Fractal-Like Kinetics for Adsorption on Heterogeneous Solid Surfaces

A physical meaning of the fractal-like concept has been represented for kinetics of adsorption on energetically heterogeneous solid surfaces. This study shows that the adsorption kinetics at the solid/solution interface in a real system with different types of surface sites and then with different affinity for adsorption can be described by a fractal-like approach. On the basis of this study, the history of process can affect the rate of process, and therefore the observed adsorption rate coefficient is a function of time. Employing this concept to extend some kinetic models leads to obtaining different fractal-like kinetic models that can be utilized to simulate adsorption kinetics in systems with heterogeneous surfaces. The simulation of experimental kinetic data with fractal-like equations for the heterogeneous surfaces and the fact that their equilibrium data follow the Langmuir-Freundlich (Sips) isotherm indicate the applicability of these equations for real systems. The obtained results show that the observed adsorption rate coefficient in heterogeneous surface systems depends on time, and it decreases by passing time.