in nonaqueous solution. Indeed, increasing acidity of a silanol group by siloxane substitution has been conjectured to explain the observed negative FSSE at low pH.7,57,58 However, polyalkoxysilanes might have yet another set of isoelectric points. There has been no systematic study of the influence of solution pH on the rate constants, but this precedent helps us rationalize how the rate constants in Figure 12 change with pHCl. As shown in Figure 12, the dimerization rate constant, k00, approaches a minimum near or above pHCl 4, while the rate constant for the end-group/end-group reaction, k11, is minimized at a lower pH, (near pHCl 2.5). The dimerization rate constants are comparable with those obtained for the water-starved systems, confirming that there is only a weak effect of (w/a)e or 〈j〉i. These results are consistent with the proposed mecha-
nism involving ionized intermediates, since we expect an increasing ionization constant and a lower isoelectric point with increasing siloxane connectivity. The monomer/end-group reaction rate constant, k01, behaves in a somewhat more complicated fashion, probably because the reaction involves a pair of reactants of different ionization constants. For a solution pH range where monomers are strongly ionized (pHCl < 2.5), the reaction should involve an ionized monomeric intermediate and a nonionized end-group and the rate constants should be determined by the former. Thus, it is not surprising that we found k01 = k00. Similarly, near the isoelectric point of the monomer, while the end-group becomes strongly ionized (pHCl > 3.5), k01 should approach k11. Negative FSSE is observed only at low pH. The minimum in k11 helps explain the strong cyclization trend observed for this range of pH. Cyclization is promoted largely because the end-group/end-group bimolecular reaction is inhibited by a strong negative FSSE in this pH range, probably owing to ionization equilibria. The effect of the degree of hydrolysis or equilibrium waterto-ethanol ratio on cyclization can be discerned by the exceptions. 29Si NMR results show that at the pH range where cyclization is ordinarily appreciable, cyclization is effectively
Polymerization of TEOS
Figure 13. Bimolecular condensation rate constant ratios for waterrich systems. (a) Rate constant ratio k11/k00 shows a minimum near pHCl 2.5. (b) Rate constant ratio k01/k00 tends to stay near unity, increasing only when k11/k00 > 1, near pHCl ) 3.5. The legends are the same as in Figure 12.
Figure 14. Apparent cyclization rate constants from eq 11 for waterrich systems, demonstrating that (a) kσ3 and (b) kσ4 decrease monotonically toward pHCl ) 4.0 while they are consistently lowered by (w/a)e or 〈j〉1. The legends are the same as in Figure 12.
suppressed only as W/Si is increased to 8. We have seen above that hydrolysis is close to completion (〈j〉i maximizes) and (w/
J. Phys. Chem., Vol. 100, No. 30, 1996 12529
Figure 15. Rate constant ratios for cyclization, demonstrating that (a) kσ3/k00 and (b) kσ4/k00 tend to stay near unity but are lowered for pHCl g 3.0. Legends are the same as in Figure 12.
a)e increases markedly as W/Si approaches a value of 8. It is possible that suppression of cyclization at W/Si ) 8 is correlated to 〈j〉i or (w/a)e (which in turn influences the activity coefficients largely via ionization). 6. Correlations with Inhomogeneity. 29Si NMR results have shown the prevalence of extensive nonrandom cyclization (high extent of reaction) over the composition range that yields homogeneous gels. Analysis of these results by kinetic modeling indicates that cyclization may be promoted by favorable solvent composition and strong negative FSSE for bimolecular reactions. Although the cause for extensive nonrandom cyclization is not clear, we note that under conditions in which cyclization is not observed, loss of NMR signal is detected. These results lead us to speculate that the competition between the processes of bimolecular reaction and cyclization plays a role in determining gel microstructural development. In conditions for which bimolecular reactions win over cyclization, we should expect that branchy, high molecular weight polymers are rapidly formed early in the reaction. Flory-Huggins theory predicts that as the polymer molecular weight increases, polymer-solvent interaction becomes increasingly unfavorable possibly because of decreasing configurational entropy of mixing, causing the polymer to phase-separate. The molecular weight limit for phase separation should decrease with branching, since the configurational entropy of mixing becomes even less favorable.4 However, phase separation may not be observed if polymerization is fast enough to establish very slowly diffusing polymers.75 (Indeed, a common method used to prevent phase separation in polymerizing systems is to predisperse huge molecular weight polymers! Demixing of these large polymers is limited by low diffusivity, so phase separation can be effectively suppressed as these polymers continue to grow.76) Results from 29Si NMR and kinetic studies indicate that at pHCl > 3 and/or at high W/Si, we should expect the formation of highly branched high molecular weight polymers since
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Ng and McCormick Summary
Figure 16. Demonstration that the 29Si NMR signal, obtained with identical NMR protocol, is diminished for t > 10 h at W/Si ) 8 and pHCl ) 3.4. Composition is [TEOS]/[EtOH]/[H2O]/pHCl ) 1.43/8.08/ 11.45/3.4.
