球形向列相液滴新缺陷态的研究

Study on New Defect States of Spherical Nematic Droplet

摘要: 基于Landau-de Gennes理论，利用二维有限差分迭代法，研究了相同条件下环(ring)结构与三缺陷结构之间的能量对比。探究了三缺陷结构稳定存在的尺寸范围、边界条件对于缺陷位置的影响以及三缺陷结构转变为环结构的动力学过程。结果表明：环结构能量最低为基态，而三缺陷结构能量相对较高为亚稳态。研究中选取固定温度并做单一弹性常数近似。对于均匀垂面锚定且锚定强度系数为w = 10⁻³ J/m²时，三缺陷结构在R ≥ 1.17 μm范围内稳定；w = 10⁻⁴ J/m²时，三缺陷结构在R ≥ 1.16 μm范围内稳定；w = 10⁻⁵ J/m²时，存在的范围为R ≥ 0.95 μm。进一步改变边界锚定强度系数，使其在边界不再是定值，而是线性变化的。在球的两极点处取最大值w_max，并取半径为26.4 μm进行研究。其他条件相同只改变w_max的值，我们发现，wmax取10⁻³ J/m²与取10⁻⁴ J/m²、10⁻⁵ J/m²相比，缺陷反而向中心轴收缩，出现反常现象。在较小的半径下，三缺陷态中的两个缺陷靠近并湮灭，最终形成环结构。

Abstract: Based on the Landau-de Gennes theory, using a two-dimensional finite-difference iterative method, the energy comparison between the ring structure and the structure of three defects under the same condition is established. In addition, the size range of the three-defect structure, the influence of boundary conditions on the location of defects and the dynamic process of the transformation of the three-defect structure into a ring structure are also discussed. As a result, the ring structure with the lowest energy is ground state, while the three-defect structure with the higher energy is metastable state. In our study, the temperature is constant; the elastic constants are approximately equal. When the homeotropic anchoring is homogenous and if we assume that the anchoring strength coefficient is w = 10⁻³ J/m², the three-defect structure is stable in the range of R ≥ 1.17 μm; as the coefficient is w = 10⁻⁴ J/m², the structure is stable in the range of R ≥ 1.16 μm; as the coefficient is w = 10⁻⁵ J/m², R ≥ 0.95 μm. Furthermore, the anchoring strength coefficient is changed so that it is no longer fixed on the boundary, but changes linearly. The maximum value of wmax was set at the two poles of the sphere, and the radius was set for 26.4 μm in the study. Other conditions are the same, the results for w_max of 10⁻³ J/m², 10⁻⁴ J/m² and 10⁻⁵ J/m², respectively, are compared. When w_max = 10−3 J/m2, instead defects moved into the central axis, and abnormal phenomena appeared. At a smaller radius, two defects of the three-defect states get close to each other and annihilate, and form a ring structure finally.