Simulation of adsorption, desorption, and exchange kinetics of mixtures on planar surfaces .2. Diffusive-controlled adsorption, desorption, and exchange kinetics for multicomponent mixtures

A quantitative theory for the diffusive-controlled adsorption, desorption, and exchange kinetics for multicomponent mixtures on a planar substrate has been developed. A power series and an asymptotic representation of the adsorption and desorption valid for short and long times are obtained for systems obeying arbitrary adsorption isotherms of multicomponent mixtures. The analytical solutions over a wide range of time are found for multicomponent mixtures satisfying arbitrary adsorption and desorption isotherms using the Consistent Time Scale (CTS) approach. It is shown that the relaxation function F(t) may be applied to describe the adsorption and desorption processes over a wide range of times. The equation in the form F(t) = log[Gamma(o)/Gamma(t) - 1] = n log(t/t(rel)) describes the diffusion-controlled adsorption and desorption processes for arbitrary adsorption isotherms. The analytical analysis is shown to be an asymptotical correlation of n = 0.5 for short and large times for adsorption isotherms of different types. The simple formulas are derived to calculate the parameters n, t(rel)(ad), and t(rel)(des) (the relaxation time for adsorption and desorption processes, respectively) and also the times of establishment of the equilibrium states for the adsorption and desorption processes for arbitrary adsorption isotherms.