Caging effects in amorphous hard-sphere solids

The caging density of a d-dimensional hard-sphere solid is introduced as the density at which the average contact number on a sphere equals the caging number, defined as the average minimal number of randomly parked neighbors which completely arrest (cage) a test sphere. The mean-field caging density, which is consistent with random (loose) sphere packing in d=2 and d=3, parallels the (always higher) d-dimensional densities of regular close packed crystals. The gap between caging and close-packing densities is ascribed to a difference in geometric optimization. This difference also explains the gap between sphere co-ordination in packings or glasses of colloidal spheres and the absolute maximum for close-packed crystals. Caging numbers appear to be an important feature of random packings in general since caging effects also account for the particle shape dependence of random thin-rod packings.