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Perspective: Basic understanding of condensed phases of matter via packing models

Author(s): Torquato, Salvatore

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Abstract: © 2018 Author(s). Packing problems have been a source of fascination for millennia 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.
Publication Date: 14-Jul-2018
Electronic Publication Date: 10-Jul-2018
Citation: Torquato, S. (2018). Perspective: Basic understanding of condensed phases of matter via packing models. Journal of Chemical Physics, 149 (2), 10.1063/1.5036657
DOI: doi:10.1063/1.5036657
ISSN: 0021-9606
Pages: 149, 020901-1 - 020901-32
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Chemical Physics
Version: Final published version. This is an open access article.
Notes: Volume 149, Issue 2, 14 July 2018, Article number 020901

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