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

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, $P(R)\sim R^{α-1}$. 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 $α$. When $α\to \infty$, 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 $α\gg 1$, 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.