Langmuir 1997, 13, 1145-1149
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On the Texture Characterization of Mixed SiO2-ZrO2 Aerogels Using the Nitrogen Adsorption-Desorption Isotherms: Classical and Fractal Methods† S. Blacher,* R. Pirard, and J. P. Pirard Service de Ge´ nie Chimique, Lie` ge University, Baˆ t. B6, B-4000 Lie` ge, Belgium
B. Sahouli and F. Brouers Physique de Mate´ riaux, Institut de Physique, Lie` ge University, Baˆ t. B5, B-4000 Lie` ge, Belgium Received October 17, 1995. In Final Form: February 22, 1996X We discuss methods to extract information on the texture from nitrogen adsorption-desorption data of mixed SiO2-ZrO2 aerogels prepared under different conditions. The data have been analyzed following two methods: (a) the classical Brunauer-Emmett-Teller (BET) theory1 and extensions2 and the “fractal FHH” theories.3,4 We show that (a) the classical methods are unable to interprete adsorption-desorption data obtained for this kind of system and (b) fractal FHH theories lead to the conclusion that mixed SiO2-ZrO2 aerogels are surface fractals, independently of the preparations conditions.
Introduction Aerogels are cluster-assembled porous materials derived from the supercritical drying of highly cross-linked inorganic or organic gels. These materials exhibit ultrafine cell/pore sizes, continuous porosity, high specific surface area, and a microstructure composed of interconnected colloidal-like particles or polymeric chains with characteristic diameters of about 10 nm. This microstructure is responsible for their unusual optical, acoustic, thermal, and mechanical properties.5 Since the potential applications of aerogels depend mostly on the pore size distribution, a study of the pore morphology is of primary importance. The microstructural differences of aerogels prepared under various conditions have been mainly studied by transmission and scanning electron microscopy (TEM and SEM), small angle neutron or X-ray scattering (SANS or SAXS), nitrogen adsorption-desorption isotherms, mercury porosimetry, and nuclear magnetic resonance (NMR) measurements.6a But the aerogel microstructure appears to be so complex that at present one can only hope that a complete picture will result from a confrontation and comparison of the information provided by several independent methods of characterization used on the same samples. Each of these methods has its advantages and drawbacks. The interest of SAXS and SANS studies is that they are nondestructive; however, it is not always easy to determine precisely the particles size, and in some instances, the variation of the scattered intensity with the wavevector is far from † Presented at the Second International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Poland/Slovakia, September 4-10, 1995. X Abstract published in Advance ACS Abstracts, September 15, 1996.
(1) Brunauer, S.; Emmet P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309. (2) Lecloux, A. J. In Catalysis, Science and Technology; Andersen, J. R., Boudard, P., Eds.; Springer-Verlag: Berlin, 1981; Vol. II, p 171. (3) (a) Avnir, D.; Jaroniec, M. Langmuir 1989, 5, 1431. (b) Yin, Y. Langmuir 1991, 7, 216. (4) (a) Pfeifer, P.; Cole, M. W. New J. Chem. 1990, 14, 221. (b) Pfeifer, P.; Obert, M.; Cole, M. W. Philos. Trans. R. Soc. London, A 1989, 423, 169. (5) Le May, J. D.; Hopper, R. W.; Hrubesh, L. W.; Pekala, R. W. MRS Bull. 1990, 30. (6) (a) Brinker, C. J.; Scherer, G. W. Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing; Academic Press: New York, 1990; Chapter 9. (b) Idem p 523.
