Pattern formation in size-polydisperse adsorption: Fractal properties and transition to order

Random sequential adsorption of particles with size polydispersity (PRSA) is investigated. For the PRSA with a power-law small-size distribution, P(R)similar to Ralpha-1, we reveal the fractal nature of the arising patterns. The fractal dimension D-f is found to decrease from 2 to D-A = 1.305..., the fractal dimension of the Apollonian packing, as a increases from 0 to infinity. We examine PRSA by a combination of exact, scaling, mean-field, and numerical approaches. We find that the scaling theory works fairly well for the whole range of alpha, while the mean-field theory (MFT) is applicable only for small alpha. We attribute this failure of the MFT to the increasing regularity of the PRSA patterns with increasing alpha. We confirm this conclusion by the direct measurement of the entropy production rate of the pattern formation process, which demonstrates the transition from an irregular regime of the pattern formation to the regular one.