Structural Modifications in Silica Sonogels Prepared with Additions of

Feb 14, 2008 - J. A. Portella,D. A. Donatti,A. Ibañez Ruiz, andD. R. Vollet* ... Unesp Universidade Estadual Paulista, Cx. P. 178, 13500-970 Rio Clar...
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J. Phys. Chem. C 2008, 112, 3552-3557

Structural Modifications in Silica Sonogels Prepared with Additions of Poly(vinyl alcohol) J. A. Portella, D. A. Donatti, A. Iban˜ ez Ruiz, and D. R. Vollet* IGCE, Departamento de Fı´sica, UnespsUniVersidade Estadual Paulista, Cx. P. 178, 13500-970 Rio Claro (SP), Brazil ReceiVed: October 16, 2007; In Final Form: December 3, 2007

Silica wet gels were prepared from acid sonohydrolysis of tetraethoxysilane (TEOS) and additions of poly(vinyl alcohol) (PVA)-water solution. Aerogels were obtained from supercritical CO2 extraction. The samples were studied by thermal gravimetric (TG) analysis, small-angle X-ray scattering (SAXS), and nitrogen adsorption. The structure of wet gels can be described as a mass fractal with dimension D equal to 2.0 on the whole length scale experimentally probed by SAXS, from ∼0.3 to ∼15 nm. Pure and low-PVA-addition wet gels exhibit an upper cutoff accounting for a finite characteristic length ξ of the mass fractal structure. Additions of PVA increase ξ without modifying D, which was attributed to a steric effect of the polymer in the structure. The pore volume fraction of the aerogels diminishes typically about 11% with respect to that of the wet gels, although nitrogen adsorption could be underestimating some porosity. The pore size distribution of the aerogels is shifted toward the mesopore region with the additions of PVA, in a straight relationship with the increase of ξ in the wet gels. The thermal stability of the pore size distribution of the aerogels was studied up to 1000 °C.

Introduction A large variety of silica-based glass and glass ceramics has been obtained by a sol-gel process from silicon alkoxide hydrolysis, particularly of tetraethoxysilane (TEOS).1 Due to the immiscibility of the TEOS-water system, a mutual solvent such as ethanol is usually employed as a homogenizing medium for the hydrolysis in the conventional sol-gel method. Sonochemistry is an alternative method to promote the solventless hydrolysis of the alkoxide by submitting the heterogeneous acidified TEOS-water mixture to ultrasound action.2 The overall process involves hydrolysis and polycondensation reactions up to the formation of a gel. The wet gel structure is frequently described as a continuous solid network embedded in a great volume fraction liquid phase. Supercritical drying (aerogels), freeze drying (cryogels), and evaporation drying (xerogels) are the usual methods in dried gel production. The pore structure and the properties of the final product were found to be strongly dependent on the starting materials and on the conditions of hydrolysis, aging, and drying of the gels,3-5 and, also, on the addition of chemical and structural modifiers. In particular, the incorporation of organic polymers in the silica structure to form organic/inorganic composites6-9 has proportioned the obtaining of materials with interesting structural properties. The pore structure associated with the gels has attracted the attention of several researchers for a wide variety of applications. The porous structure of gels has been considered as proper for preparation of catalyst support materials, complex-center doped materials for metallic ions,10 and materials for encapsulation of organic11 and inorganic compounds,12 with interesting optical and/or electronic properties. Due to its peculiar transport properties, the porous matrix of the silica gel has also been considered for the preparation of controlled-release carrier implantable materials for low weight drugs in biological systems.13 Thus, the characteristics and * Corresponding author: Telephone: +55-19 35262237. Fax: +55-19 35348250. E-mail: [email protected].

