Bulk Mediated Surface Diffusion: The Infinite System Case

TL;DR

This paper introduces an analytical model for bulk-mediated surface diffusion using CTRW, revealing sub-diffusive behavior and validating results with Monte Carlo simulations, advancing understanding of interface processes.

Contribution

It presents a novel analytical CTRW-based model for bulk-mediated surface diffusion, including asymptotic analysis and simulation validation.

Findings

Sub-diffusive regime identified for large times

Analytical results agree with Monte Carlo simulations

First visit time to the surface evaluated

Abstract

An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented. The time evolution of the effective probability distribution width on the surface is calculated and analyzed within an anomalous diffusion framework. The asymptotic behavior for large times shows a sub-diffusive regime for the effective surface diffusion but, depending on the observed range of time, other regimes may be obtained. Montecarlo simulations show excellent agreement with analytical results. As an important byproduct of the indicated approach, we present the evaluation of the time for the first visit to the surface.