Structure of Hydrophobic Ambient-Pressure-Dried Aerogels Prepared

Jan 15, 2014 - Silica wet gels with the same silica content were prepared by the sonohydrolysis of tetraethoxysilane (TEOS) with additions of dimethyl...
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Structure of Hydrophobic Ambient-Pressure-Dried Aerogels Prepared by Sonohydrolysis of Tetraethoxysilane with Additions of N,N‑Dimethylformamide William Chiappim, Jr., Carlos M. Awano, Dario A. Donatti, Fabio S. de Vicente, and Dimas R. Vollet* Departamento de Física, IGCE, Universidade Estadual Paulista (UNESP), Caixa Postal 178, 13500-970 Rio Claro (SP), Brazil ABSTRACT: Silica wet gels with the same silica content were prepared by the sonohydrolysis of tetraethoxysilane (TEOS) with additions of dimethylformamide (DMF). DMF plays a role in the overall hydrolysis/gelification/aging step of the sol−gel process, providing more consolidated wet gels with larger syneresis degrees and densities. The structure of the as-obtained wet gels can be interpreted as being built up of mass-fractal domains with fractal dimension D = 2.2 and radius of gyration decreasing from about 14 to 12 nm with increasing quantity of DMF. Monolithic hydrophobic aerogels were prepared after washing of the wet gels with isopropyl alcohol (IPA), silylation with trimethylchrorosilane (TMCS), and ambient-pressure drying (APD). The specific surface area of the APD aerogels was found to be about 900 m2/g, and the mean silica particle size was about 2.0 nm, approximately independent of the DMF quantity, whereas the porosity decreased slightly with increasing amount of DMF, fairly accompanying the behavior of the radius of gyration of the precursor wet gels. The mass-fractal characteristics were preserved in the APD aerogels, but the radius of gyration of the mass-fractal domains was reduced to values between 2.8 to 4.0 nm, with the values decreasing slightly with the DMF quantity, and the fractal domains developed a surface−mass-fractal structure with the overall washing/silylation/APD treatment. The structural characteristics of the APD aerogels as determined by SAXS were found to be in notable agreement with those inferred from nitrogen adsorption.

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INTRODUCTION The alkoxide sol−gel process has been largely used for the preparation of silica-based products with interesting optical, electronic, and structural properties.1 Alkoxide sol−gel-derived silica gels are considered to be appropriate matrixes for the preparation of doped materials with complex centers of metallic ions,2,3 materials for the encapsulation of organic4−6 and inorganic7,8 compounds, implantable materials for controlledrelease drug carriers,9,10 and substitute materials for membrane process in fuel cells.11 Wet gels are often described as a continuous solid network embedded in a large-volume liquid phase. The structure of the final dried product depends strongly on the conditions of drying. Supercritical drying (SCD) often yields monolithic aerogels with structures not far from those of the original wet gels. Conventional ambient-pressure drying (APD) yields xerogels with structures that are often very different from those of the original wet gels, because of the collapse of the silica network as a result of compressive stress imposed by the liquid surface tension upon evaporation.12,13 Fracture and crack formation caused by gradient stresses appearing on APD seriously limit the conversion of the wet gel to monolithic xerogel.12−14 The use of drying control chemical additives (DCCA) has sometimes facilitated the production of monolithic APD xerogels.1,14−21 N,N-Dimethylformamide (DMF) has been used as a basic DCCA structure modifier © 2014 American Chemical Society

that is able to successfully produce gel monoliths without cracks.22−27 The use of DMF was found to be effective in the sol−gel synthesis of crack-free APD silica xerogels25,26 and of improved-quality SCD silica aerogels.24 The low surface tension of DMF was identified as one of the effects protecting the drying gel from crack generation because the DMF vaporization together with the liquid phase during the drying process weakens the capillary force exerted on the silica network structure.27 However, DMF seems not only to work as a DCCA but also to work equally well as a catalyst, modifying the hydrolysis rate and increasing the polymerization rate,24 ultimately affecting the structure and mechanical properties of the gels.15,24−26 SCD aerogels might be limited for application in some areas because of the brittleness of the very porous silica network structure even in low-humidity environments. To diversify the applicability of aerogels in some areas, ambient-pressure drying (APD) after silylation of the silica surface has been employed to obtain hydrophobic aerogels with good monolithicity and transparency and low density.28,29 Trimethylchlorosilane (TMCS) is a typical chemical silylating agent that is often used for this purpose. Silylation replaces −H from hydrophilic Received: October 1, 2013 Revised: November 26, 2013 Published: January 15, 2014 1151

