Series expansion studies of random sequential adsorption with diffusional relaxation

TL;DR

This paper develops long series expansions and simulations to analyze the kinetics of random sequential adsorption with diffusional relaxation, revealing detailed short-term behavior and confirming large-time saturation trends.

Contribution

The authors introduce an efficient algorithm to generate long series expansions for the coverage in models of adsorption with diffusion, providing new insights into their kinetic behaviors.

Findings

Series expansions accurately describe short and intermediate time kinetics.

Large-time coverage approaches saturation as t^{-1/2}.

Simulations confirm theoretical predictions of saturation behavior.

Abstract

We obtain long series (28 terms or more) for the coverage (occupation fraction) $\theta$, in powers of time $t$ for two models of random sequential adsorption with diffusional relaxation using an efficient algorithm developed by the authors. Three different kinds of analyses of the series are performed for a wide range of $\gamma$, the rate of diffusion of the adsorbed particles, to investigate the power law approach of $\theta$ at large times. We find that the primitive series expansions in time $t$ for $\theta$ capture rich short and intermediate time kinetics of the systems very well. However, we see that the series are still not long enough to extract the kinetics at large times for general $\gamma$. We have performed extensive computer simulations employing an efficient event-driven algorithm to confirm the $t^{-1/2}$ saturation approach of $\theta$ at large times for both models, as well as to investigate the short and intermediate time behaviors of the systems.