Trimethylethoxysilane Liquid-Phase Hydrolysis Equilibrium and Dimerization Kinetics: Catalyst, Nonideal Mixing, and the Condensation Route

Article abstract of DOI:10.1021/jp990304b

Although the kinetics of organoethoxysilane hydrolytic (poly)condensation have been studied under kinetically simplified conditions, materials are actually synthesized from nonideal mixtures with high monomer and catalyst concentrations. Using ²⁹Si nuclear magnetic resonance, we study the hydrolysis of trimethylethoxysilane and the dimerization of the resulting silanol in aqueous ethanol at monomer and catalyst concentrations typical of organically modified silicate synthesis. Under acidic conditions, we find that when (and only when) the effects of solvent composition on catalyst activity are considered, it becomes clear that water-producing condensation is the dominant dimerization route. Under basic conditions, the extent of deprotonation of the weakly acidic silanol passes through a minimum during reaction, thereby producing an anomolous trend in reaction rate. This necessitates a kinetic model which is first order in both silanol and deprotonated silanol and which accounts for changing deprotonation.

Full text of DOI:10.1021/jp990304b

J. Phys. Chem. A 1999, 103, 4233-4241
4233
Trimethylethoxysilane Liquid-Phase Hydrolysis Equilibrium and Dimerization Kinetics:
Catalyst, Nonideal Mixing, and the Condensation Route
†
Stephen E. Rankin, J a´ n Sˇ ef cˇ ´ı k, and Alon V. McCormick*
Department of Chemical Engineering and Materials Science, UniVersity of Minnesota,
Minneapolis, Minnesota 55455
ReceiVed: January 25, 1999; In Final Form: March 24, 1999
Although the kinetics of organoethoxysilane hydrolytic (poly)condensation have been studied under kinetically
simplified conditions, materials are actually synthesized from nonideal mixtures with high monomer and
29
catalyst concentrations. Using Si nuclear magnetic resonance, we study the hydrolysis of trimethylethoxysilane
and the dimerization of the resulting silanol in aqueous ethanol at monomer and catalyst concentrations typical
of organically modified silicate synthesis. Under acidic conditions, we find that when (and only when) the
effects of solvent composition on catalyst activity are considered, it becomes clear that water-producing
condensation is the dominant dimerization route. Under basic conditions, the extent of deprotonation of the
weakly acidic silanol passes through a minimum during reaction, thereby producing an anomolous trend in
reaction rate. This necessitates a kinetic model which is first order in both silanol and deprotonated silanol
and which accounts for changing deprotonation.
Introduction
The issue of phase separation can only be understood, however,
once the chemical behavior of these systems has been addressed.
Hydrolytic polycondensation of alkoxysilanes, one type of
sol-gel processing, is a materials processing technique of
intense and growing interest.1-3 This interest comes from
researchers in a variety of fields including ceramics; inorganic,
organic, and “materials” chemistry; polymer chemistry and
physics; electronic materials; optical materials; and catalysis.
Materials that can be synthesized by this technique include
conventional metal oxide ceramics in novel shapes including
thin films, coatings, and near net shapes; ceramics of these
shapes and others containing highy dispersed organic modifiers;
zeolites and related molecular sieves; disordered and ordered
mesoporous silicates; amorphous silicone resins; low-dielectric
silsesquioxanes; low-molecular-weight silicone oils and crystals;
and monolayer films.
To approach this, we start with simpler systems which do not
display complicated phase behavior, here, the simplest possible
system undergoing the same chemistry, i.e., the monofunctional
alkoxysilane system.
This system undergoes the same chemistry as other alkoxy-
silanes. First, alkoxy groups are hydrolyzed (eq 1). The resulting
silanols form siloxane bonds and a condensate-either water
(eq 2) or alcohol (eq 3).
(
CH ) Si-OR + H O f (CH ) Si-OH + ROH (1)
3
3
2
3 3
(CH ) Si-OH + HO - Si(CH ) f
3 3 3 3
(
CH ) Si-O-Si(CH ) + H O (2)
3 3 3 3 2
There is considerable interest in understanding and controlling
the molecular structure of these silicates and organically
modified silicates. Since quartz is the minimum-energy structure
of silica at room temperature, both zeolites and the numerous
amorphous silica structures (including biological and synthetic
mesoscopically ordered silicates ) are metastable. Their exist-
ence is governed by dynamic processes. Increased structure
variability is introduced by organic modification. To understand
how to manipulate siloxane structure through processing condi-
tions, we must investigate the sometimes subtle interplay of all
factors influencing the rates of processes contributing to structure
evolution.
Previous investigations (including many in this journal6-10)
have yielded many insights into the behavior of network-forming
ethoxysilane precursors. However, the behavior of base-
catalyzed and template-containing systems is complicated by
phase behavior which depends not only on the overall solution
composition but also on the distribution11 of species present.
(
CH ) Si-OH + RO - Si(CH ) f
3 3
3 3
(CH ) Si-O-Si(CH ) + ROH (3)
3
3
3 3
Formerly,12 we investigated the thermodynamics of these
4
5
reactions in aqueous ethanol (R ) C2H5) and found equilibrium
coefficients near 15 for hydrolysis and 63 for water condensa-
tion. (The equilibrium coefficient for alcohol condensation is
linearly dependent on these coefficients.) We also determined
the deprotonation (eq 4) equilibrium coefficient Kd for trimethyl
silanol to be about 10 at room temperature.
