A fractal approach to adsorption on heterogeneous solid surfaces. 1. The relationship between geometric and energetic surface heterogeneities

Solid surfaces are never ideally regular, that is, geometrically and energetically homogeneous, nor are they fully irregular or fractal. Instead, real solid surfaces exhibit a limited degree of organization quantified by the fractal dimension D. We find that there is a functional relationship between the differential distribution of adsorption energies and the differential distribution of pore sizes on such "partially correlated" surfaces. We also show that the differential pore size distribution reduces to the classical fractal pore size distribution in the limit of very small pore sizes, or when the fractal dimension D approaches 3. To do this, analytical expressions are developed describing pore size correlations, and correlations between adsorption energies. These correlation functions are then used to develop a general form of the interaction term in the equations for adsorption isotherms. Finally, using our theoretical approach, existing equations describing adsorption on heterogeneous surfaces are reexamined. It is shown that some of these equations have to be revised whereas others can be generalized to take into account both energetic and geometric heterogeneity.