Misinterpretation of Dubinin–Radushkevich isotherm and its implications on adsorption parameter estimates

Dubinin–Radushkevich (D – R) isotherm remains one of the widely used adsorption models in solid/liquid interface. However, adsorption potential (ε), as a function of equilibrium concentration (C_e) and solubility (C_s) of adsorbate, is frequently expressed through a dimensionally inconsistent form i.e. ε=RTln1+1Ce, instead of the correct form i.e. ε=RTlnCsCe. Although Hu and Zhang (2019) have pointed out the misinterpretation, incorrect use of isotherm however continues. All of the 10 all-time highly cited articles on D-R isotherm and 80 out of 117 articles citing the work of Hu and Zhang (2019) adopted the incorrect or ambiguous form. Only six research articles have referred source of required C_s data, i.e. literature reported value, approximated to initial adsorbate concentration, or as an additional model parameter. Modeling of D-R isotherm using datasets extracted from three selected references suggests that using the incorrect expression would have a variable impact on maximum adsorption capacity estimates. However, sorption energy would invariably be overestimated (at least 200 times) in all data sets. In the absence of any unified approach and the practical difficulty associated with ascertaining the correct C_s value, researchers are inclined to use the inconsistent model.