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what is expected from simple fractal models. Moreover, one cannot completely eliminate errors due to multiple scattering. In mercury porosimetry, the mercury destroys the porous structure of the aerogel rather than intruding into the pores. Nevertheless useful morphological information can be obtained from a theoretical modeling of the collapsing process itself.7,8 Although electron microscopy provides some textural information, it is difficult to quantify the observed 3D structure from image analysis. In this paper, we discuss the possibility and the methodology to be used to extract information in the porous solid texture from nitrogen adsorption-desorption data of mixed SiO2-ZrO2 aerogels. To achieve this goal, nitrogen adsorption-desorption isotherms were determined for samples prepared under different conditions by varying the acidity, the hydrolysis ratio, and the Z ) Zr/(Zr + Si) molar ratio. Then, measurements were analyzed following two methods: the classic BrunauerEmmett-Teller (BET) theory1 and extensions2 and the fractal FHH theories.3,4 Experimental Section Sample Preparation. Gels were synthesized by hydrolysis of zirconium propoxide and tetraethylorthosilicate (TEOS) in ethanol. The zirconium propoxide is stabilized by methoxyethanol to avoid a too fast reaction and a premature precipitation of the oxide. The molar ratio Z ) Zr/(Zr + Si) was adjusted to 0.3, 0.5, or 0.7. The hydrolysis molar ratio h ) H2O/(Zr + Si) was adjusted to 4 or 6, and the reaction was catalyzed by H+ ions using a 1 M HCl aqueous solution or by OH- ions using a 1 M NH4OH aqueous solution. The total metallic concentration (Zr + Si) was fixed to 0.26 M by dilution with ethanol. The precursor’s sol is made by successive addition, under stirring of appropriate quantities of (1) anhydrous ethanol, (2) solution of 1 M zirconium propoxide in methoxyethanol, (3) tetraethylorthosilicate (TEOS), and (4) solution of h mol/L acidified, basified, or neutral water in ethanol (h is the hydrolyzed molar ratio as specified above). The viscosity of the solution increases immediately and gelation occurs within 1-50 min according to the composition. The gel is aged during 7 days at room temperature to let the reactions take place. The gel is finally hypercritically dried in a 1.5 L autoclave with an initial nitrogen pressure of 45 bar after adding (7) Pirard, R.; Blacher, S.; Brouers, F., Pirard, J. P. J. Mater. Res. 1995, 10, 8, 2114. (8) Scherer, G. W.; Smith, D. M. J. Non-Cryst. Solids 1995, 186, 316.
© 1997 American Chemical Society
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Figure 1. Nitrogen adsorption-desorption isotherms obtained for Z ) 0.5 aerogels with h ) 4, acid (a) and basic (b) catalyzed, and h ) 6, acid (c) and basic (d) catalyzed. 200 mL of ethanol. After closure, the temperature is raised to 600 K at a rate of 2 K/min. The pressure is limited to 110 bar. After 30 min, at maximum temperature and pressure, the hypercritical fluid is evacuated and the vessel is vented by dry nitrogen during 15 min. Thirteen samples where correctly synthesized. Let us note that the gels with Z ) 0.3, acid catalyzed, were not synthesized because the reaction is too slow and the gels Z ) 0.7, h ) 6 were not analyzed because they were not homogeneous due too a fast reaction. Density of aerogels varies between 0.013 and 0.078.
Methods The nitrogen adsorption-desorption isotherms were determined at liquid-nitrogen boiling temperature (77 K) by the classical volumetric method with Sorptomatic Carlo Erba Series 1800 apparatus controlled by an IBM Personal Computer. Nitrogen of high purity (99.98%) was used. Recently, Sherer et al.9 have shown that the adsorption methods could induce damage in the structure of silica aerogel. As shown by Ehrburger-Dolle et al.10 this damage should practically only affect the macropores. To avoid the influence of adsorption-induced measurement damage, we have limited ourselves to the relative pressure range 0.05 < p/p0 < 0.8. Analysis of the Adsorption-Desorption Isotherms. Classical Theory.1,2 The classic methodology to char(9) Scherer, G. W.; Stein, J.; Smith, D. M. Non-Cryst. Solids 1995, 186, 309. (10) Ehrburger-Dolle, F.; Dallamano, J.; Elaloui, E.; Payonk, G. M. J. Non-Cryst. Solids 1995, 186, 9.