Kd
-
-
(
CH ) Si-OH + OH {
\
} (CH ) Si-O + H O (4)
3
3
3 3
2
Grubb13 began investigating trialkylsilanol esterification and
condensation behavior in alcohols using Karl Fischer titration.
Unfortunately, this technique only gives a measure of the
combined concentrations of silanol and water. This value does
not allow one (without additional assumptions) to distinguish
changes due to esterification and hydrolysis from those due to
condensation, nor to determine the route by which condensation
*
Corresponding author.
Current address: 139-74 Beckman Institute, California Institute of
†
Technology, Pasadena, CA 91125.
1
0.1021/jp990304b CCC: $18.00 © 1999 American Chemical Society
Published on Web 05/11/1999

4234 J. Phys. Chem. A, Vol. 103, No. 21, 1999
Rankin et al.
occurs. The technique also has the disadvantage that the sample
must be disturbed by the titration, so artifacts may be introduced
by shifting equilibria.
TABLE 1: Compositions Investigated
0
Name [TMES] [H O] (M) {W} Catalyst [catalyst] (M)
0
2
0
A-1
A-2
A-3
A-4
A-5
A-6
A-7
A-8
A-9
A-10
A-11
A-12
B-1
2.0
2.0
2.2
1.85
1.85
2.0
2.0
2.0
2.0
2.0
1.85
1.85
1.95
4.0 {2.0}
4.0 {3.0}
4.4 {2.0}
7.39 {4.0}
11.1 {6.0}
0.8 {0.4}
1.4 {0.7}
2.0 {1.0}
2.5 {1.25}
3.0 {1.5}
0.629 {0.34}
1.48 {0.8}
5.05 {2.6}
HCl
HCl
HCl
HCl
HCl
HCl
HCl
HCl
HCl
HCl
HCl
HCl
NaOH
0.01
Kelling and coworkers studied in detail the kinetic behavior
0.00316
0.0022
0.00226
0.00226
0.002
0.002
0.002
0.002
0.002
0.00226
0.00226
0.029
of organodimethylsilanols in dioxane/water and toluene/
water.1
4-17
They report, for instance, that triorganosilanol
dimerization is second order with respect to silanol concentration
with acid and first-order with respect to silanol concentration
with base, and that condensation is usually first-order with
respect to catalyst concentration. However, they consider
conditions unusual for sol-gel processing (specifically, dioxane
or toluene as solvent), and the characterization technique (gas
chromatography) is invasive. What remains unclear is the role
of the solvent under conditions more typical of sol-gel
processing (where high concentrations of monomer and catalyst,
and alcoholic solvents are common). Most notably, the competi-
tion between water- and ethanol-producing condensation has
not been characterized for trimethylethoxysilane in aqueous
tween trimethylsilanol and trimethylalkoxysilanes dominates
under acidic conditions, but this has not been independently
verified and could not be proved by Karl Fischer titration alone.
22
Assink and Kay find for acid-catalyzed tetramethoxysilane that
ethanol.
Pohl and Osterholtz1
methanol-producing condensation competes with but does not
dominate water-producing condensation. On the other hand, they
report that ethanol-producing condensation is nearly negligible
8-20
performed elegant characterizations
of the behavior of mono-, di- and trifunctional organosilanols
in buffered aqueous solution by liquid-state nuclear magnetic
resonance (NMR), a noninvasive technique. They find the
expected linear dependence of condensation rate coefficient on
the concentrations of both hydroxyl ion and hydronium ion.
It is to the credit of these previous investigators that they
were able to devise experimental conditions in which specific
trends could be isolated. This investigation builds upon the
carefully controlled studies of the past to move into more
complicated compositions. Usually, sol-gel processing is done
in unbuffered solutions containing a good deal of ethanol
23
for tetraethoxysilane. The route for trimethylethoxysilane
remains unknown.
The effect of water content on catalyst activity has not been
considered in previous investigations of alkoxysilane chemistry.
This issue may have been avoided by Assink and Kay in their
23
study of tetraethoxysilane condensation by working only at
low extents of hydrolysis (only up to one-fourth water per
ethoxyl group) and therefore always with a low free water
content. We will find that accounting the for the effects of water
on catalyst activity has a major influence on the interpretation
of our kinetic experiments for the monofunctional system.
Under basic conditions, we will find that one cannot neglect
ionization equilibria when modeling the reaction kinetics of
trimethylethoxysilane. In other words, it is not possible to use
a single effective rate coefficient at a certain pH (as we have
often done in the past with acid catalyst). Instead, we must use
a rate expression accounting for ionization equilibrium even to
describe the changing rate of condensation over the course of
a single experiment.
(alcohol is frequently used as a cosolvent of the alkoxysilane
and water initially, and more alcohol forms during reaction).
With these conditions, the models applicable under controlled
conditions may begin to break down. Ethanol and water alone
mix nonideally, and hydrochloric acid activity is known to be
a function at least of the ethanol-to-water ratio.21 Also, silanols
are weakly amphiprotic, so when the solution is not buffered,
there might be shifts in overall pH (or more importantly, in the
concentration of active species) which have the potential to
change the course of reaction.
This paper focuses on how to distinguish the condensation
route (alcohol- vs. water-producing), on nonideality of ethanol/
water mixtures and on the effects of variable deprotonation of
weakly acidic silanols. These issues are explored using Si
NMRsthis nucleus is sensitive to shielding differences caused
by both hydrolysis and condensation extents, and the technique
is noninvasive.
