Saturated random packing built of arbitrary polygons under random sequential adsorption protocol

TL;DR

This paper introduces a new algorithm for generating strictly saturated random packings of arbitrary polygons via the RSA protocol, enabling detailed analysis of packing densities and microstructural properties.

Contribution

The authors develop a versatile algorithm for saturated polygon packings and analyze packing fractions and microstructure for various triangle shapes.

Findings

Maximum packing density of 0.552814 for specific triangle side ratios

Algorithm successfully generates saturated packings of any polygon type

Insights into growth kinetics and distribution of packing fractions

Abstract

Random packings and their properties are a popular and active field of research. Numerical algorithms that can efficiently generate them are useful tools in their study. This paper focuses on random packings produced according to the random sequential adsorption (RSA) protocol. Developing the idea presented in [G. Zhang, Phys. Rev. E {\bf 97}, 043311 (2018)], where saturated random packings built of regular polygons were studied, we create an algorithm that generates strictly saturated packings built of any polygons. Then, the algorithm was used to determine the packing fractions for arbitrary triangles. The highest mean packing density, $0.552814 \pm 0.000063$, was observed for triangles of side lengths $0.63:1:1$. Additionally, microstructural properties of such packings, kinetics of their growth as well as distributions of saturated packing fractions and the number of RSA iterations needed to reach saturation were analyzed.