control of the porous structure in silica gels are naturally of scientific and technological interest. In this work, we studied the structural modifications caused by additions of poly(vinyl alcohol) (PVA) in TEOS-derived silica sonogels. The volume concentration of silica in the wet sonogels was kept the same for all PVA additions in order to probe more properly the influence of PVA additions on the structure of the gels. The structural modifications were studied by small-angle X-ray scattering (SAXS) and nitrogen adsorption. In addition, the thermal stability of the pore structure was studied up to 1000 °C by nitrogen adsorption. Experimental Section The samples were prepared from the sonohydrolysis of mixtures of 25 mL of TEOS, 8 mL of deionized water, and 5 mL of 0.1 N HCl as a catalyst, so the hydrolysis water/ TEOS molar ratio was ∼6.45 and the hydrolysis pH ∼2.0. Sonohydrolysis was promoted during 10 min under a constant power (∼0.7 W/cm3) of 20 kHz ultrasonic radiation to obtain homogeneous sols. A quantity of Vx mL of a 5.5% by weight water solution of poly(vinyl alcohol) (PVA), whose density was measured in a liquid pycnometer as (1.01 ( 0.01) g/cm3, and (20 - Vx) mL of water were added to the hydrolyzed sols. Vx amounts of 0, 4, 8, 14, and 20 mL yielded the samples P0, P4, P8, P14, and P20, respectively. Sonication was applied for 2 min more for complete the homogenization. The water dilution was desired in order to obtain a set of sols with different PVA concentrations and approximately the same silica concentration (∼1.8 × 10-3 mol of SiO2/cm3). The pH values of the sols were yet increased up to about 4.5 by addition of 3.5 mL of 0.1 N NH4(OH) in order to accelerate the gelation process, before the samples were cast in sealed plastic containers for 30 days at 40 °C for gelation and aging. Monolithic pieces of wet gels were then obtained. The wet gels were studied by bulk density measurements, thermal gravimetric (TG) analysis, and small-angle X-ray scattering (SAXS).

10.1021/jp710051x CCC: $40.75 © 2008 American Chemical Society Published on Web 02/14/2008

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TABLE 1: Measured and Evaluated Structural Properties of the Wet Gels P0 P4 P8 P14 P20

Fwg (g/cm3)

FL (g/cm3)

φL (%)

(∆m/m0)L (%)

(∆m/m0)TG (%)

(∆m/m0)A (%)

(∆m/m0)TGA (%)

