On the thermodynamics of adsorption on heterogeneous surfaces

A heterogeneous surface is modeled as a collection of independent adsorption sites. The adsorption properties of a site are completely described by the energy and entropy of adsorption. If there is a very large number of adsorption site types on the surface (continuous distribution of sites in the limit), one has to consider their bi-dimensional distribution on the entropy/energy plane. It is shown how this distribution can be converted into the conventional one-dimensional distribution of adsorption sites in the free energy of adsorption, which can be determined from an experimental isotherm by the known methods of the theory of adsorption on heterogeneous surfaces. It is also shown how one can obtain from two free energy distributions at different temperatures the entropy and the energy distributions as well as the entropy/energy relationship for different adsorption sites on a heterogeneous surface. The entropy/energy relationship can serve as a test for consistency of experimental data.