Structural transitions in granular packs: statistical mechanics and statistical geometry investigations

TL;DR

This study combines experimental and simulation data to analyze the structural organization of granular sphere packings, revealing sharp transitions at specific packing fractions linked to changes in network geometry and free volume fluctuations.

Contribution

It introduces a statistical mechanics framework to identify and interpret structural transitions in disordered granular packings based on network and volume fluctuation analysis.

Findings

Sharp changes in network clustering at RLP and RCP limits

Abrupt variations in free volume fluctuations at these packing fractions

Identification of a thermodynamics-like variable linked to structural transitions

Abstract

We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is studied in terms of the network of common neighbours. This geometrical analysis reveals sharp changes in the network's clustering occurring at the packing fractions (fraction of volume occupied by the spheres respect to the total volume, $\rho$) corresponding to the so called Random Loose Packing limit (RLP, $\rho \sim 0.555$) and Random Close Packing limit (RCP, $\rho \sim 0.645$). At these packing fractions we also observe abrupt changes in the fluctuations of the portion of free volume around each sphere. We analyze such fluctuations by means of a statistical mechanics approach and we show that these anomalies are associated to sharp variations in a generalized thermodynamical variable which is the analogous for these a-thermal systems to the specific heat in thermal systems.