Temperature Effect on the Structure and Formation Kinetics of

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Temperature Effect on the Structure and Formation Kinetics of Vinyltriethoxysilane-Derived Organic/Silica Hybrids Dimas R. Vollet,* Carlos M. Awano, Fabio S. de Vicente, Alberto Iba~nez Ruiz, and Dario A. Donatti Departamento de Física, Instituto de Geoci^encias e Ci^encias Exatas, UNESP—Universidade Estadual Paulista, Cx.P. 178, 13500-970 Rio Claro (SP), Brazil ABSTRACT: The structure and formation kinetics of organic/ silica hybrid species prepared from acid hydrolysis of vinyltriethoxisilane has been studied in situ by small-angle X-ray scattering (SAXS) at 298, 318, and 333 K in a strongly basic step of the process. The evolution of the SAXS intensity is compatible with the formation of linear chains which grow, coil, and branch to form polymeric macromolecules in solution. The SAXS data were analyzed by the scattering from a persistent chain model for polymeric macromolecules in solution using a modified branching Sharp and Bloomfield global function, which incorporates a branching probability typical of randomly and nonrandomly branched polycondensates, and in a particular case, it is also valid for polydisperse coils of linear chains. Growth of linear chains and coiling dominate the process up to the formation of likely monodisperse Gaussian coils or polydisperse coils of linear chains. The link probability to form a branching point is increased with time to form nonrandomly branched polycondensates in solution. The kinetics of the process is accelerated with temperature, but all the curves formed by the time evolution of the structural parameters in all temperatures can correspondingly be matched on a unique curve by using an appropriate time scaling factor. The activation energy of the process was evaluated as ΔE = 21 ( 1 kJ/mol. The characteristics of the kinetics are in favor of a complex overall mechanism controlled by both condensation reactions and dynamical forces driven by interfacial energy up to the final structure development of the hybrids.

’ INTRODUCTION The preparation of organic/inorganic silica hybrids by incorporation of organic functional groups in the silica structure has attracted the attention of several researchers due to its wide variety of applications.1
10 In a typical process, a functional group is chemically introduced by a three-functional alkoxide while the silica inorganic network is formed by siloxane bonds by hydrolysis and condensation of the alkoxide.2
7 Vinyltriethoxysilane (VTES) has been used as a three-functional alkoxide precursor to produce organic/inorganic silica hybrids which present interesting optical and structural properties,6,7 such as good coatings with remarkable mechanical properties deposited onto substrates9 and highly monodisperse spheres via a one-step synthesis under basic conditions.1 The important feature of the organic-functionalized alkoxide polymerization is competition between the processes of hydrolysis, condensation, and phase separation, which are strongly dependent on the pH and temperature and determine the final properties of the hybrid.1,10 Structural and kinetic studies are useful tools to accompany the often nuances between these ongoing processes. Small-angle X-ray scattering (SAXS) has been shown to be a useful technique often used successfully for such purposes.11
14 We have studied the structure and the formation kinetics of VTES-derived organic/silica hybrids in strongly basic medium by means of small-angle X-ray scattering.13,14 The time evolution of the SAXS intensity was found to be compatible with formation r 2011 American Chemical Society

and evolution of linear chains which grow, coil, and branch to form macromolecules with local persistence. The persistence length is a measure of the coiling degree of the macromolecule, and because rheological properties are affected by the local persistence of the chains,15 the measure of this property is naturally of scientific interest to understand the overall process of the hybrid formation and behavior. The structure of the polymeric VTES/silica hybrids was found13,14 to evolve with time up to the apparent formation of a perfectly Gaussian persistent chain.16 The scattering curve I(q) from a perfectly Gaussian coiled chain macromolecule exhibits three characteristic regions:16 (i) the innermost part at low q follows approximately a Gaussian curve characterized by a radius of gyration Rg; (ii) the intermediate-q portion follows the relationship I(q) µ q
2 due to large subsections of the macromolecule formed by random arrangements of chain elements building an object of mass-fractal dimension D = 2; (iii) the outermost part at high q follows the scattering of a needle, I(q) µ q
1, since the small regions of the macromolecule are portions of linear chains. In a Kratky q2I(q) versus q plot, the Gaussian region drops down toward zero at q = 0, the intermediate-q portion I(q) µ q
2 becomes horizontal, and the I(q) µ q
1 tail end follows an ascending line, the extrapolation of which toward q = 0 passes Received: March 15, 2011 Revised: July 4, 2011 Published: July 07, 2011 10986

