Abstract
We review the interactions and dynamics of topological defects in liquid crystals (LCs) in quasi-twodimensional (2D) geometries. Such spatial restrictions can be realized in thin freely suspended smectic C films, in thin sandwich cells filled with nematic LCs, and under specific boundary conditions in LC shells embedded in aqueous solutions. Random defect patterns can be created by thermal quenching of the samples from lower ordered into higher ordered phases. On the other hand, well defined isolated defect configurations for the study of elementary interaction steps can be prepared by simple mechanical techniques. Observation by polarizing microscopy is straightforward. Spatial dimensions of the experimental systems as well as time scales are convenient for observation. The continuum theory of LCs is well developed so that in addition to the experimental characterization, an analytical or numerical description is feasible. From interactions and dynamic features observed in these LC systems, general conclusions on defect dynamics can be drawn.
Highlights
After having obtained the equilibrium director configurations for defect pairs in given distances and orientations, we discuss their dynamics: It is a widely used concept to assume that interacting defects moving in the liquid crystals (LCs) system pass equilibrium configurations of the director fields in an adiabatic way
Models and experiments of 2D nematic and smectic C (SmC) defect interactions and dynamics were compiled in this review
The square-root scaling was confirmed in many experiments with smectic films and nematics in sandwich cells
Summary
Topological defects occur in a wide variety of physical systems, ranging from soft matter [1,2,3,4,5,6] to quantum systems [7,8,9,10], superfluid liquids [11,12,13,14], and thin magnetic films [15,16,17] to cosmology [18,19,20,21,22]. Some liquid crystal (LC) phases are promising candidates by virtue of their easy handling, straightforward observation, convenient relaxation time scales, and diversity of structures They allow for studying defect interactions and coarsening dynamics of topological defect patterns with conventional optical polarizing microscopy. An advantage of smectic freely suspended films over nematics is that experiments with nematics in sandwich cells are not easy to interpret because of the three-dimensionality of the geometric problem. Defects, even if they are well-localized in the cell midplane, usually extend from one glass plate to the other.
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