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Switching silica aerogels from transparent to opaque
Journal of Non-Crystalline Solids 350 (2004) 364–371 www.elsevier.com/locate/jnoncrysol
Switching silica aerogels from transparent to opaque G. Reichenauer a
a,*
, J. Fricke a, J. Manara b, J. Henkel
b
Physics Department, EPII, Universita¨t Wu¨rzburg, Am Hubland, 97074 Wu¨rzburg, Germany b Bavarian Center for Applied Energy Research, Am Hubland, 97074 Wu¨rzburg, Germany
Abstract Adsorption of 2-propanol in the pores of a silica aerogel with a porosity of about 87% and a (breakthrough) pore diameter of 25 nm is accompanied by very strong light scattering. With an uptake of only a few vol.% of 2-propanol, the direct-hemispherical transmission is reduced by about 50% in the visible spectral range. The observed effect is present on both adsorption and desorption and is fully reproducible. This sorption-induced scattering vanishes as soon as the sample is either completely liquid filled or dried. From the experimental light scattering data we deduce that the mean chord length of the entities responsible for the strong light scattering is about 60–100 nm; these values indicate a structural feature significantly larger than the breakthrough pore diameter, and 25–50% smaller than the characteristic size of the density fluctuations found for the silica aerogel with no 2-propanol adsorbed. 2004 Elsevier B.V. All rights reserved. PACS: 82.33.Ln; 75.35.+c; 68.43.Hn; 42.49.Ta
1. Introduction Recently, several authors have reported the observation of an opaque phase during the adsorption or desorption of liquids such as 4He, liquid nitrogen, or ethanol in silica aerogels [1–5]. Despite numerous hints and remarks, so far only a few research groups have tried to elucidate the origin of this effect by investigating the transmission or scattering of electromagnetic radiation at different stages of pore filling [1,4]. Wong et al. [1] studied the transmission of light for a silica aerogel (porosity 95%) partly filled with liquid nitrogen at about 125 K as a function of temperature at fixed nitrogen density (pressure); while the sample showed significant optical extinction in the two-phase region (liquid/vapor), the transmission sharply increased as soon as the temperature exceeded the critical point of the confined nitrogen. *
Corresponding author. Tel.: +49 931 70564 28; fax: +49 931 70564
60. E-mail addresses: [email protected], [email protected] (G. Reichenauer). 0022-3093/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.08.235
Lurio et al. [4] investigated in situ the change of smallangle X-ray scattering during adsorption of 4He in a silica aerogel with a porosity of 98%. They found a remarkably different behavior for the scattering upon adsorption and desorption: the characteristic length scale of the scatterers only varied between 5 and 15 nm in the adsorption branch of the isotherm hysteresis, while the same quantity dropped from about 60 to 5 nm when changing the pore filling ratio from 50 to 15 vol.% upon desorption. Although the characteristic sizes, which they deduced from the scattering upon sorption, are on the same order of magnitude as the radius of curvature of 22 nm determined from the relative pressure shift of the two hysteresis branches, the data did not provide a conclusive interpretation. By accident, we also found a huge change in transparency when investigating the length change of a silica aerogel upon adsorption of 2-propanol. The linear length change of the sample in this experiment (by about 15%) was quite large (see also [6]); it was therefore not clear whether the observed effect is induced by the length change or rather is a more general feature. We therefore
G. Reichenauer et al. / Journal of Non-Crystalline Solids 350 (2004) 364–371
repeated the experiment with a much stiffer silica aerogel in order to quantify the size of the scatterers. 2. Experimental 2.1. Sample preparation and characterization The silica aerogel investigated was obtained from the high-energy group at DESY, Hamburg, Germany [7]; it was prepared from a one-step TMOS (tetramethoxysilane)-derived base-catalyzed silica gel that had been supercritically dried with respect to methanol (synthesis and processing details are given in reference [7]). To significantly increase the stiffness of the as-prepared sample, we sintered the aerogel (initial density 0.26 g cm3) to a density of about 0.29 g cm3. The nanostructure of the aerogel was characterized by ultrasmall-angle X-ray (USAXS) and nitrogen sorption analysis at 77 K (ASAP2000 by Micromeritics; software ASAP2010). The scattering experiments were performed at the SAXS instrument JUSIFA (beamline BW1) and the ultrasmall-angle scattering instrument (beamline BW4) at the German synchrotron facility HASYLAB, Hamburg. For the X-ray scattering experiments as well as for the optical investigations 1 mm thick slices were cut from the monolithic aerogel block with a diamond saw. The USAXS pattern I(q) was evaluated with a combination of a fractal structure factor S(q), a particle structure factor F(q), and a term that describes the packing of the fractal clusters U(q) [8,9]: IðqÞ ¼ F ðqÞ SðqÞ UðqÞ;
ð1aÞ
with
IðqÞ ¼ c1
1 4
1 þ 0:22 ðq RÞ 1
1þ
!
c2 1 þ 0:22ðqnÞ
1 þ p 3ðsinðqDÞ qD cosðqDÞÞ=ðqDÞ
3
;
df
lim ðI q4 Þ ¼ K ¼ 2p q2SiO2 C 2 S=m;
with qSiO2 the density of the silica backbone and C = 8.504 · 1011 m kg1 the factor converting the mass density into the corresponding electron density. The nitrogen sorption data were analyzed with respect to the specific surface area SBET/m, the total specific pore volume Vpore/m as well as the breakthrough diameter dBT [6] of the sample. The breakthrough diameter as extracted from the onset of the desorption branch of the isotherm hysteresis corresponds to the size of the largest percolating pores in the system [10]. The Youngs modulus of the aerogel was calculated from the travel time of an ultrasonic pulse according to E = m2 Æ q, with m the sound velocity and q the macroscopic density of the aerogel.