Under acidic conditions, we will investigate the interdepen-
dent roles of catalyst and water content on condensation kinetics
in mostly ethanol solutions. Three effects may contribute to
changes with the ethanol-to-water ratio: (1) The effect of
hydrolysis extent (due to water content) on the competition
between water condensation (eq 2) and alcohol condensation
Experimental Section
The initial composition of each sample (after mixing) is listed
in Table 1. Samples were prepared by first placing a solution
of monomer and ethanol in a septum-capped NMR cell (a 5
mm o.d. glass tube) and by injecting an equal volume of a
solution containing water and the desired catalyst to give the
initial composition shown in the table. Solutions were prepared
from trimethylethoxysilane [TMES] (g98%, from Aldrich),
ethanol (anhydrous grade, Aaper Alcohol & Chemical), filtered
deionized water (prepared in house), and either a normalized
hydrochloric acid solution (Aldrich) or a 1 N standardized
sodium hydroxide solution prepared from filtered deionized
water and solid NaOH (Aldrich). Chromium acetylacetonate
2
9
(eq 3), and (2) the effect of hydrolysis extent on condensation
(
Aldrich), 1 wt %, was added as a paramagnetic relaxation
reactivity, and (3) the effect of water content on the activity of
the ionic and nonionic species present.
24
agent to the solvent ethanol. All experiments were conducted
at room temperature (22 ( 0.2 °C).
Since we have chosen a monofunctional system, the only
effect of hydrolysis extent on condensation kinetics is the
competition between condensation routes. A nearest-neighbor
substituent effect (the second effect above) can be ruled out
because the only ligands besides the reactive one are always
methyl groups.
Once samples were mixed and homogeneity visually con-
firmed, the samples were inserted into the spectrometer (within
2
9
5 min from mixing). Si nuclear magnetic resonance (NMR)
spectra were gathered using a Varian VXR-500 instrument with
a broad-band probe operating at 99.309 MHz under quadrature
detection. The number of transients per spectrum was at least
eight but was increased when possible to improve the signal-
Grubb13 assumed that alcohol-producing condensation be-

Trimethylethoxysilane Liquid-Phase Kinetics
J. Phys. Chem. A, Vol. 103, No. 21, 1999 4235
Figure 1. Representative 29Si NMR spectra for reacting acidic
trimethylethoxysilane system (sample A-1). The first spectrum was
4
collected 2.1 min after mixing and /
3
min elapse between spectra.
Chemical shifts are reported relative to external tetramethylsilane in a
j
solution of ethanol with Cr(acac)
bonds and j hydroxyl groups.
3
i
. M represents a site with i siloxane
Figure 2. An example of the fitting to data of an acid-catalyzed sample
(A-1). The hydrolysis extent is fit with a constant and the inverse
monomer concentration is fit with a line. The data are taken from three
identical experiments. The fitting is done using as many points as
possible before excessive scatter and a deviation from linearity (due to
reversibility) is observed.
to-noise ratio. We waited 10 s between 60° radio frequency
pulses to allow complete relaxation of the 29Si nuclei. We
verified that quantitatively similar results are obtained with a
longer interpulse delay, confirming that the delay is long enough
to provide quantitative data.
(filled circles) is close to a constant value of 0.78 even at the
first datum.
An external sample of tetramethylsilane in ethanol containing
1
wt % Cr(acac)3 was used as a chemical shift standard. Because
We have reported on the hydrolysis pseudoequilibrium
behavior of these samples and other ethoxysilanes and have
2
5
30
of the broad signal from the glass in the probe and NMR cell,
we collected spectra with a large spectral width (17 kHz) and
with at least 32000 data points per spectrum. Exponential line
broadening of 1-3 Hz was applied to each spectrum to
maximize the signal-to-noise ratio. Decoupling at 500 MHz was
gated on during acquisition and off otherwise (to avoid a
possible negative NOE).
always measured hydrolysis equilibrium coefficients in the range
of 10-30. The pseudoequilibrium approximation is useful
because it allows us to treat hydrolysis through algebraic rather
than differential equations. It is challenging to determine the
condensation route under hydrolysis pseudoequilibrium, how-
ever, because regardless of the route, the distribution of SiOEt
and SiOH groups is “scrambled” as condensation proceeds:
Results and Discussion
fast
Acidic System. Figure 1 shows the 29Si NMR spectra
collected for a representative sample (A-1). The unhydrolyzed
monomer peak (17.5 ppm) is assigned by comparison to a
solution containing an identical concentration of TMES but
without water. The dimer peak (7.3 ppm) is easily assigned as
the monotonically growing peak, and the hydrolyzed monomer
(Me) SiOC H + H O { } (Me) SiOH + C H OH (5)
3
2
5
2
3
2
5
Because water- and alcohol-producing condensation are
nearly indistinguishable in a single experiment when hydrolysis
pseudoequilibrium holds, we do not yet assume a route and
instead use an effective condensation rate coefficient for each
experiment, defined by:
(14.3 ppm) appears after water is added but decays after reaching
a maximum. These assignments closely match those of Suda et
2
6
d[M0]
al. (who also used ethanol as a solvent) and follow the same
2
)
-k [M ]
(6)
27
eff
0
trend as those of Hook, although they differ from the latter
by up to +0.9 ppm, possibly because Hook’s solutions contain
a large concentration of d6-acetone. The chemical shift trends
do not change with composition, but the actual chemical shifts
do depend slightly on composition, with a difference of up to
dt
where [M0] is the concentration of all monomer (hydrolyzed or
not) and we expect that contributions from water and alcohol
condensation give keff ) kcw ø + 2kca ø(1 - ø). Since ø is
2
+
1 ppm observed for the unhydrolyzed monomer, up to +0.5
nearly constant for all experiments, keff is also nearly constant
and could be found by fitting the solution of eq 6 to the
experimental data.
