An analytical isotherm equation that describes the multilayer adsorption on fractal surfaces with adsorbate-adsorbate interactions (measured in terms of free energy) different from that of bulk liquid was developed. Assuming mathematical functionalities for the variation of the free energy, it is possible to evaluate the influence of the adsorbate-adsorbate interactions on the adsorption capacity of solids of high degree of surface irregularity. For those surfaces with relatively low degree of irregularity, it results that the free energy variation with the layer number in the multilayer region affects considerably the sorption capacity of the adsorbent, even for water activities lower than those corresponding to the monolayer moisture content. The energy interactions between adjacent adsorbate layers become less important as the fractal dimension of the adsorbent increases. For a fractal surface, the growing of the multilayer seems to mainly controlled by the degree of surface roughness characteristic of microporous adsorbents, where the volume and pore dimension are the true limitants to the sorption capacity. The isotherm equations obtained were tested fitting published experimental equilibrium data of various water vapor-biopolymer systems.
Part of the book: Food Engineering