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temperature and pressure for about 40 days. The procedure yielded perfect monoliths of hydrophobic APD silica aerogels, of which a typical example is shown in Figure 1. As most of the characteristics of

Si−OH groups on the silica surface for stable hydrophobic −SiR3 groups. Silylation helps to prevent the silica network from collapsing upon drying,30 and the hydrophobic surface prevents the deterioration of the structure of the aerogel in humid environments.31 In a previous work,32 we studied the structural characteristics of SCD aerogels prepared by the sonohydrolysis of TEOS with additions of DMF. We found that the addition of DMF during the sonohydrolysis step of the process yielded SCD aerogels with slightly minor porosity and mean pore size, but with apparently much improved properties for the silica network with respect to elasticity and shock resistance. This finding corroborates the idea that DMF should play a more fundamental role in the silica network structure of the aerogels, at least when ultrasound is employed in the hydrolysis step of the process. It has been pointed that the application of ultrasound during the hydrolysis step of the sol−gel process produces silica-based materials with higher densities and more homogeneous pore structures than can be obtained by conventional hydrolysis.33−38 In this work, we have synthetized silica wet gels from HClcatalyzed sonohydrolysis of TEOS with additions of DMF and silylated the wet gels with TMCS to produce hydrophobic silica aerogels after ambient-pressure drying (APD). To properly compare the structures of the samples prepared with different DMF/TEOS proportions, the same water/TEOS molar ratio and HCl concentration were used in the hydrolysis step of the process, and the thus-hydrolyzed sols were properly diluted in water to yield sols with the same silica concentration. The hydrophobic APD silica aerogels obtained after silylation of the wet gels with TMCS were studied by small-angle X-ray scattering (SAXS) and nitrogen adsorption. This study has scientific and technological interest because of the importance of the system for applications in several areas and because it demonstrates that complete structural characterization can be carried out on such a complex and ill-defined geometry associated with the gel structures. This work brings additional physical insights by illustrating how completely different techniques can notably describe the same structural picture for hydrophobic APD aerogels.

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Figure 1. About 1.5-cm-diameter hydrophobic APD aerogel prepared with a DMF/TEOS molar ratio of R = 4.0.

the wet gels were apparently preserved in the APD gels (as shown in Figure 1), which indicates extraction of the solvent without apparent substantial pore collapse, the obtained material can be called an aerogel.39 The APD silica aerogels were degassed in a vacuum at 120 °C for 24 h before being analyzed by small-angle X-ray scattering (SAXS) and nitrogen adsorption. 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) in Campinas, Brazil. The beam was monochromatized with a silicon monochromator and collimated with a set of slits defining a pinhole geometry. A twodimensional position-sensitive X-ray detector was used to obtain the isotropic SAXS intensity I(q) 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 SAXS data to be obtained from q0 = 0.0693 nm−1 to qm = 1.6793 nm−1 with a resolution of about 4 × 10−4 nm−1. The data were corrected for sample attenuation and parasitic scattering and normalized with respect to the beam intensity. Nitrogen adsorption isotherms were obtained at liquid nitrogen temperature (77 K) using an ASAP 2010 Micromeritics apparatus. The data were analyzed for the Brunauer−Emmett−Teller (BET) specific surface area (SBET), total pore volume (Vp), and pore size distribution (PSD). The PSD was determined from the adsorption branch of the isotherm using Micromeritics software (DFT Plus) with a set of kernel functions compiled in numeric form on the basis of the classical Kelvin equation and the Harkins and Jura isotherm for the adsorbed layer thickness.40 The software works by determining, through a leastsquares routine, the PSD curve that most nearly describes the experimental adsorption isotherm. One of the outputs of the software is the incremental pore volume dVp, in units of cm3/g, as a function of the pore diameter, which was used in the present work for further analysis.

EXPERIMENTAL SECTION

Silica wet gels were prepared by the sonohydrolysis of mixtures of tetraethoxysilane (TEOS), distilled and dionized water, HCl as a catalyst, and N,N-dimethylformamide (DMF). The hydrolysis was promoted for 10 min by applying ultrasonic radiation (∼0.7 W/cm3) in a fixed volume (∼40 cm3) of the reactant mixture. The hydrolysis step of the process was carried out while keeping the water/TEOS molar ratio equal to 6.4 and the concentration of HCl equal to 1.3 × 10−5 mol/cm3 but varying the DMF/TEOS molar ratio (R) from 0 to 4. The hydrolyzed sols were diluted in adequate water quantities and homogenized by ultrasound for 2 min more to yield final sols with the same silica concentration (∼1.5 × 10−3 equiv of Si per cm3). A quantity of NH4OH equivalent to about 70% of the HCl content was added to the sols to accelerate the gelation process. The sols were finally cast in sealed plastic containers and kept at 40 °C for gelation and aging for 30 days to yield monolithic wet gels. The aged wet gels were characterized by apparent density measurements, gravimetric thermal analysis, and small-angle X-ray scattering. The wet gels were thoroughly washed in isopropyl alcohol before being left immersed for a week in a 10 vol % solution of trimethylchrorosilane (TMCS) in isopropyl alcohol (with the solution renewed after each 24 h) to promote silylation of the silica surface of the gels. After being thoroughly washed again in isopropyl alcohol to remove the excess TMCS, the silylated gels were left to dry at ambient

