Cooperative sorption on porous materials

Sorption isotherms are determined by underlying molecular interactions. However, doubts have been raised whether the sorption mechanism can be understood in principle from analyzing sorption curves via a range of competing models. We have shown recently that it is possible to translate a sorption isotherm to the underlying molecular interactions via rigorous statistical thermodynamics. The aim of this paper is to fill the gap between the statistical thermodynamic theory and analyzing experimental sorption isotherms, especially of microporous and mesoporous materials. Based on a statistical thermodynamic approach to interfaces, we have derived a cooperative isotherm, as a generalization of the Hill isotherm and our cooperative solubilization model, without the need for assumptions on adsorption sites, layers, and pore geometry. Instead, the statistical characterization of sorbates, such as the sorbate-interface distribution function and the sorbate number distribution, as well as the existence of statistically independent units of the interface, underlies the cooperative sorption isotherm. Our isotherm can be applied directly to literature data to reveal a few key system attributes that control the isotherm: the cooperative number of sorbates and the free energy of transferring sorbates from the saturated vapour to the interface. The sorbate-sorbate interaction is quantified also via the Kirkwood-Buff integral and the excess numbers.