Jamming Transition and Inherent Structures of Hard Spheres and Discs

TL;DR

This study investigates how the jamming volume fraction of hard spheres depends on initial fluid configurations, revealing a sharp increase beyond a certain point and linking it to structural and dynamic properties related to glass transition theories.

Contribution

It demonstrates the dependence of jamming volume fraction on initial conditions and connects structural changes to the random first order transition theory of glass transition.

Findings

$J$ remains constant at low initial volume fractions

$J$ sharply increases when initial volume fraction exceeds the dynamic transition point

Structural properties like local order and static length scale change with initial conditions

Abstract

Recent studies show that volume fractions $\phiJ$ at the jamming transition of frictionless hard spheres and discs are not uniquely determined but exist over a continuous range. Motivated by this observation, we numerically investigate dependence of $\phiJ$ on the initial configurations of the parent fluids equilibrated at a fraction $\phiini$, before compressing to generate a jammed packing. We find that $\phiJ$ remains constant when $\phiini$ is small but sharply increases when $\phiini$ exceeds the dynamic transition point which the mode-coupling theory predicts. We carefully analyze configurational properties of both jammed packings and parent fluids and find that, while all jammed packings remain isostatic, the increase of $\phiJ$ is accompanied with subtle but distinct changes of (i) local orders, (ii) a static length scale, and (iii) an exponent of the finite size scaling. These results quantitatively support the scenario of the random first order transition theoryof the glass transition.