The inappropriate application of the regression Langmuir Q_m for adsorption capacity comparison

The Langmuir equation, the best known adsorption model in the past century, was extensively applied to describe adsorption isotherms. The saturated adsorption amount (Q_m) obtained from the Langmuir model is an essential index to evaluate the maximum adsorption capacity of the adsorbent, which was assumed to be irrelevant to the aqueous concentration of the adsorbate. Adsorption isotherms of cadmium onto soil and biochar were performed in the current study, and the regression Langmuir Q_m was demonstrated to be highly dependent on the aqueous concentration. The regression Q_m increased from 0.066 to 2.17 mg·g^-1 (by ~3-fold) for the selected soil, and from 2.12 to 48.4 mg·g^-1 (by ~23-fold) for the chosen biochar when the highest initial aqueous concentration increased from 2.34 to 887 mg·L^-1. One inappropriate application for comparison of the regression Langmuir Q_m as the adsorption capacity is found, i.e., it is difficult to directly compare the regression Q_m without neither a saturated isotherm nor considering the experimental conditions. It is also very hard to accurately predict adsorption behavior by the regressed Langmuir model obtained from a partial adsorption isotherm. It is suggested to pay more attention to the difference between the saturated adsorption capacity and the regression Q_m value derived from one unsaturated isotherm.