Is Random Close Packing of Spheres Well Defined?

Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations involved. In recent years progress on a fundamental description of jammed matter could be made by starting from a constant volume ensemble in the spirit of conventional statistical mechanics. Recent work has shown that this approach, first intr...

We answer the questions raised by Donev, Torquato, Stillinger, and Connelly in their "Comment on "Jamming at zero temperature and zero applied stress: The epitome of disorder.' " We emphasize that we follow a fundamentally different approach than they have done to reinterpret random close packing in terms of the "maximally random jammed" framework. We define the "maximally random jammed packing fraction" to be where the largest number of initial states, chosen completely rand...

We present a theoretical prediction on random close packing factor \phi_RCP^b of binary granular packings based on the hard-sphere fluid theory. An unexplored regime is unravelled, where the packing fraction \phi_RCP^b is smaller than that of the mono-sized one \phi_RCP^m, i.e., the so-called loose jamming state. This is against our common perception that binary packings should always reach a denser packing than mono-sized packings at the jamming state. Numerical evidence fur...

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in $d=3$ dimensions, and thus obtain an estimate of the random close packing (RCP) volume fraction, $\phi_{\textrm{RCP}}$, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributi...

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 meta...

O'Hern, Silbert, Liu and Nagel [Phys. Rev. E. 68, 011306 (2003)] (OSLN) claim that a special point $J$ of a "jamming phase diagram" (in density, temperature, stress space) is related to random close packing of hard spheres, and that it represents, for their suggested definitions of jammed and random, the recently introduced maximally random jammed state. We point out several difficulties with their definitions and question some of their claims. Furthermore, we discuss the con...

When are athermal soft sphere packings jammed ? Any experimentally relevant definition must at the very least require a jammed packing to resist shear. We demonstrate that widely used (numerical) protocols in which particles are compressed together, can and do produce packings which are unstable to shear - and that the probability of generating such packings reaches one near jamming. We introduce a new protocol that, by allowing the system to explore different box shapes as i...

Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B, 105 (2001)], a classification scheme of jammed packings into hierarchical categories of locally, collectively and strictly jammed configurations has been proposed. They suggest that these jamming categories can be tested using numerical algorithms that analyze an equivalent contact network of the packing under applied displa...

We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model an...

Although the concept of random close packing with an almost universal packing fraction of ~ 0.64 for hard spheres was introduced more than half a century ago, there are still ongoing debates. The main difficulty in searching the densest packing is that states with packing fractions beyond the glass transition at ~ 0.58 are inherently non-equilibrium systems, where the dynamics slows down with a structural relaxation time diverging with density; hence, the random close packing...