The initial condition for condensation kinetics is ill-defined
because there is some finite period of time required for the
hydrolysis pseudoequilibrium to be established. However, the
rate coefficient from the point of reaching hydrolysis pseu-
doequilibrium is not affected by this, so we solve eq 6 with a
perturbation to the known initial monomer concentration ac-
counting for this induction period, to find the following solution:
ppm for the hydrolyzed monomer (both with much higher water
content, see the Appendix), and the dimer chemical shift
changing little. The change in chemical shift is most likely due
to the effects of the solvent composition.28 The total integrated
intensity of the spectra remains constant in this case and in all
others except for one (sample A-5), which apparently goes
through liquid-liquid phase separation at long times (see the
Appendix).
Without exception in the range of hydrochloric acid-catalyzed
conditions studied, hydrolysis pseudoequilibrium29 is observed.
This is characterized by the extent of hydrolysis reaching its
equilibrium value before a significant condensation extent is
reached (most often by the time the first spectrum was collected).
For many cases this means that the fractional extent of
hydrolysis {ø ) [SiOH]/([SiOH] + [SiOEt])} is nearly constant
with respect to condensation extent. An example of this is shown
in Figure 2 for sample A-1. For this sample the hydrolysis extent
[M0]- ) [M0]0 + ꢀ + kefft
1
-1
where ꢀ is a constant which accounts for the induction time for
hydrolysis pseudoequilibrium to be established. An example of
the type of fit observed using this relationship is shown for
sample A-1 in Figure 2. This result is typical: data from three
separate experiments are shown and the correlation coefficient

4236 J. Phys. Chem. A, Vol. 103, No. 21, 1999
Rankin et al.
Figure 4. Results of fitting eq 12 to all measured experimental data.
The fit was restricted so that the x-intercept is greater than or equal to
Figure 3. The effect of hydrochloric acid on the apparent condensation
rate coefficient of hydrolyzed trimethylethoxysilane at 22 °C. The points
shown are for samples with a pseudoequilibrium water concentration
of about 2.8 M (A-1-A-3).
2
1 (the function fit is y ) m(1 - x) +
x
b ), and the estimated error of
each point was used to weight the residual function.
hydrolysis pseudoequilibrium). As should be expected for
homogeneous catalysis by a strong acid, we find that keff ∝
2
TABLE 2: Hydrolysis Equilibrium Values (øeq and [H O]eq)
a
and Effective Bimolecular Condensation Rate Coefficients
Measured for Acid-Catalyzed Systems
[HCl]. We might anticipate that this should be true regardless
of the condensation route and Figure 3 gives no cause to doubt
this. This dependence is easily explained by the following classic
1
sample
ø
eq
2
[H O]eq (M)
k
eff (M h)-
1
4,20
A-1
A-2
A-3
A-4
A-5
A-6
A-7
A-8
A-9
A-10
A-11
A-12
0.78
0.7
2.82
2.72
3.15
6.12
9.67
0.13
0.47
0.89
1.28
1.73
0.043
0.576
13.0 ( 1.8
5.4 ( 1.5
scheme:
+
+
2
0.79
0.88
0.91
0.26
0.45
0.60
0.64
0.72
0.11
0.45
4.3 ( 0.62
1.12 ( 0.065
1.65 ( 0.090
2.45 ( 0.27
3.07 ( 0.26
2.95 ( 0.24
2.03 ( 0.31
2.27 (0.20
1.64 ( 0.28
2.12 ( 0.25
t Si-OH + SH h t Si-OH + S
(8)
+
2
+
t Si-OH
+ XO -Si t f t Si-O-Si t + XOH (9)
where S represents a proton-accepting solvent (either ethanol
or water) and X is either a hydrogen or an ethyl group.
Assuming labile proton redistribution equilibrium (eq 8) and
that eq 9 is the rate-limiting step, we can write:
a
All rate coefficients are found by linear regression, and error
d[SiOX]
+
2
estimates are for 95% tolerence levels.
) k*[tSiOH ][tSiOX]
dt
for the fit in Figure 2 is 0.97. For all samples, at least eight
data points are used for the regression analysis and the set of
points chosen starts from the point that ø is constant and stops
when the linearity of the data deteriorates (usually because of
increased scatter as the monomer concentration drops). This
corresponds to following the decay of monomer to at least one
half of its original concentration. Points where condensation
reversibility becomes important (as determined by a clear drop
K [tSi - OH][HCl]
p
) k*
[tSiOX]
[
S] + K [tSi - OH]
p
)
k′[HCl][tSiOH][tSiOX]
(10)
where K is the protonation redistribution equilibrium coefficient
(for eq 8). Depending on X (H or R), k* and k′ apply to either
alcohol- or water-producing condensation. In writing eq 10,
complete dissociation of HCl is assumed ([HCl] ) [tSiOH ]
p
-
1
+
2
in the slope of [M0] vs time) are also excluded from the
regression analysis.
