Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement
Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement
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DOI：
10.1140/epje/e2004-00043-2
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发表时间：
2004-01-01
影响因子：
1.8
通讯作者：
Yokoyama, H
中科院分区：
文献类型：
--
作者：
Fukuda, J;Yoneya, M;Yokoyama, H
利用我们以前提出的一种自适应网格加密方法，研究了球形粒子周围液晶的取向分布和拓扑缺陷的结构。先前的工作[J. Fukuda et al.，物理评论E 65，041709（2002）]致力于研究双曲刺猬缺陷的精细结构的粒子伴随，在本文中，我们提出的土星环配置的平衡剖面。以粒子半径R-0为单位的土星环半径r（d）随x_i（x_i相干长度与R-0的比值）的增加而微弱地增加。接下来我们讨论刺猬和土星环的能量稳定性。自适应网格细化方案的使用与张量取向序参数Q（alphabeta）一起，使我们能够计算的弹性能的一个液晶没有任何假设的结构和能量的缺陷核心在以前类似的研究。在刺猬构型中，液晶的约化自由能（F）除以bar = F/L1 R 0，其中L-1为弹性常数，几乎与xi无关，而在土星环构型中，它表现出对数依赖性。这一结果清楚地表明，刺猬的能量稳定的土星环的大粒子是肯定归因于大的缺陷能量的土星环的大半径。
We investigate the orientation profile and the structure of topological defects of a nematic liquid crystal around a spherical particle using an adaptive mesh refinement scheme developed by us previously. The previous work [J. Fukuda et al., Phys. Rev. E 65, 041709 (2002)] was devoted to the investigation of the fine structure of a hyperbolic hedgehog defect that the particle accompanies and in this paper we present the equilibrium profile of the Saturn ring configuration. The radius of the Saturn ring r(d) in units of the particle radius R-0 increases weakly with the increase of xi, the ratio of the nematic coherence length to R-0. Next we discuss the energetic stability of a hedgehog and a Saturn ring. The use of adaptive mesh refinement scheme together with a tensor orientational order parameter Q(alphabeta) allows us to calculate the elastic energy of a nematic liquid crystal without any assumption of the structure and the energy of the defect core as in the previous similar studies. The reduced free energy of a nematic liquid crystal, (F) over bar = F/L1R0, with L-1 being the elastic constant, is almost independent of xi in the hedgehog configuration, while it shows a logarithmic dependence in the Saturn ring configuration. This result clearly indicates that the energetic stability of a hedgehog to a Saturn ring for a large particle is definitely attributed to the large defect energy of the Saturn ring with a large radius.