A modified Sips distribution for use in adsorption isotherms and in fractal kinetic studies

Abstract

The classical energy distribution introduced by Sips to account for the Langmuir–Freundlich adsorption isotherm is extended to the case when the exponent α of the isotherm is higher than 1. The mean free energy of desorption E₀ is estimated from the apparent dissociation constant K by the classical formula E₀ = −RT ln K. The dispersion of the energy values, which reflects the heterogeneity of the adsorbing sites, is estimated from the exponent α. The dispersion decreases when the exponent increases. Comparisons are made with the Gaussian approximation and the condensation approximation. The Sips distribution is also applied to activation energies, resulting in a Mittag–Leffler kinetic equation, as used in ‘fractal kinetic’ studies. The adsorption of the dye Basic Yellow 28 onto a surfactant-modified aluminium-pillared clay is studied as an example.