Ammonia catalyzed hydrolysis-condensation kinetics of tetraethoxysilane/ dimethyldiethoxysilane mixtures studied by 29 Si NMR and SAXS

Article abstract of DOI:10.1007/s10953-006-9117-y

In-situ ²⁹Si liquid-state nuclear magnetic resonance (NMR) was used to investigate the ammonia catalyzed hydrolysis and condensation of the mixed systems of tetraethoxysilane (TEOS) and dimethyldiethoxysilane (DDS) dissolved in methanol. With ammonia catalysis, the hydrolysis reaction orders for TEOS and DDS in the mixed systems remained first order, which is similar to that observed for their corresponding single silane component precursor systems. The hydrolysis rate constant for TEOS in the mixed systems was larger than that of TEOS in the single silane component precursor systems. Meanwhile, the hydrolysis rate constants of DDS in the mixed precursor systems were smaller than those of DDS in the single silane component precursor systems. The hydrolysis and condensation kinetics showed more compatible hydrolysis- condensation relative rates between TEOS and DDS, which remarkably affected the final microstructure of the resulting silica particles. Small angle X-ray scattering (SAXS) experiments showed a typical double fractal structure in the particulate networks. Springer Science+Business Media, LLC 2007.

Full text of DOI:10.1007/s10953-006-9117-y

J Solution Chem (2007) 36:327–344
DOI 10.1007/s10953-006-9117-y
ORIGINAL PAPER
Ammonia Catalyzed Hydrolysis-Condensation Kinetics
of Tetraethoxysilane/Dimethyldiethoxysilane Mixtures
Studied by 29Si NMR and SAXS
Yao Xu · Xianyong Sun · Dong Wu · Yuhan Sun ·
Yongxia Yang · Hanzhen Yuan · Feng Deng ·
Zhonghua Wu
Received: 8 June 2006 / Accepted: 30 August 2006 /
Published online: 6 February 2007
ꢀ Springer Science + Business Media, LLC 2007
C
Abstract In-situ 29Si liquid-state nuclear magnetic resonance (NMR) was used to investigate
the ammonia catalyzed hydrolysis and condensation of the mixed systems of tetraethoxysi-
lane (TEOS) and dimethyldiethoxysilane (DDS) dissolved in methanol. With ammonia
catalysis, the hydrolysis reaction orders for TEOS and DDS in the mixed systems remained
first order, which is similar to that observed for their corresponding single silane component
precursor systems. The hydrolysis rate constant for TEOS in the mixed systems was larger
than that of TEOS in the single silane component precursor systems. Meanwhile, the hydrol-
ysis rate constants of DDS in the mixed precursor systems were smaller than those of DDS
in the single silane component precursor systems. The hydrolysis and condensation kinetics
showed more compatible hydrolysis-condensation relative rates between TEOS and DDS,
which remarkably affected the final microstructure of the resulting silica particles. Small
angle X-ray scattering (SAXS) experiments showed a typical double fractal structure in the
particulate networks.
Keywords Reaction kinetics · 29Si NMR · Hydrolysis · Condensation · Small angle X-ray
scattering · Tetraethoxysilane (TEOS) · Dimethyldiethoxysilane (DDS)
Y. Xu ( )· X. Sun · D. Wu · Y. Sun
ꢀ
State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences,
Taiyuan 030001, China
e-mail: xuyao@sxicc.ac.cn
Y. Yang· H. Yuan · F. Deng
State Key Laboratory of Magnetic Resonance & Atomic & Molecular Physics, Wuhan Institute
of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
Z. Wu
Laboratory of Synchrotron Radiation, Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100039, China
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1 Introduction
The sol-gel process has proven to be a highly effective method for the synthesis of glasses,
ceramics, nanocrystallines and nanoscaled amorphous materials under mild conditions [1–5].
By introducing organic groups or polymers into the inorganic silica matrices, the properties
of the sol-gel derived materials can be tailored at the molecular level according to different
requirements [6, 7]. So far, a large number of SiO2-based sol-gel derived hybrid materials
have been prepared and are expected to be applied in optical devices [8], functional thin
films [9] and membranes for gas separation [10]. Although a wealth of sol-gel synthetic
approaches have been reported, a detailed understanding of the underlying reactive kinetics
in the sol-gel process currently is not fully developed. Even for a single precursor, TEOS for
example, athough the kinetics of the sol-gel reactions has been formulated at various levels
of sophistication [1, 2, 11–14], the reactive pathway is not fully understood. Besides, no
general rule can be used to guide the control of the sol-gel process [15, 16].
Reaction kinetics are highly sensitive not only to the nature of the starting precursor, but
also to the pH and the solvent polarity of the reaction medium [1, 2, 17]. When TEOS, a
commonly used inorganic precursor, is co-hydrolyzed together with an organic-substituted
ethoxysilane monomer (Rx Si(OEt)1−x, where R can be methyl, ethyl, phenyl, vinyl,
3-aminopropyl, 3-methacryloxypropyl or 3-glycidoxypropyl), many other factors add to
the complexity of the initial reaction kinetics and the subsequent sol-gel process [18–20].
Therefore, an investigation on the reaction kinetics of TEOS and an organic-substituted
monomer in a mixed precursor system becomes crucial for understanding the nature of the
hybrid sol-gel process.
