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, $P(R)\ensuremath{\sim}{R}^{\ensuremath{\alpha}\ensuremath{-}1}$, $R\ensuremath{\le}{R}_{\mathrm{max}}$. We find that the patterns become more and more ordered as $\ensuremath{\alpha}$ increases, and that the Apollonian packing is obtained at the $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$ 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.