Bulk Mediated Surface Diffusion: Finite System Case

TL;DR

This paper analyzes the diffusion of adsorbed molecules on a finite cubic lattice surface using a Master Equation approach, deriving analytical expressions and validating them with Monte Carlo simulations.

Contribution

It provides an analytical framework for surface diffusion in finite systems and compares results with simulations to validate the model.

Findings

Analytical expressions for surface dispersion over time.

Excellent agreement between theory and Monte Carlo simulations.

Insights into diffusion dynamics at finite system boundaries.

Abstract

We address the dynamics of adsorbed molecules (a fundamental issue in surface physics) within the framework of a Master Equation scheme, and study the diffusion of particles in a finite cubic lattice whose boundaries are at the $z=1$ and the $z=L$ planes where $L = 2,3,4,...$, while the $x$ and $y$ directions are unbounded. As we are interested in the effective diffusion process at the interface $z = 1$, we calculate analytically the conditional probability for finding the system on the $z=1$ plane as well as the surface dispersion as a function of time and compare these results with Monte Carlo simulations finding an excellent agreement.