A phase diagram for jammed matter

Chaoming Song, Ping Wang and Hernán A. Makse ()
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Chaoming Song: City College of New York, New York, New York 10031, USA
Ping Wang: City College of New York, New York, New York 10031, USA
Hernán A. Makse: City College of New York, New York, New York 10031, USA

Nature, 2008, vol. 453, issue 7195, 629-632

Abstract: Jammed matter: Mathematics of the spheres The search for the most efficient way of filling a container with balls is one of the oldest of mathematical puzzles. Aside from its intrinsic interest, the problem has practical relevance in systems as varied as granular processing, fruit packing, colloid behaviour and in living cells. Experiments have shown that the loosest way to pack spheres (random loose packing) gives a density of about 55% and that the most compact (random close packing, or RCP) gives a maximum density of about 64%. These values appear robust, but there is as yet no physical interpretation for them. Now Chaoming Song et al. show analytically that, indeed, spheres cannot pack in three dimensions above the 63.4% limit found by experiment. The limit arises from a statistical picture of the jammed states in which the RCP can be defined as the ground state of the ensemble of jammed matter. These results ultimately lead to a phase diagram for jammed matter that provides a unifying view of the sphere-packing problem.

Date: 2008
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DOI: 10.1038/nature06981

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