Experiments on Random Packings of Ellipsoids

Weining Man, Aleksandar Donev, Frank H. Stillinger, Matthew T. Sullivan, William B. Russel, David Heeger, Souheil Inati, Salvatore Torquato, and P. M. Chaikin

Phys. Rev. Lett. 94, 198001 – Published 19 May 2005

Abstract

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near $1.25 ∶ 1 ∶ 0.8$ can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We have fabricated ellipsoids and show that, in a sphere, the radial packing fraction $ϕ (r)$ can be obtained from $V (h)$ , the volume of added fluid to fill the sphere to height $h$ . We also obtain $ϕ (r)$ from a magnetic resonance imaging scan. The measurements of the overall density $ϕ_{avr}$ , $ϕ (r)$ and the core density $ϕ_{0} = 0.74 \pm 0.005$ agree with simulations.

Received 11 December 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.198001

Authors & Affiliations

Weining Man¹, Aleksandar Donev⁴, Frank H. Stillinger², Matthew T. Sullivan¹, William B. Russel³, David Heeger⁵, Souheil Inati⁵, Salvatore Torquato^2,4, and P. M. Chaikin¹

¹Department of Physics, and Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
²Department of Chemistry, and Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
³Department of Chemical Engineering, and Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
⁴Program in Applied and Computational Mathematics, and Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
⁵Department of Psychology and Center for Neural Science, New York University, New York, New York 10003, USA

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Vol. 94, Iss. 19 — 20 May 2005

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