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Langmuir through the origin. After the appearance of the plateau I(q) µ q
2 in the experimental data of the VTES/silica hybrid formation, the Kratky plots exhibit maxima which increase in magnitude and shift toward the low-q region with time.13,14 To account for the maxima in the Kratky plots in the VTES/ silica hybrid formation kinetics, we have proposed a modified branching Sharp
Bloomfield (BSB) approach,13,14 in which the Debye function has been replaced by a form factor which accounts for both random and nonrandom branching of polycondensates in solution and, in a particular case, for polydisperse coils of linear chains. It has been suggested13 that the modified BSB approach describes better all the stages of aggregation of VTES/silica hybrids in comparison with the classical Sharp and Bloomfield model and the unified function proposed by Beaucage et al.,15 the latter incorporating an arbitrary mass-fractal dimension. The model has been applied to study the structure and kinetics of growth of VTES/silica hybrids as a function of the concentration of NH4OH used as a catalyst.13 It is well-known that the catalyst affects the reaction rate by changing the activation energy of the process. On the other side, temperature directly affects the rate constant but, in general, does not affect the activation energy for the process. Then the effect of temperature on the structure and kinetics of formation could be completely different from that of the concentration of the catalyst, and this justifies a separate investigation. In this work, we studied by means of SAXS the temperature effects on the structure and formation kinetics of VTES-derived organic/ inorganic silica hybrids in a strongly basic condition. The kinetics and the structural evolution were analyzed by using the mentioned BSB model in describing the SAXS data. The foundation and the methodologies presented earlier in interpreting the data were outlined here for understanding the present results.

’ EXPERIMENTAL SECTION Sols of organic/silica hybrid species were prepared by acid hydrolysis (pH 2) of a mixture of VTES (47.2 mL, Aldrich, 95%), 0.1 N HCl (16 mL, as a catalyst and water source for hydrolysis), and ethanol as a mutual solvent (55 mL, Aldrich, PA). The hydrolysis was promoted at 343 K for 2 h under magnetic stirring. A sample of the stable sol at pH 2 was studied by SAXS at 298 K. For the kinetic study, 1 M NH4OH was dropped into samples of 10 mL of the sols under magnetic stirring up to a final base concentration of 0.07 M. The kinetics of the aggregation process was studied in situ by SAXS at 298, 318, and 333 K as a function of time (min) just after the base addition up to far beyond the gel point. The sol
gel threshold occurred around two-thirds of the time spent for the SAXS study in each temperature, and it was studied separately by determining the time when the sol no longer flowed when tilted. No particular SAXS event could be associated with the sol
gel threshold. The SAXS experiments were carried out using synchrotron radiation with a wavelength λ = 0.1608 nm at the SAXS beamline of the National Synchrotron Light Laboratory (LNLS), Campinas, Brazil. The beam was monochromatized by a silicon monochromator and collimated by a set of slits defining a pinhole geometry. A 2D position-sensitive X-ray detector was used to obtain SAXS intensity from isotropic systems as a function of the modulus of the scattering vector q = (4π/λ) sin(θ/2), where θ is the scattering angle. The experimental setup allowed us to obtain SAXS data from q0 = 0.077 nm
1 up to qm = 2.347 nm
1 in intervals of Δq = 4.90  10
3 nm
1. The data were corrected by sample attenuation and parasitic scattering and normalized with respect to the beam intensity. Branching Sharp
Bloomfield Global Function. The classical Sharp and Bloomfield function has been used to describe the gradual

