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Surface Fractal Characteristics of Silica Aerogels† Andrzej B. Jarze¸ bski,*,‡ Jarosław Lorenc,‡ and Lucjan Paja¸ k§ Institute of Chemical Engineering, Polish Academy of Sciences, Bałtycka 5, PL-44101 Gliwice, Poland, and Silesian University, Institute of Physics and Chemistry of Metals, Bankowa 12, PL-40007 Katowice, Poland Received January 2, 1996. In Final Form: December 2, 1996X Internal surface structure of 13 samples of base-catalyzed silica aerogels synthesized using different reactant concentrations (TEOS, H2O) was investigated by means of small-angle X-ray scattering (SAXS) and N2 adsorption. Both SAXS and Frankel-Halsey-Hill plots of adsorption isotherms, interpreted in terms of equations of Pfeifer and co-workers, consistently show fractally rough surface structure for aerogels obtained from the low water content procedure and fractally smooth surface of those obtained with overstoichiometric water content.
Introduction Effective entrapment of organic molecules, purified proteins, and whole cell extracts in silica xerogel matrices paved the way for the development of a host of new materials exhibiting unique properties.1,2 A further possible modification of this approach, most recently tested in the author’s laboratory, is the conversion of wet proteindoped gel to a highly porous aerogel structure using hypercritical drying (HD) techniques with carbon dioxide.3 The more open, mesopore-dominated aerogel structures allow for higher diffusive fluxes than those of microporous xerogels,4 which should result in higher accessibility of molecules/proteins and hence in higher reactivity of materials. This new idea provides additional incentive favoring investigations of the effect of preparation procedure on the porous texture of silica aerogels which had proved elusive until not long ago. More recently several papers reported the effect of pH and reactant concentration in an alcogel synthesis system and also the strategy of hypercritical drying (carbon dioxide HD vs methanol HD) on the texture of silica aerogels.5-7 Adsorption of nitrogen and argon at 77 K and carbon dioxide at 273 K was employed to probe internal surface structure of silica aerogels in order to show that pH of the solution and water/ silicon alkoxide molar ratio have a pronounced effect on this structure.6,7 Microporous texture was analyzed using the DubininRadushkevich equation5,6 while the texture in the mesopore size range was investigated using the FrankelHalsey-Hill (FHH) isotherm5-7 and the exponent related to the surface fractal dimension by the equations of Pfeifer * Corresponding author. † Presented at the 2nd International Symposium on Effects of Surface Heterogenity in Adsorption and Catalysis on Solids, PolandSlovakia, September 1995. ‡ Polish Academy of Sciences. § Silesian University. X Abstract published in Advance ACS Abstracts, February 15, 1997. (1) Avnir, D. Acc. Chem. Res. 1995, 28, 328. (2) Avnir, D.; Braun, S.; Lev, O.; Ottolenghi, M. Chem. Mater. 1994, 6, 1605. (3) Jarze¸ bski, A. B.; Malinowski, J. J.; Lachowski, A.; Lorenc, J.; Bielecki, S.; Antczak, T.; Galas, E. Prepr. 7th Eur. Cong. Biotech., Nice 1995, Paper MEP172. (4) Jarze¸ bski, A. B.; Lorenc, J. Chem. Eng. Sci. 1995, 50, 357. (5) Ehrburger-Dolle, F.; Holz, M.; Lahaje, J. J. Pure Appl. Chem. 1993, 65, 2223. (6) Ehrburger-Dolle, F.; Dallamano, J.; Elaloui, E.; Pajonk, G. M. J. Non-Cryst. Solids 1995, 186, 9. (7) Jarze¸ bski, A. B.; Lorenc, J.; Aristov, Y. I.; Lisitza, N. J. J. NonCryst. Solids 1995, 190, 198.