In double-precursor systems, thetime sequencebetween hydrolysis, self-condensation and
cross-condensation is highly complex and depends on the special reaction conditions, e.g.,
the pH of the initial solution and the nature and number of substituents on the Rx Si(OEt)4−x
molecule [21–25]. Some studies [22, 23, 25] have been reported that involved the time
sequence of hydrolysis, self-condensation and cross-condensation using different double-
precursor systems, but the results differ largely with different organic substitution on the
precursor. Among the limited reports on the sol-gel kinetics of double-precursor systems,
most were performed under acidic condition. Under acidic condition, hydrolysis is usually
by far faster than condensation, so that oligomers of the hydrolyzed precursor can exist
in solution and can be easily be detected by several experimental methods. Although the
reverse occurs under basic conditions [1, 26], fewer studies have been made because they
involve more difficult experiments. In the very few reports on base-catalyzed hydrolysis
[27–29], studying the hydrolysis kinetics was not the main object of the research. In fact, the
condensation species are not easy to observe because condensation is faster than hydrolysis
under basic conditions and the condensed species can hardly be detected even by in-situ 29Si
NMR.
Riegel et al. [20] studied the ammonia-catalyzed hydrolysis and condensation of TMOS
and RTMS (R = methyl, ethyl, propyl, vinyl or phenyl) by Raman spectroscopy. The main
difficulty they encountered was that no intermediate hydrolysis species or condensation
species were observed and Raman spectroscopy did not yield detailed quantitative data.
Therefore, the kinetic rate constants could not be calculated. Despite the difficulties of the
experiments, understanding the base-catalyzed sol-gel process with double-precursor sys-
tems is still necessary and important to produce proper organic-modified silica nanoparticles
whose microstructures and performances will be different from those obtained via the acid-
catalyzed route. Their wide usage will require further investigations to elucidate the early
stages of the base-catalyzed sol-gel process. In the present work, the ammonia-catalyzed
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Table 1 Reaction component
compositions
Sample Molar ratio of TEOS/DDS/H2O/NH3
(a)
(b)
(c)
(d)
(e)
(f)
0.61/0.61/1.8a/0.152
0.61/0.60/1.8a/0.243
0.61/0.61/1.8a/0.486
0.61/0.61/3.6b/0.152
0.61/0.61/5.4c/0.152
0.61/0.31/1.5a/0.152
0.61/0.15/1.35a/0.152
a MH O = 2MT + MD.
2
b MH O = 4MT + 2MD.
2
c MH O = 6MT + 3MD. Here
M
H O2 , MT and MD are the molar
2
concentrations of H2O, TEOS
and DDS, respectively.
(g)
hydrolysis kinetics of TEOS/DDS mixtures in methanol are investigated and the detailed
rate constants are determined.
2 Experimental
2.1 Materials and components
Reagent grade aqueous ammonium hydroxide (26% NH3), anhydrous methanol, deionized
water, TEOS (Acros, 99% purity) and DDS (TCI, 98% purity) were used as received. The
reaction component compositions are presented in Table 1. Solutions (a) through (e) were
prepared by the ammonia-catalyzed hydrolysis of an equimolar mixture of TEOS and DDS,
which was held constant at 0.61 mol·m−3. The effect of the ammonia concentration on the
reaction rates can be derived by comparing the results for mixtures (a), (b) and (c). The effect
of the water concentration on the reaction rates can be derived by comparing the results for
mixtures (a), (d) and (e). The effect of the DDS/TEOS ratio can be derived from comparing
the results for the mixtures (a), (f) and (g).
2.2 In-situ liquid-state 29Si NMR experiments
In-situ liquid-state 29Si NMR samples were prepared by mixing two solutions, A and B, at
the temperature of 25 ◦C. Solution A, TEOS and DDS, was dissolved in half of the total
methanol and stirred for 20 min. Solution B, deionized water and ammonia hydroxide, was
dissolved in the other half of the methanol and was stirred for 5 min. The reaction was
initiated by mixing solutions A and B. After 5 min of stirring, the sample was transferred to a
NMR sample tube (5 mm O.D.) and analyzed immediately. Chromium(III) acetylacetonate,
Cr(acac)3 (1 wt.%), was added as the spin relaxation agent. Many studies [11, 30] have
proven that Cr(acac)3 has little effect on the reaction rate or the final product distribution.
All in-situ liquid-state 29Si NMR experiments were carried out in duplicate using a UNITY
INOVA-500 Spectroscopy instrument. To achieve sufficient signal intensity, 168 scans were
acquired for each spectrum with a 3 s pulse delay using a 90◦ pulse angle. The spectral
frequency of 29Si was 99.351 MHz. The resulting spectra were internally referenced to
a tetramethylsilane (TMS) standard. The resonance peaks of the observed species were
well resolved and could be integrated quantitatively. During the experiments, gelation did
not occur and transesterification was negligible [11]. All these NMR experiments were
conducted at 25 ◦C and the temperature was controlled to within 0.1 ◦C.
As reference experiments, the individual hydrolysis of a single precursor, TEOS or DDS,
were carried out under the same reaction conditions as mentioned above. The hydrolysis
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and condensation rate constants were also calculated for comparison with those of mixed
systems.
2.3 Interface characterization of the sols
According to the synthesis parameters detailed in Table 1, the sols were prepared and
then subjected to Transmission Electron Microscopy (TEM, H600, Hitachi) and SAXS
measurements. The SAXS experiments were performed on the 4B9A beam line at the
Beijing Synchrotron Radiation Facility with a long-slit collimation system. The incident
X-ray wavelength was 0.154 nm. The scattering angle 2θ was approximately 0 to 3◦. The
fractal structures of the organo-modified SiO2 clusters were calculated.
