Characterization of void space, large-scale structure, and transport properties of maximally random jammed packings of superballs

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by vertical bar x(1)vertical bar(2p) + vertical bar x(2)vertical bar(2p) + vertical bar x(3)vertical bar(2p) <= 1, where p is an element of (0, infinity) is a deformation parameter indicating to what extent the shape deviates from a sphere. As p increases from the sphere point (p = 1), the superball tends to a cuboidal shape and approaches a cube in the p -> infinity limit. As p -> 0.5, it approaches an octahedron, becomes a concave body with octahedral symmetry for p < 0.5, and approaches a three-dimensional cross in the limit p -> 0. Previous characterization of superball packings has shown that they have a maximally random jammed (MRJ) state, whose properties (e.g., packing fraction phi, average contact number Z over bar ) vary nonanalytically as p diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings with 0.85 <= p <= 1.50. To supplement the previous work on such packings, we characterize their large-scale structure by examining the behaviors of their structure factors S(Q) and spectral densities <(chi)over tilde>(V)(Q), as the wave number Q tends to zero, and find that these packings are effectively hyperuniform for all values of p examined. We show that the mean width w over bar is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. Moreover, we compute the complementary cumulative pore-size distribution F(delta) and find that the pore sizes tend to decrease as vertical bar 1 - p vertical bar increases. From F(delta), we estimate how the fluid permeability, mean survival time, and principal diffusion relaxation time vary as a function of p. Additionally, we compute the diffusion "spreadability" S(t) [Torquato, Phys. Rev. E 104, 054102 (2021)] of these packings and find that the long-time power-law scaling indicates these packings are hyperuniform with a small-Q power law scaling of the spectral density (chi) over tilde (V) (Q) similar to Q alpha with an exponent alpha that ranges from 0.64 at the sphere point to 0.32 at p = 1.50, and decreases as vertical bar 1 - p vertical bar increases. Each of the structural characteristics computed here exhibits an extremum at the sphere point and varies nonanalytically as p departs the sphere point. We find the nonanalytic behavior in phi on either side of the sphere point is nearly linear, and determine that the rattler fraction phi(R) decreases rapidly as vertical bar 1 - p vertical bar increases. Our results can be used to help inform the design of colloidal or granular materials with targeted densities and transport properties.