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Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation

Robert S. Hoy

Jared Harwayne-Gidansky

Corey S. O’Hern

  • Department of Mechanical Engineering & Materials Science and Department of Physics, Yale University, New Haven, Connecticut, USA

  • Department of Electrical Engineering and Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut, USA

  • Department of Mechanical Engineering & Materials Science, Department of Physics, and Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut, USA

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Phys. Rev. E 85, 051403 – Published 22 May, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.051403

Abstract

We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres N, and their diversity of structure and symmetry increases with increasing N and decreases with increasing hyperstaticity H≡Nc−NISO, where Nc is the number of pair contacts and NISO=3N−6. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fraction f of nuclei with order compatible with the bulk (rhcp) crystal decreases sharply with increasing N due to a high propensity for stacking faults, five- and near-fivefold symmetric structures, and other motifs that preclude rhcp order. While f increases with increasing H, a significant fraction of hyperstatic nuclei for N as small as 11 retain non-rhcp structure. Classical theories of nucleation that consider only spherical nuclei, or only nuclei with the same ordering as the bulk crystal, cannot capture such effects. Our results provide an explanation for the failure of classical nucleation theory for hard-sphere systems of N≲10 particles; we argue that in this size regime, it is essential to consider nuclei of unconstrained geometry. Our results are also applicable to understanding kinetic arrest and jamming in systems that interact via hard-core-like repulsive and short-ranged attractive interactions.

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Phys. Rev. E 85, 051403– Published 22 May, 2012
  • Received 22 February 2012
Article part of CHORUS

©2012 American Physical Society

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