Hard sphere packings within cylinders.
Abstract
Arrangements of identical hard spheres confined to a cylinder with hard walls have
been used to model experimental systems, such as fullerenes in nanotubes and colloidal
wire assembly. Finding the densest configurations, called close packings, of hard
spheres of diameter σ in a cylinder of diameter D is a purely geometric problem that
grows increasingly complex as D/σ increases, and little is thus known about the regime
for D > 2.873σ. In this work, we extend the identification of close packings up to
D = 4.00σ 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 ≈ 2.85σ, 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 the 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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/15345Published Version (Please cite this version)
10.1039/c5sm02875bPublication Info
Fu, Lin; Steinhardt, William; Zhao, Hao; Socolar, Joshua ES; & Charbonneau, Patrick (2016). Hard sphere packings within cylinders. Soft Matter, 12(9). pp. 2505-2514. 10.1039/c5sm02875b. Retrieved from https://hdl.handle.net/10161/15345.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
Collections
More Info
Show full item recordScholars@Duke
Patrick Charbonneau
Professor of Chemistry
Professor Charbonneau studies soft matter. His work combines theory and simulation
to understand the glass problem, protein crystallization, microphase formation, and colloidal
assembly in external fields.
Joshua Socolar
Professor of Physics
Prof. Socolar is interested in collective behavior in condensed matter and dynamical
systems. His current research interests include:
Limit-periodic structures, quasicrystals, packing problems, and tiling theory;
Self-assembly and phases of designed colloidal particles;
Shear jamming and stick-slip behavior in dry granular materials;
Organization and dynamics of complex networks;
Topological elasticity of mechanical lattices.
Alphabetical list of authors with Scholars@Duke profiles.

Articles written by Duke faculty are made available through the campus open access policy. For more information see: Duke Open Access Policy
Rights for Collection: Scholarly Articles
Works are deposited here by their authors, and represent their research and opinions, not that of Duke University. Some materials and descriptions may include offensive content. More info