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学到超导流体、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，拓扑缺陷产生于对称性破缺相变过程中，随后的相互湮灭导致的多缺陷模式的粗化控制了相变的动态性。理解基本过程，缺陷对湮灭，是至关重要的基础，为更复杂的缺陷图案的动力学建模。在液晶（LC），向错是拓扑缺陷结构，可以很容易地制备和观察。这使得LC优秀的模型系统，研究缺陷相互作用的一般特征。LC相的流体动力学理论已经发展成熟。在以前的实验工作中，我们提供的证据表明，近晶薄膜中的向错相互作用的细节比目前理论所假设的要复杂得多。拓扑强度相等的互斥缺陷的研究带来了新的见解，这就要求对现有的模型进行修正和扩展。在本项目中，我们将重点研究拓扑强度相反的互斥缺陷，并对湮灭动力学进行定量描述。我们将与自由悬浮的近晶C膜的厚度范围从几个纳米到几个微米，记录和分析缺陷的轨迹在膜平面与偏光显微镜。与此同时，我们将开发一个合适的解释，并进行全面的数值和半解析modeling.The目标是基本的两个缺陷的相互作用过程的理解，为了实现近晶自支撑薄膜的向错动力学的定量理解准二维流体。

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.