Novel Features Arising in the Maximally Random Jammed Packings of Superballs

TL;DR

This study investigates the maximally random jammed packings of superballs and superdisks, revealing dramatic density increases, nontrivial correlations, and unique structural properties driven by particle shape anisotropy.

Contribution

It introduces the first detailed analysis of MRJ packings of superballs and superdisks, highlighting their nonanalytic density behavior and correlated local structures.

Findings

MRJ densities increase dramatically with shape anisotropy.

Packings are hypostatic with nontrivially correlated local arrangements.

As anisotropy increases, rattlers decrease and orientational order increases.

Abstract

Dense random packings of hard particles are useful models of granular media and are closely related to the structure of nonequilibrium low-temperature amorphous phases of matter. Most work has been done for random jammed packings of spheres, and it is only recently that corresponding packings of nonspherical particles (e.g., ellipsoids) have received attention. Here we report a study of the maximally random jammed (MRJ) packings of binary superdisks and monodispersed superballs whose shapes are defined by |x_1|^2p+...+|x_2|^2p<=1 with d = 2 and 3, respectively, where p is the deformation parameter with values in the interval (0, infinity). We find that the MRJ densities of such packings increase dramatically and nonanalytically as one moves away from the circular-disk and sphere point. Moreover, the disordered packings are hypostatic and the local arrangements of particles are necessarily nontrivially correlated to achieve jamming. We term such correlated structures "nongeneric". The degree of "nongenericity" of the packings is quantitatively characterized by determining the fraction of local coordination structures in which the central particles have fewer contacting neighbors than average. We also show that such seemingly special packing configurations are counterintuitively not rare. As the anisotropy of the particles increases, the fraction of rattlers decreases while the minimal orientational order increases. These novel characteristics result from the unique rotational symmetry breaking manner of the particles.