Modification of Langmuir isotherm in solution systems—definition and utilization of concentration dependent factor

The Langmuir isotherm, originally derived for the adsorption of gas molecules on solid surfaces, was modified to fit the adsorption isotherm of solutes onto solid surfaces in solution systems. The aim of this modification is based on the fact that direct application of the Langmuir isotherm to solution systems often leads to poor data fitting. In the present communication, it is shown that the level of data fitting to the Langmuir isotherm of literature data can be improved by a simple modification introducing a concentration dependent factor, X. The key concept of the modification lies in that the concentration of solute affects both adsorption and desorption stages. As a first approximation, we adopted a single-term polynomial for both processes of adsorption and desorption. Based on reanalysis of literature data of adsorption in solution, we confirmed that indeed the modified Langmuir isotherm more accurately describes the experimental observations. Furthermore, we proposed that the concentration dependent factor could be associated with the surface heterogeneity index that was introduced in a few other modified Langmuir isotherms. Some advantages and limitations of proposed modified Langmuir isotherm are also discussed.