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, $P(R)\sim R^{\alpha -1}$, $R\le R_{\max }$. 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.

4 pages, RevTex, 4 postscript figures. To appear in Phys.Rev.Lett

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