S0743-7463(96)00011-X CCC: $14.00
and co-workers.8,9 However, to get a deeper insight into the complexity of the internal surface structure of silica aerogels and hence possibly a better understanding of the mechanism of surface formation, it is desirable to probe the structure using several independent techniques,10 e.g., small-angle scattering methods (small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS)) and adsorption methods.11-13 Both SAXS and SANS have already been extensively used to investigate the structure of aerogel backbones. However, a broad distribution of pore sizes can contribute to power-law behavior of scattered intensity, I, over an interval of wavevector, q ) 4π/ λ sin(Θ/2), while a fractal surface can be considered to be equivalent to a polydisperse system of pores.14 Bearing this in mind it seems vital to compare predictions of the internal structure of aerogels resulting from scattering experiments with data obtained from adsorption techniques. However, instead of using the classical multiadsorption isotherms method, we decided to focus on the analysis of the multilayer nitrogen adsorption isotherm in terms of the FHH equation. This method, first proposed by Avnir and Jaroniec15 and elaborated by Pfeifer and Cole,8,9 emerges as a straightforward, convenient method for surface characterization.5-7 The prime objective of this work was to compare internal surface characteristics of silica aerogels obtained using nitrogen adsorption and SAXS to draw conclusions regarding dependence of the internal surface structure on the preparation procedure. To the best of our knowledge no such comparison has as yet been made for aerogels. Such an analysis could also provide interesting data on degree of consistency of the internal surface structure portrayals provided by these two fundamentally different techniques. Experimental Section Thirteen alcogel samples were prepared following the protocol earlier described in detail,7 using tetraethoxysilane (TEOS), ethanol, and water as reactants plus a complex basic catalyst comprising ammonium hydroxide and ammonium fluoride. The catalyst systems with fluorine anions are known for their ability (8) Pfeifer, P.; Cole, M. V. New J. Chem. 1990, 14, 221. (9) Ismail, I. M. K.; Pfeifer, P. Langmuir 1994, 10, 1532. (10) Avnir, D.; Farin, D.; Pfeifer, P. New J. Chem. 1992, 16, 439. (11) Rojanski, D.; Huppert, D.; Bale, H. D.; Dacai, X.; Schmidt, P. W.; Farin, D.; Seri-Levy, A.; Avnir, D. Phys. Rev. Lett. 1986, 56, 2505. (12) Hurd, A. J.; Schefaefer, D. W.; Smith, D. M.; Ross, S. B.; Le Mehaute, A.; Spooner, S. Phys. Rev. B 1989, 39, 9742. (13) Kaneko, K.; Sato, M.; Suzuki, T.; Fujiwara, Y.; Nishikawa, K.; Jaroniec, M. J. Chem. Soc., Faraday Trans. 1991, 98, 179. (14) Schmidt, P. W. In The Fractal Approach to Heterogeneous Chemistry; Avnir, D., Ed.; Wiley: Chichester, 1989; pp 67-79. (15) Avnir, D.; Jaroniec, M. Langmuir 1989, 5, 1431.
© 1997 American Chemical Society
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Figure 1. Scattering spectra for 6B samples. To separate the curves, intensities for the samples 6B25 and 6B15 were shifted upward. Slopes corresponding to Dm ) 3 and Ds ) 2 are given only for reference. of boosting gelation16,17 and hence appear quite attractive for the preparation of bioactive materials.2,3 The series of samples covered a broad range of reactant concentrations: TEOS volumetric concentration in ethanol, S, was varied between 5 and 60% while the water/TEOS molar ratio, W, took values of 6, 4, 2, and 1, respectively. Note that W ) 4 corresponds to the stoichiometric water content necessary for the hydrolysis of TEOS whereas W ) 2 corresponds to the stoichiometric content from the point of view of the overall gelation process (hydrolysis and condensation). In practice, due to the high porosity and surface area the actual “stoichiometric” W is about 3.5. The samples, labeled for clarity WBS, were investigated using nitrogen adsorption at 77 K (Micromeritics ASAP 2000) and SAXS (Kratky type camera made by Jeol). To obtain a broad range of the scattering vector q, two different filtered radiations were used, i.e., Co KR (λ ) 1.790 Å) and Cu KR (λ ) 1.542 Å) which, together with two different sets of slits, made it possible to cover the interval in q between 0.0025 and 0.115 Å-1 for Co KR and between 0.01 and 0.58 Å-1 for Cu KR. The samples investigated were granules loosely packed between two thin foils. The volume and weight of the material in the cell were carefully noted to give the mass density of the samples. The experimental setup corresponded to the geometry of an infinite length slit. Therefore, to obtain a desmeared power-law scattering exponent corresponding to point collimation of the primary beam, a 1 was added to the actual exponent resulting from the experimental scattering curve. The bulk density of aerogels Fa was determined by mercury porosimetry using Micromeritics Auto Pore II 9220. The results obtained are given in Table 1 together with additional characteristic parameters of the investigated samples, i.e., specific surface area, SBET, and mesopore volume, VpN2.
