Liquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA.
J Phys Condens Matter. 2013 Oct 9;25(40):404202. doi: 10.1088/0953-8984/25/40/404202. Epub 2013 Sep 11.
We explore the structure of nuclei and topological defects in the first-order phase transition between the nematic (N) and isotropic (I) phases in lyotropic chromonic liquid crystals (LCLCs). The LCLCs are formed by self-assembled molecular aggregates of various lengths and show a broad biphasic region. The defects emerge as a result of two mechanisms: (1) surface-anisotropy that endows each N nucleus ('tactoid') with topological defects thanks to preferential (tangential) orientation of the director at the closed I-N interface, and (2) Kibble mechanism with defects forming when differently oriented N tactoids merge with each other. Different scenarios of phase transition involve positive (N-in-I) and negative (I-in-N) tactoids with nontrivial topology of the director field and also multiply connected tactoid-in-tactoid configurations. The closed I-N interface limiting a tactoid shows a certain number of cusps; the lips of the interface on the opposite sides of the cusp make an angle different from π. The N side of each cusp contains a point defect-boojum. The number of cusps shows how many times the director becomes perpendicular to the I-N interface when one circumnavigates the closed boundary of the tactoid. We derive conservation laws that connect the number of cusps c to the topological strength m of defects in the N part of the simply connected and multiply connected tactoids. We demonstrate how the elastic anisotropy of the N phase results in non-circular shape of the disclination cores. A generalized Wulff construction is used to derive the shape of I and N tactoids as a function of I-N interfacial tension anisotropy in the approximation of frozen director field of various topological charges m. The complex shapes and structures of tactoids and topological defects demonstrate an important role of surface anisotropy in morphogenesis of phase transitions in liquid crystals.
我们探索了向列（N）相和各向同性（I）相之间一级相变过程中溶致液晶（LCLC）中核的结构和拓扑缺陷。LCLC 由各种长度的自组装分子聚集体形成，表现出广泛的双相区。缺陷的出现有两个原因：（1）表面各向异性，由于各向异性核（“拟晶胞”）的闭合 I-N 界面上的指向矢具有优先（切向）取向，赋予每个 N 核具有拓扑缺陷；（2）Kibble 机制，当不同取向的 N 拟晶胞相互合并时，缺陷形成。不同的相变场景涉及具有非平凡拓扑的正（N 相进入 I 相）和负（I 相进入 N 相）拟晶胞，以及具有多连通拟晶胞-拟晶胞构型的缺陷。限制拟晶胞的闭合 I-N 界面显示出一定数量的尖端；尖端两侧界面的唇瓣形成的角度不同于π。每个尖端的 N 侧包含一个点缺陷-boojum。尖端的数量表示当一个人围绕拟晶胞的闭合边界环绕时，指向矢与 I-N 界面垂直的次数。我们推导出了将尖端的尖端数 c 与简单连接和多连通拟晶胞的 N 部分中的缺陷的拓扑强度 m 连接起来的守恒定律。我们演示了 N 相的弹性各向异性如何导致不完整核心的非圆形形状。广义 Wulff 构造用于导出 I 和 N 拟晶胞的形状，作为各向异性 I-N 界面张力的函数，在各种拓扑电荷 m 的冻结指向矢场的近似下。拟晶胞和拓扑缺陷的复杂形状和结构证明了表面各向异性在液晶中相变形态发生中的重要作用。
