Abstract
We present an analytical derivation of the volume fractions for random close packing (RCP) in both and , based on the same methodology. Using suitably modified nearest neighbor statistics for hard spheres, we obtain in and in . These values are well within the interval of values reported in the literature using different methods (experiments and numerical simulations) and protocols. This statistical derivation suggests some considerations related to the nature of RCP: (i) RCP corresponds to the onset of mechanical rigidity where the finite shear modulus emerges, (ii) the onset of mechanical rigidity marks the maximally random jammed state and dictates via the coordination number , (iii) disordered packings with are possible at the expense of creating some order, and at the fcc limit acts as a boundary condition.
- Received 29 September 2021
- Accepted 8 December 2021
DOI:https://doi.org/10.1103/PhysRevLett.128.028002
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