Kinetic theory of cluster impingement in the framework of statistical mechanics of rigid disks

TL;DR

This paper develops a mean field kinetic model for island coverage on surfaces, accounting for spatial correlations among nucleation centers, and extends previous models to include correlated dot distributions using exclusion probabilities.

Contribution

It generalizes a kinetic model to include spatial correlations among nucleation centers, improving the understanding of surface coverage dynamics.

Findings

Analytical solution for random nucleation distributions.

Extension of the model to correlated nucleation centers.

Improved predictions of surface coverage kinetics.

Abstract

The paper centres on the evaluation of the function n(theta)=N(theta)/N0, that is the normalized number of islands as a function of coverage 0<theta<1, given N0 initial nucleation centres (dots) having any degree of spatial correlation. A mean field approach has been employed: the islands have the same size at any coverage. In particular, as far as the random distribution of dots is concerned, the problem has been solved by considering the contribution of binary collisions between islands only. With regard to correlated dots, we generalize a method previously applied to the random case only. In passing, we have made use of the exclusion probability reported in [S. Torquato, B. Lu, J. Rubinstein, Phys.Rev.A 41, 2059 (1990)], for determining the kinetics of surface coverage in the case of correlated dots, improving our previous calculation [M. Tomellini, M. Fanfoni, M. Volpe Phys. Rev.B 62, 11300, (2000)].