Study of Diffusion in a One-Dimensional Lattice-Gas Model of Zeolites: The Analytical Approach and Kinetic Monte Carlo Simulations

The diffusion of molecules adsorbed in a one-dimensional channel with side pockets is investigated in the framework of a one-dimensional lattice-gas model. The model can describe the molecules migration in some type of zeolites. We obtained the exact expression for the free energy of this model. Using the local equilibrium approximation we derived the analytical expressions for the diffusion coefficients. The concentration dependencies of the center-of-mass and Fickian diffusion coefficients are calculated for some representative values of the lateral interactions between molecules. The theoretical dependencies are compared with the numerical data obtained by the kinetic Monte Carlo simulations. The data obtained by the two completely different methods coincide amazingly well in the whole concentration and wide interaction regions.