Fractal formation and ordering in random sequential adsorption

Abstract

We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{α-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered as $α$ increases, and that the Apollonian packing is obtained at $α\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.