2.2. Optical characterization The optical characterization of the silica aerogel at different stages of adsorption of 2-propanol was performed with a Vis-IR spectrometer (Lambda 9 by Perkin–Elmer) combined with an integrating sphere [11]. The set-up determines the directional-hemispherical transmittance T and reflectance R. To investigate the angular dependence of the (directional-directional) light scattering, a laser beam with a wavelength of 543 nm was focused onto the sample and the scattered intensity was measured with a photodiode at different angles. Due to the rectangular geometry of the sample and the cuvette, light scattering in the forward direction could only be collected for angles between 2.5 and 60 with respect to the incident beam. These angles correspond to scat˚ 1, respectively. tering vectors q of 104 and 103 A The light scattering data Ilight were evaluated by a superposition of two two-phase media [12] contributions to account for scattering from the bulk (B) and the external surface (S) of the sample: I light ðhÞ ¼ ½Iðh; LS Þ þ Iðh; LB Þ ðeII þ e? cos2 ðhÞÞ;
ð1bÞ
where q is the scattering vector, R = dparticle/2 is the radius of the primary particles, n the size of the fractal clusters, df the mass fractal dimension of the clusters, D the hard-core cluster length, and c1,2 are prefactors that account for the number of clusters and particles as well as the scattering contrast. The fractal structure factor in Eq. (1b) is an approximation of the exact function [8]. Note that the particle structure in Eq. (1b) ignores oscillations that might appear with a narrow particle-size distribution. In addition, the specific surface area S/m was determined from the Porod constant K, which is defined as:
q!1
365
ð2Þ
with ð3aÞ
2 2
Iðh; LS;B Þ ¼ aS;B =ð1 þ ðLS;B qðhÞÞ Þ ; where
q ¼ 4p sinðh=2Þ=k;
and
ð3bÞ ð3cÞ
is the scattering vector and k and h are the wavelength of the incident laser beam and the scattering angle, respectively. The parameter a is a prefactor accounting for the intensity of the incident beam and the total scattering volume; eII and e? denote the polarization of the scattered light. LS and LB are the mean chord lengths characterizing the surface (roughness of the outer surface) and the bulk of the sample. For a statistically isotropic medium, the correlation length LB [13] is a representative measure of the extension of the inhomogeneities within a sample consisting of two phases with different electron density or dielectric
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constant; these properties are assumed to be constant within each phase. The correlation function of such a medium as a function of the distance r between two points is given by cðrÞ ¼ expðr=LB Þ;
with
LB ¼ 4 U1 U2
V ; S
ð4Þ
where Ui are the volume ratios of the two phases present, V is the total volume and S the area of the interface between the two phases. The correlation function is directly related to the scattering intensity I(q) via a Fourier transformation (see also Eq. (3)). In a partially liquid filled aerogel, a phase corresponding to a blank sample (i.e., an effective medium consisting of silica and void space) and a phase consisting of liquid-filled aerogel will be present. Geometrical arguments yield for the mean extensions (chord lengths) of the two phases [13] lfilled ¼ 4
V Ufilled S
and
lunfilled ¼ 4
V Uunfilled : S
ð5Þ
Since LB is defined as the weighted average of the two contributions LB ¼ Ufilled lfilled þ Uunfilled lunfilled
and
Ufilled þ Uunfilled ¼ 1 LB can be written as the harmonic of the chord lengths of the two contributing phases: 1=LB ¼ 1=lfilled þ 1=lunfilled :
ð6Þ
LB is therefore always smaller than the extent of the smaller of the two phases. For all optical measurements, the silica aerogel with a thickness of 1mm and a cross-sectional area of about 1 cm2 was first conditioned with respect to adsorption of 2-propanol by inserting it into a flat optical cuvette (Kronglas cuvette by Hellma GmbH & Co. KG) and placing it next to a 2-propanol-soaked tissue or aerogel in a closed box for 12–24 h to allow for proper equilibration; the procedure has been performed in a climate chamber as well as at ambient conditions. However, no difference was found for the sorption in the different environments. This simple technique allows for a gentle dosing of 2-propanol to the sample. Dosing too rapidly results in large concentration gradients across the sample that can induce cracks. We used 2-propanol as the adsorbate as it is a clear liquid, easy to handle (since not hazardous) and possesses a relatively low surface tension of 23.3 m Nm1. In addition, the index of refraction of 2-propanol (1.42) is very close to that for SiO2 (1.45), so that no third phase in terms of a different index of refraction is introduced into the system upon adsorption of 2-propanol. The sample was finally sealed in the cuvette by combining the glass cover of the cuvette, aluminium foil and Parafilm. The uptake of 2-propanol was quantified by weighing the sample including the cuvette and the material used for sealing prior and after exposing it to the 2propanol.
Eq. (6) can be transformed to yield 3. Results
lfilled lunfilled or lfilled þ lunfilled 1 lfilled lunfilled 1 LB ¼ : lunfilled lfilled þ lunfilled lunfilled LB ¼
ð7Þ
Resolving Eq. (7) for lfilled yields the volume ratio characterizing the filled phase: lfilled ¼ LB =ð1 Ufilled Þ with lfilled : Ufilled :¼ lfilled þ lunfilled
ð8Þ
The structural and mechanical properties of the silica aerogel investigated are summarized in Table 1. The hard-core cluster length D and the particle size dparticle were extracted via a fit of the experimental data with function Eq. (1b) (Table 1). The fractal dimension df and the cluster packing factor p were hereby found to be about 2 and 0.8, respectively. Although the fit is quite stable with respect to the results for the fit parameters D and dparticle, it is not very sensitive to the cluster size n.
Table 1 Structural properties of the silica aerogel (q = 0.29 g cm3)a N2 sorption 2
SBET/m (m /g) Vpore/m (cm3/g) dparticle (nm) dBT (nm)
SAXS 300 ± 5 3.0 ± 0.1 9.1 ± 0.5c 25 ± 1
Ultrasonic measurements 2 1
S/m (m g ) D (nm) dparticle (nm) dparticle (nm)
306 ± 15 32 ± 2b 8.5 ± 1.0 b 7.8 ± 0.3d
E (MPa)
95 ± 3
a dparticle, dBT, SBET/m and Vpore/m are the average particle size, the breakthrough diameter derived from the desorption branch of the nitrogen sorption isotherm, the specific surface area (BET) and the total specific pore volume detected, respectively. S/m, D and dparticle are the specific surface area as well as the hard-core cluster length and the primary particle size (SAXS). E is the Youngs modulus of the aerogel calculated from the ultrasound velocity m and the density of the sample (E = m2 Æ q). b Results from fit of Eq. (1b) to the experimental data. c Calculated via dparticle = 6/(qSiO2 Æ S/m) with qSiO2 = 2.2 g cm3. d Derived from the maximum in I Æ q4 (Fig. 1, insert).
G. Reichenauer et al. / Journal of Non-Crystalline Solids 350 (2004) 364–371
10 4
2000
Vads (cm3 STP /g)
1500
10 2
4
Intensity q (a.u.)
