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

Abstract

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 experimental and modeling work has focused on simpler isotherms—linear, convex, or concave. This paper highlights the underexplored S-shaped (sigmoidal) isotherms and their dimensionless representations, offering a comprehensive review of their physical meaning and application in modeling sorption and ion exchange equilibrium.