Coupling of orthogonal diffusion modes in two-dimensional nonhomogeneous systems

TL;DR

This paper investigates how collective diffusion in a 2D lattice gas on a nonhomogeneous substrate depends on particle jump rates and site potentials, revealing complex directional coupling and validating results with Monte Carlo simulations.

Contribution

It introduces an analytical variational approach to model coupled diffusion modes in nonhomogeneous 2D systems, aligning well with Monte Carlo simulations.

Findings

Diffusion coefficient depends nontrivially on jump rates in all directions.

Increasing perpendicular jump rate makes the diffusion approach mean field predictions.

Analytical results closely match Monte Carlo simulation data.

Abstract

Collective diffusion coefficient in a two-dimensional lattice gas on a nonhomogeneous substrate is investigated using variational approach. Particles reside at adsorption sites with different well depths potentials and jump randomly between them. The site blocking is the only particle--particle interaction mechanism. It is shown that the value of the diffusion coefficient in one lattice direction depends nontrivially on the rate and the character of the particle jumps in all directions. When the jump rate in the direction perpendicular to that along which the diffusion is observed increases, the collective diffusion coefficient approaches values predicted within the mean field approximation. Results of the Monte Carlo simulations for selected systems are very well reproduced by our analytical results.