Diffusion of interacting particles in discrete geometries: equilibrium and dynamical properties

TL;DR

This paper investigates the equilibrium and dynamical properties of interacting particles in discrete geometries, combining analytical models and kinetic Monte Carlo simulations to understand diffusion behavior and the effects of correlations.

Contribution

It introduces new analytical expressions for diffusion coefficients considering interaction strength and compares them with simulations, highlighting when correlations significantly affect diffusion.

Findings

Maxwell-Stefan diffusion can exceed self-diffusion, a novel observation.

Diffusive behavior is similar across dimensions, with correlations decreasing in higher dimensions.

Self-diffusion scales inversely with length in long one-dimensional systems.

Abstract

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their behavior is similar to that of interacting particles in porous materials. Different expressions for the particle jump rates are derived from transition state theory. Which expression should be used depends on the strength of the inter-particle interactions. Analytical expressions for the self- and transport diffusion are derived when correlations, caused by memory effects in the environment, are neglected. The diffusive behavior is studied numerically with kinetic Monte Carlo (kMC) simulations, which reproduces the diffusion including correlations. The effect of correlations is studied by comparing the analytical expressions with the kMC simulations. It is found that the Maxwell-Stefan diffusion can exceed the self-diffusion. To our knowledge, this is the first time this is observed. The diffusive behavior in one-dimensional and higher dimensional systems is qualitatively the same, with the effect of correlations decreasing for increasing dimension. The length dependence of both the self- and transport diffusion is studied for one-dimensional systems. For long lengths the self-diffusion shows a one over length dependence. Finally, we discuss when agreement with experiments and simulations can be expected. The assumption that particles in different cavities do not interact is expected to hold quantitatively at low and medium particle concentrations, if the particles are not strongly interacting.