Lattice-gas model for adsorption on fractally rough surfaces

A lattice-gas model for physical adsorption of a gas on a fractal surface is solved in mean-field approximation. Adsorption isotherms display a rich structure with first and second order transitions. Surface tension and temperature effects are analysed. The possibility of determining the surface fractal dimension on the basis of "monolayer" adsorption measurements is discussed. Results for the multilayer adsorption regime are also presented and compared with recent scaling conjectures.