8973
J. Phys. Chem. 1992, 96, 8973-8979 methylbenzene as to make the distinction very difficult indeed. This interpretation would be entirely in keeping with the suggestion of Turro, who considered the possibility of stabilized exciplexes on the excited-statesurface of exchange-energy-transfer processes.' The fate of such complexes would depend on the relative excitation energies of the free molecular partners. In the case of triplet acetone and mesitylene or durene, energy transfer is endothermic by at most 2 kcal, which may create ideal conditions for a relatively long-lived exciplex. Acknowledgment. G.L.I. and L.H.C. are grateful for postoctoral fellowships from the Conselho Nacional de Desenvolvimento Cientifico e Technologico (CNPq, Brazil). The fluorescence lifetime instrumentation was acquired with funds from the National Science Foundation (Grant CHE-8209863). We thank Professor J. W. Hastings for his continuing interest. G.L.I. expresses his gratitude to Professor Frank Quina for enjoyable and useful discussions.
References and Notes (1) Turro, N. J. Modern Molecular Photochemistry; Benjamin/Cummings: Menlo Park, CA, 1978; pp 305-309. (2),(a) Wilson, T.; Halpern, A. M. J . Am. Chem. SOC.1980, 102, 7279. Ib) Wilson. T.: H a i r " A. M. Ibid. 1981. 103. 2412. (c) Wilson.. T.:. Frve. - . S.'F.; Halkrn; A. M. ibid. 1984, 106, 3600. (d) Johnston, L. J.; Scaiano, J. C.; Wilson, T. Ibid. 1987, 109, 1292. (3) See, for example: Stevens, B. Adu. Photochem. 1971, 8, 161. (4) India. G. L.; Wilson. T. J. Photochem. Photobiol. A 1992, 63. 195. ( 5 ) Cataani, L.'H.; Wilson, T. J. Am. Chem. Soc. 1987, 109,.7458. (6) kdir= 4OOOrNRD, with the diffusion coefficient D calculated according to the empirical relation derived by Davis et ai. (Davis, H. T.; Tominaga, T.; Evans, D. F. AIChE J . 1980, 26, 313); Olea and Thomas found that this procedure leads to the best values of kdir(Olea, A. F.; Thomas, J. K. J . Am. Chem. Soc. 1988,110,4494). (7) In agreement with the conclusions of: Wagner, P. J.; Kochevar, I. J . Am. Chem. Soc. 1968, 90, 2232. (8) Porter, G.; Dogra, S.K.; Sugamori, S.E.; Yip, R. W. J . Chem. SOC., Faraday Trans. I1973, 69, 1462.
(9) Barltrop, J. A.; Coyle, J. D. Excited States in Organic Chemistry; Wiley: New York, 1975; p 194. (IO) Demas, J. N. Excited States Lifetime Measurements; Academic Press: New York, 1983; pp 812-89. ( I 1) We thank Ying-Hua Mei for performing these experiments. (12) Lechtken, P.; Turro, N. J. Angew. Chem., Int. Ed. Engl. 1973, 12, 314. Schuster, G.; Turro, N. J. Tetrahedron Lett. 1975, 2261. (13) The ratio DIP of "delayed counts" to "prompts counts" is estimated by integration of eqs 12 and 14. For Figure 1, DIP = k,/(ak,,) = 0.19; for Figure 2, DIP = (k,/a)(B/X,+ l/Xb) = 0.96. Thus D / P is five times larger in the presence of 0.18 M mesitylene, in otherwise the same conditions. (14) Bayliss, N. S.J . Chem. Phys. 1950, 18, 292. (1 5 ) Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: London, 1970; pp 110-1 16. (16) Examples: Milder. S.J. Inorg. Chem. 1989, 28, 868. (17) Cundall, R. B.; Voss, A. J. R. J . Chem. Soc., Chem. Commun. 1969, 137. (18) Nakashima, N.; Sumitani, M.; Ohmine, 1.; Yoshihara, K. J . Chem. Phys. 1980, 72, 2226. (19) Sugawara, T.; Iwamura, H. J . Am. Chem. SOC.1985, 107, 1329. (20) In the presence of acetone, the delayed luminescence of durene ought to be more intense, not less, judging from the experiment described above (IIIb, Figure 7; see also Discussion). The fact that this luminescence was apparently not a major problem in the Johnston-ScaianoM laser flash experiment at A,, = 308 nm seems to suggest that the two transients are not the same. (21) Closs, G. L.; Piotrowiak, P.; MacInnis, J. M.; Fleming, G. R. J . Am. Chem. SOC.1988, 110, 2652. These authors reported a change in an intramolecular energy transfer rate of less than a factor of 3 between hexane and acetonitrile as solvents, very similar to our solvent effects on kEA. (22) ET of acetone: 80 kcal (Borkman, R. F.; Kearns, D. R. J . Chem. Phys. 1966,44,945); 77.5 kcal (Loufty, R. 0.;Loufty, R. 0.J. Phys. Chem. 1973, 77, 336); 78.9 kcal (Handbook of Organic Photochemistry; Scaiano, J. C., Ed.; CRC: Boca Raton, FL, 1989; Vol. I, p 376). ET of mesitylene, 80.1 kcal; ET of durene, 79.8 kcal (Engel, P. S.;Monroe, B. M. Ado. Photochem. 1971, 8, 245; also ref 15). (23) McGlynn, S.P.; Azumi, T.; Kinoshita, M. Molecular Spectroscopy of the Triplet State; Prentice-Hall: Englewood Cliffs, NJ, 1969; pp 166-171. (24) Reference 1, pp 331-333. Mirbach, M. F.; Ramamurthy, V.; Mirbach, M. J.; Turro, N. J.; Wagner, P. J. Nouu.J. Chim. 1980, I , 471. Yip, R. W. Can. J. Chem. 1973, 51, 1881. (25) Loufty, R. 0.; (26) Giering, L.; Berger, M.; Steel, C. J. Am. Chem. Soc. 1974, 96, 1974.
