Size-Controlled Capacity and Isocapacity Concentration in Freundlich Adsorption

The Freundlich isotherm is a classic model widely used to analyze the equilibrium of solution-phase adsorption. Further analysis of the adsorption mechanism has, however, been hindered by the empirical nature of the Freundlich isotherm. By deriving the Freundlich isotherm from the Gibbs equation, this study presents a novel interpretation of the classic model with theoretical definitions for model parameters. The new interpretation shows that the inverse of the Freundlich power is linearly correlated with the molecular weight of an adsorbate for congeners with similar chemical structures, revealing a previously unappreciated dependence of adsorption capacity on the molecular size of the adsorbate. The new interpretation also shows a linear correlation between the Freundlich power and the logarithm of the equilibrium constant, exposing the existence of an isocapacity concentration for the adsorption of congeners. The quantitative structure-activity relationships, known as QSARs, represented by these linear correlations are validated using experimental data reported in the literature, including the adsorption of aliphatic alcohols by an activated carbon and the adsorption of aromatic hydrocarbons adsorption by an aquitard soil. These results provide an unprecedented explanatory power to understanding experimental observations of solution-phase adsorption using the Freundlich isotherm.