Series expansion studies of random sequential adsorption with diffusional relaxation

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.

35 pages. revtex. 16 eps figures. Series expansion coefficients are attached at the end of the soure/LaTex file (named diff.tex). uses fleqn.sty

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• A fast algorithm for random sequential adsorption of discs
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• Extended series expansions for random sequential adsorption