Characterization of surface roughness of MCM-41 using methods of fractal analysis

Abstract

We report here the characterization of surface roughness of the model mesoporous molecular sieve MCM-41, at various scales of resolution. This material comprises several levels of structure ¯that of the mesopores, the crystallites, the grains, and the particles ¯spanning four decades of resolution, each having its independent surface properties at its characteristic length scale. The apparent fractal dimension of this material, of various pore diameters, synthesized in our laboratory has been determined at various scales with the help of various characterization techniques such as adsorption, mercury porosimetry, small-angle X-ray and neutron scattering (SAXS and SANS). A new method for the estimation of fractal dimension from a gas adsorption isotherm is proposed which considers the effect of solid-fluid interactions and the meniscus curvature, neglected in earlier methods of fractal analysis. On the basis of the results, the MCM-41 structure is found to have a fractal dimension of 2 at molecular resolutions of 3-7 Å and is therefore highly smooth at this scale. At lower resolutions corresponding to the mesopore diameter (20-50 Å), it possesses an apparent fractal dimension of about 3, suggesting a higher roughness. While not suggestive of a fractal structure for the narrow pore size distribution of MCM-41, the roughness indicates the presence of constrictions in the mesopore channels. At still lower resolutions (80-250 Å and 0.1-0.4 µm), the structure is also found to be rough. It is also found that MCM-41 has a higher fractal dimension than HMS, and that vanadium incorporation into the structure of MCM-41 increases its roughness.