Mirror, Mirror on the Wall, Which Is the Fairest of Them All? Comparing the Hill, Sips, Koble-Corrigan, and Liu Adsorption Isotherms

Experimental equilibrium data for the adsorption of water contaminants on solid surfaces are generally correlated using suitable isotherm expressions. In most cases, adsorption isotherms are used empirically with the primary aim of finding the best fitting ones. The literature of adsorptive water decontamination is replete with such isotherm comparisons, usually evaluated on the basis of some statistical metrics such as R-2 and RMSE. For example, several studies have compared and ranked the isotherm equations of Hill, Sips, Koble-Corrigan, and Liu. These comparative evaluations imply that the four isotherms possess different data fitting abilities, and consequently it is possible to identify the most accurate one. The present study argues that this commonly held notion is incorrect. It demonstrates that the four isotherms provide the same results when fitted to three previously published data sets. This finding suggests that the four isotherms are mathematically equivalent despite apparent differences in their formulations. Indeed, a mathematical analysis unequivocally shows that the Hill, Sips, Koble-Corrigan, and Liu isotherms can be represented by a single generic equation with three arbitrary fitting parameters. As such, the four isotherms must provide exactly the same fit to a given set of isotherm data.