The Influence of Shape on Ordering of Granular Systems in Two Dimensions

We investigate ordering properties of two-dimensional granular materials using several shapes created by welding ball bearings together. Ordered domains form much more easily in two than in three dimensions, even when configurations lack long-range order. The onset of ordered domains occurs near a packing density of 0.8, a phenomenon observed previously for disks. One of our shapes, the trapezoid, has packings that remain disordered and near the transition density even after annealing by shaking. Since random packings are unstable for disks and many other shapes in two dimensions, trapezoid packings provide a new approach to studying two-dimensional randomness. We also find that the rotational symmetry of a shape is an excellent predictor of how easily it orders, and a potential guide to identifying two-dimensional shapes that remain random after annealing.