Results The scattering curves obtained using Co KR or Cu KR filtered radiations are presented in parts a and b of Figures 1-4. Superficial inspection of the figures reveals three different families of scattering curves. In the high q region all intensity curves, except for 2B60, consistently exhibit (16) Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979; p 212. (17) Tewari, P. H.; Hunt, A. J.; Lieber, J. G.; Lofftus, K. In Aerogels; Fricke, J., Ed.; Springer-Verlag: Berlin, 1986; p 142.
Table 1. Characteristic Parameters of the Silica Aerogels aerogel
Fa (g/cm3)
VpN2 (cm3/g)
1B20 1B30 1B60 2B05 2B15 2B25 2B60 4B05 4B15 4B25 6B05 6B15 6B25
0.22 0.30 0.18 0.039 0.079 0.085 0.175 0.034 0.054 0.072 0.035 0.051 0.061
0.45 1.41 2.10 3.18 3.52 3.85 0.92 1.61 1.70 0.64 1.14 0.94 0.77
lm (nm)
2π/qc (nm)
2.0 1.6 2.0
2.8 2.5 3.5
4.1 4.0 5.1 4.0 4.6 5.3
4.0 4.0 5.6 4.1 5.5 6.3
SBET (m2/g) 593 798 596 783 743 684 402 466 478 307 442 382 310
SSAXS (m2/g)
985 1173 953 492 445 378 481 413 359
surface scattering from the elementary smooth particles (Porod’s law). However, in the q-region immediately below Porod's law the intensity curves differ substantially. Those obtained from 4B and 6B samples exhibit a positive departure from Porod's law in the q interval 0.05-0.2 Å-1, (cf. Figures 1 and 2) while those obtained from 2B aerogels (Figure 3) show a slight curvature or a fairly constant slope, the magnitude of which is a signature of nonfractal surface roughness or surface fractality with Ds equal to about 2.7-2.8 for aerogels 2B15 and 2B25. Surprisingly enough the scattering curves from all 1B samples (Figure 4) show a characteristic kink below the Porod's law region and transition to a slope portraying a mass (branched polymeric) rather than a surface structure, most clearly seen in sample 1B20 and q range between 0.05 and 0.025 Å-1, with Dm equal to 2.2. With decreasing q these curves show either a constant slope (1B20), markedly larger than before, or a progressive curvature, extending over a decade or so. The magnitude of this constant slope, in the case of 1B20 in the q region 0.0250.0025 Å-1, implies a very rough surface fractal structure with Ds equal to about 2.8. This trend is less pronounced in denser samples of this series. The reason for the reversal of the conventional sequence of scattering characteristics seen in all 1B aerogels is not clear. In contrast
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Figure 2. Scattering spectra for 4B samples. To separate the curves, intensities for the samples 4B25 and 4B15 were shifted upward. Slopes corresponding to Dm ) 3 and Ds ) 2 are given only for reference.
