Chapter 12. Multilayer adsorption as a tool to investigate the fractal nature of porous adsorbents

This chapter surveys the use of physical adsorption, from a monolayer upward, as an experimental method to study the fractal surface structure found in many porous and irregular adsorbents. The fractal structure leads to power laws of the Frenkel-Halsey-Hill (FHH) type for the adsorption isotherm, with exponents depending on the fractal dimension of the surface and on whether the dominant force is the substrate potential (van der Waals wetting, low coverage) or the film-vapor surface tension (capillary wetting, high coverage). We derive the power laws from a unifying framework which treats the two forces as competing effects and automatically identifies well-defined coexistence lines in the pressure-dimension diagram between the submonolayer regime, the van der Waals wetting regime, and the capillary wetting regime. We compute the resulting phase diagram for several adsorbate/adsorbent pairs, predicting which of the two power laws will be observed in what pressure range for a given surface geometry and adsorbate. A detailed comparison of the adsorption isotherm on a fractal surface with that in a single pore exhibits many parallels and differences between the two, which we also discuss in terms of t-plots and comparison plots. The aim of the presentation is to provide a simple, but complete set of guidelines for the interpretation of experimental adsorption isotherms, with a minimum number of parameters, in a thermodynamically and geometrically consistent way. A variety of recent experimental studies using multilayer adsorption for fractal analysis are reviewed as illustrations. The examples include some important test cases and range from metal films to carbon blacks, activated carbons, carbon fibers, pyrogenic silicas, silica xerogels and aerogels, porous glasses, and cements.