Properties of packings and dispersions of superellipse sector particles

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parameterization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We compare three computational processes: pair-wise Monte Carlo simulations that look only at particle-particle geometric constraints, Monte Carlo simulations that look at how these geometric constraints play out over extended dispersions of many particles, and Molecular Dynamics simulations that allow particles to interact to form random loose and close packings. We investigate the dependence of critical random loose and close packing fractions on particle parameters, finding that both values tend to increase with opening aperture (as expected) and, in general, decrease with increasing corner sharpness. The identified packing fractions are compared with the mean-field prediction of the Random Contact Model. We find deviations from the model's prediction due to correlations between particle orientations. The complex interaction of spatial proximity and orientational alignment is explored using a generalized Spatio-Orientational Distribution Area (SODA) plot. Higher density packings are achieved through particles assuming a small number of preferred configurations which depend sensitively on particle shape and system preparation.