Schimming Cody D, Viñals Jorge
School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Phys Rev E. 2020 Mar;101(3-1):032702. doi: 10.1103/PhysRevE.101.032702.
Nematic liquid crystals exhibit configurations in which the underlying ordering changes markedly on macroscopic length scales. Such structures include topological defects in the nematic phase and tactoids within nematic-isotropic coexistence. We discuss a computational study of inhomogeneous configurations that is based on a field theory extension of the Maier-Saupe molecular model of a uniaxial, nematic liquid crystal. A tensor order parameter is defined as the second moment of an orientational probability distribution, leading to a free energy that is not convex within the isotropic-nematic coexistence region, and that goes to infinity if the eigenvalues of the order parameter become nonphysical. Computations of the spatial profile of the order parameter are presented for an isotropic-nematic interface in one dimension, a tactoid in two dimensions, and a nematic disclination in two dimensions. We compare our results to those given by the Landau-de Gennes free energy for the same configurations and discuss the advantages of such a model over the latter.
向列型液晶呈现出这样的构型，即其底层的有序性在宏观长度尺度上会发生显著变化。此类结构包括向列相中的拓扑缺陷以及向列 - 各向同性共存区域内的类晶区。我们讨论了一种基于单轴向列型液晶的迈尔 - 绍佩分子模型的场论扩展的非均匀构型的计算研究。张量序参量被定义为取向概率分布的二阶矩，这导致在各向同性 - 向列共存区域内自由能不是凸函数，并且如果序参量的本征值变得不物理，自由能会趋于无穷大。给出了一维各向同性 - 向列界面、二维类晶区和二维向列型位错的序参量空间分布的计算结果。我们将我们的结果与相同构型的朗道 - 德热纳自由能给出的结果进行比较，并讨论这种模型相对于后者的优势。
