PATTERN-FORMATION IN SIZE-POLYDISPERSE ADSORPTION - FRACTAL PROPERTIES AND TRANSITION TO ORDER

Random sequential adsorption of particles with size polydispersity (PR SA) is investigated. For the PRSA with a power-law small-size distribu tion, P(R)similar to Ralpha-1, we reveal the fractal nature of the ari sing patterns. The fractal dimension D-f is found to decrease from 2 t o 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 ex act, scaling, mean-field, and numerical approaches. We find that the s caling theory works fairly well for the whole range of alpha, while th e mean-field theory (MFT) is applicable only for small alpha. We attri bute this failure of the MFT to the increasing regularity of the PRSA patterns with increasing alpha. We confirm this conclusion by the dire ct measurement of the entropy production rate of the pattern formation process, which demonstrates the transition from an irregular regime o f the pattern formation to the regular one.