Structure of saturated RSA ellipse packings

Abstract: Motivated by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of (asymptotically) saturated RSA ellipse packings. We determine the packing fractions $\phi_{\rm s}(\alpha)$ to high precision, finding an empirical analytic formula that predicts $\phi_{\rm s}(\alpha)$ to within less than $0.1\%$ for all $\alpha \leq 10$. Then we explore how these packings' positional-orientational order varies with $\alpha$. We find a transition from tip/side- to side/side-contact-dominated structure at $\alpha = \alpha_{\rm TS} \simeq 2.4$. At this aspect ratio, the peak value $g_{\rm max}$ of packings' positional-orientational paircorrelation functions is minimal, and systems can be considered maximally locally disordered. For smaller (larger) $\alpha$, $g_{\rm max}$ increases exponentially with deceasing (increasing) $\alpha$. Local nematic order and structures comparable to the precursor domains observed in experiments gradually emerge as $\alpha$ increases beyond $3$. For $\alpha \gtrsim 5$, single-layer lamellae become more prominent, and long-wavelength density fluctuations increase with $\alpha$ as packings gradually approach the rod-like limit.