Monolayer Spreading on a Chemically Heterogeneous Substrate

TL;DR

This paper investigates the spreading dynamics of a monolayer of particles on a chemically heterogeneous substrate, revealing a logarithmic correction to the typical diffusive growth and analyzing effects of site trapping and particle interactions.

Contribution

The study introduces a mean-field theory for monolayer spreading on heterogeneous substrates with randomly placed active sites, supported by numerical simulations and analysis of particle current behavior.

Findings

Monolayer edge displacement follows a diffusive-logarithmic growth law.

Numerical simulations confirm the theoretical growth law and determine the effective diffusion coefficient.

Chemically active sites significantly influence spreading kinetics and particle current behavior.

Abstract

We study the spreading kinetics of a monolayer of hard-core particles on a semi-infinite, chemically heterogeneous solid substrate, one side of which is coupled to a particle reservoir. The substrate is modeled as a square lattice containing two types of sites -- ordinary ones and special, chemically active sites placed at random positions with mean concentration $\alpha$. These special sites temporarily immobilize particles of the monolayer which then serve as impenetrable obstacles for the other particles. In terms of a mean-field-type theory, we show that the mean displacement $X_0(t)$ of the monolayer edge grows with time $t$ as $X_0(t) = \sqrt{2 D_{\alpha} t \ln(4 D_{\alpha} t/\pi a^2)}$, ($a$ being the lattice spacing). This time dependence is confirmed by numerical simulations; $D_{\alpha}$ is obtained numerically for a wide range of values of the parameter $\alpha$ and trapping times of the chemically active sites. We also study numerically the behavior of a stationary particle current in finite samples. The question of the influence of attractive particle-particle interactions on the spreading kinetics is also addressed.