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RESULTS AND DISCUSSION Wet Gels. Figure 2 (left) shows the experimental density ρgel for the as-obtained wet gels as a function of the DMF/ TEOS molar ratio (R) as determined from mass and volume measurements. Also shown, just for discussion, is the evaluated density (ρL) of an ideal liquid mixture of (r − 2)H2O + 4EtOH + RDMF (where r is the water/TEOS molar ratio). Such a composition (except for the density) would be that of a liquid phase yielded in a sol−gel process in which the reactions of hydrolysis and polycondensation had occurred completely, without any syneresis; that is the final product would be just a gel composed by a solid phase (SiO2) and a liquid phase with the composition (r − 2)H2O + 4EtOH + RDMF. Figure 2 (right) shows the results of thermogravimetry (TG) tests 1152

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Figure 3. SAXS patterns of the gels prepared with additions of DMF. (Left) Wet gels: Solid lines (red) are fittings of the Beaucage approach (eq 1) to the experimental data (points). (Right) Hydrophobic APD aerogels: Solid lines (red) are fittings of the Beaucage approach with the additional surface−mass-fractal term Asmq−3 (according to eq 2) to the experimental data (points). The curves for both sets were shifted vertically for the sake of clarity.

Figure 2. Properties of the as-obtained wet gels prepared with additions of DMF (R = DMF/TEOS molar ratio). (Left) ρgel, experimental wet gel density; ρL, evaluated density of an ideal liquid mixture with a composition of (r − 2)H2O + 4EtOH + RDMF (r = water/TEOS molar ratio); −(Δm/m0)400, weight loss at 400 °C as measured by TG. (Right) TG of the wet gels carried out at a heating rate of 10 °C/min.

apparent in the curves of Figure 3 (left) accounting for a finite size of the primary particle building up the mass-fractal structure.41 The minimum length scale r0 that could be probed by SAXS at high q in our experimental setup was r0 > qm−1 ≈ 0.6 nm. The maximum value of qm = 1.7 nm−1 corresponds to a Bragg distance 2π/qm of about 3.7 nm. 2π/qm is often assumed to be the maximum particle diameter that can be experimentally probed by SAXS.42 The scattering from such a mass-fractal structure of the asobtained wet gels in Figure 3 (left) was consider in terms of an approach proposed by Beaucage,43 which can be cast as

carried out on the as-obtained wet gels at a heating rate of 10 °C/min. The density ρgel increased slightly with increasing DMF proportion to reach a maximum value at about R = 2.5, from which it diminishesd slightly up to R = 4.0. The maximum found in the density of the wet gels can be explained in terms of two competing effects: (i) the density of the wet gels increases with the syneresis phenomenon, often accompanying the aging of the gels, which would be favored by DMF additions because of the roles that DMF plays in the hydrolysis and polycondensations reactions,17,24 and (ii) the density of the wet gels diminishes because the density of the remnant liquid phase decreases with increasing the DMF proportion [see the estimated densities ρL under the conditions stated in Figure 2 (left)]. The density of the liquid phase decreases not only with increasing addition of DMF in the hydrolysis step but surely also because, in the syneresis phenomenon, the remnant liquid phase becomes DMF-enriched, as suggested by the TG tests [Figure 2 (right)]. In the TG tests, it was found that DMF seemed to be more difficult to release from the silica network because larger fractions of the liquid phase were retained to higher temperatures (up to ∼300 °C) as the addition of DMF increased [Figure 2 (right)]. The total weight loss [(Δm/ m0)400] up to 400 °C in the TG tests decreased slightly with increasing DMF quantity, as can be seen in Figure 2 (left), corroborating the idea of DMF enrichment of the remnant liquid phase after syneresis. This set of results is in accordance with the maximum found in the density of the as-obtained wet gels. Figure 3 (left) shows the SAXS intensities of the as-obtained wet gels prepared with different DMF/TEOS proportions. The curves can be described as the scattering from a mass-fractal structure because the intensity at intermediate and high q values obeys a power law in q of the form I(q) ∝ q−D, where D is the mass-fractal dimension, a physically acceptable value for 1 < D < 3, and presents a low-q crossover accounting for the finite size of the mass-fractal domain,41 which can be described by a generalized radius of gyration Rg. No crossover at high q is

