Fractal BET and FHH Theories of Adsorption: A Comparative Study

Two theories of multilayer adsorption of gases, namely the Brunauer-Emmett-Teller (BET) theory and the Frenkel-Halsey-Hill (FHH) theory, have recently been extended to the case of fractal substrates in a number of different ways. We present a critical evaluation of the various predictions. The principal results are the following. At high coverage, the fractal BET and FHH isotherms apply to mass and surface fractals, respectively. Both give characteristic power laws with D-dependent exponents (D = fractal dimension of the substrate). The BET isotherm additionally depends on the topological dimension D$_{top}$ of the substrate. For fractal aggregates (D$_{top}$ = 1) with D < 2, the adsorbed phase exists only in a highly disordered state. The BET theory is sensitive to multiple-wall effects (they affect prefactors); the FHH theory is not. For the FHH theory, detailed assessments of the approximations in the model are available. The predictions of the FHH theory have been observed on fractal silver surfaces.