Fractal formation and ordering in random sequential adsorption

TL;DR

This paper investigates the fractal patterns formed during random sequential adsorption of particles with a power-law size distribution, revealing a transition from irregular to ordered structures as the distribution's exponent increases.

Contribution

It introduces a scaling theory linking kinetic and structural properties and identifies a transition to highly ordered, Apollonian-like packings at large exponents.

Findings

Patterns become more ordered with increasing alpha

Transition from irregular to regular pattern formation

Development of a scaling theory connecting kinetics and structure

Abstract

We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered as $\alpha$ increases, and that the Apollonian packing is obtained at $\alpha \to \infty $ limit. We introduce the entropy production rate as a quantitative criteria of regularity and observe a transition from an irregular regime of the pattern formation to a regular one. We develop a scaling theory that relates kinetic and structural properties of the system.