Properties of packings and dispersions of superellipse sector particles

TL;DR

This paper investigates how the shape parameters of superellipse sector particles influence their packing densities and arrangements, using computational simulations and comparing results with theoretical models.

Contribution

It introduces a comprehensive analysis of superellipse sector particles' packing behavior, highlighting the effects of shape parameters and deviations from mean-field predictions.

Findings

Packing fractions increase with aperture size

Corner sharpness generally decreases packing density

Particles tend to adopt preferred configurations based on shape and preparation

Abstract

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.