Kinetic and Thermodynamic Study of the Hydrolysis of Silicon Alkoxides in Acidic Alcohol Solutions Jorge Sanchez and Alon McCormick* Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave SE. Minneapolis, Minnesota 55414 (Received: July 19, 1991; In Final Form: July 22, 1992) Though the relevant literature offers little consistency in the kinetic data of the acid-catalyzed hydrolysis of silicon alkoxides, reliable rate constants are essential for the development of kinetic models for sol-gel processing. Si-29 NMR was used in conjunction with numerical simulations to measure hydrolysis rate constants for tetraethoxysilane (TEOS), tetramethoxysilane (TMOS), and hexaethoxydisiloxane. Unlike previous efforts, we have used conditions where the effects of hydrolysis and condensation reactionscan be decoupled. We have verified our rate constants using a range of solution compositions. Implications regarding the influence of the synthesis protocol on gel homogeneity are discussed. We have also estimated the enthalpies, entropies, and activation energies for the hydrolysis of TEOS. We find that each subsequent hydrolysis reaction has a higher rate constant, confirming some earlier studies. However, we also find that each hydrolysis step becomes thermodynamically less favorable. These opposing kinetic and thermodynamic trends explain why acid-catalyzed hydrolysis produces a distribution of hydrolyzed intermediates rather than just fully hydrolyzed products. They also suggest that complete and immediate hydrolysis would be difficult to achieve except at very high water concentration.
Introduction
The chemical synthesis of ceramics and glasses by the sol-gel method has attracted much interest.l Even though silicon alkoxide systems have been among the most studied sol-gel materials, chemical engineering models remain tentative at best. Typically, a silicon alkoxide, for example tetraethoxysilane (TEOS) or tetramethoxysilane (TMOS), and a certain amount of water are dissolved in an alcohol in the presence of a catalyst. In acidic solutions, the polymerization of the silicon alkoxide can produce a transparent and porous gel.l*s The gel formed is a polymeric network of siloxane bonds (Si-0-Si) with alkoxy or
-
hydroxy side groups. The reactions are generally written hydrolysis: Si(OR)4 + nH,O Si(OR),,(OH), + nROH alcohol-producing condensation: Si-OR HO-Si SiUSi water-producing condensation: Si-OH HO-Si Si-0-Si
+
+
+ ROH + H20
The actual complexity of the process is not reflected by this simplified representation, though, because many different intermediates are formed during the reaction. The intermediate
0022-3654/92/2096-8973$03.00/0 0 1992 American Chemical Society
8974 The Journal of Physical Chemistry, Vol. 96, No. 22, 1992
Sanchez and McCormick
TABLE I: Summary of Literature Data for the Hydrolysis of TEOS and TMOS" source Aelion et
limitations overall hydrolysis irreversibility
Yang et a1.9
irreversibility pseudo-first-order
Pouxviel et al.'
assumes a particular set of reactions
Kay and Assink2
statistical model irreversibility
Ro et a1.I0
statistical model irreversible condensation
system composition TEOS: 0.21 M H20: 1.2 M HCI: 1.6 x 10-3 M dioxane TEOS: 1.89 M HzO: 7.57 M HCl: 9.6 X M ethanol TEOS: 1.28 M (1.95 M) HzO: 12.8 M (7.8 M) M HCl: 7.9 X (5.1 X lo4 M) ethanol 8.5 M (7.4 M) TMOS: 2.24 M H 2 0 : variable HCI: 1.6 x 10-3 M methanol TEOS: 9.3 M H20: 1.6 M HCI: 10-3 M ethanol 7 M
rate constants for the monomer hydrolysis kH = 0.374 L/(mol h) E, = 6.8 kcal/mol
k , = 0.86 h-"* k2 = 3.84 h-' k3 = 17.4 h-l k4 = 78 h-I k , / k - , = 0.8/0.11 L/(mol h) (0.26/0.026) k 2 / k + = 4.02/0.26 L/(mol h) (1.36/0.082) k3/k-, = 16.05/1.46 L/(mol h) (5.12/0.34) k4/k-4 = 29.18/7.3 L/(mol h) (9.22/1.54) k , = 48 L/(mol h) k2 = 36 L/(mol h) k3 = 24 L/(mol h) k4 = 12 L/(mol h) k l / k - , = 0.328/0.014 L/(mol h) k2/k-2= 0.282/0.026 L/(mol h) k3/k-, = 0.164/0.042 L/(mol h) k 4 / k , = 0.082/0.056 L/(mol h)
"In all these systems, both hydrolysis and condensation proceed to a significant extent during the kinetic measurements. Note that the rate constant units are L/((mol Si) h) (except (*) in L/h because of the assumption of first-order reactions).
