Distribution of volumes and coordination number in jammed matter: mesoscopic ensemble

TL;DR

This study examines the distribution of volumes and coordination numbers in jammed monodisperse sphere packings, comparing theoretical predictions with computer simulations, and suggests a possible order/disorder transition in the packing structure.

Contribution

It introduces a mesoscopic ensemble approach to model volume and coordination distributions in jammed matter, improving understanding of packing density limits and structural transitions.

Findings

Volume distribution deviates from exponential, better modeled by compressed exponential.

Average volume predictions match theoretical limits of RCP and RLP.

Coordination number distribution is exponential and inverse exponential, aligning with simulations.

Abstract

We investigate the distribution of the volume and coordination number associated to each particle in a jammed packing of monodisperse hard sphere using the mesoscopic ensemble developed in Nature 453, 606 (2008). Theory predicts an exponential distribution of the orientational volumes for random close packings and random loose packings. A comparison with computer generated packings reveals deviations from the theoretical prediction in the volume distribution, which can be better modeled by a compressed exponential function. On the other hand, the average of the volumes is well reproduced by the theory leading to good predictions of the limiting densities of RCP and RLP. We discuss a more exact theory to capture the volume distribution in its entire range. The available data suggests a plausible order/disorder transition defining random close packings. Finally, we consider an extended ensemble to calculate the coordination number distribution which is shown to be of an exponential and inverse exponential form for coordinations larger and smaller than the average, respectively, in reasonable agreement with the simulated data.