+
+
[SH ]), and for the last equivalence, it is assumed that [S] ∼
Table 2 presents the measured fractional hydrolysis extent
at pseudoequilibrium, water concentration at pseudoequilibrium,
and effective bimolecular condensation coefficient for all of the
acid-catalyzed samples. The water concentrations were found
using the stoichiometry of the hydrolysis and condensation
reactions, with site concentrations from the NMR spectra:
32
constant . Kp[tSi -OH].
To explore the effect of water concentration, we must consider
not only the effect of water on the hydrolysis extent (and
therefore on the condensation route) but also the effect of water
on the activity of the cations present. The simplest hypothesis
is that water content has no effect on activity coefficients. If
this is the case we expect that
[
H O] ) [H O] - [(CH ) SiOH] - [{(CH ) Si} O] (7)
2 2 0 3 3 3 3 2
2
keff ) [HCl]{k′ ø + 2k′ ø(1 - ø)}
(11)
cw
ca
The error estimates in Table 2 are determined by standard
31
analysis of the linear regression results.
which can be rearranged to give an expected linear relationship:
Some of the water concentrations in Table 2 are ap-
proximately equal (for samples A-1 to A-3), so it is possible to
observe for those concentrations how the effective bimolecular
condensation rate coefficient depends on acid concentration
without concern about the effect of the water content. Figure 3
shows the results for these samples (all of about 2.8 M water at
keff
)
[HCl]{(k′cw - 2k′ )ø + 2k′ }
(12)
ca
ca
ø
Figure 4 shows the results of fitting this functional form
(slightly modified to ensure crossing the x-axis at g1) to all of

Trimethylethoxysilane Liquid-Phase Kinetics
J. Phys. Chem. A, Vol. 103, No. 21, 1999 4237
Figure 5. Fit of eq 14 to the subset of experimental data with low
water content (samples A-6-A-12). Fitting is restricted so that the
y-intercept is greater than or equal to zero (fitting function: y ) mx +
2
Figure 6. Plot of hydrolysis extent against dimensionless time. The
-
1
-1
data (points) were scaled using a value of k ) 13 M
h
h , and the
calculation (solid curve) was scaled using K ) 18.5.
h
x
b ), and the estimated uncertainty of each coefficient was used to
Therefore it appears that the initial conclusion that ethanol-
producing condensation dominates (Figure 4) was incorrect.
Since the free water concentration decreases with decreasing
ø , the increasing value of the ordinate (with decreasing ø )
weight the residual function.
the measured rate coefficients. Estimated errors in the coef-
ficients are used to weigh the residual function for fitting. From
the values of the slope and intercept found, it appears that kcw
is on the order of 2% of the value of kca; in other words, this
treatment of the data suggests that water-producing condensation
is nearly negligible under most conditions.
eq
eq
in the figure is caused more by increased acid activity than the
competition between condensation routes. Therefore, water-
producing condensation is the most likely condensation route
for trimethylsilanol in acidic ethanol/water mixtures. We are
encouraged in this conclusion because Assink and Kay23 found
the same thing to be true in low-water tetraethoxysilane
However, Tourky et al. have investigated the variation of
acidity (HCl activity) with water content in ethanol/water
mixtures34 and report that the protonation extent of p-nitroaniline
is not constant but varies inversely with water concentration at
low water concentrations (or in other words that the activity
17
condensation. Kelling and coworkers have reported that the
rate of acid-catalyzed methanol-producing condensation of
trimethylsilanols competes with that of water-producing con-
densation. However, if the rate coefficient for ethanol-producing
condensation is over an order of magnitude lower than methanol-
+
coefficient for a solvated proton SH varies inversely with water
concentration: γSH+ ∝ [H2O] ). If we assume that the same
dependence holds for silanol protonation and take the activity
coefficient into account, we predict that
-1
17
producing condensation (as it is under basic conditions ), water-
producing condensation could indeed be dominant, as we have
observed.
keff
[HCl]
Alkaline System. The 29Si NMR spectra collected for the
alkaline sample (B-1 in Table 1) contain the same features as
the acidic system. Trimethylethoxysilane, trimethylsilanol, and
hexamethyldisiloxane are all present at approximately the same
chemical shifts as under acidic conditions. The fraction of
deprotonated silanols (discussed below) is too small to influence
)
{(k′′ - 2k′′)ø + 2k′′}
(13)
cw
ca
ca
ø
[H O]
2
or that:
k [H O]
eff
2
)
(k′′ - 2k′′)ø + 2k′′
(14)
29
cw
ca
ca
the chemical shift. We verified that the total integrated Si NMR
ø[HCl]
intensity remains constant during the course of reaction of the
alkaline system.
Figure 5 shows the results of fitting eq 14 to the experimental
data. Surprisingly, the conclusion drawn when taking the
dependence of the proton activity coefficient on water content
into account is exactly the opposite from before. Again
restricting the fit so that the x-intercept falls within reasonable
bounds (e0), we find that the y-intercept is approximately zero
and that the slope is positive. In other words, alcohol-producing
condensation appears to be negligible.
