Simões M, Bertolino W, Davincy T
Universidade Estadual de Londrina, Departamento de Fısica, Campus Universitário, 86051-990, Londrina (PR), Brazil.
Eur Phys J E Soft Matter. 2019 May 16;42(5):59. doi: 10.1140/epje/i2019-11817-8.
In this work we study the geometry of the elastic deformations of the uniaxial nematic liquid crystals at the bulk. We will show that, at this region of the sample, the elastic terms of the free energy can be separated as the sum of two kinds of elastic deformations, the first is proportional to the Gaussian curvature obtained from the director field of a three-dimensional nematic sample and the second is composed by those terms that cannot be expressed as resulting from this curvature. To achieve these results we will construct the metric of an unixial nematic sample using the fact that the director gives the direction of the anisotropy of the system. With this approach we will give analytical and geometrical arguments to show that the elastic terms determined by [Formula: see text], [Formula: see text] and [Formula: see text] are contained in a curvature term, while the terms fixed by the splay elastic term, [Formula: see text], and the bend elastic term, [Formula: see text], are not. The novelty here is that while [Formula: see text] and [Formula: see text] do not contribute the bulk elastic energy of a nematic sample, they have an important contribution to the curvature of the system.
在这项工作中，我们研究了单轴向列型液晶在本体中的弹性形变几何。我们将证明，在样品的这个区域，自由能的弹性项可以分离为两种弹性形变的和，第一种与从三维向列型样品的指向矢场得到的高斯曲率成正比，第二种由那些不能表示为由该曲率产生的项组成。为了得到这些结果，我们将利用指向矢给出系统各向异性方向这一事实来构建单轴向列型样品的度量。通过这种方法，我们将给出分析和几何论证，以表明由[公式：见原文]、[公式：见原文]和[公式：见原文]确定的弹性项包含在一个曲率项中，而由展曲弹性项[公式：见原文]和弯曲弹性项[公式：见原文]确定的项则不包含。这里的新颖之处在于，虽然[公式：见原文]和[公式：见原文]对向列型样品的本体弹性能量没有贡献，但它们对系统的曲率有重要贡献。