acterize a pore solid texture can be summarize by the following steps: (1) Identification of the experimental isotherm with one of the five Brunauer-Deming-Deming-Teller (BDDT) types. This allows the predominant pore size in the material to be determined: microporous (width (w) < 2 nm), mesoporous (width 2 nm < w < 50 nm), and macroporous (w > 50 nm). (2) Identification of the observed hysteresis loops with one of the five types described by de Boer. This allows the shape of the pores (cylindrical, spherical, ink bottle, etc.) to be determined. (3) Determination of the specific surface area, SBET, and the BET constant, CBET, which depends on the type of surface-adsorbate interaction, using the BET model. (4) Analysis of the v-t plot which compares the experimental isotherm with the standard isotherm of a nonporous material. Confirmation of the qualitative analysis described in steps 1 and 2 and measurements of the t-specific area surface St. (5) Quantitative characterization: (a) the specific surface area (SB) and the volume (VB) distributions of micropores are calculated by the Brunauer method; (b) the total microporous volume (VDR) is calculated by the Dubinin-Radushkevich equation; (c) the cumulative specific area (ScumBdB) and the cumulative specific volume (VcumBdB) of mesopores are calculated by the BroekhoffDe Boer method.
Texture Characterization of Aerogels
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Figure 2. v-t plots obtained for Z ) 0.5 aerogels with h ) 4 acid (a) and basic (b) catalyzed and h ) 6 acid (c) and basic (d) catalyzed.
This program, has been applied successfully to a large number of porous materials (monodisperse silica sphere11 and zirconium oxide xerogels,12 etc.) providing a complete description of the texture of these materials. Figure 1 shows some examples of experimental isotherms obtained for the different samples described in the previous section. Independently of the aerogel composition or the fabrication method, all isotherms have more or less the same shape. Moreover, on one hand this shape cannot be clearly identified with one of the five BDDT theoretical isotherms, and on the other hand, the observed hysteresis loops do not correspond to any of the five models proposed by De Boer. Despite the unusual shape of the measured isotherms we can first try to perform a classical analysis. Figure 2 shows some examples of the v-t plots corresponding to different samples described in the previous section. Some of these curves, in particular the one which corresponds to aerogels fabricated under basic conditions, exhibit downward deviation from the straight line passing through the origin. In that case, we can suppose that aerogels have a microporous structure. In this case, experimental isotherms might be identified with the type I BDDT isotherm and the set of texture parameters enumerated in step 5 can be determined. However detailed calculations13 lead to a contradictory (11) Lecloux, A. J.; Broncart, J.; Noville, F.; Dodet, C.; Marchot, P.; Pirard, J. P. Colloid Surf. 1986, 19, 359. (12) Lecloux, A. J.; Franc¸ ois, F.; Moshine, A.; Noville, F.; Pirard, J. P. J. Non-Cryst. Solids 1992, 147 & 148, 389. (13) Kolibos, S. MsD thesis, Lie`ge University, 1992.
