Hard sphere packings within cylinders

TL;DR

This paper explores the densest arrangements of hard spheres within cylinders up to 4 times the sphere diameter, revealing 17 new structures and complex core-shell interactions that depend on cylinder size.

Contribution

It extends the known packings of hard spheres in cylinders up to D=4.00σ using advanced optimization techniques, identifying new chiral structures and complex packing behaviors.

Findings

Identified 17 new dense sphere packings in cylinders.

Discovered core-shell and quasiperiodic packing structures.

Revealed complex interactions between shell and core configurations.

Abstract

The packing of hard spheres (HS) of diameter $\sigma$ in a cylinder has been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest packings of HS under this type of confinement, however, grows increasingly complex with the cylinder diameter, $D$. Little is thus known about the densest achievable packings for $D>2.873\sigma$. In this work, we extend the identification of the packings up to $D=4.00\sigma$ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond $D\approx2.85\sigma$, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle.