Recent studies show that volume fractions ${\phi }_J$ at the jamming transition of frictionless hard spheres and disks are not uniquely determined but exist over a continuous range. Motivated by this observation, we numerically investigate the dependence of ${\phi }_J$ on the initial configurations of the parent fluid equilibrated at a volume fraction ${\phi }_{\mathrm{eq}}$, before compressing to generate a jammed packing. We find that ${\phi }_J$ remains constant when ${\phi }_{\mathrm{eq}}$ is small but sharply increases as ${\phi }_{\mathrm{eq}}$ 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 ${\phi }_J$ is accompanied with subtle but distinct changes of local orders, a static length scale, and an exponent of the finite-size scaling. These results are consistent with the scenario of the random first-order transition theory of the glass transition.

• Received 8 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.205701