Optimal packings of superballs

Yang Jiao, F. H. Stillinger, S. Torquato

Research output: Contribution to journalArticle

104 Citations (Scopus)

Abstract

Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have considered spherical shapes, and it is only more recently that nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs (whose shapes are defined by | x1 | 2p + | x2 | 2p + | x3 | 2p ≤1) provide a versatile family of convex particles (p≥0.5) with both cubic-like and octahedral-like shapes as well as concave particles (0<p<0.5) with octahedral-like shapes. In this paper, we provide analytical constructions for the densest known superball packings for all convex and concave cases. The candidate maximally dense packings are certain families of Bravais lattice packings (in which each particle has 12 contacting neighbors) possessing the global symmetries that are consistent with certain symmetries of a superball. We also provide strong evidence that our packings for convex superballs (p≥0.5) are most likely the optimal ones. The maximal packing density as a function of p is nonanalytic at the sphere point (p=1) and increases dramatically as p moves away from unity. Two more nontrivial nonanalytic behaviors occur at pc=1.1509... and po=ln3/ln4=0.7924... for "cubic" and "octahedral" superballs, respectively, where different Bravais lattice packings possess the same densities. The packing characteristics determined by the broken rotational symmetry of superballs are similar to but richer than their two-dimensional "superdisk" counterparts and are distinctly different from that of ellipsoid packings. Our candidate optimal superball packings provide a starting point to quantify the equilibrium phase behavior of superball systems, which should deepen our understanding of the statistical thermodynamics of nonspherical-particle systems.

Original languageEnglish (US)
Article number041309
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume79
Issue number4
DOIs
StatePublished - Apr 1 2009
Externally publishedYes

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Packing
ellipsoids
Ellipsoid
symmetry
Statistical Thermodynamics
Symmetry
Phase Equilibria
Heterogeneous Materials
packing density
Granular Media
Rotational symmetry
Particle System
unity
Three-dimension
Quantify
Likely
thermodynamics

ASJC Scopus subject areas

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

Cite this

Optimal packings of superballs. / Jiao, Yang; Stillinger, F. H.; Torquato, S.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 79, No. 4, 041309, 01.04.2009.

Research output: Contribution to journalArticle

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