Defect dynamics and defect annihilation in liquid-crystal films

拓扑缺陷存在于各种各样的物理系统中，从宇宙学和量子物理到超导流体、胶体和各向异性液体。这些缺陷结构的动力学有惊人的相似之处。通常，拓扑缺陷是在对称性破缺相变过程中产生的，随后通过相互湮灭而导致的多缺陷图案的粗化控制了相的动力学。理解缺陷对湮没的基本过程是建立更复杂缺陷模型的基础。在液晶(LCS)中，错位是一种易于制备和直观观察的拓扑缺陷结构。这使得LCS成为研究缺陷相互作用的一般特征的优秀模型系统。一个完善的LC相流体力学理论是可行的。在以前的实验工作中，我们已经提供了证据，证明了近晶薄膜中位错相互作用的细节比目前理论所假设的要复杂得多。具有相同拓扑力的相互排斥缺陷的研究带来了新的见解，需要对现有模型进行修正和扩展，在拟议的项目中，我们将专注于相反拓扑力的相互吸引缺陷，并对湮灭动力学进行定量描述。我们将使用厚度从几纳米到几微米的自由悬浮近晶C薄膜，用偏光显微镜记录和分析薄膜平面上的缺陷轨迹。同时，我们将开发合适的解释，并进行全面的数值和半解析模型。目的是了解基本的双缺陷相互作用过程，以实现对近晶自支撑薄膜中准二维流体的错动动力学的定量理解。

Topological defects are found in a broad variety of physical systems, from cosmology and quantum physics to superconducting fluids, colloids and anisotropic liquids. There are striking analogies of the dynamics of those defect structures. Often, topological defects are generated during symmetry breaking phase transitions, and the subsequent coarsening of multi-defect patterns by mutual annihilation governs the dynamicsof the phase. Understanding of the underlying elementary process, defect pair annihilation, is crucial as a basis for the modeling of more complex defect patterns dynamics.In liquid crystals (LCs), disclinations are topological defect structures that can be prepared easily and observed straightforwardly. This renders LCs excellent model systems to study general features of defect interactions. A well developed hydrodynamic theory for LC phases is available. It has been employed to quantitatively predictnovel features of defect annihilation.In previous experimental work, we have provided evidence that the details of disclination interactions in smectic films are much more complex than assumed by present theory. The study of mutually repelling defects with equal topological strength has brought new insight, and it demands revision and extension of the existing models.In the proposed project, we will focus on mutually attracting defects of opposite topological strengths and develop a quantitative description of the annihilation dynamics. We will work with freely suspended smectic C films with thicknesses in range from several nanometers to few micrometers, to record and analyze defect trajectories in the film plane with polarizing microscopy. In parallel, we will develop a suitable interpretation and perform comprehensive numerical and semi-analytical modeling.The aim is the understanding of the elementary two-defect interaction processes, in order to achieve a quantitative understanding of disclination dynamics in smectic free-standing films as quasi-twodimensional fluids.