2.4 Microstructure analysis of the xerogels
Solid-state 29Si MAS NMR (MSL-400, Bruker) spectroscopy and X-ray photoelectron spec-
troscopy (XPS, PHI5300X, Perkin-Elmer) were also used to estimate the cross-condensation
properties of the TEOS/DDS hybrid gel. The wet gels were obtained by freely gelating the
sols used in the liquid-state 29Si NMR experiments. The xerogels were obtained by drying
the wet gels in air at room temperature and no further treatment was made. All of the 29Si
NMR experiments were performed on a Varian Infinityplus-400 spectrometer using a 7.5 mm
probe under magic-angle spinning conditions. The resonance frequency was 79.5 MHz. The
90◦ pulse width was measured to be 4.8 µs. A repetition delay time of 100 s was used for
the 29Si single-pulse experiments.
3 Results
3.1 29Si NMR spectra and the concentrations of soluble Si species
In order to assign the 29Si NMR chemical shifts to the different silicon species, the tra-
ditional notation was adopted [1]: thus D represents di-functional silicon in DDS, and Q
represents tetra-functional silicon in TEOS. Then, the symbols Dmn and Qmn denote the
products of hydrolysis or condensation of DDS and TEOS, respectively, where m and n, re-
spectively, are the number of siloxane bridges and the number of silanols surrounding the Si
atom.
Figure 1a shows a typical, time-dependent, 29Si NMR spectra obtained during the reaction
of the mixed precursors. Figure 1b and c show the time-dependent 29Si NMR spectra of the
single precursor DDS system and the single precursor TEOS system, respectively. The
chemical shifts of the soluble Si species shown in Fig. 1 are listed in Table 2. There were six
peaks detected in the experiments. The two resonance signals at −0.36 ppm and −2.18 ppm
correspond to D01 and D00, respectively, under basic condition [31]. The two resonance signals
at −80.4 ppm and −81.3 ppm correspond to Q10 and Q00, respectively. These four signals were
detected in every experiment. A weak resonance signal at 1.46 ppm belongs to D02, but it does
not appear in samples (d), (e), (f) or (g). A weak resonance signal at −78.3 ppm corresponds
to Q30. As can be seen from Fig. 1a, the hydrolysis of TEOS leads to the formation of Q01
(mainly) and Q30 (weak), but Q02 was not observed. This last observation was probably due
to the fast condensation of the intermediate species Q20 under basic conditions, so that its
signal intensity was below the detection limit of the liquid-state 29Si-NMR spectrometer
[11]. The biggest differences can be found among Fig. 1a–c and some signals corresponding
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Fig. 1 Time-dependent liquid-state 29Si NMR spectra of: (a) the TEOS/DDS systems with the molar ratio
of TEOS/DDS/H2O/NH3 at 0.61/0.61/1.8/0.243; (b) the single precursor DDS system, and (c) the single
precursor TEOS system
to dimers appeared in the spectra of the single precursor systems: D10 at −9.45 ppm and D11
at −8.92 ppm in Fig. 1b, Q01 at −88.4 ppm in Fig. 1c, but not in Fig. 1a of the mixed precursor
systems.
The relative concentrations of the intermediate soluble Si species were determined by
integrating the resonance peak area at a fixed individual frequency in the NMR spectra.
The integrated area of the initial Q00 peak of TEOS (0.61 mol·dm−3), observed without the
presence of catalyst or water, was taken as being 100%. The disappearance of the monomers
from their initial level and the appearance of one or more intermediate species are presented
as functions of time in Fig. 2 for each studied reaction mixture. The time dependence of
the monomer concentration (Q00 or D00) was obtained by fitting the experimental data with
an exponential decay function of first order and the time-dependence curves shown for the
intermediate species concentrations (Q01 or D01) are just to guide the eyes. The concentrations
displayed in Fig. 2 are the basis for further calculations of the rate constants.
Comparing Fig. 2a–c, the extent of decrease of monomer concentration increases with
increasing ammonia concentration. A similar trend can be seen by comparing Fig. 2a and d,
but no obvious differences can be observed from comparing Fig. 2d with e. Increasing
the concentration of DDS in the mixture speeds up the hydrolysis of the TEOS monomer
Table 2 Liquid-state 29Si NMR
chemical shift δ and the silicate
Species
Structures
δ(ppm)
structures
D02
D01
D00
Q03
Q01
Q00
(Me)2Si∗(OH)2
(Me)2Si∗(OEt)(OH)
(Me)2Si∗(OEt)2
Si∗(OEt)(OH)3
Si∗(OEt)3(OH)
Si∗(OEt)4
1.46
−0.36
−2.18
−78.3
−80.4
−81.3
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(a)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
(b)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
30 60 90 120 150 180 210 240 270 300
0
30 60 90 120 150 180 210 240 270 300
t (min)
t (min)
(d)
(c)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
30 60 90 120 150 180 210 240 270 300
0
30 60 90 120 150 180 210 240 270 300
t (min)
t (min)
(f)
(e)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
30 60 90 120 150 180 210 240 270 300
0
30 60 90 120 150 180 210 240 270 300
t (min)
t (min)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
(g)
0
30 60 90 120 150 180 210 240 270 300
t (min)
Fig. 2 Time-dependent soluble silicon species concentrations in the TEOS/DDS systems with molar ratios
of TEOS/DDS/H2O/NH3 at: (a) 0.61/0.61/1.8/0.152; (b) 0.61/0.61/1.8/0.243; (c) 0.61/0.61/1.8/0.486; (d)
0.61/0.61/3.6/0.152; (e) 0.61/0.61/5.4/0.152; (f) 0.61/0.31/1.5/0.152; (g) 0.61/0.15/1.35/0.152, Bꢀ D00, •D01,
᭿D02, ꢁ Q00, ◦ Q10, ᮀQ03
as seen by comparison of Fig. 2a, g and f, but no notable influence can be found on the
hydrolysis rate of the DDS monomer itself. Therefore, a qualitative conclusion can be easily
drawn from Fig. 2. That is, the hydrolysis of TEOS and DDS are both more sensitive to the
ammonia concentration than to the water concentration, and the addition of DDS speeds up
the hydrolysis of TEOS.