Figure 3. Scattering spectra for 2B samples. To separate the curves, intensities for the samples 2B60, 2B25, and 2B15 were shifted upward. Slopes corresponding to Dm ) 3 and Ds ) 2 are given only for reference.
to these somewhat unexpected characteristics of 1B samples, in the range of long scales all the remaining samples consistently show clear power-law behavior with the slope implying mass fractal structure, or a slight progressive curvature. The value of Dm was estimated to be equal to 2.2, 2.25, 1.9, and 1.75 for samples 2B05, 2B15, 4B05, and 6B05 in q interval 0.025-0.0025 Å-1. Specially noteworthy is the scattering curve from the 2B60 sample which shows no Porod regime in short scales but reveals instead a quite remarkable power-law behavior with an exponent implying a very rough surface fractal with Ds about 2.9 over q more than 1 decade long (above 0.025
Å-1). To investigate the relationship between specific surface area and the structure of the matrix using SAXS experiments, the intensity curves from 2B to 6B samples, except for 2B60, were analyzed in a conventional way,18 with the smooth surface assumption (due to well-defined Porod behavior in the short scales) to obtain values of SSAXS and of a mean particle diameterschord length in the solid phase, lm, given in Table 1. The volume fraction of each phase was determined from the measured mass (18) Bota, A. J. Appl. Crystallogr. 1991, 24, 635.
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Figure 4. Scattering spectra for 1B samples. to separate the curves, intensities for the samples 1B60 and 1B30 were shifted upward. Slopes corresponding to Ds ) 3 and Ds ) 2 are given only for reference.
Figure 5. FHH plots for 4B and 6B aerogels.
Figure 6. FHH plots for 2B aerogels.
predictions for the surface fractal dimension,8,9 i.e.: density while the skeletal density on a scale of a few angstro¨ms was assumed to be equal to 2.1 g cm-3.19 Examination of the surface structure using N2 adsorption isotherms was performed employing an already well established technique, i.e., the FHH scaling law
N/Nm ∝ [1/ln(P0/P)]1/m together with the additional equations derived by Pfeifer and co-workers.8,9 All N2 isotherms were plotted in the coordinate system N/Nm vs ln(P0/P), as shown in Figures 5-7, and the slopes of the linear sections were determined to obtain values of |1/m| given in Table 2. It is noteworthy that values of the exponent for 2B samples are greater than 1/3 in contrast to those for all 6B samples, which are less than 1/3. The magnitude of the exponent 1/m can be used to distinguish two adsorption regimes and to provide (19) De la Rosa, N.; Esquivias, L.; Craievich, A. F.; Zarzycki, J. J. Non-Cryst. Solids 1990, 121, 211.
for the van der Waals (VW) regime (1/m < 1/3) Ds ) 3(1 - 1/m) for capillary condensation (CC) (1/m > 1/3) Ds ) 3 - 1/m The values of Ds obtained from the above equations are given in Table 2 as Ds(CC) and Ds(VW), respectively. Discussion This section begins with the discussion of the structure of silica matrices. It is followed by a study of surface characteristics and finally of the consistency of predictions provided by the techniques applied. As already mentioned the scattering curves from the 4B and 6B samples, i.e., those obtained with overstoichiometric water content, show a positive departure from Porod's law in the short scales while those from “understoichiometric” samples do not. This positive
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Figure 7. FHH plots for 1B aerogels. Table 2. Surface and Mass Fractal Dimensions Determined from the FHH and SAXS Plots aerogel
|1/m|
1B20 1B30 1B60 2B05 2B15 2B25 2B60 4B05 4B15 4B25 6B05 6B15 6B25
0.152 0.287 0.323 0.439 0.414 0.403 0.341 0.363 0.336 0.262 0.313 0.315 0.279
a
Ds(CC)
Ds(VW)
Ds(SAXS)a
Dm(SAXS)a
2.54 2.14 2.03
2.8 2.9
2.2 2.4
2.57 2.59 2.60 2.66 2.63 2.66
2.8 2.7 2.8
2.2 2.2 1.9
2.21 2.06 2.05 2.16
1.7
For the length scales of fractal properties see text.
