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

ABSTRACT

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. $\epsilon =RTln\left(1+\frac{1}{C_e}\right)$, instead of the correct form i.e. $\epsilon =RTln\left(\frac{C_s}{C_e}\right)$. 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.

KEYWORDS:

• Dubinin–radushkevich isotherm
• inconsistency
• adsorption potential

Acknowledgments

This work is supported by the Karunya Institute of Technology and Sciences, Coimbatore, India. Standard ethical and professional conduct has been followed. There are no conflicts of interest (financial or otherwise) associated with this publication.

Disclosure statement

No potential conflict of interest was reported by the authors.

Statement of novelty

Manuscript entitled “Misinterpretation of Dubinin–Radushkevich Isotherm and its Implications on Adsorption Parameter Estimates”.

D–R isotherm is widely adopted to model adsorption at Solid/Liquid Interfaces. However, a dimensionally incorrect expression of adsorption energy is evident in a majority of the studies. Hu and Zhang has pointed out this misuse in a recent communication [Journal of Molecular Liquids 277 (2019) 646–648], but have provided no insight on possible reason for such recouurrence error or its repercussation on isotherm parameter estimates. About 69 out of 117 articles citing the work of Hu and Zhanh have continued the use of the erroneous expression.

In this communication, adopting experimental data set from three referred studies, we observed that an accurate value of sorbate solubility (required for the correct expression) is a challenge in non-linear regression. Prefixing the solubility data from reference can result in severe inaccuracy in adsorption energy estimates. It is recommended that the parametric assumption of sorbate solubility in D-R isotherm is a better choice.

Authors contributions

BM conceived the work and drafted the outline of the manuscript, redrawn the artwork, and performed mathematical analysis, and reshaped the discussion.

Availability of data and materials

Experimental data can be available from corresponding authors on reasonable request.

Supplemental data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/01496395.2023.2189050.

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.