Structure of saturated random-sequential-adsorption ellipse packings
Pedro Abritta, Robert S. Hoy
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 ${\ensuremath{\phi}}_{\mathrm{s}}(\ensuremath{\alpha})$ to high precision, finding an empirical analytic formula that predicts ${\ensuremath{\phi}}_{\mathrm{s}}(\ensuremath{\alpha})$ to within less than $0.1%$ for all $\ensuremath{\alpha}\ensuremath{\le}10$. Then we explore how these packings' positional-orientational order varies with $\ensuremath{\alpha}$. We find a transition from tip/side- to side/side-contact-dominated structure at $\ensuremath{\alpha}={\ensuremath{\alpha}}_{\mathrm{TS}}\ensuremath{\simeq}2.4$. At this aspect ratio, the peak value ${g}_{\mathrm{max}}$ of packings' positional-orientational pair correlation functions is minimal, and systems can be considered maximally locally disordered. For smaller (larger) $\ensuremath{\alpha}, {g}_{\mathrm{max}}$ increases exponentially with deceasing (increasing) $\ensuremath{\alpha}$. Local nematic order and structures comparable to the precursor domains observed in experiments gradually emerge as $\ensuremath{\alpha}$ increases beyond three. For $\ensuremath{\alpha}\ensuremath{\gtrsim}5$, single-layer lamellae become more prominent and long-wavelength density fluctuations increase with $\ensuremath{\alpha}$ as packings gradually approach the rodlike limit.