structures depend on the reaction conditions and influence the gel time as well as the characteristics of the gel (porosity, degree of branching, fractal structure, etc.). To understand these trends and to incorporate them into process engineering efforts, it is necessary to have rigorous reaction engineering models. Several attempts have been made to develop a model for the gelation of silicon alkoxide sol-gel systems,24 but success has been limited. Experimental rate constants are very scarce and show little consistency. Kinetic data for varying temperatures are practically absent, so little insight from activation energies has been obtained. Finally, proposed rationalization for kinetic trends have not been rigorously tested. For instance, it has been argued extensively that each subsequent hydrolysis of TEOS should be slower, but the literature does not convincingly prove this. Few authors have discussad thermodynamics trends that might interfere with kinetic trends. One of the reasons for these difficulties stems from the lack of mechanistic understanding. Many fundamental questions remain; for example, it is still not very well understood how the rates of hydrolysis and condensation depend on the environment of the silicon atom or why hydrolysis is incomplete before condensation starts, even though hydrolysis is considered fast relative to condensation in acidic In this paper, we focus on (i) the determination of rate constants for the hydrolysis of silicon alkoxides in acidic systems at different temperatures and (ii) the explanation of kinetic and thermodynamic trends. Unlike previous workers, and in order to be as general as possible, we assume neither irreversibility of the reactions nor pseudo-first-order in the reactant concentrations. To facilitate and improve the kinetic analysis of hydrolysis, sol-gel reactions are performed in conditions where hydrolysis is effectively separated from condensation for sufficient time. Finally, a nonlinear parameter optimization method is used to obtain the rate constants. Though the solutions studied here have gel times (on the order of several weeks) much longer than might be of practical interest, the kinetic and thermodynamic trends thus derived are of general interest.
Hydrolysis of Silicon Alkoxides Importance of Hydrolysis Kinetics. The hydrolysis of silicon alkoxide monomers consists of four consecutive reactions producing hydrolyzed monomers. These monomers are the building units from which the oligomers and gel evolve, and it is reasonable to think that the gel structure and gel time will largely depend o n
the concentrations of the originating monomers. Quantifying the kinetics and the relative stabilities of the five monomers is thus absolute essential for the development of a comprehensive gelation model. The importance of the hydrolyzed monomers was recognized early. For example, since small-angle X-ray scattering experiments have demonstrated that homogeneous gels produced with acid catalysts are formed by a weakly branched network,'^^ Keefer6 initially assumed that the rate of monomer hydrolysis becomes slower for each successive hydrolysis so the less hydrolyzed monomers are favored. This hypothesis was justified on the basis of the electronic inductive effect: since OH groups are better electron attractors than OR groups, hydrolysis results in a decreased electron density at the site of remaining OR groups. Assuming that the hydrolysis rate is governed by the rate of electrophilic attack of H30+on the OR ligand, the reactivity of the OR groups should decrease when the Si atom to which they are attached carries more OH groups. This hypothesis is subscribed to by several authors.'-25However, other results contradict this trend,7*9causing the issue to become even more mysterious. Given the complexity of the system, we are led to believe that gel structure and overall rate result from balancing trends of hydrolysis and condensation rates and perhaps even from the relative thermodynamic stability of the intermediates. For this reason we seek an accurate understanding of hydrolysis in particular. Hydrolysis Rate Constant. Several authors have reported rate constants for the hydrolysis of silicon alkoxides, but there is little consistency among the reported kinetic trends. We briefly review these results in Table I. The statistical model developed by Kay and Assink2 assumes equal and independent reactivities of the functional groups in the hydrolysis of TMOS, and it neglects reversibility of the reactions. In other words, because of the decrease of the number of OR groups to hydrolyze, this model assumes linearly decreasing rate constants for the four consecutive monomer hydrolysis reactions of TMOS. Using this model, Doughty et a1.* found that the hydrolysis of hexamethoxydisiloxanewas about 5 times slower than the hydrolysis of TMOS. However, the experimental results of Yang et al.9and Pouxviel et al.7 for TEOS systems show that each consecutive monomer hydrolysis seems to proceed more quickly. Moreover, Pouxviel's' and Ro's'O results indicate reversibility. It should be noted, however, that they did not attempt a rigorous determination of
