Polydisperse Adsorption: Pattern Formation Kinetics, Fractal Properties, and Transition to Order

TL;DR

This paper explores how polydisperse particles with a power-law size distribution adsorb randomly, revealing pattern formation kinetics, fractal properties, and a transition from irregular to ordered structures.

Contribution

It introduces a mean-field theory for polydisperse adsorption and identifies a sharp transition to ordered patterns at high size distribution exponent.

Findings

Pattern formation relates to structural properties of the adsorbed particles.

A mean-field theory accurately describes the process for small exponents.

A transition from irregular to ordered patterns occurs near jamming coverage for large exponents.

Abstract

We investigate the process of random sequential adsorption of polydisperse particles whose size distribution exhibits a power-law dependence in the small size limit, $P(R)\sim R^{\alpha-1}$. We reveal a relation between pattern formation kinetics and structural properties of arising patterns. We propose a mean-field theory which provides a fair description for sufficiently small $\alpha$. When $\alpha \to \infty$, highly ordered structures locally identical to the Apollonian packing are formed. We introduce a quantitative criterion of the regularity of the pattern formation process. When $\alpha \gg 1$, a sharp transition from irregular to regular pattern formation regime is found to occur near the jamming coverage of standard random sequential adsorption with monodisperse size distribution.