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Figure 1. Time evolution of the SAXS intensity in the aggregation process of VTES/silica hybrids in solution with a NH4OH concentration of 0.07 M at different temperatures. The red straight line accounts for a q
1 trend at high q. transition between power law
2 scaling and power law
1 scaling in persistence polymers that can be written as16 IðqÞ ¼ Ið0ÞfgðxÞ þ ð2lp =LÞ½ð4=15Þ þ ð7=15xÞ
½ð11=15Þ
ð7=15xÞ expð
xÞg

ð1Þ

where I(0) is the intensity extrapolated to q = 0, lp the persistence length, L the contour length (the length of the hypothetically fully extended molecule), and g(x) = (2/x2)[exp(
x)
(1
x)] the Debye function,16 with x = (Llp/3)q2 since Rg = (Llp/3)1/2 for a Gaussian coil. Equation 1 was found to describe well the first structural evolution of the aggregation of VTES-derived organic/silica hybrids, but eq 1 could not describe well the appearance of a plateau and in no way the maxima in the Kratky plots.13,14 We have proposed a modified Sharp and Bloomfield function to account for the appearance of maxima in the Kratky plots,13,14 which is characteristic of randomly and nonrandomly branched polycondensates and polydisperse coils of linear chains.17 The basic idea is to replace the Debye function g(x) in eq 1 by a form factor valid for both randomly and nonrandomly branched polycondensates and, in a particular case, for polydisperse coils of linear chains, which can be written as17 gðxÞ ¼ ð1 þ Cx=3Þ=½1 þ ð1 þ CÞx=62

ð2Þ

2 2

where x = Rg q and C is a dimensionless constant which is a function of the link probability for the formation of a chain point and the link probability for the formation of a branching point in a given macromolecule. Equation 2 has been used instead of the Debye function in eq 1 by keeping the constraint Rg2 = Llp/3, and such a modified branching Sharp
Bloomfield model has been applied with success in studying VTES/silica hybrid formation kinetics.13,14

’ RESULTS AND DISCUSSION Figure 1 shows the time evolution of SAXS intensity in the aggregation process of VTES/silica hybrids in solution with a NH4OH concentration of 0.07 M carried out at 298, 318, and 333 K. The general behavior of the scattering with time is to increase the intensity at low and intermediate q without substantially changing the intensity at high q, where the intensity was found to follow a power law regime with the scattering exponent approximately equal to
1, as shown by the q
1 trend plotted in Figure 1 at high q. The SAXS intensity exhibits an abrupt upturn at very low q on passing from the acid to the basic step of the 10987

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Figure 2. Fitting (full line) of the modified branching Sharp
Bloomfield global function (eqs 1 and 2) to the experimental data (points) along all stages of the aggregation process of VTES/silica hybrids at different temperatures. The curves are vertically shifted for the sake of clarity in the same sequence time as shown in Figure 1.

process; this effect is accentuated with increasing temperature. This upturn at very low q was attributed to a rapid aggregation of a fraction of the primary polymeric particles with a radius of gyration of about 1.4 nm already present in the earlier sol at pH 2, as evaluated through Guinier’s law in the apparent plateau at low q exhibited by the SAXS curve of the sol in Figure 1. The increase of the intensity at low and intermediate q with aggregation time seems to overlap with that upturn at low q caused by the rapid acidic to basic change. Figure 2 shows the Kratky plots for the data as a function of temperature. The SAXS intensity evolves with time up to the appearance of a plateau I(q) µ q
2 in the Kratky plots, and after that, it displays maxima at low q in the Kratky plots, which increase in magnitude and shift toward the low-q region. The overall process is accelerated with temperature following closely the general behavior observed elsewhere13 by increasing the NH4OH concentration. The linear trend at high q passing through the origin is not so obvious in the Kratky plots of Figure 2 because the curves were vertically shifted for the sake of clarity. One could think that the upturn at high q in the Kratky plots is due to a background scattering from the liquid present in the gel. However, we have studied similar systems of wet gels derived from hydrolysis of TEOS (tetraethoxysilane),18 and it was found that the contribution of the liquid scattering can be neglected in comparison with the scattering from the silica particles, since, under this condition, the scattering at high q approximates a power law q
2, characterizing a mass fractal structure with dimensionality 2, in agreement with results from other techniques. Then the q
1 trend at high q shown in Figure 1 was attributed to the scattering from linear sections of the macromolecule. This overall picture is compatible with formation of linear chains which grow, coil, and branch to form persistent chain polymeric macromolecules in solution. Accordingly, the data were analyzed by the modified branching Sharp
Bloomfield global function through eqs 1 and 2. Figure 2 shows that the modified branching Sharp
Bloomfield global function (eqs 1 and 2) fits very well to the experimental data along all stages and temperatures of the aggregation process of the VTES/silica hybrids. The fitting process was carried out using a nonlinear least-squares routine