Silicon Alkoxides in Acidic Alcohol Solutions the rate constants by optimal curve fitting. In addition, their kinetic model includes a great number of condensation reactions, which makes their rate constants even less reliable. Although the hydrolysis rate constants reported in the literature by various authors cannot be compared because of different systems and conditions, it appears, though, that the kinetics trends depend on the model used and the assumptions made. Many of the solutions studied gelled so quickly that it should be quite difficult to analyze the hydrolysis rate constants alone. That some studies show an increase in subsequent rate constant suggests that the electrophilic attack of protons on the alkoxy groups might not govern the reaction kinetics; therefore, one must also consider the rate of nucleophilic substitution and the departure of leaving groups" as well as steric effects. Finally, some studies suggests significant rates of reverse hydrolysis (sometimes referred to as re-esterification), so we must examine whether the reaction steps approach pseudoequilibrium over the course of the reaction.I2
Kinetic and Thermodynamic Calculations Analytical Method. Most of the analytical methods that have been commonly used to study the hydrolysis reaction, including Raman spectroscopy or the molybdic acid reagent method,' can only measure a global rate of hydrolysis since they cannot distinguish the individual molecules. In order to unambiguously measure rate constants for the different hydrolysis steps of TEOS, Si-29 NMR is the method of choice since it allows the monitoring of the concentrations of hydrolyzed intermediates. However, because of low sensitivity and long relaxation times, Si-29 NMR is a slow method; a reasonable spectrum typically takes at least several minutes to acquire. The relaxation time can be greatly reduced by adding a chemically inert paramagnetic relaxing agent to the system (typically Cr(acac), for alcoholic solutions). To ensure that hydrolysis does not proceed to a significant extent during the recording time, it is necessary for the reaction to be slow. Another limitation is that although hydrolysis is much faster than conden~ation,~?' condensation typically begins while the hydrolysis is still taking place. This complicates the kinetic analysis because many condensation reactions can occur, and very quickly Si-29 NMR cannot distinguish which oligomer is formed since it only reveals site connectivities. In contrast, for the monomers, the silicon resonances unambiguously belong to specific molecules. Moreover, the determination of rate constants from the experimental data by numerical methods becomes more difficult and less reliable when many reactions are taking place simultaneously, and previous authors have made severe assumptions to limit the complexity of the kinetic analysis. To overcome these difficulties, we chose to add only very small amounts of acid catalyst. The benefit13J4is that the condensation becomes so slow that a long time elapses during which only hydrolysis proceeds with a significant rate. During this 'condensation-free period" (CFP), the formation of condensed species is negligible, and only hydrolysis reactions of the monomers need to be considered for kinetic modeling. Long CFP's allow us to record a large enough number of NMR spectra so that we can accurately monitor the formation of hydrolyzed monomers. The length of the CFP depends on the concentration of water, the amount of catalyst, and the temperature. In the range of system composition we studied, it is typically of the order of 1 h or more. Because condensation is much slower than hydrolysis, calculated hydrolysis rate constants were not significantly affected by the choice of the CFP length, as long as condensed species concentrations are in small quantities compared to monomer concentrations. If this is not the case, we observed that the curve fitting of the experimental data worsened toward the end of the curve, a consequence of the buildup of condensed species, but the changes in the calculated rate constants remained within the optimization method uncertainties. An additional benefit to this approach is that we are able to quantify kinetics in low ionic strength solutions and thus can identify the influence of ionic strength as [H+] increases. Kinetic Equations. For TEOS and TMOS, we can write hydrolysis reactions as follows:
The Journal of Physical Chemistry,
+ H20 = Qol + Qol + H20 = Qo2 + Q: + H 2 0 = QO3+ Qoo
QO3+ H 2 0 = QO4+ where the subscript of the Q's is the number of siloxane bonds and the superscript is the number of silanols, and k, and k-, represent forward and reverse rate constants. Thus, when TEOS is used as precursor, R is Et and Qoo,Qol,Qo2,QO3, and QO4 are respectively Si(OEt)4 (Le., TEOS), (EtO),SiOH, (EtO),Si(OH),, EtOSi(OH),, and Si(OH)4. Note that we allow each reaction to be reversible and that the rate constants (L/(mol h)) possess units of moles of silicon units (which for monomers correspond to molecules) rather than moles of functional groups (e.g., OR or OH). The evolution of the component concentrations is described by a system of coupled differential equations: d[QoOl /dt = k-I[Qo'l [ R W
- ki [QoOI [I4201
d[Qo'l /dt = ki [Qool[I3201 + k-2[Qo21[ROHI MQo11 [H201 - k-I [Qo'l [ROHI
+ M Q o I I [I3201 k-2[Qo21 [ R W - k3[Qo21W2OI d[Qo31/dt = k3[Qo21W2OI + U Q o 4 1 P O H I k-3[Qo31[ROW - k4[Qo31W 2 0 1 d[Qo41/dt = k4[Qo31W2OI - U Q o 4 1 [ROW d[Qo21/dt = k-3[Qo31[ROHI
d[ROHl/dt Iki[Qoo1 + M Q o I I + k3[Qo21 + k4[Qo311 X [HzOI - Ik-i[Qo'l + k-2[Qo21 + k-3[Qo31 + k-dQo41J[ROHl d[H,O]/dt = -d[ROH]/dt with the initial conditions [Qo'lo = [Qo210 = [Qo310
[Qo410= 0
[QoOIO= [Si(OR)4lmitia1 [H~OIO = [H20linitiai [ROHIO= [ROHlinitia~ A similar system of differential equations can be written for the hydrolysis of the silicon sites in hexaethoxydisiloxane. NumericalTechniques.These equations were numerically solved using the Adams-Moulton a1g0rithm.l~ The calculated curves for the monomer concentrations versus time were then fitted with the experimental data using nonlinear parameter optimization methods. These methods determine the best parameters minimizing the objective function defined as m
