Structure of saturated RSA ellipse packings

TL;DR

This study investigates the structure of saturated RSA ellipse packings, providing a precise empirical formula for packing fractions and analyzing how positional and orientational order vary with aspect ratio, revealing a transition in contact types and emergence of nematic order.

Contribution

The paper introduces an accurate empirical formula for saturated RSA ellipse packing fractions and characterizes the structural transition and order development as a function of aspect ratio.

Findings

Empirical formula predicts packing fractions within 0.1% for all aspect ratios up to 10.

Identifies a transition from tip/side- to side/side-contact dominance at aspect ratio ~2.4.

Shows emergence of nematic order and lamellae structures as aspect ratio increases.

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.