Defects in liquid crystals: surface and interfacial anchoring effects

Abstract 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. Introduction Liquid crystals are endowed with continuous symmetries and physical prevalence of correlations of orientation over correlations of position and thus show rich and complex variety of topological defects. Defects in liquid crystals are of various dimensionalities, not only line defects, but also points, walls, and "configurations" (walls, topological solitons). In this review, we consider basic properties (mainly static) of defects in the simplest types of liquid crystals, nematics and smectics, mostly in relationship to the experimental studies and effects that the bounding surfaces have on defects. The experimental techniques of regular polarizing microscopy and more recent fluorescent confoca

Lassoing saddle splay and the geometrical control of topological defects

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): both point and ring topological defects can occur within each hole and around the system, while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create novel defect structures, including an array of disclination lines, reminiscent of those found in liquid crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.Comment: 9 pages, 7 figures, 1 supplementary figur

Modeling planar degenerate wetting and anchoring in nematic liquid crystals

We propose a simple surface potential favoring the planar degenerate anchoring of nematic liquid crystals, i.e., the tendency of the molecules to align parallel to one another along any direction parallel to the surface. We show that, at lowest order in the tensorial Landau-de Gennes order-parameter, fourth-order terms must be included. We analyze the anchoring and wetting properties of this surface potential. In the nematic phase, we find the desired degenerate planar anchoring, with positive scalar order-parameter and some surface biaxiality. In the isotropic phase, we find, in agreement with experiments, that the wetting layer may exhibit a uniaxial ordering with negative scalar order-parameter. For large enough anchoring strength, this negative ordering transits towards the planar degenerate state

Landau levels of cold atoms in non-Abelian gauge fields

The Landau levels of cold atomic gases in non-Abelian gauge fields are analyzed. In particular we identify effects on the energy spectrum and density distribution which are purely due to the non-Abelian character of the fields. We investigate in detail non-Abelian generalizations of both the Landau and the symmetric gauge. Finally, we discuss how these non-Abelian Landau and symmetric gauges may be generated by means of realistically feasible lasers in a tripod scheme.Comment: 13 pages, 9 figure

Elasticity-mediated self-organization and colloidal interactions of solid spheres with tangential anchoring in a nematic liquid crystal

Using laser tweezers and fluorescence confocal polarizing microscopy, we study colloidal interactions of solid microspheres in the nematic bulk caused by elastic distortions around the particles with strong tangential surface anchoring. The particles aggregate into chains directed at about 30 degrees to the far field director and, at higher concentrations, form complex kinetically trapped structures. We characterize the distance and angular dependencies of the colloidal interaction forces.Comment: 6 pages, 5 figure