Statistical analysis of adsorption isotherm models and its appropriate selection

In adsorption research, there was a good amount of adsorption data on various absorbent-adsorbate systems and many isotherm models were studied but there was no study on applicability of models to a group of adsorbent-adsorbate systems. In order to establish this, adsorption data obtained from literature for activated carbon with different solutes/sorbate(s) were considered and modelled with various adsorption models. The molecular mass of the solutes varies from 78.118(Benzene) to 932(Direct blue 2B dye) g.mol−1 and adsorbent surface area varies from 516 to 1100 m2 g−1. In this work, twelve commonly known isotherms models were employed to correlate the adsorption data. For modelling polymath® software has been used. The input data for the polymath® software were amount of adsorbate per unit amount of adsorbent, qe vs. concentration, ce. Nonlinear optimization of isotherm data gives model parameters. The correlating ability of the various models was compared in terms of arithmetic average relative deviation (AARD) calculated based on qe. The lowest overall AARD% values were observed for Baudu Isotherm and Langmuir-Freundlich and the corresponding AARD% values were 2.6 and 2.8 respectively. The highest overall AARD% value was observed for Marczewski-jaroniec isotherm and the corresponding AARD% is 23.5. Corrected Akaike’s information criterion (AICcorrected) was employed to known the best model. We observed lowest AICcorrected(15.859) value for Langmuir-Freundlich isotherm and the highest AICcorrected(59.283) value for Marczewski-jaroniec isotherm. AICcorrected reveals that Langmuir-Freundlich isotherm was efficient in correlating the isotherm data. Further, Pair-t test was performed between Baudu isotherm and other model. •The correlating ability of various adsorption models for adsorbent-absorbate system was identified.•Twelve isotherms models were employed to correlate the adsorption data.•Pair-t test was performed between Baudu isotherm and other model.•Polymath® Software was used for this analysis.•Langmuir-Freundlich isotherm is efficient in correlating the isotherm data.