Microporous and heterogeneous surface adsorption isotherms arising from Levy distributions

We show that for adsorption on heterogeneous and microporous surfaces, the Freundlich isotherm power-law exponent α is directly related to the Levy tail index of the distribution of the Langmuir parameter b and to the expected value and the variance of the adsorption energy distribution. This allows us to view adsorption at low pressure in these systems as a rare event dominated phenomena. Based on this discussion, a generalized isotherm formulation is proposed and applied to the interpretation of recent data on activated carbons.