Why is Random Close Packing Reproducible?

TL;DR

This paper explores why the random close packing density of spheres is consistently around 0.64 by linking it to the thermodynamics of colloidal suspensions and the disappearance of accessible states.

Contribution

It proposes a new conjecture connecting the reproducibility of phi_rcp to a divergence in accessible states, relating it to the equation of state for hard sphere fluids.

Findings

phi_rcp is approximately 0.64 across studies

The divergence in accessible states explains the reproducibility

Connection established between packing density and fluid thermodynamics

Abstract

We link the thermodynamics of colloidal suspensions to the statistics of regular and random packings. Random close packing has defied a rigorous definition yet, in three dimensions, there is near universal agreement on the volume fraction at which it occurs. We conjecture that the common value of phi_rcp, approximately 0.64, arises from a divergence in the rate at which accessible states disappear. We relate this rate to the equation of state for a hard sphere fluid on a metastable, non-crystalline branch.