Packing of Ellipsoids : M&M’s Pack Denser Than Ball Bearings

As part of a general study of how particle shape affects assembly, order and macroscopic properties, we discovered that pouring ellipsoids with axis ratios of 0.8:1:1.25 into a container produces randomly packed arrangements that fill it as densely and as rigidly as spheres arranged one by one on their densest lattice. Spheres on a lattice fill space to 74% (with 12 touching neighbors, n.n.), spheres poured in a container fill to 64% (6 n.n.), M&M’s (ellipsoids of revolution with aspect ratio ~2:1) fill to 69% (10 n.n.), and “optimized” ellipsoids (axis ratios 0.8:1:1.25) fill to 74% (12 n.n.). We found that crystalline arrangements of ellipsoids can do even better, up to 77% so far (14 n.n.). It is noteworthy that ellipsoids, unlike cylinders, cubes etc., can be transformed into spheres by stretching (i.e., for M&M’s, simply double the short axis). The higher densities for ellipsoids relate to the additional rotational degrees of freedom when compared to spheres and the increase in the number of neighbors to constrain them. These findings should be useful for high quality/high density ceramics as well as for fundamental understanding of melting and glass formation.