Structure of jammed ellipse packings over a wide range of aspect ratios

Motivated by the recent observation of liquid glass in suspensions of ellipsoidal colloids [J. Roller et al., Proc. Nat. Acad. Sci. 118, e2018072118 (2021)], we examine the structure of jammed ellipse packings over a much wider range of aspect ratios α than has been previously examined. We determine φ_J(α) to high precision, and find an empirical analytic formula that predicts φ_J(α) to within less than 0.1% for all α ≤ 10. Then we explore how these packings’ positional-orientational order varies with α. Local nematic order and structures comparable to the precursor domains observed in experiments gradually emerge as α increases beyond 3. For α ≥ 5, single-layer lamellae become more prominent, and long-wavelength density fluctuations increase with α as packings gradually approach the rod-like limit. We compare these jammed packings to saturated RSA ellipse packings, with the aim of understanding why both the density maximum and the transition from tip/side- to side/side-contact-dominated structure occur at different α.