Revisiting the Temkin Isotherm: Dimensional Inconsistency and Approximate Forms

The Temkin isotherm equation is increasingly being used to correlate adsorption isotherms of water contaminants. This research note shows that the Temkin isotherm as used in environmental adsorption research suffers from a fundamental flaw of dimensional inconsistency. In addition, an important but frequently overlooked issue concerns the approximate nature of the Temkin isotherm which limits its ability to fit type I isotherms: it has neither a Henry's law limit at low loadings nor a finite saturation limit at high loadings. A different approximate Temkin isotherm, which approaches a linear isotherm at low concentrations and commences at the (0,0) origin, is shown to outperform the commonly used Temkin isotherm in terms of fitting ability and resembles the Langmuir and Freundlich isotherms in describing adsorption data without a saturation plateau. It is hoped that the material presented in this research note will lead to a better comprehension of the Temkin isotherm.

Automated summary

The Temkin isotherm equation is commonly used in correlating adsorption isotherms of water contaminants, but it suffers from a fundamental flaw of dimensional inconsistency and limited fitting ability. A different approximate Temkin isotherm, which outperforms the commonly used Temkin isotherm in terms of fitting ability, approaches a linear isotherm at low concentrations and commences at the (0,0) origin, resembling Langmuir and Freundlich isotherms.