Hard sphere packings within cylinders

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 $D\approx 2.85\sigma$, 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.

11 pages, 11 figures

References in corpus (3)

• Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
• Can the packing efficiency of binary hard spheres explain the glass-forming ability of bulk metallic glasses?
• Theory of cylindrical dense packings of disks

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• Theory of rotational columnar structures of soft spheres
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• Inherent Structure Landscape of Hard Spheres Confined to Narrow Cylindrical Channels
• Competing Hexagonal and Square Lattices on a Spherical Surface
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• Transitions between phyllotactic lattice states in curved geometries
• Exact anisotropic properties of hard spheres in narrow cylindrical confinement
• Positional ordering of hard adsorbate particles in tubular nanopores
• Shape multistability in flexible tubular crystals through interactions of mobile dislocations
• Controlled transitions between phyllotactic states of repulsive particles confined on the surface of a cylinder
• Chiral Packings in Cylinders are Ultrasensitive to Confinement Deformation
• Formation of cylindrical shells via sphere packing from fluidized beds