1.06 ( 0.02 1.05 ( 0.02 1.03 ( 0.02 1.03 ( 0.02 1.05 ( 0.02

0.911 0.911 0.911 0.910 0.910

88 ( 2 89 ( 2 91 ( 2 91 ( 2 89 ( 2

76 ( 2 77 ( 2 80 ( 2 80 ( 2 77 ( 2

81.2 ( 0.2 80.7 ( 0.2 80.6 ( 0.2 82.5 ( 0.2 80.9 ( 0.2

73 ( 2 75 ( 2 78 ( 2 78 ( 2 75 ( 2

73.8 ( 0.2

For the obtaining of aerogels, the liquid phase of the wet gels was first exchanged by ethanol at room temperature. A share of the polymer in the liquid phase filling the pores of the wet gels was found to be driven out of the gels during the ethanol exchange, since the precipitation of polymeric forms in the leaching ethanol was observed. Then, ethanol was exchanged by liquid CO2 in an autoclave followed by supercritical CO2 extraction. Monolithic 1-cm-diameter, 2-cm-high cylindrically shaped samples of aerogels were obtained after the supercritical CO2 extraction. The aerogels were studied as obtained by nitrogen adsorption and SAXS. For the heat treatment of the aerogels, the samples were held for 5 h at each temperature (up to 1000 °C), so the same sample was used for the subsequent treatment at higher temperature. The SAXS experiments were carried out using synchrotron radiation with a wavelength λ ) 0.1608 nm. The experiments were conducted using the SAXS beamline of the LNLS synchrotron radiation facility, Campinas, Brazil.14 The beam was monochromatized by a silicon monochromator and collimated by a set of slits defining a pinhole geometry. A one-dimensional position sensitive X-ray detector was used to record SAXS intensity 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 get SAXS data from q0 ) 0.068 nm-1 to qm ) 3.3 nm-1 with increments of ∆q ) 2.56 × 10-3 nm-1. The data were corrected by the sample attenuation and the parasitic scattering, and normalized with respect to the beam intensity and the logarithm of the attenuation, which is proportional to the thickness of the sample. Nitrogen adsorption isotherms were obtained at liquid nitrogen temperature using an ASAP 2010 Micromeritics apparatus. The samples were degassed at 120 °C for no less than 24 h before the adsorption tests. The adsorption data were analyzed for the BET specific surface SBET, the total pore volume per mass unit Vp, as the total adsorbed volume of nitrogen at a single point close to the saturation pressure, the pore mean size lBET ) 4Vp/SBET, and the pore size distribution (PSD), as determined by the classical Kelvin equation and the Harkins and Jura model for cylindrical pores.15 Results Wet Gels. Table 1 shows the bulk density of the wet gels, Fwet, as determined by mass and volume measurements. The mean value for Fwet is 1.04 g/cm3 with a small dispersion with the PVA additions. Figure 1 (bottom) shows the mass loss ∆m/ m0 for the wet gels as determined by thermal gravimetric (TG) analysis carried out with a heating rate of 5 °C/min. The TG testing was carried out for the wet gels as obtained, i.e., after 30 days aging in sealed conditions at 40 °C, and after exchanging the liquid phase by pure ethanol. Figure 1 (top) shows the derivative of the TG signal. Practically all the mass-loss curves of both classes of wet gels in Figure 1 could be, respectively, matched approximately onto a unique curve, suggesting that both classes of wet gels have, correspondingly, approximately the same silica content and practically the same liquid-phase density.

74.6 ( 0.2 74.2 ( 0.2 73.4 ( 0.2

Most of the mass loss up to about 250 °C was associated with the evaporation of the liquid phase of the gels. Table 1 shows the mass loss (∆m/m0)TG up to 250 °C for the original nonexchanged wet gels together with (∆m/m0)TGA corresponding to the alcohol-exchanged wet gels. (∆m/m0)TG was about 81 wt % and (∆m/m0)TGA was about 74 wt %, fairly independent of the PVA additions. The lower value for (∆m/m0)TGA is in accordance with the lower density of the liquid phase of the alcohol-exchanged wet gels. The additional mass loss from 250 to 600 °C was found to be between about 1 and 1.5 wt % for pure wet gels and between about 2 and 3 wt % for the wet gels with PVA additions. The maximum weight percentage of polymer in the wet gel, which was used in the case of preparation of the sample P20, was estimated as about only 1.7 wt %. Then, little of the mass loss above 250 °C could be associated with the degraded-polymer oxidation or other residual carbon oxidation in the structure of the gel, after the liquid-phase evaporation, which means that hydrolysis and polycondensation reactions were practically 100% complete. Under the conditions of 100% hydrolysis and polycondensation in sealed containers and neglecting the polymer concentration in the gel liquid phase, we expect the liquid phase of nonexchanged wet gels to be a mixture of ethanol and water in a molar ratio equal to 4:(rw - 2), respectively, where rw is the total water/TEOS molar ratio. Assuming an ideal mixture, the density of the liquid phase FL was estimated and, thus, the volume fraction of the liquid phase φL by the equation φL ) (FS - Fwg)/(FS - FL), where FS is the density of the solid particles (silica), assumed to be 2.2 g/cm3 as frequently quoted for fused silica. The mass fraction (∆m/m0)L of the liquid phase was obtained through (∆m/m0)L ) (FL/Fwg)φL. Table 1 shows the values of FL, φL, and (∆m/m0)L for the nonexchanged wet gels. The evaluated (∆m/m0)L was slightly lower than, but in reasonable agreement with, the experimental (∆m/m0)TG. The bulk density FwgA and the mass fraction (∆m/m0)A of the liquid phase (ethanol) of the alcohol-exchanged wet gels (Table 1) were evaluated in an analogous way to the nonexchanged wet gels, assuming that φL does not change with the alcohol-exchanging process and FA ) 0.790 g/cm3 for the liquid phase (ethanol) of the alcohol-exchanged wet gels. Then, FwgA ) FS - φL(FS - FA) and (∆m/m0)A ) (FA/FwgA)φL. The evaluated (∆m/m0)A values are in reasonable agreement with the corresponding experimental (∆m/m0)TGA values from TG data. Figure 2 shows the SAXS intensity I(q) for the wet gels. The plots in Figure 2 show characteristics of the scattering from a mass fractal system. A mass fractal structure with dimensionality D (a physically acceptable value when 1 < D < 3) can be recognized by a typical power-law decrease on q of the SAXS intensity as16