departure can be attributed either to a narrow pore size distribution or a narrow particle size distribution.20,21 The former is quite likely. Indeed, PSDs obtained from N2 adsorption show a fairly pronounced narrow peak of small mesopores and markedly smaller dispersed peak of larger mesopores 6-50 nm for all 6B and 4B25 samples. Yet a narrow pore size distribution does not rule out a narrow particle size distribution. To investigate this matter in more detail, we adopted the most recent results of simulations of scattering from monodisperse and polydisperse systems.21 These demonstrate clearly that the mean particle diameter a0 is related to the effective standard deviation, σeff ) σ/a0, and to the value of wavevector corresponding to the crossover between the Porod and fractal regime, qc, by the equation a0 ) 2π (1-1.6 σeff)/qc. (Actually, qc is the locus of maximum in Iq3 vs q plots). Table 1 gives values of 2π/qc, i.e. corresponding to a0 for a monodisperse system. It is noteworthy that these values are somewhat higher than those of lm (chord length in the solid phase) for all 4B and 6B samples, whereas for samples 2B they are markedly higher. Hence, assuming that lm corresponds to the “real” mean particle diameter, one may conclude that particles in “overstoichiometric” samples are fairly monodisperse (σeff < 0.1) while those in the samples obtained from substoichiometric water regime are polydisperse (σeff > 0.2). On the whole the particle diameters determined in this study are markedly smaller than those observed in conventional base catalyzed aerogels (about 20-30 nm22) and similar to those estimated for neutral aerogels. A (20) Wang, P.; Emmerling, A.; Tappert, W.; Spormann, O.; Fricke, J.; Haubold, H. G. J. Appl. Cryst. 1991, 24, 777. (21) Hasmy, A.; Vacher, R.; Jullien, R. Phys. Rev. B 1994, 50, 1305. (22) Posselt, D.; Pedersen, J. S.; Mortensen, K. J. Non-Cryst. Solids 1992, 145, 128.
comparison of the particle diameters given in Table 1 (confirmed by TEM examination of selected samples23 ) with the values of lower cutoffs of the fractal region (q ≈ 0.025 Å-1 for lighter samples, cf. scattering curves in Figures 1-3), and hence lower limits of the scale of polymeric structure (clusters), shows their very good coincidence. Moreover, a shift of these cutoffs toward lower q values with increase in particle diameter (sample density) is also clearly observed (cf. Figure 1). This not only agrees with physical expectations but also provides strong experimental evidence in favour of the use of the equation proposed by Hasmy et al.21 Finally, it seems worth recalling that PSDs from all 2B samples show a very pronounced dispersed peak of pores in the range 2-40 nm, in contrast to overstoichiometric samples.7 Thus the polymeric clusters in overstoichiometric aerogels appear to be fairly compact (with little pore volume in intracluster structure) whereas in those from substoichiometric aerogels a remarkable (intracluster) pore volume (VpN2) is observed. The structure of the 2B60 sample is different as may be concluded from the intensity curve and the extent of rough surface fractality. This is a sort of infinitecluster structure most probably formed by the mechanism related to the one named “poisoned-Eden” growth, which occurs with defective reaction limited aggregation.24,25 Also the PSD of 2B60 (not shown here) appeared to be markedly different from that exhibited by other 2B samples. Although a pronounced presence of mesopores was detected, the mesopore volume function gradually decreased with the rise in pore diameter. We do not intend to speculate on the structure of 1B samples. The high density of these samples, especially 1B20 and 1B30, is clear evidence of a dramatic collapse of the structure during hypercritical drying. The most affected are the tenuous samples, i.e., with low TEOS content. The very low mesopore volume of the 1B20 sample and lower than expected of the 1B30 sample contrast with that of 1B60 and indicate the collapse of inter- and intracluster structure. An outcome of this process, a fairly rough surface structure observed in samples 