Figure 3. Time evolution of the structural parameters as obtained by fitting the modified branching Sharp
Bloomfield model to the experimental curves of the VTES/silica hybrid formation kinetics at different temperatures. Zero time (t = 0, open circle) corresponds to the very stable sol at pH 2.

(Levenberg
Marquardt algorithm) to obtain the parameters L, lp, C, and I(0) that minimize the square of the difference between q2I(q) and the experimental values in the Kratky plots. Figure 3 shows the time evolution of the fitted parameters I(0), L, lp, and C at the studied temperatures. The radius of gyration Rg was evaluated from L and lp through the constraint equation Rg2 = Llp/3. The curves of time evolution of the radius of gyration were found to be very similar to those of I(0) when seen on a monolog scale as that plotted in Figure 3 for I(0). The persistence length lp diminishes rapidly from a value of about 2.1 nm (value not shown in Figure 3) to a value of about 1.4 nm on passing from the acidic (t = 0, pH 2) to the basic ([NH4OH] = 0.07 M) step of the process, while the length contour L increases correspondingly from about 4.8 to 12 nm. These results mean a rapid growth and coiling of the linear chains by abruptly increasing the pH. The intensity I(0) extrapolated to q = 0 increases in a closely exponential law with the time of aggregation at the basic step of the process (Figure 3). The increase of I(0) is readily accelerated with increasing temperature. The time evolution of I(0) is a good measure of the kinetics of the transformation of the aggregation process since I(0) µ cM for polymeric macromolecules in solution, where c is the mass concentration and M the mass of the macromolecule in solution.16 The contour length L increases accompanying approximately the same behavior of I(0) with time of aggregation in the basic step of the process, while lp diminishes rapidly at the beginning of the process and tends to a constant value at stages close to the appearance of the plateau in the Kratky plots (Figure 2). After the appearance of the plateau in the Kratky plots the diminution in lp 10988

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Langmuir is accelerated again up to lp to reach values comparable with the monomer size. The parameter C was found to be essentially equal to 1 at the first stages of the process. The value C = 1 is compatible with the formation of polydisperse coils of linear chains in solution or branched polycondensates of randomly f-functional elements.17 The properties of linear chains are obtained by setting either the branching probability to zero or the functionality of the branching units to f = 2.17 The parameter C diminishes abruptly from a determined time of the aggregation process (Figure 3), this stage being shifted to minor time values with increasing temperature. Maxima in the Kratky plots (Figure 2) arise when C < 1/3. The diminution of C means that the link probability to form nonrandomly branched polycondensates17 is increased, and it is compatible with the diminution found in lp at advanced stages of aggregation. The increase of the branching probability together with the diminution of the persistence length lp means that the macromolecule continuously loses its network flexibility, becoming gradually more rigid. Figure 3 shows that the variations in the structural parameters I(0), L, lp, and C are in general accelerated with increasing temperature, suggesting a thermally activated process. We wonder if the process could be governed by a common mechanism so the curves of the time evolution of each one of the structural parameters in each temperature could be matched onto a unique curve just by a scaling time. We consider the time t = t* necessary for the system to reach the transformation degree associated with the value I(0) = 1 on the arbitrary scale of Figure 3. The time t* was chosen because all the kinetic curves in each temperature apparently exhibit a similar behavior up to approximately t = t*, when, in addition, all curves present a similar change of behavior. We have obtained, from the intercepts between the extrapolations of the experimental curves I(0) versus t in each temperature with the straight line drawn at I(0) = 1 (Figure 3), the values t* = 100 min, t* = 63.6 min, and t* = 40.4 min for 298, 318, and 333 K, respectively. Figure 4 shows the plots of the time evolution of the structural parameters on the relative time scale t/t* as obtained at 298, 318, and 333 K. The set of curves of each one of the structural parameters obtained at different temperatures was found, correspondingly, to be reasonably matched to a unique curve. Thus, there is a common mechanism governing the aggregation process of VTES/silica hybrids in the range of temperature studied in the present work. A very similar picture resulted from studying this system elsewhere13 by varying the [NH4OH] concentration in the range of 0.05
0.09 M at room temperature. Therefore, increasing the temperature is, in a certain proportion, equivalent to increasing the base concentration in the range of values to which the present kinetic study refers. The rate of aggregation kinetics increases with the catalyst concentration because the sticking probability for a reaction is increased. On the other side, the relative population of species with activation energy necessary for the aggregation process is increased with temperature and so the rate constant. The first is clearly in favor of a reactionlimited aggregation process, and the second could equally well be assigned to a reaction-limited or a diffusion-controlled mechanism, since both the relative contribution to the diffusion motions and the sticking frequency increase with temperature. It is possible that both processes could be active together in the aggregation of the present system. Interestingly, the variation of both the independent variables, catalyst concentration and temperature, yields the development of very similar final structures for the hybrids.