I(q) ∼ q-D

(1)

in a length scale ξ . q-1 . a, where ξ is the characteristic length of the fractal structure and a is the characteristic length of the primary particles building up the structure. Equation 1 fits well to the SAXS intensity with a para-

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Figure 1. (bottom) Thermal gravimetric (TG) tests carried out under a heating rate of 5 °C/min for the as-obtained and alcohol-exchanged wet gels as a function of additions of PVA. (top) Derivative of the TG signal.

Figure 2. SAXS intensity for wet gels as a function of additions of PVA. The curves are shown once more after shifting vertically by different factors, for the sake of clarity. The linear fittings to the straight portions of the curves are shown. The small circle lines are the fittings of eq 2 to the experimental P0 and P4 data, using a nonlinear-leastsquares iteration routine (Levenberg-Marquardt algorithm).

meter D essentially equal to 2, in practically whole the experimental q-range probed by SAXS (from q0 ) 0.068 nm-1 to qm ) 3.3 nm-1), except for the pure P0 system and for the low-PVA-addition P4 system, for which a crossover in the power law is apparent at low q. Table 2 shows the parameter D obtained from linear fitting in the straight portion of the curves. A crossover in the power-law regime at low q accounts for the finite characteristic length ξ of the mass fractal structure, and a crossover at high q accounts for the finite characteristic length a of the primary particle. No crossover was found at high q (Figure 2), so the characteristic length a of a primary silica particle should be less than about qm-1 ∼ 0.3 nm. The effect of the upper (ξ) and lower (a) cutoffs on the scattering from mass fractal-like structures has been treated by Sinha17 and Teixeira.18 An approximation accounts for the upper cutoff (ξ), which is applicable to low- and intermediary-q regions of the scattering curve from a mass fractal structure built up by very small primary particles, so no crossover in the power-law behavior at high q is observable, has been proposed by Vacher et al.19 That can be cast as

Figure 2 shows the fitting of eq 2 to the experimental data for the samples P0 and P4, using a nonlinear-least-squares fitting routine (Levenberg-Marquardt algorithm) and fixing the parameter D as obtained by linear fitting in the straight portion of the curves. Table 2 shows the parameter ξ obtained from the fitting process. Evidently, eq 2 could not be applied to other samples with high PVA additions since there is no crossover in the power law at low q. For samples with higher PVA additions, the characteristic length ξ would be greater than ∼15 nm, as a limit from the inverse of the experimental q0. Aerogels. Figure 3 shows the SAXS intensity from the aerogels P0, P8, and P20 compared to the corresponding wet gels. The scattering from aerogels is accordingly more intense than that from the wet gels due to the increase in the electronic density contrast resulting from the supercritical extraction of the gel liquid phase. At low- and intermediary-q regions, the curves of the aerogels are fairly parallel to those of the corresponding wet gels, more precisely for the samples with high PVA concentrations. The parameter D was evaluated (Table 2) through eq 1 in the low- and intermediary-q regions for the aerogels with high PVA concentrations. The approach apparently does not apply to the low- and intermediary-q regions for pure P0 and P4 aerogels. The SAXS curves of the aerogels apparently cross over at about qa ∼ ξa-1 to a distinct power law decaying I(q) ∼ q-R in

