IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i23p5362-5379.html
   My bibliography  Save this article

A first-order phase transition defines the random close packing of hard spheres

Author

Listed:
  • Jin, Yuliang
  • Makse, Hernán A.

Abstract

Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ∼64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated with the observed packing limit. Here we show that RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the “freezing point” in a first-order phase transition between ordered and disordered packing phases. Despite the athermal nature of granular matter, we show the thermodynamic character of the transition in that it is accompanied by sharp discontinuities in volume and entropy. This occurs at a critical compactivity, which is the intensive variable that plays the role of temperature in granular matter. Our results predict the experimental conditions necessary for the formation of a jammed crystal by calculating an analogue of the “entropy of fusion”. This approach is useful since it maps out-of-equilibrium problems in complex systems onto simpler established frameworks in statistical mechanics.

Suggested Citation

  • Jin, Yuliang & Makse, Hernán A., 2010. "A first-order phase transition defines the random close packing of hard spheres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5362-5379.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:23:p:5362-5379
    DOI: 10.1016/j.physa.2010.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110006928
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2010.08.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Amir Haji-Akbari & Michael Engel & Aaron S. Keys & Xiaoyu Zheng & Rolfe G. Petschek & Peter Palffy-Muhoray & Sharon C. Glotzer, 2009. "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra," Nature, Nature, vol. 462(7274), pages 773-777, December.
    2. Chaoming Song & Ping Wang & Hernán A. Makse, 2008. "A phase diagram for jammed matter," Nature, Nature, vol. 453(7195), pages 629-632, May.
    3. Jixiang Zhu & Min Li & R. Rogers & W. Meyer & R. H. Ottewill & W. B. Russel & P. M. Chaikin, 1997. "Crystallization of hard-sphere colloids in microgravity," Nature, Nature, vol. 387(6636), pages 883-885, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bailera, Manuel & Pascual, Sara & Lisbona, Pilar & Romeo, Luis M., 2021. "Modelling calcium looping at industrial scale for energy storage in concentrating solar power plants," Energy, Elsevier, vol. 225(C).
    2. Kyeyune-Nyombi, Eru & Morone, Flaviano & Liu, Wenwei & Li, Shuiqing & Gilchrist, M. Lane & Makse, Hernán A., 2018. "High-resolution of particle contacts via fluorophore exclusion in deep-imaging of jammed colloidal packings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1387-1395.
    3. Liu, Lufeng & Lu, Peng & Meng, Lingyi & Jin, Weiwei & Li, Shuixiang, 2016. "Order metrics and order maps of octahedron packings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 870-882.
    4. Yue Deng & Deng Pan & Yuliang Jin, 2024. "Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    5. Ilya Svetlizky & Seongsoo Kim & David A. Weitz & Frans Spaepen, 2023. "Dislocation interactions during plastic relaxation of epitaxial colloidal crystals," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    6. Zhihua Cheng & Matthew R. Jones, 2022. "Assembly of planar chiral superlattices from achiral building blocks," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    7. Sangmin Lee & Sharon C. Glotzer, 2022. "Entropically engineered formation of fivefold and icosahedral twinned clusters of colloidal shapes," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    8. Yoshio Kono & Koji Ohara & Nozomi M. Kondo & Hiroki Yamada & Satoshi Hiroi & Fumiya Noritake & Kiyofumi Nitta & Oki Sekizawa & Yuji Higo & Yoshinori Tange & Hirokatsu Yumoto & Takahisa Koyama & Hirosh, 2022. "Experimental evidence of tetrahedral symmetry breaking in SiO2 glass under pressure," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    9. Agapie Stefan C. & Whitlock Paula A., 2010. "Random packing of hyperspheres and Marsaglia's parking lot test," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 197-209, January.
    10. Stéphan T. Grilli & Mike Shelby & Olivier Kimmoun & Guillaume Dupont & Dmitry Nicolsky & Gangfeng Ma & James T. Kirby & Fengyan Shi, 2017. "Modeling coastal tsunami hazard from submarine mass failures: effect of slide rheology, experimental validation, and case studies off the US East Coast," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 86(1), pages 353-391, March.
    11. Tejada, Ignacio G., 2011. "A new statistical mechanics approach to dense granular media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2664-2677.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:389:y:2010:i:23:p:5362-5379. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.