Dense random packings of simple hard spheres were studied, both experimentally and theoretically, for several decades; however, the physical understanding of these systems is still very poor. In particular, many different experimental protocols indicate that disordered systems of hard spheres reach their maximal packing density when the spheres constitute 64% of the total volume of the system, known as the “random close packing” (RCP) density limit. Similarly, many protocols indicate that the loosest mechanically-stable random packing of spheres occurs when these spheres occupy 55% of the total volume; this is called the “random loose packing” (RLP) density limit. Importantly, while mechanically-stable states denser than the RCP limit or looser than the RLP limit can readily be constructed, the entropy of RCP and RLP states has never been characterized; as a consequence, the physical meaning of the RLP and the RCP limits is still not established and the mutual relation between these two limits is unclear.

We employ analytical centrifugation and confocal microscopy to study non-crystalline colloidal frictional sediments, prepared by centrifugation from a thermodynamically- equilibrated suspension of simple hard spheres. We demonstrate that our system allows the density and the entropy of these solid packings to be tuned in a controllable way, between the RLP and the RCP limits, by changing the density of the initial fluid. The most random fluids, where the volume fraction of colloidal spheres approaches zero, form RLP packings; this suggests the RLP limit to be interpreted as the maximally-random jammed (MRJ) density of frictional spheres[1], for which the number of mechanically stable structures is maximized. Moreover a critical packing density exists, where all fluid states in our suspensions get extinguished. This critical density coincides with the well-known RCP limit, allowing the RCP and the RLP limits to be mutually related by a simple fully-deterministic computer model, which perfectly reproduces our experimental results.

 [1] L. E. Silbert, Soft Matter 6, 2918 (2010).