Comparative Evaluation\nof the Dubinin–Radushkevich\nIsotherm and Its Variants

The\nDubinin–Radushkevich (DR) isotherm is a well-established\nmodel for describing adsorption equilibria in vapor–solid systems.\nIts adaptation for liquid–solid systems, especially in water\ncontaminant adsorption research, has led to several modified forms.\nIn this study, we refer to the original formulation as the traditional\nDR equation, which incorporates a term representing saturation concentration.\nA simplified variant eliminates the need for this term, enhancing\npracticality. Additionally, three other variants address dimensional\ninconsistencies identified in a previous DR adaptation. This study\nevaluates the performance of the traditional DR equation and these\nfour variants in characterizing the adsorption of antibiotic contaminantsspecifically\ntetracycline, sulfamethoxazole, and ciprofloxacinfrom aqueous\nsolutions using published data. Notable differences emerge in the\nfit of each equation to the data and in the estimation of key parameters\nsuch as maximum adsorption capacity and characteristic energy of adsorption.\nTo address these discrepancies, we introduce the Dubinin–Radushkevich–Misra\n(DRM) equation, a lesser-known variant. Preliminary results suggest\nthat the DRM equation provides a promising alternative, yielding robust\ndata fits and parameter estimates that align closely with experimental\nvalues.