Laplacian growth in self-consistent Laplacian field : Effect of the long-range interparticle interactions on the fractal dimension of structures formed by their aggregation-limited diffusion

TL;DR

This paper investigates how long-range interparticle interactions influence the fractal morphology of structures formed by aggregation-limited diffusion, using numerical simulations and comparing results with experimental data.

Contribution

It introduces a model incorporating binary Laplacian potentials to simulate the effect of surface stress fields on aggregation structures.

Findings

Interparticle interactions alter the fractal dimension of aggregates.

The external fractal dimension is more sensitive to the potential.

Model results align with experimental observations for antimony and silver clusters.

Abstract

We numerically simulate the dynamics of aggregation of interacting atomic clusters deposited on a surface. We show that the shape of the structures resulting from their aggregation-limited random walk is affected by the presence of a binary interparticle Laplacian potential due to, for instance, the surface stress field. We characterize the morphologies we obtain by their Hausdorff fractal dimension as well as the so-called external fractal dimension, which appears more sensitive to the potential. We demonstrate the relevance of our model by comparing it to previously published experimental results for antymony and silver clusters deposited onto graphite surface.