A critical review of adsorption isotherm models for aqueous contaminants: Curve characteristics, site energy distribution and common controversies

The quantitative description of the equilibrium data by the isotherm models is an indispensable link in adsorption studies. The previous review papers focus on the underlying assumptions, fitting methods, error functions and practical applications of the isotherm models, usually ignoring their curve characteristics, selection criteria and common controversies. The main contents of this review include: (i) effect of the model parameters on the isotherm curves; (ii) determination of the site energy distribution; (iii) selection criteria of the isotherm models; and (iv) elimination of some common controversies. It is of great significance to reveal the curve characteristics for selecting a proper isotherm model. The site energy distribution is conducive to understanding the physicochemical properties of the adsorbent surface. The complete isotherm is recommended to be correlated with the experimental data. The model parameter qmax should be cautiously adopted for comparison of the adsorbent performance. The residual plot can be used to diagnose the fitting quality of the isotherm models further. This review also addresses some common mistakes and controversies and thereby avoids their propagation in future publications.