Insights into the S-shaped sorption isotherms and their dimensionless forms

Isotherms are of paramount importance for the interpretation of adsorption and ion exchange mechanisms and the design of separation and catalytic processes. Although the literature on sorption isotherms is rich, most of experiments and models employed are limited to systems that obey simple equilibrium isotherms, such as linear, favorable (convex-upward) or unfavorable (concave-upward). This paper deals with the rather overlooked S-shaped isotherms and their dimensionless forms, which are of great importance for the modeling of separation processes and interpretation of equilibrium data. A review on the physical significance and applications of S-shaped isotherms in adsorption and ion exchange process is also presented.