Intensity (cm2/g)
10 3
10 1
367
1000
30 vol %
500
10 0
6 vol % 0
10 -1 0.001
0.1 0.2 0.3 -1 scattering vector (A )
0.01
0 0
0.1
Fig. 1. Small-angle X-ray scattering pattern I(q) for the dry silica aerogel; only every third experimental point is shown. The full line corresponds to a fit with function Eq. (1b) over the full range. The insert shows I(q) multiplied by q4, with q the scattering vector. The horizontal line indicates the value of the Porod constant.
0.8
1
1
directional-hemispherical transmittance T, reflectance R
Eq. (9) represents the expression for the first maximum of a spherical particle structure factor times q4 in case of a narrow particle-size distribution (see first term in Eq. (1)). The pronounced maximum in the experimen˚ 1 can be translated into a tal data at qmax = 0.072 A diameter of 7.8 nm. This value has to be considered as a lower limit for the particle size since Eq. (9) corresponds to a system of highly diluted particles and thus neglects scattering due to interparticle interferences; with increasing packing of the particles the maximum will shift towards larger q-values [15,16]. Applying Eq. (2) to evaluate the average value of I Æ q4 above ˚ 1 (Fig. 1) yields a specific surface area of q = 0.5 A 2 1 306 m g (with qSiO2 = 2.2 g cm3). The I Æ q4 vs. q plot further shows no significant micropore contribution since the signal does not increase drastically towards larger q-values. The nitrogen sorption analysis exhibits a type IV isotherm [10] with very steep adsorption and desorption branches defining the hysteresis loop (Fig. 2). The breakthrough diameter dBT determined from the onset of the desorption branch was found to be 25 nm (Table 1). Light scattering in the visible and NIR range is strongly affected by adsorbed 2-propanol in the silica aerogel (Figs. 3–5). Except for an almost constant contribution due to the cuvette and absorption caused by adsorbed water (1100–2000 nm) and –OH and Si–O fun-
0.6
Fig. 2. Nitrogen sorption isotherm (amount of nitrogen adsorbed vs. relative pressure p/p0) taken at 77 K for the investigated silica aerogel. The line connecting the data points is a guide to the eye. The numbers indicate the positions in the isotherm that correspond to 6 and 30 vol.% of filling.
The particle diameter dparticle can also be derived from an I Æ q4 vs. q representation of the SAXS data (Fig. 1, insert) using the relationship [14,15] ð9Þ
0.4
p/p0
1
scattering vector (A-1)
qmax d=2 ¼ 2:74:
0.2
0.8
0.6
0.4 R T R+T T cuvette R cuvette
0.2
0 500
1000
1500
2000
Wavelength (nm) Fig. 3. Directional–hemispherical transmittance T and reflectance R in the Vis-IR range for the aerogel (including cuvette) with about 30 vol.% of 2-propanol adsorbed as well as for the blank cuvette (T cuvette, R cuvette).
damentals (above 2200 nm) [17], the blank sample shows a significant scattering only below 500 nm (Fig. 4). In contrast, the samples with adsorbed 2-propanol exhibit drastically increased scattering in the visible and NIR regime. Above 1300 nm, absorption bands dominate, while in the visible range the transmission is characterized by a very broad and smooth extinction curve. Fig. 3 shows that most of the extinction in this range is due to scattering rather than absorption.
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Fig. 4. Direct–hemispherical transmittance T in the VIS-IR range of the silica aerogel (including the cuvette) investigated as a function of 2-propanol adsorbed. The corresponding photographs visualize the transparency of the sample in the different stages.
Fig. 5. Log–Linear plot of the light scattering patterns for the aerogel with different amounts of 2-propanol adsorbed. The lines represent the fit of a superposition of 2 two-phase media contributions (Eq. (3)) to the data.
The fit of the light scattering data with a superposition of two two-phase media models provides the characteristic lengths LS and LB listed in Table 2. It has to be pointed out that the sample used for the blank run is not identical to the one investigated with adsorbed 2-propanol, but it was cut from the same aerogel block. Since the manual sample preparation with respect to gentle adsorption of 2-propanol was very time consuming, the quantitative optical characterization was only performed for three samples; however, earlier observations with 2-propanol at room temperature and nitrogen
at 77 K show that strong scattering is present upon adsorption as well as upon desorption and vanishes as soon as the sample is completely filled with liquid.
4. Discussion The structural characterization of the sintered aerogel investigated exhibits an almost micropore-free silica backbone with a well-defined particle diameter; the pronounced maximum in the I Æ q4 vs. q-plot (Fig. 1, insert)
G. Reichenauer et al. / Journal of Non-Crystalline Solids 350 (2004) 364–371 Table 2 Chord lengths of the surface and the bulk scattering contributions LS and LB, respectively, derived via fitting a combination of 2 two phase models (Eq. (3)) to the light scattering data taken for a silica aerogel with different amounts of adsorbed 2-propanol. The statistical error of the data is ±5% 2-propanol adsorbed (vol.%)
LS (nm)
LB (nm)
LB/(1 Ufilled) (nm)
0 4 6 30
911* 614 524 -
134 110 105 57
134 114 111 81
*
This sample was not identical to that used for the other investigations, but taken from the same batch.
