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

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 E 0 is estimated from the apparent dissociation constant K by the classical formula E 0 = − 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. A modified Sips' energy distribution is proposed to account for Langmuir-Freundlich adsorption isotherms and Mittag-Leffler fractal kinetics.