General Cluster Sorption Isotherm

Adsorption isotherms are an essential tool in chemical physics of surfaces. However, several approaches based on a different theoretical basis exist and for some isotherms existing approaches can fail. Here, the sorbate-sorbate interaction is not limited to an orientation vertical to the adsorbent surface. Instead, a formal orientationindependent clustering, also comprising the possibility of multilayers as a special case, is underlain. The flexible clusters are described by classical thermodynamics including a free energy relationship depending on the cluster size. In this paper a rigorous unified treatment of the adsorbate-adsorbate-adsorbent interaction is shown to result in a general isotherm equation which is applied to literature data both concerning type IV isotherms of argon and nitrogen in ordered mesoporous silica, and type II isotherms of disordered macroporous silica. The new isotherm covers the full range of partial pressure (10-6 - 0.7). The determination of surface areas is not possible by this isotherm because the cross-sectional area of a cluster is unknown. Based on the full description of type IV isotherms, most known isotherms including BET are accessible by respective simplifications. The presented model is an extension of the classical derivation of the zeta-isotherm which was shown to describe type IV isotherms restricted to adsorbates with very strong tendency of clustering such as water on hydrophobic surface (Phys. Chem. Chem. Phys. 21 (2019) 5614).