@(k) = XIQICxP- Q,"I'(k)I2 i- 1
with the constraint k 1 0, where k is a vector containing the rate constants that are to be optimized, m is the number of data points, QiCXPare the experimental data (concentrations measured by NMR), and Qiaic ate the calculated concentrations. Several algorithms have been described in the literature to solve this constrained minimization prob1em.l6'* The choice of the optimization method is important, as it is known that different algorithms can behave very differently for a given problem. Thus, special care was taken in selecting the optimization method. Using a simulated collection of data calculated for a given set of rate constants, several methods were tested and compared; the comparison of the efficiency of an optimization algorithm was based on its rate of convergence and the accuracy of the calculated set of rate constants compared to the 'true" solution. The stability of the algorithm was also tested by introducing random error in
8976 The Journal of Physical Chemistry, Vol. 96, No. 22, 1992
the simulated data to see how the convergence was affected. All calculations were performed on a Cray X-MP supercomputer,and when needed, derivatives were calculated by finite-difference approximations. It was found that a Levenberg-Marquardt least-squares algorithm" was the best optimization method in our case. The use of very high precision arithmetic, apart from being much slower, did not increase significantly the accuracy of the results. Although great care was taken to ensure the determination of the best rate constants fitting the experimental data, a nonlinear parameter estimation can be sensitive to errors. Not including experimental errors of the NMR data, a source of inaccuracy is the fact that there is no guarantee that the solution obtained is the global minimizer rather than just a local minimizer. To increase the odds of reaching the best possible solution, the optimization program was run for various initial guesses. In addition, an error analysis of the results was done by calculating the variancecovariance matrix of the parameters.22 The diagonal of this matrix contains an estimate of the variances of each parameter, and thus their statistical uncertainties can be calculated. The rate constants for the first three hydrolysis reactions were found to be quite robust with respect to the choice of the initial guess. When convergence is achieved, their calculated values are insensitive to the initial guess. Their uncertainties were in the range 5-10% and often much better. The values for the last hydrolysis appear to be more sensitive to the choice of the initial guess. A "good" guess, close enough to the solution, is necessary to obtain convergence and reproducibility. The activation energies for a TEOS system were calculated from an Arrhenius plot by measuring the rate constants at various temperatures ranging from 5 to 25 "C. EquilibriumConstants. Previous workI3 suggests that a quasi-equilibrium may be reached between the different monomers. That is, though condensation may proceed, the hydrolysis reactions remain at a state of quasi-equilibrium. [This is the situation, sometimes referred as pre-equilibri~m,'~ wherein concentrations of reactants and products of the reaction remain almost exactly in their equilibrium proportions, though a small rate of net forward reaction occurs.] We estimate the equilibrium constant for the ith hydrolysis as
Sanchez and McCormick
1
-72
1
I -71
I -75
-74
Time ( m n )
I
I
-7b
-77
I -78
I -79
.do
-81 I
wm
.
-
"."
.
3
L Y
.
I 1.51
z 0
10
20
30
40
50
60
70
Time (mn) Figure 1. TMOS system: [TMOS] = 3.32 M, [MeOH] = 10.96 M, [ H 2 0 ] = 6.25 M, and [HCI] = 1.47 X lo4 M at 20 OC. (top) Stack plot of Si-29 NMR spectra at different times. The chemical shifts are referenced to tetramethylsilane (TMS). (bottom) Experimental data and optimized fitting curves for the time evolution of the monomers.
52 28 22
nnruuVL--------
K,= k,/k-, Experiment. In a 10-mm NMR glass tube, TEOS (99%+), TMOS (98%), or hemthoxydisiloxane was dissolved in an alcohol (methanol for the TMOS systems and absolute ethanol for the others) containing about 1 wt % chromium pentanedionate (paramagnetic relaxing agent). Deionized water and controlled amount of a standard 0.095 N HCl solution were then added to obtain the desired composition. Hexaethoxydisiloxane was synthesized by reacting hexachlorodisiloxane with triethyl orthoformate, adapting a method described by Doughty et a1.* The concentrations of species in the system were monitored by 29SiNMR on a GE-500NMR spectrometer at 99.36 MHz. The spectra were aquired with a pulse width of 25 ps (corresponding to a 90" tip angle) and a pulse delay of 12 s. Ti's were of the order of 3 s for TEOS and smaller for the hydrolyzed species. We observed a constant total Si signal intensity for all spectra, so they are considered quantitative.
Results
TMOS System. Figure 1 shows an example of the sequence of NMR spectra and the simulated kinetic curves for a TMOS system with composition 3.32 M TMOS, 10.96 M MeOH, 6.25 M H 2 0 , and 1.47 X lo4 M HCl at 20 "C. The sum of the monomer concentrations remained nearly unchanged, confirming that the extent of condensation is negligible in this time period. The hydrolysis rate constants (expressed in L (mol Si)-I h-l) and the estimated equilibrium constantsare reported in Table 11. Note that the "-" entry in this table indicates that we were unable to measure any significant rate of reverse hydrolysis (reesterification). TEOS Systems. Figure 2 shows the NMR spectra sequence for a TEOS system at 25 "C with composition 2.07 M TEOS,
C
.-0 E w
--.
1.6 -
-*.* .
1.2 7
C aa 0 C
404 A
* - . *-
..
