Structure of jammed ellipse packings with a wide range of aspect ratios.

Abstract

Motivated in part by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of jammed two-dimensional ellipse packings over a much wider range of particle aspect ratios (<i>α</i>, the ratio of the major and minor axis lengths) than has been previously attempted. We determine the jamming densities <i>ϕ</i>_J(<i>α</i>) to high precision, and find empirical analytic formulae that predict <i>ϕ</i>_J(<i>α</i>) to within less than 0.1% for all 1≤<i>α</i>≤10, for three different particle dispersities. Then we explore how these packings' local structural order varies with <i>α</i>. We find that the densest packings possess unusually-well-defined nearest-neighbor shells, including both a higher fraction <i>f</i>_<i>Z</i>=6 of particles with exactly six contacts and a previously-unreported short-range order marked by "kinetically suppressed" regions in their positional-orientational pair correlation function <i>g</i>(<i>r</i>,Δ<i>θ</i>). We also show that the previously-reported approach to isostaticity (coordination number <i>Z</i>_J → <i>Z</i>_iso ≡ 6) with increasing <i>α</i> is interrupted and then reversed as local nematic order increases: <i>Z</i>_J(<i>α</i>) drops towards 4 as ellipses are more often trapped by contacts with a parallel-oriented neighbor on either side and a perpendicularly-oriented neighbor on either end. Finally we show that <i>ϕ</i>_J/<i>ϕ</i>_s (where <i>ϕ</i>_s is the saturated RSA packing density) is nearly α-independent for systems that do not develop substantial local hexatic or nematic order during compression.