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由刚性棒状分子构成的向列相液晶是最简单也是理论上研究最多的液晶模型.当液晶分子在边界上的指向受到拓扑约束时,液晶材料内部可能会产生缺陷.预测液晶缺陷的分布和构型是近年来研究的热点和难点.本文在Landau-de GenneS张量模型的基础上,通过数值模拟,结合理论分析,研究三维圆柱区域内液晶缺陷在不同边界条件下的构型.本文的主要结论为,线缺陷比点缺陷更常见也更稳定;边界条件带来的拓扑约束会对线缺陷的构型产生质的影响.
The nematic liquid crystal composed of rigid rod-shaped molecules is the most simple and theoretically the most studied liquid crystal model.When the orientation of the liquid crystal molecules in the boundary is topologically constrained, defects may be generated inside the liquid crystal material, and the distribution and structure of the liquid crystal defects are predicted Based on the Landau-de GenneS tensor model, the thesis studies the configuration of liquid crystal defects in three-dimensional cylindrical regions under different boundary conditions by numerical simulation and theoretical analysis.The main contributions of this paper are as follows: The conclusion is that line defects are more common and more stable than point defects. Topological constraints caused by boundary conditions can have a qualitative effect on the line defect configuration.