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 isotherms including capillary condensation existing approaches can fail. Here, a general isotherm equation is derived and 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). It relies firstly on the classical thermodynamics of cluster formation, secondly on a relationship defining the free energy during the increase of the cluster size. That equation replaces the Lennard-Jones potentials used in the classical density functional theory. 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 are accessible by respective simplifications.