Physics Colloquium - Friday, October 9th, 2009, 4:00 P.M.

Paul Chaikin
Physics Department and
Center for Soft Condensed Matter Research
New York University

Packing problems, how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction f ~ 0.74. It is also well-known that the corresponding random (amorphous) jammed packings have f ~0.64. The density of packings in lattice and amorphous forms is intimately related to the existence of liquid and crystal phase and is responsible for the melting transition. We have studied the crystal-liquid transition in spherical colloidal systems on earth and in microgravity.

There is much more flexibility in colloidal architecture if we use non- spherical particles as building blocks. A first step is to understand how such systems densely pack. Here we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely; up to f ~0.68 - 0.71 for spheroids with an aspect ratio close to that of M&M`s Candies, and even approach f ~0.75 for general ellipsoids. We suggest that the higher density relates directly to the higher number of degrees of freedom per particle. We support this claim by measurements of the number of contacts per particle Z, obtaining Z ~10 for our spheroids as compared to Z ~ 6 for spheres. We have also found the ellipsoids can be packed in a crystalline array to a density, f ~.7707 which exceeds the highest previous packing.