Microscopic model for spreading of a two-dimensional monolayer

TL;DR

This paper models the spreading dynamics of a two-dimensional monolayer on a crystalline surface, deriving explicit relations for the monolayer edge displacement influenced by temperature and particle interactions.

Contribution

It introduces an analytically solvable mean-field model to describe monolayer spreading, identifying critical parameters for different spreading regimes.

Findings

The monolayer edge displacement follows a square root law with time.

The prefactor depends on temperature and particle interactions.

Critical parameters determine spreading, partial wetting, or dewetting regimes.

Abstract

We study the behavior of a monolayer, which occupies initially a bounded region on an ideal crystalline surface and then evolves in time due to random hopping motion of the monolayer particles. In the case when the initially occupied region is the half-plane $X \leq 0$, we determine explicitly, in terms of an analytically solvable mean-field-type approximation, the mean displacement $X(t)$ of the monolayer edge. We find that $X(t) \approx A \sqrt{D_{0} t}$, in which law $D_{0}$ denotes the bare diffusion coefficient and the prefactor $A$ is a function of the temperature and of the particle-particle interactions parameters. We show that $A$ can be greater, equal or less than zero, and specify the critical parameter which distinguishes between the regimes of spreading ($A > 0)$, partial wetting ($A = 0$) and dewetting ($A < 0$).