1B20 and 1B30, is consistently depicted in larger scales by scattered intensity and N2 adsorption isotherms. From the FHH plots it is clear that the surface of all 6B and 4B25 samples is fractally smooth in the relative pressure range of 0.7-0.95 (cf. Figure 5 and Table 2) which, converted to length scales via the classical Kelvin equation, corresponds to intracluster mesopores of diameters larger than 6 nm. In contrast, the surface of 4B25 and 2B samples consistently shows a (fractally) rough structure in the relative pressure range of 0.35-0.94, and hence the range of mesopore diameters of 2-30 nm (cf. Figure 6 and Table 2). While for all overstoichiometric samples intensity curves show a Porod region in short scales and a highly branched, polymeric structure in longer scales, the scattering curves from 2B samples reveal a rough surface in the range of 2-15 nm (1-20 nm for 2B60). The q-interval over which a rough surface structure is observed is rather narrow (except for 2B60), but the length scale of real surface roughness is longer by a factor π,14 which agrees well with the predictions from FHH plots. Particularly interesting, in this respect, is the excellent agreement of predictions of both Ds and the range of surface fractality observed in samples 2B60 and 1B20, which exhibit extraordinary but quite different surface structures. The specific surface areas of the samples evaluated from (23) Aristov, Y. I.; Lisitza, N.; Zaikovski, V. I.; Lorenc, J.; Jarze¸ bski, A. B. React. Kinet. Catal. Lett., in press. (24) Schaefer, D. W. Science 1989, 243, 1023. (25) Cao, Q.-z.; Wong, P.-z. Phys. Rev. Lett. 1991, 67, 77.
Surface Fractal Characteristics of Silica Aerogels
the nitrogen adsorption and the X-ray scattering curves are in fair agreement, and the decrease of the area with increase in particle diameters is consistently predicted by the methods. However, SSAXS values appear to be slightly higher than those of SBET, particularly for the samples exhibiting a more tenuous structure (2B). This can be explained by different resolutions characteristic for the two techniques employed as well as by the pore closure (intracluster collapse), more likely to happen in the more tenuous aerogels. On the basis of the presented results, it is not possible to offer a simple general conclusion regarding consistency of the surface structure predictions provided by SAXS and analysis of FHH plots. Although for aerogels obtained using overstoichiometric water content the FHH plots predict fractally smooth surface structure in the range of 6-40 nm, SAXS “sees” in this range a branched polymeric structure (mass fractal). If, however, the surface structure of silica aggregates is fairly rough (fractally), as observed in 2B aerogels, this is consistently revealed both by SAXS and FHH plots. Thus both methods complement each other and a complete, coherent portrayal of the porous materials structure can be obtained provided that both methods are used together.
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The following conclusions may be formulated concerning internal surface structure of silica aerogels and its characterization using SAXS and FHH plots of adsorption isotherm: (i) water content in the alcogel synthesis system appears to be the chief factor governing surface structure; (ii) internal surface of aerogels obtained from the overstoichiometric water content procedure is fractally smooth (Ds ≈ 2.0-2.2) while that of aerogels synthesized with substoichiometric water is fractally rough (Ds ≈ 2.5-2.9); (iii) both SAXS and FHH plots, interpreted in terms of the equations of Pfeifer and co-workers, provide consistent predictions of surface fractal structure of silica aerogels; however, to obtain a coherent, complete picture of the porous structure, the use of both methods is recommended. Acknowledgment. A.B.J. wishes to thank D. Avnir, F. Ehrburger-Dolle, P. Pfeifer, and W. Rudzin´ski for stimulating discussions. The authors gratefully acknowledge the financial support of the State Committee for Scientific Research (KBN) for this work under Grant 3T09C-022 09. LA960011Z
