The theory of diffusion in a binary mixture of molecules coadsorbed on a two-dimensional lattice

Abstract

The diffusion in the binary mixture of molecules coadsorbed on a square lattice is investigated by a theoretical approach and the Monte Carlo simulations. Using a lattice gas model I have derived a system of equations describing the diffusion of the molecules in the Fickian and Onsager representations. Also, I have obtained the analytical expressions for the Fickian diffusion coefficients. These expressions are derived taking into account the lateral interactions between the molecules and the interactions of the activated molecules in the saddle points of the lattice potential relief with their surroundings. The diffusion equations in the Fickian representation coincide with the corresponding classical counterparts, but the Onsager-like equations differ significantly from their standard lore – the cross terms are absent. It occures that the new transport coefficients describing the diffusion in the new Onsager representation are expressed in a rather nontrivial way via the phenomenological coefficients entering the classical equations. The Monte Carlo simulations have been used to test the correctness of the new expressions. There is a very good coincidence between the thermodynamic and kinetic data in the whole coverage region and in the wide range of the lateral interactions. The interactions substantially influence on the behavior of the thermodynamic quantities and the tracer and Fick diffusivities. These results demonstrate that the classical description of the molecule diffusion in the Onsager representation is not universal and may be not applied for some lattice gas systems.