0
0
10
2.0
30
40
50
Time (mn) Figure 2. TEOS system: [TEOS]= 2.07 M, [EtOH]= 7.94 M, [H20] = 4.15 M, and [HCI] = 5.04 X IO4 M at 25 OC. (top) Stack plot of Si-29 N M R spectra at different times. Note that dimeric Si sites (QI' and Q12)only become significant after about 50 mn. (bottom) Expcrimental data and optimized fitting curves for the time evolution of the monomers.
7.94M EtOH, 4.15 M water, and 5.04 X lo+ M HCl. Both the enthalpy and the entropy of reaction for each consecutive hydrolysis were constant over the temperature range considered. Unlike previous works,' the rate constants we measured appear relatively insensitive to the system composition (at constant acid concentration), at least for the range of compositions studied, which is an indication of their robustness. This is shown in Table
Silicon Alkoxides in Acidic Alcohol Solutions
The Journal of Physical Chemistry, Vol. 96, No. 22, 1992 8917
i' 0
0 2
0 4
P
k
08
06
1
1 2
16
1 4
pi'] i o 3 ( m o l i l ) Figure 3. Dependence of the forward rate constants with the acid concentration for a TEOS system at 5 OC. System composition: [TEOS]/[EtOH]/[H,O] = 1.55 M/9.94 M/4.15 M. Q,2
.
Q13
I 'S
I 60
I
I
I
82
94
~ 8 6
1.4
mm
,
QI'
I -88
Q2
Q 10
A
_._
I
I
1
90
-35
-34
1 96
1
20 30 40 50 Time (mn) Figure 4. Hexaethoxydisiloxane system: [hexaethoxydisiloxane] = 1.3 M, [EtOH] = 7.94 M, [H,O] = 4.15 M, and [HCl] = 5.04 X 10" M at 25 OC. (top) Stack plot of Si-29 NMR spectra at different times. (bottom) Experimental data and optimized fitting curves for the time evolution of the dimeric Si sites. 0
10
111, where the hydrolysis rate constants and pseudoequilibrium constants at 5 "C are given for three different systems at constant acid concentration. The rate constants for the hydrolysis of a TEOS system are plotted versus the acid concentration in Figure 3. It can be seen that the curve is initially linear, confirming earlier report^.^^^^ However, a deviation from linearity is observed at acid concentration higher than about 10-3M, corresponding to the DebyeHuckel limit.I9 Hexaethoxydisiloxane System. Hexaethoxydisiloxane is a dimeric precursor formed during the condensation of TEOS. Thus, it is of great interest to compare the rate constants of hydrolysis in this system and in the TEOS system. The sequence of NMR spectra for the hydrolysis of hexaethoxydisiloxanefor the system 1.3 M hexaethoxydisiloxane (thus an initial concentration of QIo sites of 2.6 M) and the same concentrations of ethanol, water, and acid as in the previous TEOS system appears in Figure 4.
Discussion Kinetic Trends. Our results show several interesting trends: (1) The first and second hydrolysis steps for TEOS and TMOS are virtually irreversible, but reversibility is increasingly evident for subsequent hydrolysis steps. The first hydrolysis of hexaethoxydisiloxane also appears to be quasi-irreversible.
8978 The Journal of Physical Chemistry, Vol. 96, No. 22, 1992
Sanchez and McCormick
TABLE III: Rate Constants (in L (mol Si)-1h-l) and Pseudoequilibrium Constants for Three Different Systems at 5 OC and at Same Acid Concentration ([HCI] = 5.04 X lo-' M) composition TEOS/EtOH/H,O (M) kilk-1 (K,) k l k - 2 (K2) kdk-3 (4) k4lk-4 (K,) 1.03/11.93/4.15 0.10/- (>50) 0.281- (>50) 0.91 10.06 (1 5) 4.311.3 (3.3) 1.55/9.94/4.15 0.081- (>50) 0.29/- (>50) 1.0/0.07 (1 3.4) 3.9/1.1 (3.5) 2.07/7.94/4.15 0.09/- (>50) 0.4/- (>50) 1.65/0.14 (11.8) 4.9/1.2 (4.0) 25
I
-+- Dimer
20
/
1
forward
1
15'
0
1 3 4 Number of OH Groups on Si
5
Figure 5. Forward and reverse rate constants for the TEOS and hexaethoxydisiloxane systems at 25 OC and at same acid concentration. TMOS results were not included in this figure because they were obtained at much smaller acid concentration. System compositions: [TEOS]/[EtOH]/[H,O]/[HCl] = 2.07 M/7.94 M/4.15 M15.04 X 10-4 = 1.3 M/7.94 M/ M; [hexaethoxydisiloxane]/[EtOH]/[H,O]/[HCI] 4.15 Ml5.04 X M.