I(q) = G exp(−R g 2q2 /3) + B{(1/q)[erf(qR g /61/2)]3 }D (1)

where G and B are prefactors so that B/G = DΓ(D/2)/RgD, where Γ(D/2) is the gamma function of the argument D/2. Although the prefactor B is constrained by B = DΓ(D/2)G/RgD, it is desirable to keep it as an independent parameter in eq 1 to avoid inherent difficulties in precisely normalizing the intensity from samples with different attenuations and eventually different numbers of scattering centers in the irradiated volume, just by working with the B/G ratio, as we will show. Figure 3 (left) shows the good fitting of eq 1 to the experimental I(q) data of the wet gels. Table 1 reports the values of the fitted parameters Rg, D, and B/G of the wet gels. The radius of gyration Rg of the mass-fractal domains was found to decrease with increasing DMF/TEOS molar ratio, whereas the mass-fractal dimension D was found to be essentially Table 1. SAXS Mass-Fractal Properties of the Wet Gels

1153

R

Rg (nm)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

13.8 14.2 13.3 13.7 13.1 12.1 12.5 12.0 11.7

(3) (3) (3) (3) (3) (3) (3) (3) (3)

D 2.2 2.1 2.2 2.1 2.2 2.2 2.2 2.2 2.2

(1) (1) (1) (1) (1) (1) (1) (1) (1)

B/G (10−3 nm−D) 5.7 6.2 6.9 6.5 7.0 8.0 7.4 8.4 8.5

(4) (4) (4) (4) (5) (5) (5) (6) (6)

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constant at approximately 2.2. The diminution of Rg might mean the development of a more consolidated structure upon aging of the gels, although the internal structure of the massfractal domains keeps the same fractal dimension as the DMF/ TEOS proportion is changed. The evolution of B/G is discussed in another section in connection with the results for the APD aerogels. Hydrophobic APD Aerogels: SAXS. Figure 3 (right) shows the SAXS intensity I(q) of the hydrophobic silylated APD aerogels prepared with different DMF/TEOS proportions in the hydrolysis/gelification/aging steps of the process. The curves in Figure 3 (right) have characteristics that can essentially be described by the same mass-fractal model as used for the wet gels (Figure 3, left), although great structural modifications can readily be observed: (i) The power law I(q) ∝ q−D becomes restricted to only the high-q region, even though the mass-fractal dimension apparently maintains approximately the same value (D ≈ 2.2); (ii) the low-q crossover from the power law I(q) ∝ q−D shifts from a lower-q to an intermediate-q region; and (iii) an additional contribution to the intensity is apparent at very low q. Accordingly, the intensity at intermediate and high q of the APD aerogels was described in terms of the same mass-fractal structure approach as used for the wet gels and given by eq 1. Although the power law I(q) ∝ q−D is restricted to a small highq range, so it would be questionable to extend the validity of the fractal concept to the aerogels,44 there are two reasons that justify this approach: (i) The power law I(q) ∝ q−D seems to extend beyond the maximum measured qm value with the same value for the exponent D as found in the wet gels, which means a similar structure at high resolution in both kind of gels. (ii) The benefits in describing power-law objects as fractal, even in a limited range, outweigh the issue of perhaps applying an erroneous fractal label, mainly because of the fact that the power law condenses the description of an often-complex geometry and provides a simple model and appropriate language and symbolism to describe ill-defined geometries, even though it does not imply fractality at all.44 The additional contribution at very low q was considered in terms of a surface−mass-fractal scattering45,46 that would result from the development of a surface fractal evolving the massfractal domains, probably originating from the processes of silylation and APD of the aerogels. A good schematic illustration of a mass fractal bounded by a surface fractal is presented in the work by Wong and Cao.45 It has been shown45,46 that, for values of q sufficiently greater than the reciprocal of the characteristic cutoff size of the surface fractal scaling, the intensity is a power law in q of the form I(q) ∝ q−(3+D−Ds), where D and Ds are the correlated mass-fractal and surface-fractal dimensions, respectively. Because our SAXS data did not explore the low-q region sufficiently to precisely identify a surface−mass-fractal scaling, we would have no precision in determining the exponent −(3 + D − Ds) and then Ds. However, D and Ds are often of the same order of magnitude, so we expect the exponent −(3 + D − Ds) to be quite close to −3.46 Therefore, to minimize the parameters to be fitted, the low-q contribution associated with the surface−mass-fractal scaling was simply approximated as a power law in q of the form Ism(q) = Asmq−3, where Asm is a constant. Thus, the overall data for the APD aerogels were fitted by the equation

