A granocentric model captures the statistical properties of monodisperse random packings

TL;DR

This paper extends the granocentric model to accurately describe local fluctuations in monodisperse sphere packings, providing insights into the microscopic structure and thermodynamics of jammed matter.

Contribution

The authors generalize the granocentric model to include monodisperse packings, capturing local fluctuations without considering particle positions, and validate it with experimental data.

Findings

Model accurately predicts local parameter distributions in monodisperse packings.

Distributions align well with experimental measurements.

Model enables calculation of thermodynamic quantities like compactivity.

Abstract

We present a generalization of the granocentric model proposed in [Clusel et al., Nature, 2009, 460, 611615] that is capable of describing the local fluctuations inside not only polydisperse but also monodisperse packings of spheres. This minimal model does not take into account the relative particle positions, yet it captures positional disorder through local stochastic processes sampled by efficient Monte Carlo methods. The disorder is characterized by the distributions of local parameters, such as the number of neighbors and contacts, filled solid angle around a central particle and the cell volumes. The model predictions are in good agreement with our experimental data on monodisperse random close packings of PMMA particles. Moreover, the model can be used to predict the distributions of local fluctuations in any packing, as long as the average number of neighbors, contacts and the packing fraction are known. These distributions give a microscopic foundation to the statistical mechanics framework for jammed matter and allow us to calculate thermodynamic quantities such as the compactivity in the phase space of possible jammed configurations.