Diversity of order and densities in jammed hard-particle packings

Abstract

Recently the conventional notion of random close packing has been supplanted by the more appropriate concept of the maximally random jammed (MRJ) state. This inevitably leads to the necessity of distinguishing the MRJ state among the entire collection of jammed packings. While the ideal method of addressing this question would be to enumerate and classify all possible jammed hard-sphere configurations, practical limitations prevent such a method from being employed. Instead, we generate numerically a large number of representative jammed hard-sphere configurations (primarily relying on a slight modification of the Lubachevsky-Stillinger algorithm to do so) and evaluate several commonly employed order metrics for each of these packings. Our investigation shows that, even in the large-system limit, jammed systems of hard spheres can be generated with a wide range of packing fractions from $\phi \approx 0.52$ to the fcc limit $(\phi \approx 0.74).$ Moreover, at a fixed packing fraction, the variation in the order can be substantial, indicating that the density alone does not uniquely characterize a packing. Interestingly, each order metric evaluated yielded a relatively consistent estimate for the packing fraction of the maximally random jammed state $({\phi }_{\mathrm{MRJ}}\approx 0.63).$ This estimate, however, is compromised by the weaknesses in the order metrics available, and we propose several guiding principles for future efforts to define more broadly applicable metrics.