The alkaline TMES system does not show instantaneous
hydrolysis equilibrium like the acidic solutions do. Instead,
Figure 6 shows that ø takes several minutes to reach a constant
(equilibrium) value. Since we see a relatively slow hydrolysis
transient, we comment on hydrolysis kinetics. We should be
able to measure from the initial monomer decay a forward
hydrolysis rate coefficient (kh). However, hydrolysis is a little
too fast for this: the extent of hydrolysis is over 60% by the
first measured NMR spectrum. We can, however, place a lower
bound on the hydrolysis rate coefficient using a simplified
analysis of these data. Neglecting the effects of condensation
on hydrolysis extent, we write
Given this large difference in the interpretation depending
on the assumption about the activity of protonated silanols, one
might wonder which result to believe. First of all, it is clear
that, at high ethanol contents in ethanol/water mixtures contain-
ing hydrochloric acid, acid strength (as measured for instance
34
by Hammett acidity ) decreases with increasing water con-
0
0
2
1,35
tent.
It would be unwise to ignore this effect as the water
d[M
]
0
0
1
0
)
-k [H O][M ] + k [EtOH][M ]
(15)
concentration varies over an order of magnitude (see Table 2).
Also, we know that tetraethoxysilane does not interact strongly
h
2
e
dt
3
6
with ethanol, so we have reason to expect that the presence
of the organosilicon compounds does not strongly interfere with
the acidity behavior observed in ethanol/water mixtures.
The water concentration is a function of time in this equation,
but we can use the stoichiometry of the hydrolysis reaction to
write

4238 J. Phys. Chem. A, Vol. 103, No. 21, 1999
Rankin et al.
1
0
[
H O](t) ) [H O] - [M ](t)
2
2
0
and
1
0
[
EtOH](t) ) [EtOH] + [M ](t)
0
Substituting this in to eq 15 gives
dø
E
Kh
)
W + ø -(W + 1) -
+ ø(1 - 1/Kh)
(16)
{
}
dk [M ]t
h
0
where ø is defined earlier, W ) [H2O]0/[M0], E ) [EtOH]0/
M0], Kh ) kh/ke, and [M0] is the total monomer concentration.
[
Since W and E are fixed by our experiment, only Kh is truly
adjustable on the right hand side of this equation. This equation
is expressed in a dimensionless form. If it is valid, it should be
possible to match the equation to the experimental data simply
by (1) finding a Kh value consistent with the long-time behavior
of the data and (2) finding a kh value which scales the measured
data to the numerical solution of this equation.
Figure 7. Relationship between inverse monomer concentration and
integral of the square of hydrolysis extent for the base-catalyzed sample.
The dashed line is a guide to the eye through the experimental data,
and the dotted line is a linear fit to the first few data points.
-
that the rate of condensation is proportional to [SiOH][SiO ]
For the first step, we find that the long-time hydrolysis extent
is consistent with Kh ) 18.5. This value falls within the range
2
rather than strictly to [SiOH] . The question, then, is whether
the ratio of deprotonated species changes during reaction.
If deprotonation happens much more quickly than condensa-
tion, we can assume a deprotonation pseudoequilibrium for this
system, which allows us to use our measured deprotonation
coefficient to calculate the fraction of deprotonated silanols. We
1
2
of hydrolysis equilibrium coefficients measured previously.
For the second step of matching to the experimental data, we
-
1
-1
find that kh ) 13 M ‚h . An excellent match between the
hydrolysis kinetics model and the data is shown in Figure 6.
The estimate of kh should be regarded as a lower bound, since
some monomer is in fact being consumed during the approach
to hydrolysis pseudoequilibrium.
12
know the Kd ) 10, so we can write
-
[
SiO ][H O]
2
Although the extent of hydrolysis is not constant, we should
be able to use the measured values to find the condensation
rate coefficient for this system. To do this, we go back to the
equation we would write for the rate of decay of monomer by
water-producing condensation:
)
K ) 10
(19)
d
[SiOH][OH-]
Neglecting deprotonated alcohol, we can approximate that all
added sodium hydroxide is present either as a hydroxyl anion
-
-
or as a silanol anion, in which case [OH ] + [SiO ] ) [NaOH]0.
We also presume that the water concentration is known from
the stoichiometry hydrolysis and condensation at each datum
and that the NMR peak for hydrolyzed monomer includes both
d[M0]
2
2
)
-k ø [M ]
(17)
cw
0
dt
-
Earlier, we assumed that ø could be determined from an
equilibrium coefficient or could be measured and was ap-
proximately constant. Since in this case ø does change with
time, we simply retain the time dependence and solve the
differential equation:
deprotonated and normal silanols ([SiO ] + [SiOH] )
[Si]ø(1 - R) where R ) [M1]/[Si]). Substituting these relation-
ships and solving the resulting quadratic equation gives
[SiO-]
fd )
-
(
[SiOH] + [SiO ])
1
M0]
1
t
2
-
) kcw
∫
ø (t′)dt′
(18)
([NaOH]
+ [Si](1 - R)ø + [H
[Si](1 - R)ø
O]/10)
2
0
0
[
[M ]
0 0
)
-
2
2
If the data vary slowly with time (and in this case they do),
we can approximate the integral in this equation with a
trapezoidal integration of the experimental data. We then expect
a linear relationship between the inverse monomer concentration
and this approximate integral. It turns out that this equation does
not fit all of the experimental data, however (Figure 7). As the
figure shows, a linear fit to the first data points fails to match
the experimental data at longer times.
x(
[NaOH] + [Si](1 - R)ø + [H O]/10) - 4[NaOH] [Si](1 - R)ø
0
2
0
2
[Si](1 - R)ø
(20)
Does this equation predict that the fraction of deprotonated
silanols changes significantly with time? We plot in Figure 8
the results of eq 20 applied to our data as a function of time.