I(q) = A sm q−3 + G exp( −R g 2q2 /3) + B{(1/q)[erf(qR g /61/2)]3 }D

(2)

The fitting procedure was carried out by fixing the massfractal dimension D equal to that of the wet gels (D = 2.2), to minimize the parameters to be fitted even more, and proceeding with the determinations of the radius of gyration Rg of the mass-fractal domains and of the prefactors G, B, and Asm. Figure 3 (right) shows the good fitting of eq 2 to the experimental data for the hydrophobic APD aerogels. Table 2 lists the results for the fitted parameters Rg, B/G, and Asm/G. The Asm/G prefactor ratio was found to be about 10−4 nm−3. Table 2. SAXS Structural Parameters of the Hydrophobic APD Aerogels Evaluated Using the Approach Given by Eq 2 with D = 2.2 R

Rg (nm)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

3.05 4.02 3.71 3.41 3.72 3.25 3.30 3.26 2.85

B/G (10−1 nm−D)

(4) (5) (5) (4) (5) (4) (4) (4) (3)

1.9 1.1 1.3 1.6 1.4 1.8 1.6 1.5 2.1

(3) (2) (2) (2) (2) (3) (2) (2) (3)

Asm/G (10−4 nm−3) 7 5 3 3 3 5 5 2 5

(2) (2) (1) (1) (1) (2) (2) (1) (2)

The values of the radius of gyration Rg of the mass-fractal domains of the hydrophobic APD aerogels (Table 2) were typically found to range between 3 and 4 nm, generally decreasing with increasing DMF quantity. These typical values are much smaller than those obtained for the wet gels (between 12 and 14 nm, Table 2), although the mass-fractal dimension seemed to be essentially the same (D ≈ 2.2). These results suggest the profound modifications that the thorough washing, silylation, and ambient-pressure drying processes can have on the gels. To diminish Rg without changing D, the mass-fractal domains should be modified/destroyed mainly on their external shell layers, where the local mass density is smaller. The radial mass density ρ(r) of a fractal object decreases with r as47

ρ (r ) ∝ r D − 3

(3)

because the mass m(r) inside a sphere of radius r of a fractal object scales as m(r) ∝ rD.41 Then, the radial mass density decreases rapidly with r in the mass-fractal domains, which would facilitate the modification/destruction of the more external shell layers with the mentioned treatments. However, the decrease of Rg was not the only modification affecting the external shell layers of the hydrophobic APD aerogels; there was also found a qualitative modification in producing the surface fractal (as inferred from the additional contribution of Asmq−3 at low q), equally affecting the external shell layers of the hydrophobic APD aerogels. The typical B/G ratio for the hydrophobic APD aerogels (Table 2) was found to be about 102 times the typical value for the wet gels (Table 2). This result is in agreement with the meaning of the B/G ratio for a mass-fractal object, which can be cast as43 B /G = D Γ(D/2)R g −D 1154

(4)

