Structure of jammed ellipse packings with a wide range of aspect ratios
Motivated in part by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of jammed ellipse packings over a much wider range of particle aspect ratios ($α$) than has been previously attempted. We determine $ϕ_{\rm J}(α)$ to high precision, and find empirical analytic formulae that predict $ϕ_{\rm J}(α)$ to within less than 0.1% for all $1 \leq α\leq 10$, for three different particle dispersities. We find that the densest packings possess unusually-well-defined nearest-neighbor shells, including both a higher fraction $f_{\rm Z = 6}$ 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 $Z_{\rm J} \to Z_{\rm iso} \equiv 6$) with increasing $α$ is interrupted and then reversed as local nematic order increases: $Z_{\rm J}(α)$ 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 $ϕ_{\rm J}/ϕ_{\rm s}$ (where $ϕ_{\rm s}$ is the saturated RSA packing density) is nearly $α$-independent for systems that do not develop substantial local hexatic or nematic order during compression.