Most author^^,^**^ have assumed irreversible hydrolysis reactions in their kinetic models. Our attempts to fit the data assuming irreversible reactions always resulted in poor fits for the last two hydrolysis steps. (2) Both the forward and reverse reactions are faster for each consecutive hydrolysis as shown in Figure 5 where the forward and reverse rate constants have been plotted as a function of the number of OH groups on the silicon. This trend, which is observed for the three precursors studied, refutes the assumption of a reaction mechanism governed by the partial charges on the OR groups and the rate of electrophilic attack on those groups. On the contrary, these results support a bimolecular nucleophilic substitution mechanism (SN2):Ip2O the fast protonation of the alkoxy groups is followed by a slower and ratelimiting nucleophilic attack of water on the silicon atoms and finally the elimination of alcohol. OR is a bad leaving group and water is a weak nucleophilic species, explaining the relative stability of TEOS in neutral water-alcohol ~olution,'~ but O+RH is a much better leaving group and the reaction can proceed faster. The electron deficiency on Si increases when more OH groups are attached to it, because of the higher electronegativity of thisgroup compared to OR,21and thus, the Si atom becomes more vulnerable to water addition. Because the attack of the nucleophile is done from the opposite direction of the leaving group, steric effects are also important in explaining the upward trend of the hydrolysis reactivity. The more bulky OR groups tend to hinder more the nucleophilic attack than the OH groups. The importance of steric effects is evidenced by comparing the rate constants for TEOS and hexacthoxydisiloxane. While the inductive effect would predict a higher reactivity for silicon sites on dimer at same acid concentration, we actually observed slower rate constants for the dimer as seen in Figure 5 . This decrease in hydrolysis reactivity between the monomer and dimer is a consequence of steric effects. Thermodynamic Treads. The behavior of the K,'s shows that the reactions become thermodynamically less favorable for each subsequent hydrolysis step. This is clearly apparent for all three precursors studied. The kinetic and thermodynamic trends thus oppose each other. Examining Moand ASo in Table I1 reveals that the reason for the thermodynamic trend seems to be enthalpic and not entropic: the entropy actually seems to become more favorable, a possible consequence of a decreased order in the system, as water
is consumed by the reaction. Instead, the reason that each s u b sequent hydrolysis becomes less favored is solely an enthalpic effect, as the enthalpy of reaction decreases. We thus expect that the equilibrium distribution of hydrolyzed monomers is a strong function of temperature (by the van't Hoff relation).
Conclusion It was earlier thought that homogeneous gels consisting of weakly branched silicate networks resulted from increasingly slower hydrolysis with each subsequent step. Later, this view met experimental contradictionwhen it was found that the actual trend was an increase in the rate constants with each subsequent step. Our results unambiguously confirm this increase, but they also show that each subsequent hydrolysis is thermodynamically less favored. This explains why, depending on the reaction conditions and particularly the water concentration, there can be a large inventory of unhydrolyzed or partially hydrolyzed species even though the hydrolysis is 'fast". Therefore, the hydrolysis of silicon alkoxides does not necessarily produce only fully hydrolyzed intermediates even when the water amount is stoichiometrically sufficient. Acknowledgment. We acknowledge the support of NSF (Contract CTS-8910423), ONR, and the Center for Interfacial Engineering at the University of Minnesota. Registry No. TEOS, 78-10-4; TMOS, 681-84-5; hexaethoxydisiloxane, 2157-42-8.
References and Notes (1) Brinker, C. J.; Scherer, G. W. Sol-Gel Science; Academic Press: New York, 1990. (2) Kay, B. D.; Assink, R. A. J. Non-Cryst. Solids 1988,99,359; 1988, 104, 112; 1988, 107, 35. (3) Peppas, N. A.; Scranton, A. B.; Tsou, A. H.; Dawn, E. E. In Better Ceramics through Chemistry IIfi Brinker, C. J., Clark, D. E.. Ulrich, D. R., Eds.; Material Research Society: Pittsburgh, 1988; p 43. (4) Bailey, J. K.; MeCartney, M. L.; Macosko, C. W. J. Non-Cryst. Solids 1990, 125, 208. ( 5 ) Schaefer, D. W.; Keefer, K. D. In Better Ceramics through Chemistry; Brinker, C. J., Clark, D. E., Ulrich, D. R., Eds.; Elsevier North-Holland: New York, 1984; p 1. (6) Keefer, K.D. In Better Ceramics through Chemistry; Brinker, C. J., Clark, D. E., Ulrich, D. R., Eds.;Elsevier North-Holland: New York, 1984; p 15. (7) Pouxviel, J. C.; Boilot, J. P. J. Non-Crysl. Solids 1987, 94, 374. (8) Doughty, D. H.; Assink, R. A.; Kay, B. D. Ado. Chem. Ser. 1990, No. 224, 241. (9) Yang, H.; Ding, Z.; Jiang, Z.; Xu,X . J . Non-Cryst. Solids 1989,112, 449. (10) Ro, J. C.; Chung, J. J . Non-Cryst. Solids 1989, 110, 26. (1 1) Benson, D. Mechanisms of Inorganic Reactions in Solution; McGraw-Hill: New York, 1968. (12) Smith, J. M. Chemical Engineering Kinetics; McGraw-Hill: New York. 1981. (1 3) Sanchez, J.; McCormick, A. V. In Chemical Processing of Aduanced Materials; Hench, L. L., West, J., Eds.; Wiley: New York, 1992. (14) Jada, S. S . J. Am. Ceram. Soc. 1987, 70, 298. (1 5) Burden, R. L.; Faires, J. D. Numerical Analysis; Prindle, Weber & Schmidt: Boston, 1985. (16) Dennis, J. E.; Schnakl, R. B. Numerical Methods for Unconstraiwd Optimization and Nonlinear Equations; Prentice-Hall: Englewood Cliffs, NJ, 1983. (17) Fletcher, R. Practical Methods of Optimization; Wiley: New York, 1980. (18) Gill, P. E.; Murray, W.; Wright, M. H. Practical Optimization; Academic Press: New York, 1981. (19) Atkins, P. W. Physical Chemistry; Oxford University Prcss: Oxford, 1982. (20) Corriu, R. J. P.; Leclerq, D.; Vioux, A.; Pauthe, M.;Phalippou, J. In Ultrastructure Processing of Aduanced Ceramics; Ulrich, D. R., Mackenzie, J. D., Eds.; Wilcy: New York, 1988. (21) Huheey, J. E.J . Phys. Chem. 1965, 69, 3285.