is very similar to the features found for silica aerogels derived from high-temperature supercritical drying (e.g., [18]), where Ostwald ripening is thought to result in a narrowing of the size distribution of primary particles and a smoothening of the necks between adjacent entities. According to the SAXS data, the primary particles with a diameter of 8–10 nm form small clusters (Table 1) with about three to four times their size. Assuming spherical geometry, the primary particle diameter derived from the maximum in the I Æ q4-plot yields a specific surface area of about 360 m2 g1 (for a particle density of 2.2 g cm3). This value is about 20% larger than the specific surface area determined from the Porod-constant (Eq. (2)) and the sorption data (Table 1); the discrepancy is probably due to a particle-packing-induced shift of the maximum in the I Æ q4-plot towards larger q-values. The light scattering of the dry aerogel shows significant forward scattering indicating a mean chord length for phases with a different average index of refraction of 130 nm (Table 2). This behavior has been reported earlier by other authors for both silica aerogels as well as their gel precursors (e.g., [19–23]); the scattering was found to depend strongly on the pH of the sol and the solid phase fraction [21] or the degree of shrinkage induced upon subcritical drying [20]. For high pH silica gels, Knoblich and Gerber [21] claim that with increasing pH clusters with decreasing size are forming; these entities arrange into larger associations, however, maintaining as large of a distance as possible. The characteristic sizes that the other authors extracted from light scattering, USAXS, SEM, or AFM are on the order of 40–100 nm depending on the density and the pre-treatment of the sample. The value of 75–90 nm given by Marliere et al. [23] for the aggregates in a sintered aerogel with a porosity of about 87% is on the same order as the mean chord length derived from the light scattering data for our blank aerogel (Table 1). Assuming a closed packed bed of aggregates the volume in between neighboring entities would be on the order of 1/3 of the aggregate volume; applying Eqs. (6) and (8) and assuming a phase with different density instead of a liquidfilled volume, the extent l of the interaggregate phase
369
would be on the order of 200 nm, i.e., a factor 6–8 times larger than the breakthrough pore diameter and the hard-core cluster length detected (Table 1). So far it is still unclear whether the space in between the associations or aggregates is represented by just voids or by aerogel with different density as compared to the one of the aggregates. For instance Hua et al. [20] suggest large pores surrounding the aggregates, while Scherer [24] argued that if a significant number of macropores would be present, they would percolate and dominate the fluid transport properties. The hypothesis of pores with sizes above 50 nm also seems to contradict the findings of our nitrogen sorption analysis especially since nitrogen sorption at 77 K is thought to be sensitive only to pores smaller than 50 nm. As the total specific pore volume of 3 g cm3 detected for our sample (Table 1) equals the one theoretically expected, V pore =m ¼
1 1 q qSiO2
ð10Þ
with the aerogel density q = 0.29 g cm3 and the silica backbone density qSiO2 = 2.2 g cm3, all pores present have to be either micro- or mesopores. This argument of course is based on the assumption that the models that are used to interpret the sorption data also hold for aerogels, which do not contain pores in the sense of an enclosed void. On the other hand, evaluating the SAXS data at an absolute scale provides an additional option to check the variation of average density as a function of length scale by calculating the invariant Q [13,19,25] with C a constant (see Eq. (2)): Z Q ¼ I q2 dq ¼ ðqSiO2 qÞ 2p2 C 2 ð11Þ The integral of the experimental data (Fig. 1) over a ˚ 1 results range in scattering vector from 0.0027 to 0.8 A 3 in a lower limit of 1.7 g cm for the difference (qSiO2 q) in densities; with a silica density of qSiO2 = 2.2 g cm3, this yields an estimate for the average aerogel density of 0.5 g cm3 at a length of about 50– 100 nm. This value is within the error bars of ±0.15 g cm3 close to the macroscopic density of the sample and does not allow for a high percentage of larger voids. We therefore have to assume that the structural features causing the light scattering in the blank sample are density fluctuations rather than voids. In addition, in the early stage of adsorption, large voids are not expected to be filled and thus are unlikely to be responsible for the strong scattering in that regime. The fit of the light scattering data provides two mean chord lengths with LS (Table 1) exceeding LB by a factor of 5–10. The fact that LS is different for the two samples taken from the same batch, but does not significantly vary with adsorption of 2-propanol, strongly suggests that this contribution is due to scattering off the external surface of the (sawed) aerogel platelet (see also Ref.
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[19]). With increasing amount of adsorbed 2-propanol the second mean chord length, LB decreases from about 130 to 60 nm. Keeping in mind that LB always provides the lower limit for the extent of the phases in a twophase model (Eq. (6)), the values indicate a structural entity that is clearly larger than the breakthrough diameter detected for the aerogel. While part of the broadening of the light-scattering curve has to be attributed to an increase in multiple scattering contributions (about 25–30% of the signal at 30 vol.% filling), the dominant effect still seems to be due to scattering from the sample itself. At an amount of adsorbed 2-propanol that corresponds to the range of inner surface coverage (Fig. 2), the scattering is slightly enhanced compared to the dry sample; the scattering strongly increases however with the transition from adsorption at the inner surface of the aerogel to capillary condensation (Fig. 2). The effect is so drastic that the forward scattering at angles below 10 is completely masked. Since the sample turns opaque, both upon adsorption as well as on desorption, viscous fingering [26] can be excluded as an explanation for the observed behavior. We also can neglect the influence of a possible contraction and re-expansion of the sample upon of capillary filling [6] since the aerogel investigated is relatively stiff (see Table 1) and the haze upon sorption is also observed with adsorbates with small or even negligible surface tension [1,4]. The fact that the size of the scatterers changes with progressing adsorption (see also Ref. [4]) excludes the hypothesis that the aggregates also present in the dry aerogel are homogeneously filled with 2-propanol. In this case, only the contrast and thus the amplitude of the scattering would change, rather than the extent of the scatterers being effective. Lurio et al. [4] found an increase of the characteristic lengths with increasing volume-filling ratio upon adsorption as well as on desorption, which is contrary to our findings. Although Lurio et al. investigated the scattering in a q-range below the one related to light scattering, so far we do not have a consistent explanation that combines both observations. The scattering entities that cause the strong extinction in the visible and NIR range can either be blobs or clusters of liquid resulting e.g., from the filling of interconnected pores (see also simulations by Gavalda et al. [27]) or be due to an inhomogeneous distribution of pores sizes within the aggregates thus favoring the partial filling of certain regions. Although we can not distinguish between these two options on the base of the experimental data, the fact that the density fluctuations in the dry aerogel are on the same order of magnitude as the entities causing the strong scattering in the partially liquid filled sample suggests that the two features are related, i.e., the increasing light scattering is essentially due to the enhancement of a morphological property imprinted in the aerogel under investigation.
The experimental data indicate that a two-phase model might not be sufficient to describe the observed behavior. Further experiments are therefore needed to develop a suitable model. Especially helpful will be the evaluation of well calibrated, in situ measured light and USAXS data at different stages of filling upon adsorption and desorption, which not only allows for the extraction of the size of the scattering entities but also the contrast between the different phases contributing. It would further be interesting to study the effects for aerogels with different morphology (e.g., derived under acid or base-catalyzed conditions) and density.
5. Conclusions Partial filling of a silica aerogel with a transparent liquid results in strong light scattering. The characteristic lengths of the phases (100 nm) causing the scattering are hereby on the same order as the size of the density fluctuations found for the dry aerogel. So far the experimental data do not provide enough information to distinguish between blobs of liquid and local fluctuations in the pore-size distribution that would result in an inhomogeneous filling with liquid and thus a modulation of the dielectric constant.
Acknowledgments The authors are indebted to M. Wiener and T. Schliermann, Wu¨rzburg University, for performing the SAXS measurements and the evaluation of the raw data. We also would like to thank Professor G.W. Scherer, Princeton University, and N. Mulders, University of Delaware, for fruitful discussions.
