An exponential kinetic model for adsorption at solid/solution interface

Abstract

An exponential kinetic model has been proposed for modeling of adsorption kinetics at the solid/solution interface. This new equation was compared with pseudo first-order (PFO) and pseudo second-order (PSO) equations as the well-known two parametric models. Based on numerically generated data points (t,q) by using of statistical rate theory equation for homogeneous surfaces, it has been shown that we can use the new model for homogeneous solid surfaces as well as the pseudo second-order model. Moreover, the driving force of new model is a combination of driving forces of PFO and PSO equations. However, using Langmuir–Freundlich equation to generate kinetic data for heterogeneous surfaces, it has been shown that the kinetic data can be described by PFO model when the adsorption rate coefficient is smaller than the desorption rate coefficient; but, when the adsorption rate coefficient is bigger than the desorption rate coefficient, which is more favorite for practical application, the new exponential model shows better agreement with kinetic data. The main advantage of using the new model for heterogeneous systems is its simplicity in comparison with Langmuir–Freundlich kinetic model which there is no analytical solution for it. Finally, the results of fitting to the experimental data represent that exponential model can describe kinetics of adsorption for both homo- and heterogeneous systems very well.