ABSTRACT

Orientation of nematic liquid crystal (NLC) around a topological defect is expressed by the equation, $\psi =s\varphi +{\varphi }_0$, where $\psi$, $s$, $\varphi$ and ${\varphi }_0$ are the director spatial phase, topological charge, azimuthal angle and a spatial phase shift, respectively. Conventionally, defect array is modelled by simply adding the $\psi$ fields of all the defects. The resultant array is a combination of the defects imposed by design (${\psi }_s$) and the defects due to the lattice geometry (${\psi }_g$). However, defect arrays generated in homeotropic confinement show hyperbolic hedgehogs (${\psi }_h$) between the ${\psi }_s$s, which are out of the scope of the conventional model. In this research, two-dimensional defect ‘crystals’ with various lattice structures (square and hexagonal), various defect shapes (radial or circular) and various lattice constants (pixel size) are generated by pixelated patterned electrodes in homeotropic NLC cells. The results verify the two selection rules, 1) The total $s$ must be zero, 2) ${\varphi }_0$ must be a constant throughout the array, and a new model composed of ${\psi }_s$, ${\psi }_g$ and ${\psi }_h$ is established. Calculation proves that the selected modelled array has minimum free energy. The ${\psi }_s$-${\psi }_g$-${\psi }_h$ model is versatile and easy to apply, which benefits the design of new topological defect arrays.

摘要

拓扑缺陷周围的向列液晶 (NLC) 的取向由以下方程表示， $\psi =秒\phi +{\phi }_0$， 在哪里 $\psi$, $秒$, $\phi$ 和 ${\phi }_0$分别是指向矢空间相位、拓扑电荷、方位角和空间相移。传统上，缺陷阵列是通过简单地添加$\psi$所有缺陷的领域。由此产生的阵列是设计强加的缺陷的组合（${\psi }_{秒}$) 和由于晶格几何形状引起的缺陷 (${\psi }_G$）。然而，在垂直约束中产生的缺陷阵列显示双曲刺猬（${\psi }_H$） 在。。之间 ${\psi }_{秒}$s，这超出了常规模型的范围。在这项研究中，具有各种晶格结构（方形和六边形）、各种缺陷形状（径向或圆形）和各种晶格常数（像素大小）的二维缺陷“晶体”由垂直 NLC 单元中的像素化图案电极产生。结果验证了两个选择规则，1）总$秒$ 必须为零，2) ${\phi }_0$ 必须是整个数组中的常量，并且新模型由 ${\psi }_{秒}$, ${\psi }_G$ 和 ${\psi }_H$成立。计算证明所选的建模阵列具有最小的自由能。这${\psi }_{秒}$——${\psi }_G$——${\psi }_H$ 模型通用且易于应用，有利于新拓扑缺陷阵列的设计。