Structure of Random Porous Materials: Silica Aerogel

Abstract

Using small-angle x-ray scattering, we show that porous silica aerogel has a fractal backbone structure. The observed structure is traced to the underlying chemical (polymerization) and physical (colloid aggregation) growth processes. Comparison of scattering curves for aerogel with silica aggregates confirms this interpretation.In spite of the importance of random porous media in nature and in technology, the structure of these materials has eluded characterization.In this paper we show that certain classes of porous materials can be characterized through fractal geometry and that the appropriate geometry can be determined by small-anglex-ray scattering. We report the structure of a silica aerogel prepared by critical-point drying of an alcoholic (sic) silica gel. This material is chosen because of its exceedingly low density (0.09 g/cm3) and concomitant high porosity. We show that the porosity in this material is due to a random colloid aggregation process in the solution precursor. To our knowledge, this is the first time that the structure of a porous material has been explained in terms of random growth. Classical models of porosity-dependent properties are based on highly simplified geometrical structures like packed spheres or bottlenecked bubbles. ' Recently, fractal2 structures (percolation networks, fractal surfaces) have also been postulated to explain fluorescence3 and adsorption4 5 data for porous media. Although there have been many attempts to characterize the microstructure of porous materials, modeldependent geometric assumptions, like those above, have doomed all indirect methods.A primary goal of our work is to establish the existence of a fractally porous solid. To this end, we first outline the expected scattering patterns for simple fractal structures. The key to our interpretation is based on a qualitative distinction between surface and volume fractals. We find that the low-density aerogel has purely mass-fractal character and find no evidence for fractally rough surfaces.Scattering Pom Pactals. -To interpret scattering curves it is useful to distinguish between bulk and surface scattering. In systems without distinct surfaces, such as polymers in solutions, the scattered intensity,

Structure of Low-Density Nanoporous Dielectrics Revealed by Low-Vacuum Electron Microscopy and Small-Angle X-ray Scattering

“…Such mass fractal ranges shorter than an order of magnitude are, however, typical for silica AGs. 1,4,6,21 In addition, inhomogeneities in the pore size distribution (resulting in density fluctuations), with the presence of large pores of ∼ 200 − 300 nm in diameter, revealed by LVSEM for α-AlOOH and GeO 2 , can explain the power law slopes in SAXS curves for q < 5 × 10 −2 nm −1 for these AGs (and not for the γ-AlOOH AG, which has a more uniform structure [ Fig. 2]).…”

“…Since scattering curves of nanoporous dielectrics are typically interpreted based on a fractal model (see, for example, Refs. 4,6,[20][21][22], below we will use it to interpret SAXS data from Fig. 4.…”

“…26 However, how exactly R g1 and R g2 are related to a and ξ strongly depends on the shape and size distribution of scatterers. [20][21][22] For a non-speculative interpretation of SAXS data, information from direct imaging methods is required. For example, values of R g1 from Table I translate into a mean particle diameter of 2 5/3R g1 ≈ 13 nm for the α-AlOOH AG (with roughly spherical particles as building blocks), 20 into a mean ligament width of 2 4/3R g1 ≈ 45 nm for the GeO 2 AG (with rod-like ligaments), 24 and into a mean nanoleaflet thickness of 2R g1 ≈ 5 nm for the γ-AlOOH AG (with leaflet-like ligaments).…”

Characterization and structural investigation of fractal porous-silica over an extremely wide scale range of pore size

“…The It is well-known that porous materials such as active carbon, Vycor glass and aerogels have fractal geometry with limited size-scale over only one decade or less around 10 nm [26][27][28][29].…”

“…Therefore, it would be fruitful to briefly address the comparison between the scattering results and the present results here. In the scattering experiments on porous samples, two kinds of fractal dimension can be observed, surface fractal dimension D s and mass fractal dimension D, which emerge as the dependences of scattering intensity I (q) on wave number q (q = 2/r, r: pore size), can be observed, where I (q) q -(6-Ds) and I (q) ~ q -D [27,29,30]. Roughly speaking, the former and latter dependences are observed in the scale ranges below and above the smallest pore size, respectively.…”