Algorithms to generate saturated random sequential adsorption packings built of rounded polygons

TL;DR

This paper introduces an algorithm for generating saturated random packings of rounded polygons, enabling the study of their properties and packing densities, with applications in modeling molecular monolayers.

Contribution

The paper presents a novel algorithm for creating saturated random packings of rounded polygons, expanding the tools for studying complex shape packings.

Findings

Packing fraction peaks for rounded triangles.

Packing density approaches that of disks with more sides and rounding.

Rounded polygons can be slightly denser than disks even at high side counts.

Abstract

We present the algorithm for generating strictly saturated random sequential adsorption packings built of rounded polygons. It can be used to study various properties of such packings built of a wide variety of different shapes and in modelling monolayers obtained during the irreversible adsorption processes of complex molecules. Here, we apply the algorithm to study the densities of packings built of rounded regular polygons. Contrary to packings built of regular polygons, where packing fraction grows with an increasing number of polygon sides, the packing fraction reaches its maximum for packings built of rounded regular triangles. With a growing number of polygon sides and increasing rounding radius, the packing fractions tend to the limit given by a packing built of disks. However, they are still slightly denser, even for the rounded 25-gon, which is the highest-sided regular polygon studied here.