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

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

1998-06-26

arxiv.org/abs/cond-mat/9806331v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, LaTeX, 5 figures, to appear in Phys.Rev.E

Scientific paper

10.1103/PhysRevE.58.3530

We investigate the process of random sequential adsorption of polydisperse particles whose size distribution exhibits a power-law dependence in the small size limit, $P(R)\sim R^{\alpha-1}$. 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 $\alpha$. When $\alpha \to \infty$, 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 $\alpha \gg 1$, 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.

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