In a search for a shape maximizing packing fraction for two-dimensional random sequential adsorption

TL;DR

This study investigates various two-dimensional shapes in random sequential adsorption to identify which shape achieves the highest saturated packing fraction, finding that elongated ellipses with a specific axis ratio perform best.

Contribution

The paper compares multiple 2D shapes in RSA to determine the shape with the maximum packing fraction, highlighting ellipses with a 1.85 axis ratio as optimal.

Findings

Maximum packing fraction is approximately 0.58405.

Ellipses with a 1.85 axis ratio yield the highest packing.

Elongated shapes outperform other studied geometries.

Abstract

Random sequential adsorption (RSA) of various two dimensional objects is studied in order to find a shape which maximizes the saturated packing fraction. This investigation was begun in our previous paper [Cie\'sla et al., Phys. Chem. Chem. Phys. 17, 24376 (2015)], where the densest packing was studied for smoothed dimers. Here this shape is compared with a smoothed $n$-mers, spherocylinders and ellipses. It is found that the highest packing fraction out of the studied shapes is $0.58405 \pm 0.0001$ and is obtained for ellipses having long-to-short axis ratio of $1.85$, which is also the largest anisotropy among the investigated shapes.