I(q) ) AΓ(D + 1) sin[(D - 1) arctan(qξ)]/ (1 + q2ξ2)(D-1)/2(D - 1)qξ (2) where Γ(x) is the gamma function and A is a constant for a given D and ξ. TABLE 2: Structural Parameters of the Wet Gels and Aerogels wet gel P0 P4 P8 P14 P20

aerogel

D ((0.02)

ξ (nm)

D ((0.1)

ξa (nm)

R ((0.03)

Dm ((0.02)

Ds ((0.05)

2.02 2.02 1.98 2.01 1.99

8.9 ( 0.2 15 ( 1 >15c >15c >15c

a a 2.0 2.1 2.2

2.3 ( 0.1 2.2 ( 0.1 2.3 ( 0.1 2.1 ( 0.1 1.9 ( 0.1

2.82 2.85 2.86 2.90 2.91

(2.46-2.58)b 2.56 2.57 2.60 2.62

(2.10-2.34)b 2.27 2.28 2.30 2.33

a No clear large-domain power law at low q in the SAXS intensity. b Meso- and micropore regimes. c No crossover at low q in the SAXS intensity to fit eq 2.

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Figure 3. SAXS intensity for samples of aerogel as a function of PVA additions. The curves were shifted vertically by different factors for clarity. The data of the corresponding wet gels were drawn as dotted lines for direct comparison. The straight lines at low q for the samples with high additions of PVA are linear fittings of eq 1. The straight lines at high q (q > ξa-1) for the aerogels are linear fittings of the power law decaying I(q) ∼ q-R, with the exponent R close to 3.

the high-q region, with the exponent R being quite close to 3. This seems the only one which applies to the samples P0 (pure) and P4 (low PVA addition). The values of the parameters ξa and R of the aerogels are shown in Table 2. Figure 4 shows the nitrogen adsorption isotherms for the aerogels. The isotherms are more properly classified as type IV, according to IUPAC classification.20 Table 3 shows the values as determined from nitrogen adsorption for the BET specific surface area (SBET), the total pore volume per mass unit (Vp), the pore mean size (lBET), and also for the particle mean size lS ) 4VS/SBET, as an analogy to the pore mean size so VS ) 1/FS, with FS ) 2.2 g/cm3 as frequently assumed for fused silica. The bulk density F and the pore volume fraction φ of the aerogels (Table 3) were evaluated by 1/F ) (1/FS) + Vp and φ ) (FS - F)/FS, respectively. The specific surface SBET diminishes slightly while Vp and lBET increase more accentually with the addition of PVA. The particle mean size lS increases in accordance with the diminution of the specific surface, since lS ∝ 1/SBET in the case of constant FS. Figure 5 shows the pore size distribution (PSD) of the aerogels. The PSD is shifted toward the macropore region with the additions of PVA. The presence of larger pores in the aerogels was associated with the size of the mass fractal domain at low q in the SAXS data in the original wet gels. Figure 5 also shows the evolution with temperature up to 1000 °C of the PSD in the aerogels. Figure 6 shows the

Figure 4. Nitrogen adsorption isotherms for the aerogels as a function of additions of PVA. The open circles represent the desorption branch.

evolution of the structural parameters of the aerogels as a function of temperature. The mesopore structure is fairly stable up to about 700 °C, with the pore volume being slow and continuously eliminated with temperature. Above about 800 °C, the process of elimination of the porosity is promptly accelerated. Discussion The structure of wet gels can be described as mass fractal with dimension D essentially equal to 2, independent of the additions of PVA in the studied range. The fundamental role of the additions of PVA on the structure is to extend the fractality range toward the low-q region, or to increase the characteristic length ξ of the mass fractal structure, without, however, changing the mass fractal dimension D. The mass fractal dimension D ∼ 2 was attributed to a characteristic of the silica structuring in the sonogels, since D was found to be independent of the additions of PVA. We have found D essentially equal to 2 in studying several high-porosity TEOS-derived wet sonogels.21,22 A mechanism in which the characteristic length ξ is increased with the PVA additions could be associated with steric effects of the polymer in the liquid phase of the wet gels. In the aggregation process to form the gel, the polymer chains lodge preferentially in the external regions between the growing silica clusters, or in the liquid phase in larger pores. The steric effect of the polymer could ensure space enough at high correlation distances to avoid approximation between the aggregating silica particles to allow the formation of more opened silica structures up to a higher

