title: Organizing principles for dense packings of nonspherical hard particles: not all shapes are created equal.
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 [Torquato and Jiao, Phys. Rev. E 81, 041310 (2010)]. 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.
authors.affiliation: Department of Chemistry, Princeton Center for Theoretical Science, Program of Applied and Computational Mathematics, Princeton Institute of the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA. torquato@princeton.edu
authors.forename: Salvatore
authors.initials: S
authors.lastname: Torquato
authors.forename: Yang
authors.initials: Y
authors.lastname: Jiao
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D006244:Hardness; D008956:Models, Chemical; D015233:Models, Statistical; D010316:Particle Size
chemical_list: D003102:Colloids