J. Phys. Chem. 1992,96,8979-8982 (22) Diehl, P.; Kcllerhals, H.; Lustig, E. NMR Basic Principles and Progress; Diehl, P., Fluck, E., Kosfeld, R., Eds.; Springer-Verlag: Berlin,
1912. (23) Aelion, R.; Loebcl, A.; Eirich, F. J. Am. Chem. Soc. 1950,72,5705.
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(24) Babushkin, V. I.; Matveyev, G. M.; Mchedlov-Petrossyan, 0. P. Thermodynamics of Silicates; Springer-Verlag: Berlin, 1985. (25) Matsuyama, 1.; Satoh, S.; Katsumoto, M.; Susa, M. J . Non-Crys?. Solids 1991, 135, 22.
Electrochemlcal Measurements on the Blndlng of Sodium Dodecyl Sulfate and Dodecyltrimethylammonium Bromide wlth a- and B-Cyciodextrlns W. M. Z. Wan Yunus, J. Taylor, D. M. Bloor, D. G.Hall, and E. Wyn-Jones* Department of Chemistry and Applied Chemistry, University of Salford, Saljord M5 4WT, U.K. (Received: April 8, 1992; In Final Form: June 8, 1992)
The binding of ionic surfactants (S)to a-and 8-cyclodextrins (CD) has been investigated using surfactant-selectiveelectrodes. These electrochemical measurements have shown that S(CD) and S(CD)2inclusion complexes are formed between sodium dodecyl sulfate and both a-and /3-cyclodextrinsand also between dodecyltrimethylammonium bromide and a-cyclodextrin. On the other hand, the cationic surfactant only forms a 1:l complex with 8-cyclodextrin. From the data the equilibrium binding constants for the formation of each of the complexes have been evaluated.
Introduction Cyclodextrins are cyclic carbohydrates consisting of 6, 7, or 8 glucose units respectively called a-,8-,and 7-cyclodextrin.' To a first approximation they can be regarded as cylinders with a hydrophilic exterior and a hydrophobic interior. In aqueous solutions, the insertion of a hydrophobic guest into the cyclodextrin molecule results in complexation in which no covalent bonds are formed.14 Surfactants are ideal guests which allow a systematic study of complexation with cyclodextrins since both their hydrophobic and hydrophilic moieties can be systematically changed.s-'8 In this paper, we report a study of the equilibrium properties of complexes formed between a-and 8-cyclodextrins with the surfactants sodium dodecyl sulfate (SDS) and dodecyltrimethylammoniumbromide (DTAB). A literature survey reveals that, after an initial period that p r o d u d sometimes ambiguous and inconclusive information,s-18it is now generally regarded that the existence of 1:l and 2:l cyclodextrin/surfactant complexes has been confirmed. Despite this progress, there has been a paucity of data concerning the determination of the actual individual equilibrium binding constants for both steps in the formation of these complexes. Indeed, as far as we are aware, only one publication has been rep~rted'~ in which both equilibrium constants have been evaluated. The main reason concerning the lack of quantitative information on these systems is that most of the techniques that have been used for studying surfactant cyclodextrin complexes in the past have used indirect methods or techniques that essentially measure the macroscopic properties of the solution (e.g., conductivity). As we have shown previously on systems involving cationic surface active drugs and a-cyclodextrins, one of the key parameters that is required in order to understand binding of this kind is to be able to measure the monomer guest concentration in a formulation consisting of cyclodextrin and guest."*' Recently we have been extremely successful in the application of surfactant-selective membrane electrodes to investigate the equilibrium properties of aqueous solutions of surfactants containing various additives.'g-21 The advantage of these electrodes is that monomer concentration of surfactants can be monitored directly in these various formulations. We report here on studies involving emf measurements of surfactant electrodes selective to SDS and DTAB in their complexation with both u- and B-cyclodextrins.
Experimental Section 1. Electrodes. The surfactant-selective membrane electrodes used in the present work were constructed using a method which has been described previously.22-2sThe membrane comprises a specially conditioned poly(viny1 chloride) and a commercially available polymeric plasticizer. For the anionic surfactants the poly(viny1 chloride) used in the present work contains positively charged groups; for the cationics the PVC contains negatively charged groups. In order to make membranes selective to SDS and DTAB, the respective poly(viny1 chlorides) are neutralized by the oppositely charged surfactant ions before use. For SDS the monomer surfactant activities in various solutions can be obtained from emf measurements from the following cell
i
surfactant (SDS) test solution containing ommercial bromide selective electrode a constant amount of selective electrode cyclodextrin and [mol dm-3] sodium bromide
*Author to whom correspondenceshould be addressed.
0022-3654/92/2096-8979$03.00/00 1992 American Chemical Society
