由柱狀粒子所組成的液體廣泛存在於自然界中，柱狀粒子比圓形粒子多具有旋轉自由度，使得其系統的結構與運動更為複雜。在高密度二維柱狀液體中，當長寬比等於3時，會產生tetratic結構，這種結構是由柱狀粒子互相平行或垂直排列所組成，且移動與轉動的馳豫時間在低溫時會被分離。我們利用數值模擬的方法，改變一個由類似液晶分子的棒狀粒子的長寬比，觀察其對於液體微觀結構與動力行為的影響。當長寬比從3逐漸縮短時，液體的微觀結構會由tetratic排列結構轉變為質心六角晶格結構，且長寬比介於1.5到2.5之間時，微觀結構不會出現有序的組態。在微觀結構與動力行為上，我們發現有序排列會增加粒子移動所需的馳豫時間。然而，粒子轉動只與自身的長短有關，故粒子長寬比增長時，粒子愈難以做旋轉運動。
長寬比較大的一端，好的tetratic結構會同時抑制粒子的移動與轉動。另一方面，長寬比較小的一端，好的六角晶格結構同樣會抑制粒子移動，但粒子自身的轉動卻會被激發，其原因在於，好的六角晶格結構給予短粒子足夠的空間旋轉，而差的六角晶格結構會使得粒子靠得更近，並壓縮粒子的旋轉空間。

Liquids composed of elongated particles such as dumbbells, ellipsoid, spherocylinders, or rod-like bio-molecules and nano-particles, widely exist in nature. The anisotropic shape of elongated particles gives additional rotational degree of freedom, which breaks isotropic symmetry and enriches micro-packing and motion under thermal agitation. In previous works, the 2D cold liquid composed of spherocylinders with shape aspect ratio (SAR) greater than 3 exhibits tetratic ordered domains with parallel or perpendicular aligned particles, and separation of rotational and translational hopping time scales. In this work, we numerically investigate the micro-structures and motions of the 2D cold liquids composed of short rods by reducing SAR from 3 to 1.35. It is found that the quasi-long range tetratic alignment order and the hexagonal bond-orientation order, respectively at the two SAR ends, are both destroyed in the intermediate SAR regime around SAR=2. The poor particle packing of the disordered structure makes the translational hopping time reach minimum. However, long rods give a strong rotational topological constraint with rod alignment ordering, so the rotational hopping time monotonically increases with increasing SAR, and the rotational and the translational hopping time scales are separated at the small aspect ratio end, after the cross-over of their rate in the intermediate regime.
At the high aspect ratio end, the good local tetratic order has the same positive effects on suppressing rotational and translational hoppings. At the low aspect ratio end, the local hexagonal order has opposite effects on rotational and translational hoppings. The smaller minimum bond length to the nearest neighbors from a site with poor hexagonal ordering is the key for making tighter rotational caging to suppress rotational hopping.
In a 2D system, the packing density and temperature are also significant factors. With increasing packing density or decreasing temperature, the crystalline ordered domains with 4-fold tetratic alignment order increases for SAR > 2. Furthermore, the separation of translational and rotational hopping time scales is weakened for decreasing packing density and increasing temperature for SAR < 2.

Contents
1. Introduction 1
2. Background 4
2.1 2D Cold Liquids composed of spherical particles ............ 4
2.2 2D Cold Liquids composed of rod-like particles ............. 6
3. Simulation 8
3.1 Simulation Model ................................................ 8
3.1.1 Equation of Motion ..................................... 8
3.1.2 Mutual Interaction ...................................... 10
3.1.3 Friction Coefficient and Thermal Perturbation ...... 11
3.1.4 Parameter Setting ........................................ 13
3.2 Boundary Condition ............................................. 14
4. Resultanddiscussion 16
4.1 SAR Effect on Micro-structures and motion ................... 16
4.1.1 Micro-structures with decreasing SAR .............. 16
4.1.2 Micro-motions with decreasing SAR ................ 21
4.1.3 Correlating local translational and rotational motions with local structural orders .................... 26
4.2 Packing Density and Temperature Effect on Micro- structures and motions .......................................... 35
4.2.1 Micro-structures with changing ρ and T ................. 35
4.2.2 Micro-motions with changing ρ and T .................... 37
5. Conclusion 39
6. Bibliography 41

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