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3.2 Hydrolysis kinetics
3.2.1 Hydrolysis-condensation mechanism and sol-gel kinetics model
Under basic conditions it is likely that water dissociates to produce nucleophilic hydroxyl
anions in a rapid first step; the hydroxyl anion then attacks the silicon atom. Iler [32] and
Keefer [33] proposed an SN2–Si mechanism. Equation (1), in which OH− displaces OR−
with inversion of the silicon tetrahedron, is as follows:
In Eq. (1), R = OEt for TEOS and R = CH3 for DDS. This mechanism is affected by both
steric and inductive factors; however, steric factors are more important because silicon
acquires a little charge in the transition state. The most widely accepted mechanism for the
condensation reaction involves the attack of a nucleophilic deprotonated silanol on a neutral
silicate species, which was proposed by Iler [32] to explain condensation reactions in aqueous
silicate systems. Pohl and Oserholtz [34] and Voronkov et al. [35] proposed essentially the
same mechanism, Eqs. (2) and (3), to account for deuteroxide (hydroxyl) anion and general
base-catalyzed condensation of silicon alkoxide.
In above-mentioned rudimentary hydrolysis and condensation mechanism, how the vari-
ous functional groups, (OR), (OH), and (OSi) are distributed on the silicon atoms is ignored.
At this level, only three reactions and three rate constants are necessary to describe the
functional group kinetics (Eqs. (4)–(6)), where h denotes hydrolysis, cw the condensation of
water and ca the condensation of alcohol:
kh
SiOR + H2O −→ SiO + ROH
(4)
(5)
(6)
kcw/2
2SiOH −→ 2(SiO)Si + H2O
kca/2
SiOH + SiOR −→ 2(SiO)Si + ROH
In practice, hydrolysis and condensation occur concurrently, and at the nearest functional
group level there are 15 distinguishable local chemical environments. Kay and Assink [36,
37] have represented the 15 silicate species in matrix forms. At this more sophisticated level,
there are 165 distinguishable rate coefficients: 10kh, 55kcw and 100kca, considering only
the forward reactions. If one goes further to the next-to-nearest functional group level, the
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resulting number of rate constants will be huge. Thus, based on the above consideration, the
precise sol-gel kinetics (including all of the determined rate constants) will be impossible
to quantify experimental methods. Therefore, a simple sol-gel kinetic model proposed by
Lee et al. [38] was adopted for the following kinetics calculations. This is a total model
for hydrolysis and condensation kinetics, not a detailed rudimentary reaction model, so the
obtained reaction orders must be fractional. These fractional reaction orders reflect the true
complicated sol-gel process.
A simple sol-gel reaction kinetics model for TEOS is as follows:
kTh1
Q00 + H2O −→ Q10 + ROH
(7)
(8)
kTh2
Q10 + 2H2O −→ Q30 + 2ROH
kTc1
Q10 + Q10 −→ Q01 + H2O
(9)
kTc2
Q30 + Q30 −→ Q41 + H2O
(10)
As for DDS, the sol-gel reaction kinetics model is similar to that of TEOS and is as follows:
kDh1
D00 + H2O −→ D01 + ROH
(11)
(12)
(13)
(14)
kDh2
D01 + H2O −→ D02 + ROH
kDc1
D01 + D01 −→ D10 + H2O
kDc2
D02 + D02 −→ D12 + H2O
3.2.2 Hydrolysis kinetics of TEOS in TEOS/DDS mixtures
In reactions (7) to (10), all the reactive rates are dependent on [NH3] and [H2O], so the rate
expression for the initial hydrolysis of TEOS is given by:
ꢀ
ꢁ
d Q00
ꢀ
ꢁ
α
rT = −
= kTh1 Q00 [NH3]β[H2O]γ
(15)
dt
The exponents α, β and γ here are the reaction orders belonging to the TEOS monomer,
NH3 and H2O, respectively. Because NH3 was used as a catalyst during the hydrolysis and
condensation processes, its concentration remained constant; the change of water concen-
tration was less than 5% of the initial amount [38] so it was also regarded as being invariant
when calculating reaction rate constants. If we define
kT1h = kTh1[NH3]β[H2O]γ
(16)
then the rate expression Eq. (15) can be simplified to
ꢀ
ꢁ
d Q00
ꢀ
ꢁ
α
rT = −
= kT1h Q00
(17)
dt
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Fig. 3 Time-dependent TEOS
monomer concentrations in the
TEOS/DDS systems with the
molar ratio of
TEOS/DDS/H2O/NH3 at: (a)
0.61/0.61/1.8/0.152; (b)
0.61/0.61/1.8/0.243; (c)
0.61/0.61/1.8/0.486; (d)
0.61/0.61/3.6/0.152; (e)
0.61/0.61/5.4/0.152; (f)
(a)
(f)
(b)
(g)
(c)
(d)
(e)
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
-3.5
-4.0
0.61/0.31/1.5/0.152; (g)
0.61/0.15/1.35/0.152. The slopes
of the straight lines yield the
pseudo-first-order rate constants
kT1h for TEOS hydrolysis
0
30 60 90 120 150 180 210 240 270 300
t (min)
As can be seen from Fig. 2, the exponentially fitted time-dependent concentration of Q00
is a good approximation to the experimental data. In this case, it is assumed that the reaction
(7) is of first order, i.e., α = 1, so the rate expression (17) reduces to:
ꢀ
ꢁ
d Q00
ꢀ
ꢁ
rT = −
= kT1h Q00
(18)
dt
Integration of Eq. (18) then yields
ꢀ
ꢁ
ꢀ
ꢁ
ln Q00 = ln Q00 − kT1h
t
(19)
0
Thus, a plot of ln[Q00] versus t should yield a straight line with −kT1h as the slope and ln[Q00]0
as the intercept. Figure 3 shows the relation between ln[Q00] and t. The observed good
linearity proves that α = 1. Furthermore, taking the natural logarithm of Eq. (16) yields,
ln kT1h = ln kTh1 + β ln[NH3] + γ ln[H2O].
