Small-Sample Corrected Akaike Information Criterion: An appropriate statistical tool for ranking of adsorption isotherm models

Abstract

Ranking of seven equilibrium isotherm models with various numbers of parameters (Langmuir, Freundlich, Redlich–Peterson, Sip, Langmuir–Freundlich, Fritz–Schlunder-3 parameter and Fritz–Schlunder-4 parameter)for the adsorption of Cu2+ and Cd2+ onto Bentonite and modified Bentonite clay was done using the smallsample-corrected Akaike information criterion (AICc). It was observed that the Freundlich model ranked first among the adsorption isotherm models considered. Inmost cases, using the AICc, the Langmuir model was ranked the second best isotherm model. Modification of Geothite, Humic acid, and Goethite+Humic acid with increase in temperature was observed to affect the Relative Akaike Weight (RAW) which describes the performance of adsorption models relative to the adsorption model with the minimum AICc estimate. The AICc was found to rank adsorption isotherm models better than error functions because it is more sensitive to model deviations and takes into consideration the number of parameters in an equilibrium isotherm model. AICc was found to be more reliable in resolving very close performance of adsorption isotherms. This study showed that the conventional isotherm model, Freundlich, is a better model for describing experimental data from adsorption of Cu2+ and Cd2+ onto Bentonite and modified Bentonite adsorbents than models derived from them and having a higher number of parameters.