A New Two-Parameter Isotherm for Modeling Adsorptive Removal of Water Contaminants

The two-parameter Elovich isotherm is increasingly being used to describe the adsorption of water contaminants on solid materials. This isotherm is derived from a modified version of Langmuir’s kinetic theory for saturable adsorption. However, despite incorporating a saturation capacity parameter, the Elovich isotherm fails to predict an adsorption maximum at high concentrations. As a result, there are disparities between the estimated and observed saturation capacities. In this study, we have identified a conceptual flaw within the Elovich isotherm responsible for this anomaly. By introducing modifications to the theoretical derivation of the Elovich isotherm, we have rectified the conceptual defect. The modified isotherm retains the two parameters of the Elovich isotherm but possesses a different mathematical structure. In contrast to the Elovich isotherm, the new isotherm provides estimated saturation capacities that align closely with the observed values. A comparative analysis demonstrates the superiority of the new isotherm over the Elovich isotherm in fitting data featuring a plateau. However, the new isotherm is loading-implicit, posing challenges in data fitting. To overcome this limitation, we have developed a novel method to convert the loading-implicit isotherm into an explicit form. This conversion enables convenient data fitting and facilitates the evaluation of the site energy distribution of heterogeneous adsorbents.