(20)
Therefore, a linear plot of ln kT1h versus ln[NH3] with a slope β will yield the reaction order
β for NH3 when [H2O] is assumed to remain constant (i.e., samples (a), (b) and (c)). This
plot is shown in Fig. 4. Similarly, a linear plot of ln kT1h versus ln[H2O], shown in Fig. 5, will
yield the reaction order γ of H2O when [NH3] remains constant (i.e., samples (a), (d), (e)).
Values of β = 0.98 and γ = 0.795 have been determined directly from the TEOS branches
of Figs. 4 and 5. The relative deviations for β and γ are less than 5%, and originated from
uncertainties in the area integration of the NMR peaks. Applying the value of kT1h obtained
from Fig. 3, and using values of β and γ in Eq. (20), the values of kTh1 were calculated
(see Table 3). Finally, the initial hydrolysis rate equation for TEOS in the mixed TEOS/DDS
system is
rT = 9.33 × 10−3[TEOS][NH3]0.98[H2O]0.795
(21)
From Eqs. (7) and (9), the disappearance of species Q10 is accompanied by the appearance
of the condensation product species Q01, or a cross-condensed species and another intermedi-
ate species Q30. Because the intermediate Q10 is so active that it has little time to accumulate,
a steady-sate concentration is reached after the Q10 concentration approaches its maximum
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Fig. 4 Pseudo-first-order
-4.4
-4.6
-4.8
-5.0
-5.2
-5.4
-5.6
-5.8
-6.0
hydrolysis rate constants kT1h and
TEOS
DDS
kD1 h versus the NH3 concentration
in the TEOS/DDS systems (the
linear correlation coefficients are
0.99996 and 0.99999 for TEOS
and DDS, respectively)
-2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4
ln[NH3]
value. According to the steady-state approximation [39], the following equation is obtained:
ꢀ
ꢁ
d Q10
ꢀ
ꢁ
ꢀ
ꢁ
= kTh1 Q00 − kTc1 Q10 ≈ 0
(22)
ss
ss
dt
where [Q10]ss and [Q00]ss are the steady-state concentrations of [Q01] and [Q00], respectively.
Hence, the condensation rate constant kTc1 can be defined by:
ꢀ
ꢀ
ꢁ
ꢁ
Q00
Q01
ss
ss
kTc1 = kTh1
(23)
The kTc1 data are also listed in Table 3. Because Q30 does not appear in experiments (f) and
(g), kTh2 and kTc2 that are defined by reactions (5) and (7) are not taken into account.
3.2.3 Hydrolysis kinetics of DDS in TEOS/DDS mixtures
Applying an analysis process similar to that used for TEOS for calculating the hydrolysis
kinetics of DDS in the mixed TEOS/DDS system, reaction (11), three plots of ln[D00] versus
Fig. 5 Pseudo-first-order
TEOS
DDS
hydrolysis rate constants kT1h and
-4.8
-5.0
-5.2
-5.4
-5.6
-5.8
-6.0
kD1 h versus the H2O concentration
in the TEOS/DDS systems (the
linear correlation coefficients are
0.999905, and 0.99992 for TEOS
and DDS, respectively)
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
ln([H2O])
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Table 3 Rate constants for hydrolysis and condensation in the TEOS/DDS systems
Sample
akTh1 × 103 (TEOS) akDh1 × 103 (DDS) akTc1 × 103 (TEOS) akDc1 × 103 (DDS)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Average
10.64 0.5
9.42 0.5
9.39 0.45
9.09 0.45
8.83 0.42
9.02 0.45
9.54 0.48
8.77 0.44
9.50 0.48
9.16 0.48
28.14 1.4
61.29 3.2
69.04 3.5
63.76 2.2
65.47 3.3
67.69 3.4
67.95 3.4
70.01 3.5
66.5 0.5
63.69 3.2
54.08 2.7
51.65 2.6
53.1 2.7
60.47 3.1
57.88 2.9
56.12 2.8
56.7 0.48
35.19 1.8
8.72 0.44
9.68 0.48
9.53 0.48
9.67 0.48
9.06 0.45
9.33 0.47
bReference 7.41 0.4
157.2 0.4
aThe errors of kh and kc were estimated assuming a 5% uncertainty for the integration areas, and subscripts
h and c indicate hydrolysis and condensation reactions, respectively.
bReference experiments refer to the individual hydrolysis of single precursor species under the same reactive
conditions as used in this paper.
t, ln kD1 h versus ln[NH3], and ln kD1 h versus ln[H2O] have been drawn and are shown in Fig. 6;
the DDS branch of Fig. 4 and the DDS branch of Fig. 5, respectively. Consequently, the
hydrolysis rate equation for DDS was obtained as:
rD = 9.16 × 10−3[DDS][NH3]0.75[H2O]0.26
(24)
Using the steady-state approximation [39], the condensation rate constant kDc1 has also been
defined and its values are listed in Table 3.
