Organizing principles for dense packings of nonspherical hard particles

Not all shapes are created equal

Salvatore Torquato, Yang Jiao

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

We have recently devised organizing principles to obtain maximally dense packings of the Platonic and Archimedean solids and certain smoothly shaped convex nonspherical particles. Here we generalize them in order to guide one to ascertain the densest packings of other convex nonspherical particles as well as concave shapes. Our generalized organizing principles are explicitly stated as four distinct propositions. All of our organizing principles are applied to and tested against the most comprehensive set of both convex and concave particle shapes examined to date, including Catalan solids, prisms, antiprisms, cylinders, dimers of spheres, and various concave polyhedra. We demonstrate that all of the densest known packings associated with this wide spectrum of nonspherical particles are consistent with our propositions. Among other applications, our general organizing principles enable us to construct analytically the densest known packings of certain convex nonspherical particles, including spherocylinders, "lens-shaped" particles, square pyramids, and rhombic pyramids. Moreover, we show how to apply these principles to infer the high-density equilibrium crystalline phases of hard convex and concave particles. We also discuss the unique packing attributes of maximally random jammed packings of nonspherical particles.

Original languageEnglish (US)
Article number011102
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume86
Issue number1
DOIs
StatePublished - Jul 5 2012
Externally publishedYes

Fingerprint

organizing
Packing
pyramids
Catalan Solid
Proposition
Concave polyhedron
Square-based pyramid
Antiprism
Archimedean solid
Platonic solid
Prism
Pyramid
Dimer
polyhedrons
prisms
Lens
Attribute
lenses
dimers
Distinct

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

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abstract = "We have recently devised organizing principles to obtain maximally dense packings of the Platonic and Archimedean solids and certain smoothly shaped convex nonspherical particles. Here we generalize them in order to guide one to ascertain the densest packings of other convex nonspherical particles as well as concave shapes. Our generalized organizing principles are explicitly stated as four distinct propositions. All of our organizing principles are applied to and tested against the most comprehensive set of both convex and concave particle shapes examined to date, including Catalan solids, prisms, antiprisms, cylinders, dimers of spheres, and various concave polyhedra. We demonstrate that all of the densest known packings associated with this wide spectrum of nonspherical particles are consistent with our propositions. Among other applications, our general organizing principles enable us to construct analytically the densest known packings of certain convex nonspherical particles, including spherocylinders, {"}lens-shaped{"} particles, square pyramids, and rhombic pyramids. Moreover, we show how to apply these principles to infer the high-density equilibrium crystalline phases of hard convex and concave particles. We also discuss the unique packing attributes of maximally random jammed packings of nonspherical particles.",
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