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Switching silica aerogels from transparent to opaque G. Reichenauer a
a,*
, J. Fricke a, J. Manara b, J. Henkel
b
Physics Department, EPII, Universita¨t Wu¨rzburg, Am Hubland, 97074 Wu¨rzburg, Germany b Bavarian Center for Applied Energy Research, Am Hubland, 97074 Wu¨rzburg, Germany
Abstract Adsorption of 2-propanol in the pores of a silica aerogel with a porosity of about 87% and a (breakthrough) pore diameter of 25 nm is accompanied by very strong light scattering. With an uptake of only a few vol.% of 2-propanol, the direct-hemispherical transmission is reduced by about 50% in the visible spectral range. The observed effect is present on both adsorption and desorption and is fully reproducible. This sorption-induced scattering vanishes as soon as the sample is either completely liquid filled or dried. From the experimental light scattering data we deduce that the mean chord length of the entities responsible for the strong light scattering is about 60–100 nm; these values indicate a structural feature significantly larger than the breakthrough pore diameter, and 25–50% smaller than the characteristic size of the density fluctuations found for the silica aerogel with no 2-propanol adsorbed. 2004 Elsevier B.V. All rights reserved. PACS: 82.33.Ln; 75.35.+c; 68.43.Hn; 42.49.Ta
1. Introduction Recently, several authors have reported the observation of an opaque phase during the adsorption or desorption of liquids such as 4He, liquid nitrogen, or ethanol in silica aerogels [1–5]. Despite numerous hints and remarks, so far only a few research groups have tried to elucidate the origin of this effect by investigating the transmission or scattering of electromagnetic radiation at different stages of pore filling [1,4]. Wong et al. [1] studied the transmission of light for a silica aerogel (porosity 95%) partly filled with liquid nitrogen at about 125 K as a function of temperature at fixed nitrogen density (pressure); while the sample showed significant optical extinction in the two-phase region (liquid/vapor), the transmission sharply increased as soon as the temperature exceeded the critical point of the confined nitrogen. *
Corresponding author. Tel.: +49 931 70564 28; fax: +49 931 70564
60. E-mail addresses: [email protected], [email protected] (G. Reichenauer). 0022-3093/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.08.235
Lurio et al. [4] investigated in situ the change of smallangle X-ray scattering during adsorption of 4He in a silica aerogel with a porosity of 98%. They found a remarkably different behavior for the scattering upon adsorption and desorption: the characteristic length scale of the scatterers only varied between 5 and 15 nm in the adsorption branch of the isotherm hysteresis, while the same quantity dropped from about 60 to 5 nm when changing the pore filling ratio from 50 to 15 vol.% upon desorption. Although the characteristic sizes, which they deduced from the scattering upon sorption, are on the same order of magnitude as the radius of curvature of 22 nm determined from the relative pressure shift of the two hysteresis branches, the data did not provide a conclusive interpretation. By accident, we also found a huge change in transparency when investigating the length change of a silica aerogel upon adsorption of 2-propanol. The linear length change of the sample in this experiment (by about 15%) was quite large (see also [6]); it was therefore not clear whether the observed effect is induced by the length change or rather is a more general feature. We therefore
G. Reichenauer et al. / Journal of Non-Crystalline Solids 350 (2004) 364–371
repeated the experiment with a much stiffer silica aerogel in order to quantify the size of the scatterers. 2. Experimental 2.1. Sample preparation and characterization The silica aerogel investigated was obtained from the high-energy group at DESY, Hamburg, Germany [7]; it was prepared from a one-step TMOS (tetramethoxysilane)-derived base-catalyzed silica gel that had been supercritically dried with respect to methanol (synthesis and processing details are given in reference [7]). To significantly increase the stiffness of the as-prepared sample, we sintered the aerogel (initial density 0.26 g cm3) to a density of about 0.29 g cm3. The nanostructure of the aerogel was characterized by ultrasmall-angle X-ray (USAXS) and nitrogen sorption analysis at 77 K (ASAP2000 by Micromeritics; software ASAP2010). The scattering experiments were performed at the SAXS instrument JUSIFA (beamline BW1) and the ultrasmall-angle scattering instrument (beamline BW4) at the German synchrotron facility HASYLAB, Hamburg. For the X-ray scattering experiments as well as for the optical investigations 1 mm thick slices were cut from the monolithic aerogel block with a diamond saw. The USAXS pattern I(q) was evaluated with a combination of a fractal structure factor S(q), a particle structure factor F(q), and a term that describes the packing of the fractal clusters U(q) [8,9]: IðqÞ ¼ F ðqÞ SðqÞ UðqÞ;
ð1aÞ
with
IðqÞ ¼ c1
1 4
1 þ 0:22 ðq RÞ 1
1þ
!
c2 1 þ 0:22ðqnÞ
1 þ p 3ðsinðqDÞ qD cosðqDÞÞ=ðqDÞ
3
;
df
lim ðI q4 Þ ¼ K ¼ 2p q2SiO2 C 2 S=m;
with qSiO2 the density of the silica backbone and C = 8.504 · 1011 m kg1 the factor converting the mass density into the corresponding electron density. The nitrogen sorption data were analyzed with respect to the specific surface area SBET/m, the total specific pore volume Vpore/m as well as the breakthrough diameter dBT [6] of the sample. The breakthrough diameter as extracted from the onset of the desorption branch of the isotherm hysteresis corresponds to the size of the largest percolating pores in the system [10]. The Youngs modulus of the aerogel was calculated from the travel time of an ultrasonic pulse according to E = m2 Æ q, with m the sound velocity and q the macroscopic density of the aerogel.