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Figure 4. Evolution of the structural parameters of the polycondensates as a function of the relative time scale t/t*. Zero relative time means sol at pH 2 and 298 K. The set of curves for different temperatures of the structural parameters can be reasonably well matched to a unique curve in each case.

The results from Figures 3 and 4 suggest that the aggregation kinetics, as measured by the time evolution of I(0), I(0,t), could be well represented within the time interval t e t* approximately by an exponential function given by Ið0;tÞ ¼ A expðktÞ

ð3Þ

where A is a constant and k a true constant rate which depends exclusively on the temperature (and pH naturally). The values for the rate constant k were obtained by linear fitting of eq 3 to the experimental data of I(0) versus t in Figure 3 in the range t e t*. It was found that k = (196 ( 5)  10
4 min
1, k = (321 ( 7)  10
4 min
1, and k = (472 ( 12)  10
4 min
1 for 298, 318, and 333 K, respectively. In addition, from the properties of the plots of I(0) versus t/t* in Figure 4, it is inferred that there is a quantity β, with k = β/t*, which is a constant value independent of the temperature in the range studied. Therefore, the quantity t*
1 is also a measure proportional to an overall constant rate of the aggregation process in the range t e t*. Figure 5 shows the plots on a log scale of the rate constants k together with the values t*
1 (proportional to the overall rate constants) as a function of the inverse of temperature, 1/T. The plots were found to obey reasonably well a typical Arrhenius equation between the rate constant k (and t*
1) and 1/T in the temperature range studied. The energy of activation for the process was determined by linear fitting of the Arrhenius equation to the experimental data (Figure 5), and it was found that ΔE = (20.6 ( 0.9) kJ/mol from k and ΔE = (21.1 ( 2.3) kJ/mol from t*
1, both values yielding ΔE = (21 ( 1) kJ/mol as an average value. We have found no values in the literature for the activation energy in the aggregation process of organic/silica hybrids prepared from pure VTES. Values between 25 and 30 kJ/mol have been reported for polycondensation in acidic medium in the 10989

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At advanced stages of aggregation, C goes readily to zero so the scattering form of eq 2 goes to the Debye
Bueche form24 gðqÞ ¼ 1=ð1 þ a2 q2 Þ2

Figure 5. Arrhenius equation fitting the rate constant k and t*
1 (the latter proportional to an overall rate constant) with the inverse of temperature.