result: in spite of the assumption that the isotherms are of type I or that the material has a microporous structure, one finds that the ratio between ScumBdB* (calculated with the extremus shape factor 1, corresponding to cylindrical meniscus2) and SBET are in the interval 0.3 < ScumBdB*/ SBET < 0.5, depending on the aerogel composition and the fabrication method, which indicates that the part of the porosity corresponding to the mesopores is important. On the other hand, some of the v-t curves, in particular the one that corresponds to aerogels fabricated in undert acidic condition, exhibit some slightly upward deviation from the straight line. Then mesopores exist and we can suppose that the capillary condensation phenomenon is present. In this case, the experimental isotherms might be identified with the theoretical BDDT type IV and as a consequence, the material should have a mesoporous structure. Calculations of the texture parameters give a ratio between ScumBdB** (calculated with the extremus shape factor 1, corresponding to cylindrical meniscus2) and SBET in the interval 0.6 < ScumBdB**/SBET < 0.9 depending on the considered aerogel. This corresponds to an important contribution of micropores which is in contradiction with the previous assumption. In fact, a careful observation of the v-t plots shows a very small deviation from the straight line passing through the origin. To explain this feature, there are two possibilities: (1) the aerogels have smooth surfaces or (2) the nonclear deviation downward or upward of the experimental curve from the straight line is the result of a competition between the surface-adsorbate potentials and
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Table 1. Summary of the Experimental Resultsa Z) Zr/(Zr + Si) catalytic SBET SB ScumBdB* ScumBdB** (%) h medium (m2/g) (m2/g) (m2/g) (m2/g) 30 30 30 30 50 50 50 50 50 50 70 70 70 70 70 70 a
4 4 6 6 4 4 4 6 6 6 4 4 4 6 6 6
B N B N A B N A B N A B N A B N
551 442 762 538 474 715 353 420 643 370 285 280 280 291 761 333
620 441 672 415 472 607 344 418 551 343 291
197 143 210 173 188 190 144 202 177 124 149
436 347 489 367 451 472 335 360 391 300 276
287
139
253
653
216
514
the experimental isotherm m 2.44 2.43 3.50 3.21 2.54 3.41 2.55 2.13 3.56 2.81 2.34 3.18 2.48 1.76 4.15
The signification of the comumn headings is given in the text.
the surface tension (capillary condensation), both present in the adsorption phenomena. The large SBET measured in all cases excludes the possibility of a smooth surface; therefore the second possibility appears to be plausible. Classical methods of computation of volume and specific surface distribution are based on the assumption of the existence of pores which have well-defined shapes and dimensions. We know that aerogels, as shown by TEM, SEM, SANS, and SAXS measurements,6a have a structural diversity which includes all pore sizes, arranged in a complex self-similar geometry. Table 1 presents SB, ScumBdB*, ScumBdB**, and SBET values obtained for all the samples described before. These results can be summarized as follows: (a) The SBET of the studied aerogels decreases as Z increases. (b) For des aerogels prepared under acidic and neutral conditions SB ≈ SBET, which indicates that they have mainly a microporous structure. (c) In all cases ScumBdB* * 0, which indicates the presence of mesopores. (d) Mixed SiO2-ZrO2 aerogels prepared under basic conditions have a larger SBET than the aerogels prepared under acidic or neutral conditions. This trend, which seems opposite to generally observed pure silica aerogel, has been already noticed on some silica aerogels6b and depends strongly on the fabrication method. Fractal Theories. The BET and FHH classical theories1,14 have been extended to characterize fractal surfaces. As we have shown elsewhere15 the fractal BET theory assumptions16 are not appropiate to determine the fractal surface dimension of aerogels. The classical FHH equation describes the continuous growth of an adsorbate film with thickness z on a flat surface when x f 1 as14
N 1 ≈ ln Nm x
( ( ))
-1/m
(2)
and in general 2 e m e 3. Fractal FHH type equations were proposed by Avnir et al.,3a Pfeifer et al.4 and Yin.3b In spite of the different adsorption mechanism for multilayer formation considered by Avnir et al.3a and Yin,3b they obtained the following isotherm
N 1 ≈ ln Nm x
( ( ))
-(3-Ds)
(3)
