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 (α, the ratio of the major and minor axis lengths) than has been previously attempted. We determine the jamming densities ϕ_J(α) to high precision, and find empirical analytic formulae that predict ϕ_J(α) to within less than 0.1% for all 1≤α≤10, for three different particle dispersities. Then we explore how these packings’ local structural order varies with α. We find that the densest packings possess unusually-well-defined nearest-neighbor shells, including both a higher fraction f_Z=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 g(r,Δθ). We also show that the previously-reported approach to isostaticity (coordination number Z_J → Z_iso ≡ 6) with increasing α is interrupted and then reversed as local nematic order increases: Z_J(α) 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 ϕ_J/ϕ_s (where ϕ_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.