2.2. Optical characterization The optical characterization of the silica aerogel at different stages of adsorption of 2-propanol was performed with a Vis-IR spectrometer (Lambda 9 by Perkin–Elmer) combined with an integrating sphere [11]. The set-up determines the directional-hemispherical transmittance T and reflectance R. To investigate the angular dependence of the (directional-directional) light scattering, a laser beam with a wavelength of 543 nm was focused onto the sample and the scattered intensity was measured with a photodiode at different angles. Due to the rectangular geometry of the sample and the cuvette, light scattering in the forward direction could only be collected for angles between 2.5 and 60 with respect to the incident beam. These angles correspond to scat˚ 1, respectively. tering vectors q of 104 and 103 A The light scattering data Ilight were evaluated by a superposition of two two-phase media [12] contributions to account for scattering from the bulk (B) and the external surface (S) of the sample: I light ðhÞ ¼ ½Iðh; LS Þ þ Iðh; LB Þ ðeII þ e? cos2 ðhÞÞ;
ð1bÞ
where q is the scattering vector, R = dparticle/2 is the radius of the primary particles, n the size of the fractal clusters, df the mass fractal dimension of the clusters, D the hard-core cluster length, and c1,2 are prefactors that account for the number of clusters and particles as well as the scattering contrast. The fractal structure factor in Eq. (1b) is an approximation of the exact function [8]. Note that the particle structure in Eq. (1b) ignores oscillations that might appear with a narrow particle-size distribution. In addition, the specific surface area S/m was determined from the Porod constant K, which is defined as:
q!1
365
ð2Þ
with ð3aÞ
2 2
Iðh; LS;B Þ ¼ aS;B =ð1 þ ðLS;B qðhÞÞ Þ ; where
q ¼ 4p sinðh=2Þ=k;
and
ð3bÞ ð3cÞ
is the scattering vector and k and h are the wavelength of the incident laser beam and the scattering angle, respectively. The parameter a is a prefactor accounting for the intensity of the incident beam and the total scattering volume; eII and e? denote the polarization of the scattered light. LS and LB are the mean chord lengths characterizing the surface (roughness of the outer surface) and the bulk of the sample. For a statistically isotropic medium, the correlation length LB [13] is a representative measure of the extension of the inhomogeneities within a sample consisting of two phases with different electron density or dielectric
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constant; these properties are assumed to be constant within each phase. The correlation function of such a medium as a function of the distance r between two points is given by cðrÞ ¼ expðr=LB Þ;
with
LB ¼ 4 U1 U2
V ; S
ð4Þ
where Ui are the volume ratios of the two phases present, V is the total volume and S the area of the interface between the two phases. The correlation function is directly related to the scattering intensity I(q) via a Fourier transformation (see also Eq. (3)). In a partially liquid filled aerogel, a phase corresponding to a blank sample (i.e., an effective medium consisting of silica and void space) and a phase consisting of liquid-filled aerogel will be present. Geometrical arguments yield for the mean extensions (chord lengths) of the two phases [13] lfilled ¼ 4
V Ufilled S
and
lunfilled ¼ 4
V Uunfilled : S
ð5Þ
Since LB is defined as the weighted average of the two contributions LB ¼ Ufilled lfilled þ Uunfilled lunfilled
and
Ufilled þ Uunfilled ¼ 1 LB can be written as the harmonic of the chord lengths of the two contributing phases: 1=LB ¼ 1=lfilled þ 1=lunfilled :
ð6Þ
LB is therefore always smaller than the extent of the smaller of the two phases. For all optical measurements, the silica aerogel with a thickness of 1mm and a cross-sectional area of about 1 cm2 was first conditioned with respect to adsorption of 2-propanol by inserting it into a flat optical cuvette (Kronglas cuvette by Hellma GmbH & Co. KG) and placing it next to a 2-propanol-soaked tissue or aerogel in a closed box for 12–24 h to allow for proper equilibration; the procedure has been performed in a climate chamber as well as at ambient conditions. However, no difference was found for the sorption in the different environments. This simple technique allows for a gentle dosing of 2-propanol to the sample. Dosing too rapidly results in large concentration gradients across the sample that can induce cracks. We used 2-propanol as the adsorbate as it is a clear liquid, easy to handle (since not hazardous) and possesses a relatively low surface tension of 23.3 m Nm1. In addition, the index of refraction of 2-propanol (1.42) is very close to that for SiO2 (1.45), so that no third phase in terms of a different index of refraction is introduced into the system upon adsorption of 2-propanol. The sample was finally sealed in the cuvette by combining the glass cover of the cuvette, aluminium foil and Parafilm. The uptake of 2-propanol was quantified by weighing the sample including the cuvette and the material used for sealing prior and after exposing it to the 2propanol.
Eq. (6) can be transformed to yield 3. Results
lfilled lunfilled or lfilled þ lunfilled 1 lfilled lunfilled 1 LB ¼ : lunfilled lfilled þ lunfilled lunfilled LB ¼
ð7Þ
Resolving Eq. (7) for lfilled yields the volume ratio characterizing the filled phase: lfilled ¼ LB =ð1 Ufilled Þ with lfilled : Ufilled :¼ lfilled þ lunfilled
ð8Þ
The structural and mechanical properties of the silica aerogel investigated are summarized in Table 1. The hard-core cluster length D and the particle size dparticle were extracted via a fit of the experimental data with function Eq. (1b) (Table 1). The fractal dimension df and the cluster packing factor p were hereby found to be about 2 and 0.8, respectively. Although the fit is quite stable with respect to the results for the fit parameters D and dparticle, it is not very sensitive to the cluster size n.
Table 1 Structural properties of the silica aerogel (q = 0.29 g cm3)a N2 sorption 2
SBET/m (m /g) Vpore/m (cm3/g) dparticle (nm) dBT (nm)
SAXS 300 ± 5 3.0 ± 0.1 9.1 ± 0.5c 25 ± 1
Ultrasonic measurements 2 1
S/m (m g ) D (nm) dparticle (nm) dparticle (nm)
306 ± 15 32 ± 2b 8.5 ± 1.0 b 7.8 ± 0.3d
E (MPa)
95 ± 3
a dparticle, dBT, SBET/m and Vpore/m are the average particle size, the breakthrough diameter derived from the desorption branch of the nitrogen sorption isotherm, the specific surface area (BET) and the total specific pore volume detected, respectively. S/m, D and dparticle are the specific surface area as well as the hard-core cluster length and the primary particle size (SAXS). E is the Youngs modulus of the aerogel calculated from the ultrasound velocity m and the density of the sample (E = m2 Æ q). b Results from fit of Eq. (1b) to the experimental data. c Calculated via dparticle = 6/(qSiO2 Æ S/m) with qSiO2 = 2.2 g cm3. d Derived from the maximum in I Æ q4 (Fig. 1, insert).
G. Reichenauer et al. / Journal of Non-Crystalline Solids 350 (2004) 364–371
10 4
2000
Vads (cm3 STP /g)
1500
10 2
4
Intensity q (a.u.)
