Basic Understanding of Condensed Phases of Matter via Packing Models

TL;DR

This paper reviews theoretical and computational studies of packing models, highlighting their role in understanding the structure and properties of condensed matter, including jammed states and dense packings across various dimensions.

Contribution

It provides a comprehensive overview of packing models, emphasizing the geometric-structure approach and covering diverse particle types and packing states, with insights into future challenges.

Findings

Unified characterization of jammed packings via jamming categories and order maps

Analysis of densest, maximally random, and lowest-density jammed states

Survey of packings of spheres, polydisperse, and nonspherical particles

Abstract

Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.