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analogy with the mean pore size lp through the relation ls = 4(1/ρs)/SBET, where ρs is the particle density (assumed to be that of fused silica, 2.2 g/cm3) so 1/ρs represents the silica specific volume. The density (ρ) and porosity (ϕ) of the aerogels were estimated (Table 3) by the equations (1/ρ) = (1/ρs) + Vp and ϕ = Vp/[Vp + (1/ρs)]. The measured SBET values and the estimated ls parameters in Table 3 were found to be very similar for all of the hydrophobic APD aerogels, independent of the DMF quantity used in the earlier hydrolysis/aging step. This means that the primary particle building up the (fractal) structure of the aerogels is essentially the same, independent of the DMF additions and of the subsequent washing/silylation/APD process. The typical value for the specific surface area (∼900 m2/g) found for hydrophobic APD aerogels in this work is only about 10% smaller than the typical value found in supercritical-dried aerogels also prepared with additions of DMF.32 The measured Vp and lp (and correlated ϕ) parameters in Table 3 were found to exhibit a slight general tendency to decrease with increasing DMF quantity. This result is in agreement with the syneresis process observed upon aging of the wet gels responsible for the increase in the density of the wet gels upon aging (Figure 2, left). The values of Vp and lp (and ϕ) in this set of APD aerogels were found to be somewhat smaller than those typically found in supercritical-dried aerogels also prepared with additions of DMF.32 This suggests that the overall washing/ silylation/APD process has an additional effect on the porosity and pore size distribution with respect to the supercritical drying process. Figure 5 (right) shows the pore size distribution as determined from the nitrogen adsorption isotherms. The pore size distribution curves exhibit a moderate plateau approximately between pore diameters of about 1.4−8 nm, which was found to be very similar for all of the hydrophobic APD aerogels but exhibited a slight general tendency to shift toward smaller pores as the DMF quantity increased. The characteristics of the pore size distribution curves of the present APD aerogels are rather different from those of the supercritical-dried aerogels also prepared with DMF additions,32 although both sets of aerogels exhibit the same general tendency to shift toward smaller pores as DMF increases. However, the pore size distribution curves of the supercriticaldried aerogels were all found to shift to larger pores (which means larger Vp and lp and smaller ρ values), and the supercritical-dried aerogels presented a considerable fraction of micropores,32 which was definitely not found in the present hydrophobic APD aerogels. SAXS and Nitrogen Adsorption Data Correlation. As mentioned, no crossover at high q is apparent in the SAXS curves of Figure 2 (for either the APD aerogels or the wet gels), accounting for a finite size of the primary particle building up the mass-fractal structure. The minimum length scale r0 that could be probed by SAXS at high q in our experimental setup was r0 > qm−1 ≈ 0.6 nm, which corresponds to a Bragg distance of about 3.7 nm, a criterion often adopted as a conservative position in small-angle literature42 to define the maximum particle diameter that can be experimentally probed by SAXS. The mean particle size ls inferred from nitrogen adsorption was found to be about 2.0 nm (Table 3). Thus, direct determination from SAXS of the specific surface area of the APD aerogels through a crossover to Porod’s law at high q, for instance (which means resolving the primary particle size), is not possible.

If D is a constant, as was found for both the wet gels and the APD aerogels, this would give simply B/G ∝ Rg−D. Then, the diminution of Rg by a factor of F in the hydrophobic APD aerogels with respect to the wet gels would lead to an increase by a factor FD in the B/G ratio. Figure 4 shows a plot of B/G versus Rg and the good correlation found by using eq 2, and indirectly eq 4, in describing the structures of both the wet gels and the APD aerogels.

Figure 4. Wet gels and hydrophobic APD aerogels were found to be well correlated by the same mass-fractal scaling properties.

Hydrophobic APD Aerogels: Nitrogen Adsorption. Figure 5 (left) shows the nitrogen adsorption isotherms

Figure 5. (Left) Isotherms of nitrogen adsorption (solid symbols) and desorption (open symbols) of the hydrophobic APD aerogels. For the sake of clarity, the isotherms were shifted by 100 cm3/g with respect to each other. (Right) Pore size distribution of the APD aerogels as obtained from the nitrogen adsorption isotherms.

obtained for the hydrophobic APD aerogels prepared with additions of DMF. The isotherms are more properly described as those of type IV in the general IUPAC classification, accounting for a mesoporous structure.48 Table 3 reports the values of the BET specific surface area (SBET), total pore volume per unit mass (Vp), and mean pore size (lp = 4Vp/SBET) obtained from the nitrogen adsorption isotherms of the hydrophobic APD aerogels. V p was determined as the volume of nitrogen condensed at a point close to the saturation pressure of liquid nitrogen (p/p0 ≈ 1). The mean particle size (ls) was estimated (Table 3) in an 1155

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Table 3. Structural Properties of the APD Aerogels as Determined by Nitrogen Adsorption SBET (m2/g)

R 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

878 939 927 938 939 894 930 908 935

Vp (cm3/g)

(8) (8) (8) (8) (8) (8) (8) (8) (8)

0.66 0.81 0.74 0.72 0.75 0.64 0.69 0.64 0.65

lp (nm)

ls (nm)

3.0 3.5 3.2 3.1 3.2 2.9 3.0 2.8 2.8

2.1 1.9 2.0 1.9 1.9 2.0 2.0 2.0 2.0

(1) (1) (1) (1) (1) (1) (1) (1) (1)

(1) (1) (1) (1) (1) (1) (1) (1) (1)

I(q) = A sm q

2

2 2

+ G /(1 + q aDAB )

(1) (1) (1) (1) (1) (1) (1) (1) (1)

0.89 0.79 0.84 0.85 0.83 0.92 0.88 0.92 0.91

ϕ

(1) (1) (1) (1) (1) (1) (1) (1) (1)