Intensity (cm2/g)
10 3
10 1
367
1000
30 vol %
500
10 0
6 vol % 0
10 -1 0.001
0.1 0.2 0.3 -1 scattering vector (A )
0.01
0 0
0.1
Fig. 1. Small-angle X-ray scattering pattern I(q) for the dry silica aerogel; only every third experimental point is shown. The full line corresponds to a fit with function Eq. (1b) over the full range. The insert shows I(q) multiplied by q4, with q the scattering vector. The horizontal line indicates the value of the Porod constant.
0.8
1
1
directional-hemispherical transmittance T, reflectance R
Eq. (9) represents the expression for the first maximum of a spherical particle structure factor times q4 in case of a narrow particle-size distribution (see first term in Eq. (1)). The pronounced maximum in the experimen˚ 1 can be translated into a tal data at qmax = 0.072 A diameter of 7.8 nm. This value has to be considered as a lower limit for the particle size since Eq. (9) corresponds to a system of highly diluted particles and thus neglects scattering due to interparticle interferences; with increasing packing of the particles the maximum will shift towards larger q-values [15,16]. Applying Eq. (2) to evaluate the average value of I Æ q4 above ˚ 1 (Fig. 1) yields a specific surface area of q = 0.5 A 2 1 306 m g (with qSiO2 = 2.2 g cm3). The I Æ q4 vs. q plot further shows no significant micropore contribution since the signal does not increase drastically towards larger q-values. The nitrogen sorption analysis exhibits a type IV isotherm [10] with very steep adsorption and desorption branches defining the hysteresis loop (Fig. 2). The breakthrough diameter dBT determined from the onset of the desorption branch was found to be 25 nm (Table 1). Light scattering in the visible and NIR range is strongly affected by adsorbed 2-propanol in the silica aerogel (Figs. 3–5). Except for an almost constant contribution due to the cuvette and absorption caused by adsorbed water (1100–2000 nm) and –OH and Si–O fun-
0.6
Fig. 2. Nitrogen sorption isotherm (amount of nitrogen adsorbed vs. relative pressure p/p0) taken at 77 K for the investigated silica aerogel. The line connecting the data points is a guide to the eye. The numbers indicate the positions in the isotherm that correspond to 6 and 30 vol.% of filling.
The particle diameter dparticle can also be derived from an I Æ q4 vs. q representation of the SAXS data (Fig. 1, insert) using the relationship [14,15] ð9Þ
0.4
p/p0
1
scattering vector (A-1)
qmax d=2 ¼ 2:74:
0.2
0.8
0.6
0.4 R T R+T T cuvette R cuvette
0.2
0 500
1000
1500
2000
Wavelength (nm) Fig. 3. Directional–hemispherical transmittance T and reflectance R in the Vis-IR range for the aerogel (including cuvette) with about 30 vol.% of 2-propanol adsorbed as well as for the blank cuvette (T cuvette, R cuvette).
damentals (above 2200 nm) [17], the blank sample shows a significant scattering only below 500 nm (Fig. 4). In contrast, the samples with adsorbed 2-propanol exhibit drastically increased scattering in the visible and NIR regime. Above 1300 nm, absorption bands dominate, while in the visible range the transmission is characterized by a very broad and smooth extinction curve. Fig. 3 shows that most of the extinction in this range is due to scattering rather than absorption.
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Fig. 4. Direct–hemispherical transmittance T in the VIS-IR range of the silica aerogel (including the cuvette) investigated as a function of 2-propanol adsorbed. The corresponding photographs visualize the transparency of the sample in the different stages.
Fig. 5. Log–Linear plot of the light scattering patterns for the aerogel with different amounts of 2-propanol adsorbed. The lines represent the fit of a superposition of 2 two-phase media contributions (Eq. (3)) to the data.
The fit of the light scattering data with a superposition of two two-phase media models provides the characteristic lengths LS and LB listed in Table 2. It has to be pointed out that the sample used for the blank run is not identical to the one investigated with adsorbed 2-propanol, but it was cut from the same aerogel block. Since the manual sample preparation with respect to gentle adsorption of 2-propanol was very time consuming, the quantitative optical characterization was only performed for three samples; however, earlier observations with 2-propanol at room temperature and nitrogen
at 77 K show that strong scattering is present upon adsorption as well as upon desorption and vanishes as soon as the sample is completely filled with liquid.
4. Discussion The structural characterization of the sintered aerogel investigated exhibits an almost micropore-free silica backbone with a well-defined particle diameter; the pronounced maximum in the I Æ q4 vs. q-plot (Fig. 1, insert)
G. Reichenauer et al. / Journal of Non-Crystalline Solids 350 (2004) 364–371 Table 2 Chord lengths of the surface and the bulk scattering contributions LS and LB, respectively, derived via fitting a combination of 2 two phase models (Eq. (3)) to the light scattering data taken for a silica aerogel with different amounts of adsorbed 2-propanol. The statistical error of the data is ±5% 2-propanol adsorbed (vol.%)
LS (nm)
LB (nm)
LB/(1 Ufilled) (nm)
0 4 6 30
911* 614 524 -
134 110 105 57
134 114 111 81
*
This sample was not identical to that used for the other investigations, but taken from the same batch.
