Organizing Principles for Dense Packings of Nonspherical Hard Particles: Not All Shapes Are Created Equal

TL;DR

This paper generalizes organizing principles to determine the densest packings of a wide variety of convex and concave nonspherical particles, enabling analytical construction and better understanding of their packing behaviors.

Contribution

It introduces four generalized organizing principles for dense packings of nonspherical particles and validates them across numerous shapes, including convex and concave forms.

Findings

All densest packings tested are consistent with the principles.

Enabled analytical construction of densest packings for several particle types.

Provided insights into high-density phases and packing attributes of nonspherical particles.

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. We apply and test all of these organizing principles to the most comprehensive set of both convex and concave particle shapes 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.