Defect dynamics and defect annihilation in liquid-crystal films

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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.