Dynamics of Chainlike Molecules on Surfaces

TL;DR

This paper investigates how chainlike molecules diffuse on surfaces, revealing that entropy-driven repulsion causes increasing diffusion coefficients at low to intermediate coverages, with theoretical and simulation results aligning well with experiments.

Contribution

It introduces a combined simulation and mean field theoretical approach to explain the diffusive behavior of chainlike molecules on surfaces, emphasizing entropy effects.

Findings

Density profiles show steep edges due to diffusive properties.

Diffusion coefficient $D_C(\theta)$ increases then decreases with coverage.

Good agreement between theory, simulations, and experiments.

Abstract

We consider the diffusion and spreading of chainlike molecules on solid surfaces. We first show that the steep spherical cap shape density profiles, observed in some submonolayer experiments on spreading polymer films, imply that the collective diffusion coefficient $D_C(\theta)$ must be an increasing function of the surface coverage $\theta$ for small and intermediate coverages. Through simulations of a discrete model of interacting chainlike molecules, we demonstrate that this is caused by an entropy-induced repulsive interaction. Excellent agreement is found between experimental and numerically obtained density profiles in this case, demonstrating that steep submonolayer film edges naturally arise due to the diffusive properties of chainlike molecules. When the entropic repulsion dominates over interchain attractions, $D_C(\theta)$ first increases as a function of $\theta$ but then eventually approaches zero for $\theta \to 1$. The maximum value of $D_C(\theta)$ decreases for increasing attractive interactions, leading to density profiles that are in between spherical cap and Gaussian shapes. We also develop an analytic mean field approach to explain the diffusive behavior of chainlike molecules. The thermodynamic factor in $D_C(\theta)$ is evaluated using effective free energy arguments, and the chain mobility is calculated numerically using the recently developed dynamic mean field theory. Good agreement is obtained between theory and simulations.