preparation of hybrids from mixtures of TEOS and VTES.19 For the pure TEOS system, the energy of activation for silica gelation in acidic medium was found to vary largely between 36 and 96 kJ/mol, depending on the catalyst and the water content for the previous hydrolysis, in the same range of temperature as that in the present work.20 Particularly, a value of 19.4 kJ/mol was reported for silica gelation in pure the TEOS system with no catalyst.20 This picture suggests that the energy of activation for the aggregation process of organic/silica hybrids prepared from mixtures of VTES and TEOS diminishes with increasing VTES concentration and pH, which is in agreement with the value 21 kJ/mol obtained from the pure VTES system in the present work. The value for the activation energy is also compatible with that of a condensation reaction controlling the process. The kinetic exponential law found in accordance with eq 3 in the present study is typical of a phase separation mechanism by spinodal decomposition,21 which would involve long-range dynamical forces driven by interfacial energy. However, the lack of clear maxima in SAXS intensity curves with time does not support the definition of a characteristic size accounting for the length scale of the initial separated phases of the spinodal decomposition.21 In addition, eq 3 can be associated with a much more severe growth law than other growth laws described by power laws with time with an exponent typically between 1/3 and 1/2, which are characteristic of diffusion-controlled mechanisms.22 Then the characteristics of the kinetics seem to discard diffusion-controlled mechanisms and are in favor of a complex overall mechanism controlled by both condensation reactions and dynamical forces driven by interfacial energy up to the final structure development of the hybrids. Indeed, the kinetic exponential law of eq 3 in which the transformed quantity x is proportional to exp(kt) revels an autocatalytic component in the process since the rate equation dx/dt is also proportional to x. This could be due to the increase of the chemical quenching caused by the diminution of solubility as the macromolecules grow in solution, often triggering mechanisms of phase separation in which dynamical forces driven by interfacial energy are important.23

ð4Þ

where a is the correlation distance of the structure so it could be assigned to Rg/6 to match to eq 2. The Debye
Bueche form is applied to inhomogeneous solids with a distribution of holes of random shapes and sizes in the solid,24 for which the correlation function in real space r is an exponential γ(r) = exp(
r/a). This characteristic to which the system tends at high stages of aggregation is compatible with a high degree of network rigidity and compaction reached by the macromolecules there. We think that small species of hybrids eventually present in the early sol at pH 2 should be completely hydrolyzed and partially condensed because of the severe acid hydrolysis undergone by the VTES solution at pH 2. Certainly some polycondensation has occurred even in the early sol at pH 2 since we have found there polycondensates with a radius of gyration of about 1.4 nm, as mentioned. Perhaps some random cross-linking could be formed even in the early sol, but we think that the probability of crosslinking should be very low because of the steric effects due to the vinyl group presence, which would favor the linking that would result in a linear chain formation with parallel (or antiparallel) alignment of the vinyl groups. Such a tendency seems to be maintained along the stages of the aggregation process at the basic step. This picture is supported by the fairly well-defined rodlike power law
1 regime found at high q in the sol and along the stages of the aggregation at the basic step (Figure 1). Note that linear chain formation is not the case in the aggregation of the TEOS system, in which branched polycondensates formed from 4-functional monomers were found in the stable hydrolyzed sol at pH 2 and along the aggregation process at the basic step (pH 4.5),18 where fractal structures with dimensionality 2 were found but no rodlike power law
1 regime was observed at high q.18 In the aggregation process of the present study, the number of (very small) primary particles present even in the early sol apparently diminishes as the size of the macromolecules in solution increases, in a mechanism in which the volume fraction of the particles j (and then the mass concentration c) should remain constant. In this mechanism, the integrated intensity over the reciprocal space q, a property known as invariant given by16 Z ∞ Q ¼ q2 IðqÞ dq ¼ 2π2 ðΔFÞ2 jð1
jÞV ð5Þ 0

ΔF being the difference in the electronic density between the particles and the liquid matrix and V the irradiated sample volume, should remain constant. The invariant Q could not be obtained with surety from our experimental data for the lack of a wider measured range at high q, which would allow us to extrapolate the integration of eq 5 up to infinity, typically through Porod’s law.16 It could be argued that Q should be essentially constant in a process of particle growth at the expense of smaller ones. This would be corroborated by the isosbestic point apparently exhibited by the intensity curves at high q in Figure 1. In this sense, the gain in the integration of q2I(q) at low and intermediate q with time would be counterbalanced by the loss in the integration at high q, because of the diminution of I(q) above the isosbestic point. To check the reasonability of such a hypothesis, we carried out the integration of eq 5 over the experimental q range and estimated the integration above the experimental q range by using the intensities Ie(q) extrapolated 10990

