(272c) Searching for Ordered Dense Packings of Particle Systems

The problem of how particles pack at high density is an old one, dating back at least to the work of Johannes Kepler who conjectured that cubic close packing would yield the maximum density achievable through the packing of spheres [1]. From a more recent perspective this problem emerges in the context of understanding the structure of molecular solids [2], as well the ordered structures formed by self assembly of colloidal particles [3]. While the Kepler conjecture now has a mathematical proof [4], there is little formal guidance as to the close packed structures formed by mixtures of spheres or by nonspherical particles. Some time ago as part of a project on understanding the packing of hard chain models of n-alkane solids [5] we developed a simulated annealing method for locating ordered close packed structures through progressive compression of a system of particles consisting of a unit cell and its nearest neighbor cells. In this paper we present more refined versions of this method and illustrate its application to several particle packing problems. We have developed two forms of the simulated annealing method. In one the space group is fixed, while in the other the only restriction is on the number of particles in a unit cell. The second method allows a wider ranging search for close packed structures at the cost of somewhat slower convergence. We will describe suitable annealing schedules for implementing these methods. We will present applications of the methods to several systems including: i) hard dumbbells [6]; ii) mixtures of additive hard spheres [7]; iii) mixtures of nonadditive hard spheres [8]; iv) models of chiral molecules [9].

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