0.60 0.64 0.62 0.61 0.62 0.58 0.60 0.58 0.59

(1) (1) (1) (1) (1) (1) (1) (1) (1)

Thus, the determination of aDAB at low and intermediate q is sufficient to check the specific surface area (SDAB) of the random distribution hypothesis, just by using the equation49

However, we wondered whether it might be possible to approximate the mass-fractal approach described by eq 1 in the whole q-range probed by SAXS by a more fundamental approach able to describe the low-q and most of the intermediate-q SAXS data and that could be useful to estimate at least a share of the specific surface area. We considered that the mass-fractal structure could be, in large part, wellapproximated by a random distribution of holes and solid, according to the Debye−Anderson−Brumberger (DAB) model,49 for which the correlation function g(r) is an exponential of the form g(r) = exp(−r/aDAB), where aDAB is the DAB correlation distance of the structure. The scattering from a DAB model is given by IDAB(q) = G/(1 + q2aDAB2)2, where G has the same meaning as in the Guinier term G exp(−Rg2q2/3) in eq 1. It is easy to show (by expanding both functions for q → 0) that aDAB = Rg/61/2. The scattering from the hydrophobic APD aerogels was then considered in terms of the DAB approach together with the mentioned low-q surface− mass-fractal Asmq−3 contribution as −3

ρ (g/cm3)

SDAB = (1/ρ)4ϕ(1 − ϕ)/aDAB

(6)

In addition, the mean pore size lpDAB and the mean particle size lsDAB of the random distribution system can be obtained through the relations49 lpDAB = aDAB /(1 − ϕ)

and

lsDAB = aDAB /ϕ

(7)

Table 4 lists the structural parameters of the hydrophobic APD aerogels as evaluated from the DAB approach just by Table 4. SAXS Structural Parameters of the Hydrophobic APD Aerogels as Evaluated from the DAB Approach Using the Fitted Parameters in Table 2 and Setting aDAB = Rg/61/2 R 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

(5)

Figure 6 shows eq 5 plotted using the same parameters G, aDAB = Rg/61/2, and Asm as fitted earlier (Table 3) for the APD

aDAB (nm) 1.25 1.64 1.51 1.39 1.52 1.33 1.35 1.33 1.16

(1) (2) (2) (1) (2) (1) (1) (1) (1)

SDAB (m2/g) 866 711 741 804 748 798 810 796 914

(9) (8) (8) (9) (8) (9) (9) (9) (9)

lpDAB (nm) 3.1 4.6 4.0 3.6 4.0 3.2 3.4 3.2 2.8

(1) (1) (1) (1) (1) (1) (1) (1) (1)

lsDAB (nm) 2.1 2.6 2.4 2.3 2.4 2.3 2.2 2.3 2.0

(1) (1) (1) (1) (1) (1) (1) (1) (1)

setting aDAB = Rg/61/2. The values of the specific surface area SDAB of the APD aerogels (Table 4) obtained from SAXS were found to be in reasonable agreement with the values of SBET (Table 3) obtained from nitrogen adsorption, with the values of SDAB typically only about 10% smaller than those of SBET. The somewhat smaller values found for SDAB with respect to SBET can be explained because nitrogen adsorption records the more internal share of the porosity belonging to the mass-fractal structure (associated with the high-q scattering), for which the random distribution (DAB model) left to be applied. The values for lpDAB and lsDAB (Table 4) were accordingly also found to be in reasonable agreement with the lp and ls (Table 3), naturally taking into account the somewhat smaller values found for SDAB. Finally, as the mass-fractal structure measured by SAXS for the APD aerogels could be approximated at low and intermediate q to obtain the specific surface area (and then lpDAB and lsDAB), we wondered whether the pore size distribution as measured from nitrogen adsorption could be approximated to obtain the mass-fractal structure at high q (correspondingly in the small-pore region). We considered an approach50 to generate a mass-fractal structure using a

Figure 6. Plot showing that the DAB approach is a good approximation for the mass-fractal structure (just by setting aDAB = Rg/61/2) in the low- and intermediate-q regions. This result applies to all of the other APD aerogels.

aerogel with R = 2.5. The plots for other samples of APD aerogels were very similar, showing that the approximation through eq 5 is very satisfactory up to about q ≈ 1 nm−1, when the mass-fractal scattering seems to surpass that from the random distribution hypothesis (DAB model). Although the DAB model exhibits only an asymptotic transition to Porod’s law [I(q → ∞) ∝ q−4], its practical usefulness is that just one parameter (aDAB) is necessary to describe the whole scattering curve (from q = 0 to q → ∞). 1156