3.3 Results of 29Si MAS NMR and XPS measurements on xerogels
Figure 7a and b shows the solid-state 29Si MAS NMR spectra of the hybrid gels (a) and (g),
respectively, where the superscripts m and n in the symbols Qm and Dn denote the number of
Si−O−Si bridges. As to gel (a), mainly the D2 peak of DDS condensation and the Q4 peak
of TEOS condensation are simultaneously observed. As for gel (g), the strong Q4 signal
reveals the high extent of condensation of TEOS, but DDS has a very low condensation
Fig. 6 Time-dependent DDS
(a)
(f)
(b)
(g)
(c)
(d)
(e)
monomer concentrations in the
TEOS/DDS systems with the
molar ratio of
TEOS/DDS/H2O/NH3 at: (a)
0.61/0.61/1.8/0.152; (b)
0.61/0.61/1.8/0.243; (c)
0.61/0.61/1.8/0.486; (d)
0.61/0.61/3.6/0.152; (e)
0.61/0.61/5.4/0.152; (f)
0.61/0.31/1.5/0.152; (g)
0.61/0.15/1.35/0.152. The slopes
of the straight lines yield the
pseudo-first-order rate constants
kD1 h for DDS hydrolysis
-0.4
-0.8
-1.2
-1.6
-2.0
-2.4
-2.8
0
30 60 90 120 150 180 210 240 270 300
t (min)
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Fig. 7 Solid-state 29Si MAS
NMR spectra of TEOS/DDS
hybrid gels (a) and (g)
(a)
Q4
D2
Q3
50
0
-50
-100
-150
(g)
-200
Chemical shift /ppm
Q4
Q3
Q1
D1
2
D
50
0
-50
-100
-150
-200
Chemical shift /ppm
extent because both D resonance signals appear, including D1 (for partial condensation) and
D2 (for complete condensation).
The atomic content (AC) of carbon on the hybrid SiO2 particle surface was calculated
from the integral area of the carbon peak of the XPS spectrum. For hybrid gel (a), the AC
is as high as 50.45%, which means there was enrichment of methyl groups on the surface
of the SiO2 particles. The error of the AC value originated from the relative uncertainty of
about 5% of the integral area.
3.4 Results of SAXS and TEM
The SAXS technique has been successfully applied to the characterization of nano-scale
microstructures [40–43], especially the fractal structure of sols, although it cannot provide
chemical kinetic information for a sol. The SAXS of a typical fractal system has an ex-
ponential decrease of the scattering intensity that is given by I(q)αq−Dm(1 ≤ Dm < 3) or
I(q)αqDs−6 (2 < Ds < 3) for mass-fractal systems (the fractal dimension is Dm) or surface-
fractal systems (the fractal dimension is Ds), respectively [45], where q = (4π/λsin(θ/2))
is the scattering wave vector, λ is the wavelength of the incident X-ray and θ is the scattering
angle. Thus, a fractal curve of ln[I(q)] versus ln(q) will possess a linear range with −Dm as its
slope. The fractal dimension can be determined from the slope of the linear range. According
to Craievich [45] and Marliere et al. [46], it is possible for double-fractal structures to exist.
That is, a complex fractal structure is present that includes two fractal dimensions.
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Fig. 8 TEM photographs of
TEOS/DDS hybrid sol
The detailed fractal data are collected in Table 5 from which two fractal dimensions can
be found for the TEOS/DDS hybrid sols. Both Dm1 and Dm2 are mass-fractals and 2 < Dm1
< 3, 1 < Dm2 < 2. This double-fractal structure can be confirmed from the TEM photograph
shown in Fig. 8. In Fig. 8, two circles indicate the spacial scale of the double-fractal structure,
of which the small one is for primary particles (corresponding to Dm1) and the large one for
particulate networks (corresponding to Dm2). Obviously, the primary particles are linked
together into some loose networks.
4 Discussion
4.1 Comparison with the hydrolysis and condensation of a single precursor
The main reason for studying the hydrolysis and condensation of the TEOS/DDS mixed
systems is to understand the hybrid sol-gel process at a molecular level along with the
subsequent microstructure and chemical homogeneity of the derived hybrid materials. A
clear analysis of the hydrolysis kinetics will provide us with effective directions to synthesize
hybrid materials in the light of special material design requirements. Thus, the first thing
to be dealt with is identifying both why and what kind of differences occur between the
hydrolysis kinetics of the mixed double-precursor system and those of the single precursor
systems.