Clearly the fraction of deprotonated silanols is predicted to
increase significantly after hydrolysis pseudoequilibrium is
established, passing through a minimum at about 0.5 h and
doubling from this value over the next four hours. This change
could explain why the rate of condensation appears to increase
with time.
One reason eq 18 fails to match the measured data is that we
have assumed that the rate coefficient is constant when in reality
the composition of the solution changes with time. We can be
sure that the observed deviation is not due to condensation
reversibility because the slope of the curve increases with time;
if reversibility were the problem, the rate would drop. The
composition might, however, feed back to the condensation rate
through a dependence on the concentration of ionic species. It
has in fact been proposed that base-catalyzed condensation of
Incorporating this value into our original expression from the
condensation rate:
d[M0]
†
2
2
)
-k f (t)ø (t)[M ] (t)
cw d 0
1
6,20
silanols proceeeds through a deprotonated intermediate,
so
dt

Trimethylethoxysilane Liquid-Phase Kinetics
J. Phys. Chem. A, Vol. 103, No. 21, 1999 4239
Figure 8. Fraction of deprotonated silanols in the base-catalyzed
trimethylethoxysilane system as a function of time. The dashed line is
provided as a guide to the eye.
Figure 10. Fraction of NaOH consumed by silanols as a function of
time for sample B-1. Dashed line is only a guide to the eye.
sodium hydroxide which is consumed by silanols. This fraction
is not equal to one and is not even constant for our sample. If
the silanol concentration were very large or if Kd were larger,
the assumption of a constant deprotonated silanol concentration
might be better met. This particular composition illustrates,
however, why first-order kinetics have been observed under
some but not all conditions for alkaline silanol condensation.
Conclusions
We have monitored the kinetics of hydrolytic dimerization
of trimethylethoxysilane in nonideal conditions. The behavior
in both acidic and basic solutions had to be analyzed with more
complex models than had been used previously.
Under acidic conditions, facile hydrolysis pseudoequilibrium
prevails in all samples. This makes it difficult to distinguish
the route of condensation (alcohol vs water producing). By
studying this monofunctional monomer, we have ruled out the
possibility of substitution effects on reactivity. Accounting for
the effect of addition of small amounts of water to mostly
ethanol solutions (which tends to lower the activity of hydrogen
ions), we have concluded that the water-producing route
dominates the condensation of trimethylsilanol over a wide range
of water concentrations (even if the net effect of water addition
on condensation rate is negative).
Under alkaline conditions, we examined another common
occurrence in realistic synthesis conditions: the use of a very
high concentration of catalyst. First, we find that hydrolysis does
reach pseudoequilibrium during the measured interval but more
slowly than with acid. We also find that the deprotonation
equilibrium shifts during reaction. The extent of deprotonation
of the silanols passes through a minimum with respect to time;
the subsequent increase in deprotonation leads to an increase
in dimerization rate late in reaction. When we properly account
for this, we are able to write a set of equations for trimethyl-
ethoxysilane hydrolytic dimerization with variable hydrolysis
and deprotonation extents which matches the data.
Figure 9. Plot of inverse monomer concentration as a function of the
integral of the experimental product of the fraction of deprotonated
silanols and the square of the hydrolysis extent for sample B-1. The
dashed line is a least-squares fit to the data points.
Again, taking the measured values of fd and ø at each point
allows us to test the following relationship:
1
1
†
cw
t
2
-
) k
∫
f (t′)ø (t′)dt′
(21)
d
0
[
M0] [M ]
0 0
Where the integral is approximated by trapezoidal integration
of the experimental data plotted with respect to time.
Figure 9 shows that the relationship in eq 21 is able to match
+
cw
-1
the experimental data with k ) 32.6 ( 0.5 (M h) . So
unlike the acid-catalyzed case where the fraction of protonated
silanols remains constant during reaction, we must account for
the changing balance of deprotonation as a weak acid (silanol)
is generated, titrated, and consumed during base-catalyzed
hydrolytic condensation of trimethylethoxysilane.
The necessity of including this changing deprotonation may
seem surprising compared to previous reports. Previously, it has
been suggested that silanol homocondensation should be first
order with respect to silanol and first order with respect to
Acknowledgment. The authors thank the Center for Inter-
facial Engineering at the University of Minnesota and Dow
Corning Corporation for research support. S.E.R. also thanks
the National Science Foundation and the University of Min-
nesota Graduate School for support through graduate fellow-
ships. We thank Shayne Kirchner for preparing the base-
catalyzed sample. We also thank Dr. Gary Wieber of Dow
Corning for helpful discussions.
1
4
hydroxide anion. This is actually a simplification of eq 20
and 21 when Kd is large enough and [H2O] is small enough
-
that [SiO ] ∼ [NaOH]0 at all times. Keeping the water content
low is easy to do when one starts with silanols and works in
nonalcoholic solvents. When ethanol is present, however, water
is needed (due to esterification) to keep the hydrolysis extent
high, so these conditions are not as easily met.
Appendix: Observation of Phase Separation
To see how our sample compares to those where first-order
kinetics apply, we plot in Figure 10 the fraction of original
In one case noted in the text (sample A-5), the integrated
intensity of the Si NMR spectra did not remain constant. Figure
29

4240 J. Phys. Chem. A, Vol. 103, No. 21, 1999
Rankin et al.
kind of decay expected for second-order kinetics. In fact, the
curve passing through the data points in Figure 12 is a fit of
the following function to the early-time data (up to 20 min of
reaction):
[
M0]0
[
M ] )
(22)
0
1
+ k [M ] t
eff
0 o
Notice that the function continues to match to monomer
concentration well even after the “mystery” species appears and
the signal begins to be lost. That the monomer concentration
does not decrease more quickly than homogeneous second-order
kinetics would dictate suggests that the monomer is not part of
the overall signal being lost from this sample.