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geometries, even though it applies only to a limited range of the length scale and does not imply fractality at all.44

sequence of approximations, starting from a homogeneous solid with the density of fused silica (ρs = 2.2 g/cm3) and probing the resulting bulk density ρ(r) that results as each incremental pore volume per unit mass dVp(r) is gradually incorporated into the structure. The process can be cast as

■

CONCLUSIONS Hydrophobic silica aerogels were successfully prepared by the sonohydrolysis of tetraethoxysilane (TEOS) with additions of dimethylformamide (DMF), after washing, silylation, and ambient-pressure drying (APD) of the wet gels. DMF was found to play a role in the hydrolysis and polycondensation reactions during the hydrolysis/gelification/ aging steps of the process, apparently providing more consolidated wet gels with larger syneresis degrees and densities. The structure of the as-obtained wet gels can be described as a mass-fractal structure built up by fractal domains with fractal dimension D = 2.2 and radius of gyration fairly decreasing in the range between 14 and 12 nm with increasing DMF quantity. Washing with isopropyl alcohol and silylation with trimethylchlorosilane of the wet gels produced monolithic hydrophobic aerogels after ambient-pressure drying (APD). The specific surface area of the APD aerogels was found to be about 900 m2/g, and the mean silica particle size was about 2.0 nm, approximately independent of the DMF quantity, whereas the mean pore size was found to decrease in the range between 3.5 and 2.8 nm with increasing DMF quantity. The mass-fractal domains originally present in the wet gels were preserved in the structure of the hydrophobic APD aerogels, but their radii of gyration were reduced to values between 2.8 and 4.0 nm, with the values decreasing slightly with DMF additions, and the fractal domains developed a surface− mass-fractal structure with the overall washing/silylation/APD treatment. The general structural characteristics of the APD aerogels as determined by SAXS are in notable agreement with those inferred from nitrogen adsorption.

r

1/ρ(r ) = (1/ρs ) +

∑ dVp(r) 0

(8)

The density ρ(r) was evaluated through eq 8 for the APD aerogels from the incremental pore volume per unit mass (Figure 5, right) as determined from nitrogen adsorption, by using the pore diameter d as a gauge length to probe the radial distance r of the supposed fractal structure. Naturally, eq 8 tends to the value of the density ρ of the aerogels (Table 3) as r → ∞. Assigning ρ(r) as evaluated from eq 8 to the local density, eq 3 should hold in the case of the pore structure able to build the mass-fractal structure, or ρ(r) ∝ rD−3. Figure 7 shows a plot of the experimental ρ(r) versus r on a log−log scale for all of the APD aerogels. The graphs of all

■

AUTHOR INFORMATION

Corresponding Author

Figure 7. Mass-fractal properties of the APD aerogels from the pore size distribution as determined by nitrogen adsorption. For the sake of clarity, the curves were multiplied by the following factors: R = 0 (1.00), R = 0.5 (1.25), R = 1.0 (1.50), R = 1.5 (1.75), R = 2.0 (2.00), R = 2.5 (2.35), R = 3.0 (2.65), R = 3.5 (3.00), and R = 4.0 (3.40). All of the oblique lines were drawn with the same slope equal to −(3 − D) = −0.8, which gives D = 2.2. The horizontal lines at the right correspond to the asymptotic values of the aerogel density ρ (Table 3), and those at the left correspond to the silica density ρs = 2.2 g/cm3. A vertical line at r = 4.4 nm was drawn as a reference for the radius of a sphere (Rsph) with radius of gyration ⟨Rg⟩ = (3/5)1/2Rsph, the average value for the crossover Rg determined by SAXS (Table 2).

*Phone: +55-19 35269180. Fax: +55-19 35269179. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

REFERENCES

This research partially supported by National Synchrotron Light Laboratory (LNLS; Campinas, Brazil), FAPESP (São Paulo, Brazil), and CNPq (Brasilia, Brazil).

samples exhibit a linear behavior at the small-pore side, the slope of which is, in all cases, quite close to the exponent D − 3 of eq 3, with D = 2.2. A vertical line at r = 4.4 nm is also shown in Figure 7 that corresponds to the radius of a sphere (Rsph) with a radius of gyration of ⟨Rg⟩ = (3/5)1/2Rsph, the average value of the crossover Rg determined by SAXS (Table 2). These results are in notable agreement with the mass-fractal characteristics obtained from SAXS. The description of power-law objects as fractals condenses the details of an often-complex geometry and provides a simple model and appropriate language and symbolism to describe ill-defined

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