According to our previous work [31], the individual hydrolysis rate equations for the
single TEOS and DDS systems are of the following type:
rT = 7.41 × 10−3[TEOS][NH3]0.333[H2O]0.227
rD = 2.814 × 10−2[DDS][NH3]0.652[H2O]0.080
(25)
(26)
Comparing Eq. (18) with (22), and Eq. (21) with (23), it is obvious that the reaction orders
of NH3 and H2O become larger in the mixed double-precursor system than in the single-
precursor system. This result indicates that the hydrolysis of TEOS and the hydrolysis of
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DDS are more sensitive to the concentrations of NH3 and H2O in the mixed-precursor
system than in the single-precursor system. In addition, the reactive order with respect to the
NH3 concentration is always larger than that of H2O, which shows a stronger sensitivity of
the hydrolysis to the concentration of NH3 than to H2O. These results reveal an important
phenomenon: TEOS and DDS both follow their original reaction pathways even in mixed
systems and the sequence of sensitivity is still in the order TEOS (DDS) > NH3 > H2O.
Thus, one need not worry about a possible irregular change in the sensitivity sequence. This
conclusion is useful for the design of hybrid materials.
In the reference experiments for the single-precursor systems, the hydrolysis rate constants
k
k
Th1 for TEOS and kDh1 for DDS are listed in the row “reference” of Table 3. It was found that
Th1 increases from 7.41 × 10−3 to 9.33 × 10−3 when the situation for TEOS is changed from
the single-precursor system to the mixed-precursor system. On the contrary, kDh1 decreases
from 28.14 × 10−3 to 9.16 × 10−3 when the situation of DDS is changed from the single
to the mixed-precursor system. However, the value of kT c1 decreases from 157.2 × 10−3 to
66.5 × 10−3 and the value of kDc1 increases from 35.19 × 10−3 to 56.7 × 10−3. If we define
the following two variables KT = kTc1/kTh1 for TEOS and KD = kDc1/kDh1 for DDS, the
relative rates between the condensation and hydrolysis reactions can be seen more clearly. The
obtained values of KT and KD are collected in Table 4. Interestingly, the divergence between
the values of KT and KD decreases from 21.2 to 1.2 and from 7.5 to 6.1, respectively, when
the TEOS and DDS situations are changed from the single-precursor system to the mixed-
precursor system, which shows that a more compatible sol-gel process occurs between TEOS
and DDS. This information should benefit the fabrication of hybrid materials with higher
homogeneity.
Comparing the condensation rates for systems (g), (f), (a) in Table 3, some useful infor-
mation can be obtained. With the increasing concentration of DDS in the mixed-precursor
systems, the condensation rate of TEOS decreases whereas the condensation rate of DDS
increases. This can be understood from the reduction of the average functionality for silicon
atoms of TEOS a phenomenon that prevents formation of the siloxane network. The reverse
case occurs for DDS.
In summary, hydrolysis becomes more active and the reactive behavior of TEOS and
DDS becomes more compatible in the TEOS/DDS mixed-precursor system, compared with
the corresponding single-precursor systems. All these phenomena indicate the possibility of
forming a product with high homogeneity.
4.2 Estimation of cross condensation and particle growth
Although the hydrolysis kinetics and the simple condensation rate constants of the mixed
TEOS/DDS systems have been determined, the condensation kinetics, especially the cross-
condensation kinetics, are impossible to study using the liquid-state NMR technique under
Table 4 Relative rates for
hydrolysis and condensationa
KT (TEOS)
KD (DDS)
Mixed precursor system
Single precursor system
7.5
21.2
6.1
1.2
aKT = kTc1/kTh1 and KD = kDc1/kDh1, where kTc1 and
k
Th1 are the condensation and hydrolysis rate constants
for TEOS, and kDc1 and kDh1 are the condensation and
hydrolysis rate constants for DDS.
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basic condition. This is because the condensation reaction occurs faster than the hydrolysis
reaction and the formed condensation species immediately participate in nucleation and
become inaccessible to liquid-state NMR measurements. The defined condensation rate
constants kT c and kDc are just overall rate constants for TEOS and DDS, and no cross-
condensation reaction kinetics were described. After gelation occurs, the solid-state 29Si
NMR method is suitable for analyzing the local chemical environment in the hybrid materials.
But, no appropriate technique is available to study the condensation kinetics and growth
kinetics of particles that occur just in the “blind” region between the liquid-state NMR
detection range and the solid-state NMR detection range.
However, we can still approximately understand the cross-condensation properties using
the solid-state 29Si MAS NMR and XPS methods. Figure 7 shows the solid-state 29Si MAS
NMR spectra of the hybrid gels resulted from samples (a) and (g). As to sample (a), the
strong Q4 and D2 signals reveal a high extent of condensation of TEOS and DDS. However,
for sample (g), the DDS precursor shows a very low extent of condensation because all
of the D resonance signals from D1 (partial condensation) to D2 (complete condensation)
coexist. This contradictory situation should not occur when cross condensation between the
hydrolyzed TEOS and DDS is intense. The XPS result shows that the concentration of carbon
on the surface of the hybrid-gel particle is 50.45%. Thus, the methyl groups introduced by
the DDS-TEOS cross condensation are mainly distributed on the surface of the hybrid gel.
Combining the results from the solid-state 29Si MAS NMR and XPS measurements, we
deduce that cross condensation is weak for the hybrid sol-gel process under basic conditions.
But, from the hydrolysis kinetics measurements, the hydrolysis and condensation rates of
TEOS and DDS are more compatible. In spite of this extent of cross condensation, it is
closely related to the particle growth.
