Are the pore and surface morphologies of real catalysts fractal?

Abstract

log–log plots of one property vs. another (such as dimension) have been employed since the inception of science. Mandelbrot has proposed that linear log–log plots with fractional slopes could be characteristic of idealized structures called fractals. Fundamental to these idealized ‘fractal’ structures is the concept of self-similarity by which spatial relationships are translated to higher (or lower) dimensions. This paper will assess whether this concept of self-similarity (i.e. fracticality) is applicable to real catalyst pore structures, as has been proposed and is being exercised extensively in the current theoretical and modelling literature. We analyse the data available for the characterization of pore structure and compare these data to the properties of idealized fractals. As a specific example, a Menger sponge (an idealized three-dimensional fractal) is analysed. We find that the void fractions, adsorption/desorption and Hg porosimetry data for known, practical catalysts are inconsistent with a fractal pore network. However, fractal concepts may be useful in our understanding of surface roughness. Thus, the bounds on the applications of fractal analyses to real catalysts are placed in perspective. No known industrial catalysts have pore structures that can be realistically represented by idealized fractal structures.