论文标题
饱和RSA椭圆包装的结构
Structure of saturated RSA ellipse packings
论文作者
论文摘要
通过最近观察到椭圆形胶体悬浮液的液体玻璃的动机，我们检查了（渐近）饱和的RSA椭圆包装的结构。我们将包装分数$ ϕ _ {\ rm s}（α）$确定为高精度，找到一个经验分析公式，该公式可以预测$ ϕ _ {\ rm s} $ to to by $α\ leq 10 $的$ 0.1 \％$ $ 0.1 \％$。然后，我们探索这些包装的位置定向顺序如何随$α$变化。我们发现在$α=α_ {\ rm ts} \ simeq 2.4 $的$α=α_ {\ rm TS} \ simeq 2.4 $下的尖端/侧面/侧面接触式结构的过渡。在此长宽比下，包装的位置 - 定向配对函数的峰值$ g _ {\ rm max} $最少，并且可以将系统视为最大的本地混乱。对于较小的（较大）$α$，$ g _ {\ rm max} $随着（增加）$α$的指数增加。随着$α$的增加，与实验中观察到的前体域相当的局部列表和结构逐渐出现超过$ 3 $。对于$α\ gtrsim 5 $，随着包装逐渐接近类似杆状的极限，单层薄片变得更加突出，而长波长密度的波动随着$α$而增加。
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 $ϕ_{\rm s}(α)$ to high precision, finding an empirical analytic formula that predicts $ϕ_{\rm s}(α)$ to within less than $0.1\%$ for all $α\leq 10$. Then we explore how these packings' positional-orientational order varies with $α$. We find a transition from tip/side- to side/side-contact-dominated structure at $α= α_{\rm TS} \simeq 2.4$. 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) $α$, $g_{\rm max}$ increases exponentially with deceasing (increasing) $α$. Local nematic order and structures comparable to the precursor domains observed in experiments gradually emerge as $α$ increases beyond $3$. For $α\gtrsim 5$, single-layer lamellae become more prominent, and long-wavelength density fluctuations increase with $α$ as packings gradually approach the rod-like limit.