for micropores and mesopores size distribution where 2 < Ds < 3 is the surface fractal dimension. In the Pfeifer et al.4 approach the same fractal law distribution is found in the case where mesopores are predominant, otherwise the determination of the surface fractal dimension cannot be determined unambigously. Equation 3 has been used recently to determine the surface fractal dimension of silica aerogels.17-19 Table 1 shows the values obtained for m. For equiconcentration SiO2-ZrO2 mixed aerogels, prepared in acidic and neutral catalyst conditions, we found 2 < m < 3, for all h. In contrast, for aerogels prepared in basic conditions we found 3 < m, for all h. It was noted20 that the microporosity increases the value of m and that the capillary condensation decreases it. In our case, this trend is confirmed as we found the greatest SB for basic aerogels (see Table 1). This behavior is conserved for higher values of Z, but for Z ) 0.3, h ) 4, m is always smaller than 3. If eq 3 is used, we obtain 2.59 < Ds < 2.64 for aerogels prepared in acidic and neutral catalyst conditions and 2.69 < Ds < 2.72 for aerogels prepared on basic conditions. It must be reminded that this apparent fractal dimension depends of the type of probe use to measure it. This is why it is necessary to use these values with great care and compare them with the results of other independent methods of measurements. Discussion
where R and m depend on the solid-adsorbate interaction. The value of m is determined experimentally by plotting
Our calculations using a classical approach to determine the pore size distribution of SiO2-ZrO2 aerogels from nitrogen adsorption-desorption measurements does not give satisfactory results. Indeed these materials have a large multiscale pore size distribution which is not compatible with the assumptions on the shape and dimension of pores in the classical theories. The use of the concept of an effective surface fractal dimension appears as a possible way to describe the effect of the various physical and chemical parameters on the aerogel morphology. The fractal characterization of silica aerogels is made from usually SAXS and SANS measurements which can probe the range 0.5-200 nm. From these measurements, silica aerogels have been described as “polymeric mass fractals” formed by lightly cross-linked chains of particles (1 < D < 2) or “colloidal surface fractals” formed by compact branched cluster aggregates (2 < D < 3). The first class has been associated with silica aerogels synthesized under acidic conditions and the second class
(14) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: London, 1982; p 89. (15) Blacher, S.; Pirard, R.; Pirard, J. P.; Brouers, F.; Germain, M. In Advances in Porous Materials; Komarneni, S., Smith, D. M., Beck, J. S., Eds.; Materials Research Society: Pittsburgh, PA, 1995; Vol. 371, p 523. (16) Cole, M. W.; Holder, N. S.; Pfeifer, P. Phys. Rev. B 1986, 33, 8806.
(17) Erburger-Dolle, F.; Holz, M.; Mauzac, C.; Lahaye, J.; Pajonk, G. M. J. Non-Cryst. Solids 1992, 145, 185. (18) Erburger-Dolle, F.; Dallamo, J.; Elauli, E.; Pajonk, G. M. J. NonCryst. Solids 1995, 186, 9. (19) Jarzebsi, A.; Lorenc, J.; Aristov, Y.; Lisitza, N. J. Non-Cryst. Solids 1995, 190, 198. (20) Carrott, P. J. M.; Sing, K. S. W. Pure Appl. Chem. 1989, 61, 1835 and references herewith.
(1x) ) zR
ln
m
(1)
Texture Characterization of Aerogels
with silica aerogels synthesized under neutral and basic conditions. From considerations based on the dynamic of the hydrolysis-condensation equilibria between monomers and cluster aggregates which is strongly pH dependent, polymeric type aerogels are modeled by cluster-cluster growth type models (DLCA) and colloidal type aerogels by monomer-cluster growth type models (RDLA). In the context of nitrogen adsortion-desorption measurements, this classification loses its meaning because this technique probes the surface rugosity in a range from 0.35 nm (N2 monolayer) to more or less 20 nm. This scale is not large enough to allow us “to see” the global structure of the aerogel; it provides only information on the rugosity of the system at the molecular length scale. Our calculations using the fractal FHH theory lead to the conclusion that the mass or surface fractal character is not a clear-cut
Langmuir, Vol. 13, No. 5, 1997 1149
classification. Mass or surface fractal character might depend on the scale at which the aerogel is probed. Aerogels appear to be multiscaling objects. This means that the fractality is scale dependent and depends on the various steps of the growth process. Acknowledgment. The authors are very much indebted to Professor D. Avnir for an illuminating explanation. The authors thank the “Service de la Recherche Scientifique du Ministe`re de l’Education, de la Recherche et de la Formation de la Communaute´ Franc¸ aise de Belgique” and the “Ministe`re de la Re´gion Wallonne, Direction Ge´ne´rale des Technologies et de la Recherche”, for financial support. LA950883L
