Defects in Liquid Crystals: Surface and Interfacial Anchoring Effects

This review discusses static properties of topological defects, such as line defectsdisclinations and dislocations, point defects hedgehogs (monopoles) and boojums; focal conic domains and tilt grain boundaries in basic types of liquid crystals: uniaxial and biaxial nematics, cholesterics and smectics. We present the most popular experimental techniques to study defects in soft matter, namely, polarizing microscopy and fluorescence confocal polarizing microscopy. The role of bounding surfaces and the so-called surface anchoring that lifts the degeneracy of the order parameter in stability of defects is discussed. Because of the surface anchoring, the equilibridm state of a bounded liquid crystal might contain topological defects. For example, nematic bubbles nucleating during the first-order phase transition from the isotropic melt, might contain point defects (hedgehogs and boojums) and disclination loops when their size is larger than the anchoring extrapolation length defined by the ratio of the Frank elastic constant of the director curvature and the (polar) anchoring coefficient. Depending on the strength of surface anchoring, an edge dislocation might be expelled from the system with ID positional order or be stabilized in the bulk. Furthermore, focal conic domains play the role of "surface anchoring facets" by providing the necessary orientation of the liquid crystal director at the smectic boundary.