bimolecular reactions are fast. This condition may lead to phase separation. Since NMR spectroscopy is sensitive to the mobility of the nuclei (exhibited by T1), a progressive loss of NMR signal at a constant relaxation delay as polymerization proceeds may indicate of polymer phase separation. Indeed, we find that at pHCl ) 3.4 and W/Si ) 8, a significant amount of NMR signal is lost within 10 h of the reaction time (Figure 16) . At W/Si ) 2 and pHCl ) 3.5, significant 29Si NMR signal, from branched sites, is lost only for t > 300 h (Figure 17). Moreover, increased molecular concentration at the liquidliquid interface can also promote bimolecular reactions. Indeed, under conditions of high acid and low water concentrations, which should produce homogeneous gels in the single phase, the polymerization of TEOS in multiphase systems can produce silica particles.77,78 The 29Si NMR spectra appear similar to those observed for base-catalyzed TEOS systems in solution. Gelation can also occur for acid-catalyzed TEOS systems in a microemulsion79 for which the 29Si NMR spectra showed no cycles. These results suggest that favorable bimolecular reactions at the liquid-liquid interface can cause phase separation to produce particles.
For acid-catalyzed polymerization of TEOS, we have monitored the evolution of well-specified small oligomers including three-membered and four-membered rings up to a conversion of 40% over the initial compositions (mol/L) [TEOS]/[EtOH]/ [H2O]/[HCl] ) (1.43-2.86)/(5.28-10.71)/(2.86-11.45)/(4 × 10-4 to 2 × 10-2). Decreasing pHCl generally favors cyclization. This pH effect is magnified at high W/Si. This effect is less important in systems that are both dilute ([TEOS] < 2) and low in the initial water-to-silicon ratio (W/Si e 2), where cyclization is highly favorable regardless of pH. Cyclization is favored by low to moderate W/Si (1-4) and by high initial ethanol concentration. The compositions that favor cyclization (low pHCl and W/Si) correlate well with the compositions that produce homogeneous microporous gels.70 The gels are expected to be made of polymers of low fractal dimension but with segments containing small cycles such as the double threering structure. This is consistent with SAXS results.37,38 We confirm that hydrolysis equilibrium is established rapidly in the systems studied so that, regardless of the initial composition, the average degree of hydrolysis for each silicon site becomes practically constant after a short initial transient period and before significant changes in the concentration of (i + 1) siloxy-substituted silicon sites occur. This allows us to monitor the bimolecular and cyclization condensation rate constants using a molecular kinetic model. Results show favorable cyclization can be rationalized by the trends in the apparent rate constants. The apparent dimerization rate constant decreases with solution pH and water-to-ethanol ratio at equilibrium (or the average degree of hydrolysis). The end-group/end-group to dimerization rate constant ratio shows a minimum near pHCl 2.5. As the pHCl increases, bimolecular end-group/end-group reaction competes effectively with cyclization and may explain the observed precipitation at high pHCl presumably caused by the formation of highly branched polymers that are incompatible with the solvents. Moreover, the minima in the dimerization rate constant and the end-group/end-group to dimerization rate constant ratio, with respect to pHCl, are consistent with a reaction mechanism
Figure 17. Demonstration that the 29Si NMR signal from branched site peaks is diminished for t > 300 h at W/Si ) 2 and pHCl ) 3.5. Composition is [TEOS]/[EtOH]/[H2O]/pHCl ) 2.02/8.11/4.04/3.5. The last three spectra are acquired with 128 scans, while others are acquired with 32 scans.
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