is very similar to the features found for silica aerogels derived from high-temperature supercritical drying (e.g., [18]), where Ostwald ripening is thought to result in a narrowing of the size distribution of primary particles and a smoothening of the necks between adjacent entities. According to the SAXS data, the primary particles with a diameter of 8–10 nm form small clusters (Table 1) with about three to four times their size. Assuming spherical geometry, the primary particle diameter derived from the maximum in the I Æ q4-plot yields a specific surface area of about 360 m2 g1 (for a particle density of 2.2 g cm3). This value is about 20% larger than the specific surface area determined from the Porod-constant (Eq. (2)) and the sorption data (Table 1); the discrepancy is probably due to a particle-packing-induced shift of the maximum in the I Æ q4-plot towards larger q-values. The light scattering of the dry aerogel shows significant forward scattering indicating a mean chord length for phases with a different average index of refraction of 130 nm (Table 2). This behavior has been reported earlier by other authors for both silica aerogels as well as their gel precursors (e.g., [19–23]); the scattering was found to depend strongly on the pH of the sol and the solid phase fraction [21] or the degree of shrinkage induced upon subcritical drying [20]. For high pH silica gels, Knoblich and Gerber [21] claim that with increasing pH clusters with decreasing size are forming; these entities arrange into larger associations, however, maintaining as large of a distance as possible. The characteristic sizes that the other authors extracted from light scattering, USAXS, SEM, or AFM are on the order of 40–100 nm depending on the density and the pre-treatment of the sample. The value of 75–90 nm given by Marliere et al. [23] for the aggregates in a sintered aerogel with a porosity of about 87% is on the same order as the mean chord length derived from the light scattering data for our blank aerogel (Table 1). Assuming a closed packed bed of aggregates the volume in between neighboring entities would be on the order of 1/3 of the aggregate volume; applying Eqs. (6) and (8) and assuming a phase with different density instead of a liquidfilled volume, the extent l of the interaggregate phase
369
would be on the order of 200 nm, i.e., a factor 6–8 times larger than the breakthrough pore diameter and the hard-core cluster length detected (Table 1). So far it is still unclear whether the space in between the associations or aggregates is represented by just voids or by aerogel with different density as compared to the one of the aggregates. For instance Hua et al. [20] suggest large pores surrounding the aggregates, while Scherer [24] argued that if a significant number of macropores would be present, they would percolate and dominate the fluid transport properties. The hypothesis of pores with sizes above 50 nm also seems to contradict the findings of our nitrogen sorption analysis especially since nitrogen sorption at 77 K is thought to be sensitive only to pores smaller than 50 nm. As the total specific pore volume of 3 g cm3 detected for our sample (Table 1) equals the one theoretically expected, V pore =m ¼
1 1 q qSiO2
ð10Þ
with the aerogel density q = 0.29 g cm3 and the silica backbone density qSiO2 = 2.2 g cm3, all pores present have to be either micro- or mesopores. This argument of course is based on the assumption that the models that are used to interpret the sorption data also hold for aerogels, which do not contain pores in the sense of an enclosed void. On the other hand, evaluating the SAXS data at an absolute scale provides an additional option to check the variation of average density as a function of length scale by calculating the invariant Q [13,19,25] with C a constant (see Eq. (2)): Z Q ¼ I q2 dq ¼ ðqSiO2 qÞ 2p2 C 2 ð11Þ The integral of the experimental data (Fig. 1) over a ˚ 1 results range in scattering vector from 0.0027 to 0.8 A 3 in a lower limit of 1.7 g cm for the difference (qSiO2 q) in densities; with a silica density of qSiO2 = 2.2 g cm3, this yields an estimate for the average aerogel density of 0.5 g cm3 at a length of about 50– 100 nm. This value is within the error bars of ±0.15 g cm3 close to the macroscopic density of the sample and does not allow for a high percentage of larger voids. We therefore have to assume that the structural features causing the light scattering in the blank sample are density fluctuations rather than voids. In addition, in the early stage of adsorption, large voids are not expected to be filled and thus are unlikely to be responsible for the strong scattering in that regime. The fit of the light scattering data provides two mean chord lengths with LS (Table 1) exceeding LB by a factor of 5–10. The fact that LS is different for the two samples taken from the same batch, but does not significantly vary with adsorption of 2-propanol, strongly suggests that this contribution is due to scattering off the external surface of the (sawed) aerogel platelet (see also Ref.
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[19]). With increasing amount of adsorbed 2-propanol the second mean chord length, LB decreases from about 130 to 60 nm. Keeping in mind that LB always provides the lower limit for the extent of the phases in a twophase model (Eq. (6)), the values indicate a structural entity that is clearly larger than the breakthrough diameter detected for the aerogel. While part of the broadening of the light-scattering curve has to be attributed to an increase in multiple scattering contributions (about 25–30% of the signal at 30 vol.% filling), the dominant effect still seems to be due to scattering from the sample itself. At an amount of adsorbed 2-propanol that corresponds to the range of inner surface coverage (Fig. 2), the scattering is slightly enhanced compared to the dry sample; the scattering strongly increases however with the transition from adsorption at the inner surface of the aerogel to capillary condensation (Fig. 2). The effect is so drastic that the forward scattering at angles below 10 is completely masked. Since the sample turns opaque, both upon adsorption as well as on desorption, viscous fingering [26] can be excluded as an explanation for the observed behavior. We also can neglect the influence of a possible contraction and re-expansion of the sample upon of capillary filling [6] since the aerogel investigated is relatively stiff (see Table 1) and the haze upon sorption is also observed with adsorbates with small or even negligible surface tension [1,4]. The fact that the size of the scatterers changes with progressing adsorption (see also Ref. [4]) excludes the hypothesis that the aggregates also present in the dry aerogel are homogeneously filled with 2-propanol. In this case, only the contrast and thus the amplitude of the scattering would change, rather than the extent of the scatterers being effective. Lurio et al. [4] found an increase of the characteristic lengths with increasing volume-filling ratio upon adsorption as well as on desorption, which is contrary to our findings. Although Lurio et al. investigated the scattering in a q-range below the one related to light scattering, so far we do not have a consistent explanation that combines both observations. The scattering entities that cause the strong extinction in the visible and NIR range can either be blobs or clusters of liquid resulting e.g., from the filling of interconnected pores (see also simulations by Gavalda et al. [27]) or be due to an inhomogeneous distribution of pores sizes within the aggregates thus favoring the partial filling of certain regions. Although we can not distinguish between these two options on the base of the experimental data, the fact that the density fluctuations in the dry aerogel are on the same order of magnitude as the entities causing the strong scattering in the partially liquid filled sample suggests that the two features are related, i.e., the increasing light scattering is essentially due to the enhancement of a morphological property imprinted in the aerogel under investigation.
The experimental data indicate that a two-phase model might not be sufficient to describe the observed behavior. Further experiments are therefore needed to develop a suitable model. Especially helpful will be the evaluation of well calibrated, in situ measured light and USAXS data at different stages of filling upon adsorption and desorption, which not only allows for the extraction of the size of the scattering entities but also the contrast between the different phases contributing. It would further be interesting to study the effects for aerogels with different morphology (e.g., derived under acid or base-catalyzed conditions) and density.
5. Conclusions Partial filling of a silica aerogel with a transparent liquid results in strong light scattering. The characteristic lengths of the phases (100 nm) causing the scattering are hereby on the same order as the size of the density fluctuations found for the dry aerogel. So far the experimental data do not provide enough information to distinguish between blobs of liquid and local fluctuations in the pore-size distribution that would result in an inhomogeneous filling with liquid and thus a modulation of the dielectric constant.
Acknowledgments The authors are indebted to M. Wiener and T. Schliermann, Wu¨rzburg University, for performing the SAXS measurements and the evaluation of the raw data. We also would like to thank Professor G.W. Scherer, Princeton University, and N. Mulders, University of Delaware, for fruitful discussions.
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