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Figure 6. (Left) Linear mass density (as a measure proportional to I(0)/L) and (right) invariant Q (as obtained from extrapolation of the intensities up to qp = 3.5 nm
1) as a function of the relative time scale t/t*. Zero time means sol at pH 2 and 298 K. The horizontal dashed lines were drawn to guide the eyes.

by eq 1, evaluated with the fitted parameters, up to a value qp, and assuming the validity of Porod’s law [Ie(q) µ q
4] above qp, the latter bringing an additional contribution to Q in the range from qp up to infinity equal to qp3Ie(qp). Figure 6 shows the evaluation of Q carried out for qp = 3.5 nm
1 as a function of t/t* at each temperature, suggesting that Q is a fairly constant value along all the process. The value of Q really increases with qp, but it was found that it is still a fairly constant value for a large range of values of qp centered at 3.5 nm
1, which suggests strongly that j (and so the mass concentration c) remains constant along the process. The gradual transition from the flexible network to the compact and rigid behavior of the macromolecule could be alternatively analyzed from the evolution of the mass linear density of the linear chain. Since I(0) µ cM, it follows that I(0)/L is proportional to the linear mass density M/L of the linear chain, if c is a constant value. Figure 6 shows the evolution of the linear mass density M/L, in arbitrary units, on the relative time scale t/t*. It was found that M/L is practically a constant value up to stages close to t/t* = 1, which means that the thickness of the linear chains remains essentially constant during this stage. Afterward, M/L increases gradually with the advance of the process, which means a thickening of the linear chains. The thickening process could be drastic at very advanced stages of aggregation when C f 0 and the branching degree is high. It may be that the persistence length loses its physical meaning and the constraint equation Rg = (Llp/3)1/2 could not be used there for the present persistence chain model to be valid yet.

’ CONCLUSIONS The structure and formation kinetics of organic/silica hybrid species prepared from acid hydrolysis of VTES has been studied in situ by SAXS at different temperatures. The evolution of the SAXS intensity is compatible with the formation of linear chains which grow, coil, and branch to form polymeric macromolecules in solution. Growth of linear chains and coiling dominate the process up to the formation of likely monodisperse Gaussian coils or polydisperse coils of linear chains. Branching increases with the aggregation process to form nonramdomly branched polycondensates in solution, while the persistence length diminishes at advanced stages of aggregation. The increase of the branching

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degree and diminution of the persistence length mean that the macromolecule continuously loses its network flexibility. The linear mass density of the linear chain remains approximately constant up to a few beyond the formation of Gaussian coils or polydisperse coils of linear chains, while the macromolecules maintain certain flexibility. Afterward, there is a thickening process in which the linear mass density increases gradually, increasing the compaction and rigidness of the macromolecule network. The kinetics of the process is accelerated with temperature, but all the curves formed by the time evolution of the structural parameters in all temperatures can correspondingly be matched on a unique curve by using an appropriate time scaling factor. The activation energy of the process was evaluated as ΔE = (21 ( 1) kJ/mol. The characteristics of the kinetics are in favor of a complex overall mechanism controlled by both condensation reactions and dynamical forces driven by interfacial energy up to the final structure development of the hybrids.

’ AUTHOR INFORMATION Corresponding Author

*Phone: +55-19 35269180. Fax: +55-19 35269179. E-mail: vollet@ rc.unesp.br.

’ ACKNOWLEDGMENT This research was partially supported by the LNLS, Fundac-~ao de Amparo a Pesquisa do Estado de S~ao Paulo (FAPESP), and Conselho Nacional de Desenvolvimento Científico e Tecnol ogico (CNPq), Brazil. ’ REFERENCES (1) Deng, T. S.; Zhang, Q. F.; Zhang, J. Y.; Shen, X.; Zhu, K. T.; Wu, J. L. J. Colloid Interface Sci. 2009, 329, 292–299. (2) Chong, A. S. M.; Zhao, X. S. Catal. Today 2004, 93
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