It is difficult for the actual growth mechanism of particles to be completely characterized
because of the complex effects from the solvent and reaction compositions. Only for the
simplest system TEOS/EtOH/H2O/NH3 is the growth mechanism of SiO2 particles consid-
ered to be clear. That is, a standard reaction-limited growth occurs with no formation of
new particles and no agglomeration of existing particles [27]. In addition, the effect of the
solvent on the particle growth is an important aspect. Mine and co-workers [28] investigated
the effect of different alcohol solvents on the particle growth rate and found that differences
in the dielectric constant of the solvent and the particle surface potential determined the
magnitudes of the inter-particle repulsion and the corresponding order of the particle growth
rate. Concerning our binary precursor systems, the mechanism of particle growth should be
more complex than for the single precursor system. The true situation may be the following:
TEOS hydrolyzes and self-condenses into some silica nuclei; simultaneously, the hydrolyzed
DDS reacts with these nuclei and modifies the surface of the silica particles with methyl
groups that then prevents particle agglomeration and adds to the insolubility of the colloidal
silica particles.
4.3 Double fractal structure in TEOS/DDS hybrid sol
There is still the question as to how the double-fractal structures come into being in the
hybrid sols, even though the reaction kinetics and the cross condensation have been studied.
To answer this question, the relative hydrolysis rate between DDS and TEOS, rT/rD, is the
key. In the above-mentioned discussion about KT and KD, a better compatibility between
the hydrolysis and condensation of TEOS or DDS was found. It accounts qualitatively for
the easier hybrid formation between TEOS and DDS. The ratio rT/rD can be used to explain
how the starting condition of the hybrid sol affects the double-fractal structure. The values
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Table 5 Values of rT/rD and the
detailed double-fractal structure
parametersa
Sample
rT/rD
Dm1 Dm2
(a)
(b)
(d)
(g)
1.05
1.17
1.52
3.27
2.31
2.22
2.29
2.26
1.26
1.11
1.21
1.07
aDm1 and Dm2 are the
mass-fractal dimensions; rT/rD
=
1.02[TEOS][NH3]0.23[H2O]0.53/[DDS].
of rT/rD (its relative deviations are less than 5%, which originates from uncertainties in the
area integration of the NMR peaks) are calculated from Eqs. (21) and (24) as follows:
9.33 × 10−3[TEOS][NH3]0.98[H2O]0.795
rT/rD
=
9.16 × 10−3[DDS][NH3]0.75[H2O]0.26
= 1.02[TEOS][NH3]0.23[H2O]0.535/[DDS]
(27)
The detailed rT/rD values are collected in Table 5. Comparing samples (a) with (b), (a) with
(d), and (a) with (g), respectively, it is found that the rT/rD values increase with [NH3], [H2O]
and the ratio of TEOS to DDS. Simultaneously, the amounts of Dm2 increase against this
sequence.
TEOS hydrolyzes and self-condenses into the compact silica nuclei with Dm1 being
greater than two. The simultaneously hydrolyzed DDS monomers cross condense with the
Si−OH groups on the surface of the compact silica nuclei and further link them into a loose
network with Dm2 being smaller than two. In this process, the relative hydrolysis rates
between TEOS and DDS determine how loose the particulate network will be. For example,
the value of rT/rD of sample (a) is 1.05 and is much smaller than 3.27 of sample (g), which
mean that a smaller difference between the hydrolysis rates occurs between TEOS and DDS
for sample (a) than for (g). Thus, the hydrolyzed DDS will quickly cross condense with
the hydrolyzed TEOS to block further growth of SiO2 particles. This growth prevention is
remarkable so that DDS has a good condensation rate (see the 29Si MAS NMR result of
Fig. 7a).
Taking the particle size into account, the sol (a) undergoes faster particulate growth than
sol (g). Therefore, TEOS and DDS must hybridize into a somewhat more compact network
in sol (a) than in sol (g). This can be verified by their fractal dimension Dm2, as seen in
Table 5. Although the particulate networks of sol (a) and sol (g) all possess typical double-
fractal structures, the Dm2 of sol (a) is larger than that of sol (g). Based upon the comparative
analysis between rT/rD and Dm2 of the hybrid sols (a) and (g), these two parameters are only
different aspects of the same nature. Thus it is reasonable to find such concordant results by
different methods.
5 Conclusion
Because the condensation of siloxane is much faster than its hydrolysis under basic condi-
tions, and the species formed by condensation participate by nucleation immediately and
become insoluble, it is difficult to detect the liquid-state 29Si NMR signal of the condensed
species. Therefore, only the kinetics of the initial hydrolysis of the TEOS/DDS mixed systems
have been observed. The most valuable conclusion is that the hydrolysis and condensation
of TEOS and DDS become more compatible in the double-precursor system than in single-
precursor system. Assisted by information gained from the solid 29Si MAS, NMR and XPS
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measurements, weak cross condensation between two precursors can be deduced. The true
hybrid sol-gel process may be the following: TEOS hydrolyzes and self-condenses into
silica nuclei, simultaneously the hydrolyzed DDS modifies the surface of the silica nuclei
and results in double-fractal clusters through cross condensation with the silica nuclei. Thus,
in-situ liquid-state 29Si NMR provides a powerful tool for studying the initial hydrolysis
kinetics, which is crucial for formation of the structure and homogeneity of the final hybrid
material. Although no appropriate experimental technique could be utilized to obtain directly
the condensation kinetics, the cross-condensation mechanism can still be estimated with the
assistance of solid 29Si MAS NMR and XPS and SAXS measurements. This supplements
the kinetics studies.
Acknowledgments Financial support from the National Key Native Science Foundation (No. 20133040) is
gratefully acknowledged.
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