Precise algorithm to generate random sequential adsorption of hard polygons at saturation

TL;DR

This paper introduces a generalized algorithm for generating saturated random sequential adsorption packings of two-dimensional polygons, accurately determining their saturation densities without extrapolation, extending previous work on spherical particles.

Contribution

The authors extend a previously developed algorithm for spheres to polygons, enabling precise calculation of saturation densities for various regular polygons.

Findings

Saturation densities for polygons with 3 to 10 sides were determined.

Results are consistent with previous extrapolation-based studies.

The algorithm effectively reaches the saturation limit in finite time.

Abstract

Random sequential adsorption (RSA) is a time-dependent packing process, in which particles of certain shapes are randomly and sequentially placed into an empty space without overlap. In the infinite-time limit, the density approaches a "saturation" limit. Although this limit has attracted particular research interest, the majority of past studies could only probe this limit by extrapolation. We have previously found an algorithm to reach this limit using finite computational time for spherical particles, and could thus determine the saturation density of spheres with high accuracy. In this paper, we generalize this algorithm to generate saturated RSA packings of two-dimensional polygons. We also calculate the saturation density for regular polygons of three to ten sides, and obtain results that are consistent with previous, extrapolation-based studies.