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, $P(R)\ensuremath{\sim}{R}^{\ensuremath{\alpha}\ensuremath{-}1}.$ We reveal a relation between pattern formation kinetics and structural properties of arising patterns. We propose a mean-field theory that provides a fair description for sufficiently small $\ensuremath{\alpha}.$ When $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\alpha}}\ensuremath{\infty},$ 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 $\ensuremath{\alpha}\ensuremath{\gg}1,$ 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.