TABLE 3: Characteristics of the Pore Structure of the Aerogels As Determined from Nitrogen Adsorption Data P0 P4 P8 P14 P20

SBET ( m2/g)

Vp (cm3/g)

lBET (nm)

lS (nm)

F (g/cm3)

φ (%)

976 ( 5 923 ( 5 941 ( 4 888 ( 4 804 ( 4

1.39 ( 0.02 1.44 ( 0.02 1.58 ( 0.02 1.64 ( 0.02 1.57 ( 0.03

5.7 ( 0.1 6.2 ( 0.1 6.7 ( 0.1 7.4 ( 0.1 7.8 ( 0.1

1.86 ( 0.05 1.97 ( 0.05 1.93 ( 0.05 2.05 ( 0.05 2.26 ( 0.05

0.54 ( 0.01 0.53 ( 0.01 0.49 ( 0.01 0.48 ( 0.01 0.49 ( 0.01

75 ( 1 76 ( 1 78 ( 1 78 ( 1 78 ( 1

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F(r) ) FS(r/a)D-3

Figure 5. Pore size distribution (PSD) for the aerogels as a function of additions of PVA and temperature of heat treatment.

to grant the mass fractal behavior in all the length scale r between ξ and a. The presence of larger pores in the aerogels with high additions of PVA could be due to the ethanol exchanging process of the liquid phase of the wet gel (a mixture of ethanolwater-polymer), before the autoclave supercritical process. A share of the polymeric material was found to be driven out from the pores of the gels together with water in the leaching ethanol, since a polymeric precipitation in the leaching ethanol during the exchanging process was observed. It could be due to the preferential solvation of the polymer by water molecules.23 Surely a share of the polymeric material remains in the gel structure after the aerogel processing, since the gels prepared with additions of PVA have shown a slightly yellowish color under heat treatment at temperatures above 150 °C. The yellowness was more intense the greater the additions of PVA. Oxidation of residual polymeric material in the structure of the aerogels could account for the slight diminution of the pore mean size lBET and the slight increase of the specific surface SBET at about 400 °C in the samples with high additions of PVA (Figure 6). The typical value for the pore volume fraction φ of the aerogels (Table 3) is about 11% smaller than that of typical φL of the wet gels (Table 1). This suggests that a share of the porosity is eliminated in the overall exchange and supercritical CO2 extraction. However, the porosity could be underestimated in the adsorption method because nitrogen should not necessarily fill all the great pores in the case of aerogels, since most of the solid surface of the aerogel has a positive curvature, disturbing the nitrogen condensation with consequent underestimation of the porosity.24 A structural modification accompanying the autoclave process seems to occur at a high resolution level scale, since the SAXS curves of the aerogels were found to be substantially different from those of the corresponding wet gels at high q. The value of the exponent R, which was found to be close to ∼3, is high enough to be associated exclusively with a mass fractal structure. It could also be associated with a contribution of a rough surface resulting from the overall autoclave process, for which a positive deviation from Porod’s law I(q) ∼ q-4 would be expected.25 A correlated surface/mass fractal,26 with mass fractal dimension Dm and surface fractal dimension Ds, scatters as a power law I(q) ∼ q-R in Porod’s region, so that26

R ) 2Dm - Ds

Figure 6. Evolution of structural parameters of the aerogels as a function of temperature.

characteristic length ξ. The spectacular result here is that the external-PVA-richer-more-opened structure shows the same mass fractal behavior with D ∼ 2 as the internal-purer-silica structure, to allow the mass fractal density Fξ to diminish with the increase of the characteristic length ξ according to the scaling law19