The concentration of dimer (M1) sites increases as expected
for the first 20 min of reaction, but as soon as an appreciable
concentration of the mystery peak appears, M1 begins to
disappear below the value expected by second-order kinetics.
The curve passing through the M1 data in Figure 12 is a fit of
the following empirical function:
Figure 11. 29Si NMR spectra collected for sample A-5. A totally new
peak is observed (*) which has not previously been observed in
homogeneous systems. The first spectrum is collected 3.2 min after
mixing and 2.7 min evolve between spectra.
[
M ] - [M ]
t < 18 min
t g 18 min
0
0
0
[
M ] )
(23)
1
-kps(t-18 min)
[
(
[M ] - [M ]) e
0
0
0
It is not clear how to interpret the ability of this function to fit
the data. The exponential decay coefficient kps can be interpreted
as a pseudo-first-order phase separation rate coefficient, but this
does not have a rigorous physical justification.
Coincident with the loss of dimer signal near 20 min of
reaction, the “mystery species” appears. The concentration of
this species plateaus quickly, however, at a concentration of
0
.125 M. Because this sample eventually forms two liquid
phases, it seems reasonable that this new peak and the loss of
M1 signal represented in Figure 12 are both associated with the
early stages of phase separation. Since M0 does not disappear
any more quickly than second-order kinetics would dictate at
any time, it appears that the species being lost from the NMR
spectra are mainly M1 sites. Three factors may contribute to
loss of signal from M1 in this newly formed phase. (1)
Presuming that the new phase is less polar than the majority of
the solution, the relaxation agent (chromium acethylacetonate)
may partition preferentially in the polar phase. Decreased
relaxation in the new apolar phase would lead to easier spin
saturation and eventually to loss of signal compared to the signal
expected from fully-relaxed nuclei. (2) The new apolar phase
is of lower density and may migrate out of the measurement
volume (the sample is large enough for this to occur). (3) The
new apolar phase might be initially present in small domains
in which molecular motion is restricted, leading to slowed spin-
lattice relaxation (due to inhibited molecular tumbling) and to
broadening of the signal.
Figure 12. Plot of concentrations from 29Si NMR data. Concentrations
of M , M , and the new “mystery” species are determined by
0 1
comparison to the intensity of a nonreactive monomer solution of equal
concentration. The signal lost is the difference between the measured
0 1
concentrations of M and M and the known silicon concentration.
1
1 shows how the spectra evolve. The peaks observed are nearly
identical to those of the homogeneous monofunctional systems
although shifted somewhat due to the changed composition:
0.5 ppm for the silanol and +1 ppm for the ethoxysilane)
(
+
with the important exception of one new peak (labeled with an
asterisk in Figure 11). This peak appears slightly downfield of
the dimer (M1) peak, indicating nuclei in a better shielded
environment.
At very long times compared to those shown in Figure 11,
two distinct liquid phases can be observed in the sample. Neither
29
phase contains a species giving the Si NMR peak marked with
an asterisk in Figure 11, so it is clear that this is an intermediate
species. We can learn more about the nature of this species by
examining the concentration transients of this sample.
Since the new “mystery” peak appears as phase separation
occurs, it most likely arises from M1 sites in a new environment,
possibly on the surface of the domains of the new phase or in
nuclei of the new phase.
Figure 12 shows how the concentrations of M0 and M1 vary
with time, along with the concentration of the mystery species
and the “lost” signal (the difference between the added silicon
concentration and the measured concentrations of M0 and M1).
These concentrations are determined by assuming that the
absolute signal intensity measured by NMR is proportional to
the number of silicon nuclei of that type present in the solution,
an assumption justified normally because of complete relaxation
While the details of what is going on in sample A-5 are not
entirely clear, it is evident that some sort of phase separation is
occurring after 20 min of reaction, leading to loss of NMR
signal. Since this system does not produce solid precipitates,
this demonstrates that the formation of a solid phase is not
29
necessary to explain loss of Si NMR signal in sol-gel solutions.
This suggests that, in alkoxysilane systems that do form
particles, the observed loss of NMR signal upon phase separa-
2
9
between Si pulses.
The monomer (M0) concentration behaves just like the
monomer concentration in a homogeneous system, showing the
3
7
tion could happen as soon as liquid-liquid phase separation

Trimethylethoxysilane Liquid-Phase Kinetics
J. Phys. Chem. A, Vol. 103, No. 21, 1999 4241
begins and does not require exceptionally fast condensation in
the newly formed phase to explain the lack of intermediates
and products in the liquid-satate 29Si NMR spectra.
(17) Spitzner, H.; Wandschneider, S.; Lange, D.; Kelling, H. J. Prakt.
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One final note: if the new peak we observe in the 29Si NMR
spectra is a good indicator of phase separation, it appears that
one point on the two-phase boundary of this multicomponent
system is (the composition at 20 min) 54 mol % ethanol, 40
mol % water, 0.31 mol % trimethylethoxyilane, 3.6 mol %
trimethylsilanol, and 1.7 mol % hexamethyldisiloxane (with
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0
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(
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(
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(
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33
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(
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(