Comparative Evaluation of the Dubinin–Radushkevich Isotherm and Its Variants

The Dubinin–Radushkevich (DR) isotherm is a well-established model for describing adsorption equilibria in vapor–solid systems. Its adaptation for liquid–solid systems, especially in water contaminant adsorption research, has led to several modified forms. In this study, we refer to the original formulation as the traditional DR equation, which incorporates a term representing saturation concentration. A simplified variant eliminates the need for this term, enhancing practicality. Additionally, three other variants address dimensional inconsistencies identified in a previous DR adaptation. This study evaluates the performance of the traditional DR equation and these four variants in characterizing the adsorption of antibiotic contaminants─specifically tetracycline, sulfamethoxazole, and ciprofloxacin─from aqueous solutions using published data. Notable differences emerge in the fit of each equation to the data and in the estimation of key parameters such as maximum adsorption capacity and characteristic energy of adsorption. To address these discrepancies, we introduce the Dubinin–Radushkevich–Misra (DRM) equation, a lesser-known variant. Preliminary results suggest that the DRM equation provides a promising alternative, yielding robust data fits and parameter estimates that align closely with experimental values.