Kralj S, Virga E G, Zumer S
Department of Physics, Faculty of Education, University of Maribor, Koroska 160, 2000 Maribor, Slovenia.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Aug;60(2 Pt B):1858-66. doi: 10.1103/physreve.60.1858.
We study the biaxial structure of both line and point defects in a nematic liquid crystal confined within a capillary tube whose lateral boundary enforces homeotropic anchoring. According to Landau-de Gennes theory the local order in the material is described by a second-order tensor Q, which encompasses both uniaxial and biaxial states. Our study is both analytical and numerical. We show that the core of a line defect with topological charge M=1 is uniaxial in the axial direction. At the lateral boundary, the uniaxial ordering along the radial direction is reached in two qualitatively different ways, depending on the sign of the order parameter on the axis. The point defects with charge M=+/-1 exhibit a uniaxial ring in the plane orthogonal to the cylinder axis. This ring is in turn surrounded by a torus on which the degree of biaxiality attains its maximum. The typical lengths that characterize the structure of these defects depend both on the cylinder radius and the biaxial correlation length. It seems that the core of the point defect does not depend on the far nematic director field in the bulk limit.
我们研究了限制在毛细管内的向列型液晶中线缺陷和点缺陷的双轴结构，该毛细管的侧向边界强制垂直锚定。根据朗道 - 德热纳理论，材料中的局部有序性由二阶张量Q描述，它涵盖单轴和双轴状态。我们的研究包括解析和数值两方面。我们表明，拓扑电荷M = 1的线缺陷的核心在轴向是单轴的。在侧向边界，沿径向的单轴有序性通过两种定性不同的方式实现，这取决于轴上序参量的符号。电荷M = ±1的点缺陷在与圆柱轴正交的平面内呈现一个单轴环。这个环又被一个环面围绕，在该环面上双轴性程度达到最大值。表征这些缺陷结构的典型长度既取决于圆柱半径，也取决于双轴关联长度。似乎在体极限情况下，点缺陷的核心不依赖于远处的向列指向矢场。
