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Self-assembled clusters of spheres related to spherical codes

Carolyn L. Phillips1,*, Eric Jankowski2,†, Michelle Marval3, and Sharon C. Glotzer1,2,3,‡

  • 1Applied Physics Program, University of Michigan, Ann Arbor, Michigan, 48109, USA
  • 2Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, 48109, USA
  • 3Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan, 48109, USA

  • *Present address: Computation Institute, Argonne National Laboratory, Lemont, Illinois, USA.
  • †Present address: University of Colorado at Boulder, Boulder CO 80309.
  • ‡sglotzer@umich.edu
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Phys. Rev. E 86, 041124 – Published 15 October, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.041124

Abstract

We consider the thermodynamically driven self-assembly of spheres onto the surface of a central sphere. This assembly process forms self-limiting, or terminal, anisotropic clusters (N-clusters) with well-defined structures. We use Brownian dynamics to model the assembly of N-clusters varying in size from two to twelve outer spheres and free energy calculations to predict the expected cluster sizes and shapes as a function of temperature and inner particle diameter. We show that the arrangements of outer spheres at finite temperatures are related to spherical codes, an ideal mathematical sequence of points corresponding to the densest possible sphere packings. We demonstrate that temperature and the ratio of the diameters of the inner and outer spheres dictate cluster morphology. We present a surprising result for the equilibrium structure of a 5-cluster, for which the square pyramid arrangement is preferred over a more symmetric structure. We show this result using Brownian dynamics, a Monte Carlo simulation, and a free energy approximation. Our results suggest a promising way to assemble anisotropic building blocks from constituent colloidal spheres.

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Outline

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Phys. Rev. E 86, 041124– Published 15 October, 2012
  • Received 15 January 2012

©2012 American Physical Society

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