TY - JOUR
T1 - Perspective
T2 - Basic understanding of condensed phases of matter via packing models
AU - Torquato, S.
N1 - Funding Information:
I am deeply grateful to Frank Stillinger, Paul Chaikin, Aleksandar Donev, Obioma Uche, Antonello Scardicchio, Weining Man, Yang Jiao, Chase Zachary, Adam Hopkins, Étienne Marcotte, Joseph Corbo, Steven Atkinson, Remi Dreyfus, Arjun Yodh, Ge Zhang, Duyu Chen, Jianxiang Tian, Michael Klatt, Enrqiue Lomba, and Jean-Jacques Weis with whom I have collaborated on topics described in this review article. I am very thankful to Jaeuk Kim, Duyu Chen, Zheng Ma, Yang Jiao, Ge Zhang, and Gerardo Odriozola for comments that have greatly improved this article. The author’s work on packing models over the years has been supported by various grants from the National Science Foundation, including the current Award No. DMR-1714722.
Publisher Copyright:
© 2018 Author(s).
PY - 2018/7/14
Y1 - 2018/7/14
N2 - 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.
AB - 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.
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U2 - 10.1063/1.5036657
DO - 10.1063/1.5036657
M3 - Article
C2 - 30007388
AN - SCOPUS:85049868168
SN - 0021-9606
VL - 149
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 2
M1 - 020901
ER -