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Experiments show that the loosest way to pack spheres (random loose packing) gives a density of approx 55 per cent. On the other hand, the most compact way to pack spheres (random close packing) results in a maximum density of approx 64 per cent. These values are experimentally robust, although not very well understood theoretically. In this paper the authors present an approximate statistical theory of different kinds of random packings ('jammed' states) of spheres. From their formulation, random close packing emerges as the ground state of the ensemble of jammed matter. They also find that random packings of spheres in three dimensions cannot exceed a density limit of approx 63.4 per cent. Random close packing and random loose packing states appear as special lines on a phase diagram illustrating the effects of density and friction on the system.
Reference: Song, C., Wang, P. and Makse, H. A. Nature 453, 629-632 (2008).
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