Fξ ) FS(ξ/a)D-3 The local mass fractal density F(r) should scale as3

(3)

(4)

(5)

The mass fractal and the surface fractal characteristics could be separate from independent investigations. We have employed an independent method27 for the generation of a mass fractal structure from the PSD curve. We start from a homogeneous solid with density FS (equal to that of the fused silica) and follow by incorporating to the structure the incremental pore volume per mass unit of silica δVp(ri) to probe the resulting bulk density F(r), assumed as the local density. The process can be written as ri)r

1/F(r) ) 1/FS +

∑ δVp(ri)

(6)

ri)0

Figure 7 shows the function F(r) in a log-log scale with the structure length scale as probed by the pore width 2r. Equation 4 was fitted to the experimental F(r) below about the maximum pore width 2rξ. From the slope D - 3 of the linear fittings, one obtains the values D ) Dm shown in Table 2. For pure P0

Silica Sonogels Prepared with PVA Additions

J. Phys. Chem. C, Vol. 112, No. 10, 2008 3557 Aerogels obtained by exchange and supercritical CO2 extraction exhibited pore size distributions which were shifted toward the mesopore region as the addition of PVA was increased. The larger pore size distribution was associated with the greater characteristic length ξ of the mass fractal structure of the original wet gel. The setting of larger pores in the aerogels could be due to the partial polymer drag together with water by the leaching ethanol in the previous alcohol exchange before the CO2 autoclave process. The pore volume fraction of the aerogels diminishes typically about 11% with respect to that of the wet gels, although nitrogen adsorption could be underestimating the porosity in the aerogels. The mass fractal structure of the original wet gels seems to evolve to a mass/surface fractal structure at a high-resolution level in the aerogels. The mesopore structure of the aerogels is fairly stable up to about 700 °C. A process of pore elimination is promptly accelerated above about 800 °C. Acknowledgment. Research partially supported by LNLS (National Synchrotron Light Laboratory), FAPESP, CAPES, and CNPq, Brazil.

Figure 7. Local bulk density F(r) as evaluated from the PSD of the aerogels. The straight lines are linear fittings of eq 4 to the straight portions of the curves.

sample, there are two linear regimes in the log F(r) vs log 2r plot. Apparently, P0 exhibits a more opened structure in the mesopore region (Dm ∼ 2.46) in comparison to that in the micropore region (Dm ∼ 2.58). Using eq 5, we determine Ds (Table 2) from the measured Dm and R. Ds increases slightly with the additions of PVA, suggesting that the surface roughness increases with the additions of PVA. For pure P0 sample, the surface seems more rough at a level of the micropore region and more smooth at a level of the mesopore region. The lack of a crossover in the plots of Figure 7 in the mesopore region of the aerogels with additions of PVA, which could account for the minor values for D (between 2.0 and 2.2) obtained by the SAXS intensity at low q (Figure 3), could be due to the underestimation of the mesoporosity in the adsorption method, as pointed out earlier.24 A greater incremental pore volume in the mesopore region would give a more accentuated dropping of the function F(r) in the mesopore region of Figure 7, yielding lower values for Dm there, which would be in better agreement with the SAXS curves at low q in Figure 3. Conclusions The structure of silica wet gels prepared from acid sonohydrolysis of TEOS followed by additions of PVA-water solution can be described as a mass fractal with dimension D essentially equal to 2.0, in practically the whole characteristic length scale experimentally probed by SAXS, from ∼0.3 to ∼15 nm. For pure TEOS and low-PVA-addition sonogels, an upper cutoff associated with a finite characteristic length ξ of the mass fractal structure is apparent. The main effect of the addition of PVA on the structure of the wet gels is to increase the characteristic length ξ of the mass fractal structure, without changing the mass fractal dimension D. This result was attributed to steric effects of the polymer in the structure of the gel.

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