Universality of Random Close Packing ?

In 1611 Kepler proposed that the densest packing of spheres could be achieved by stacking close-packed planes of spheres. In such a packing, the spheres occupy π/ √ 18 ≈74.05% of space. The Kepler conjecture was (almost certainly) proved in 1998 by Thomas Hales. When we pour a large number of equal-sized spheres in a container and shake them down, we do not obtain the Kepler packing. Rather a disordered structure forms in which the spheres occupy approximately 64% of the available space. It has long been debated if this density of “random close packing” (RCP) is well defined. The Bible seems to suggest it is: “Give, and it will be given to you. A good measure, pressed down, shaken together and running over, will be poured into your lap” (Luke 6:38) but, of course, we should not use the Bible as a source of scientific information (otherwise we would have to accept that π=3). The quantitative study of random close packing seems to have started with J.D. Bernal’s experiments on the packing of ball bearings [1]. His experiments (and those of many others) suggested that it is impossible to compress disordered sphere packings beyond a volume fraction of approximately 64%. However, this observation does not necessarily imply that there is a welldefined density of random close packing. It could just as well be that the rate at which the density of a disordered hard-sphere packing increases with “shaking” becomes very slow around a volume fraction 64% – very slow, but not zero. If that were the case, RCP would not have a clear mechanical definition. Indeed, in 2000, Torquato, Truskett and Debenedetti [2] argued that states with a density above 64% can always be obtained by increasing the local order. This observation implies that the “mechanical” route to random close packing is ill defined. At high-enough densities, ordered structures are always favored because they occupy a larger fraction of configuration space than disordered structures.