Polydisperse adsorption: Pattern formation kinetics, fractal properties, and transition to order

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)similar to Ralpha-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 alpha. When alpha-->(infinity), 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 alpha much greater than 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.