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

Source: [Polydisperse Adsorption: Pattern Formation Kinetics, Fractal Properties, and Transition to Order](<https://www.sota2.com/research/paper/68fa248f2c2a3760193a5d26>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T02:58:37.529Z

Authors: N.V.Brilliantov, Yu.A.Andrienko, P.L.Krapivsky, J.Kurths

Published: 1998-06-26T17:40:24.000Z

## 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, $P(R)\\sim R^{\\alpha-1}$. 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9806331>)

[PDF](<https://arxiv.org/pdf/cond-mat/9806331.pdf>)