Hard sphere packings within cylinders.
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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.
Published Version (Please cite this version)10.1039/c5sm02875b
Publication InfoFu, 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.
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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.
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; Organization and dynamics of complex networks; Topological elasticity of mechanical lattices.
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