An adsorption isotherm from a micro-state model

The present study is dedicated to the derivation of an alternative adsorption isotherm for liquid-solid interfaces from a micro-state model, where adsorption is predominantly of a chemical nature. We describe adsorption-desorption on a liquid-solid interface starting from a partition function. In the new model the surface site occupation number is controlled by the Pauli principle (monolayer condition) and additional an attractive or repulsive surface potential, which depends on the overall surface coverage (nonlinearity). The effective potential represents adsorbate adsorbent interaction, as well as an influence of adsorbate adsorbate interactions on the surface potential. A Langmuir equivalent isotherm is recovered in the limit of a weak potential. The proposed model and Langmuir's isotherm are compared using data of humic acid (HA) adsorption on Brazilian Oxisol soil samples. Both models parameterize the experimental data well, but only the new model seems to be self-consistent.