Distinctive features arising in maximally random jammed packings of superballs

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 vertical bar x(1)vertical bar(2p) + ... + vertical bar x(d)vertical bar(2p) <= 1 with d = 2 and 3, respectively, where p is the deformation parameter with values in the interval (0, infinity). As p increases from zero, one can get a family of both concave (0 < p < 0.5) and convex (p >= 0.5) particles with square symmetry (d = 2), or octahedral and cubic symmetry (d = 3). In particular, for p = 1 the particle is a perfect sphere (circular disk) and for p -> infinity the particle is a perfect cube (square). We find that the MRJ densities of such packings increase dramatically and nonanalytically as one moves away from the circular-disk and sphere point (p = 1). Moreover, the disordered packings are hypostatic, i.e., the average number of contacting neighbors is less than twice the total number of degrees of freedom per particle, and yet the packings are mechanically stable. As a result, 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 as measured by the tetratic and cubatic order parameters increases. These characteristics result from the unique manner in which superballs break their rotational symmetry, which also makes the superdisk and superball packings distinctly different from other known nonspherical hard-particle packings.