Topological defects in two-dimensional liquid crystals confined by a box

Abstract

When a spatially uniform system that displays a liquid-crystal ordering on a two-dimensional surface is confined inside a rectangular box, the liquid crystal direction field develops inhomogeneous textures accompanied by topological defects because of the geometric frustrations. We show that the rich variety of nematic textures and defect patterns found in recent experimental and theoretical studies can be classified by the solutions of the rather fundamental, extended Onsager model. This is critically examined based on the determined free energies of different defect states, as functions of a few relevant, dimensionless geometric parameters.

A Bidimensional Gay-Berne Calamitic Fluid: Structure and Phase Behavior in Bulk and Strongly Confined Systems

“…As temperature increases, those domain walls disappear and two point defects arise close to the corners of the square. The structural behavior of the LC sample under square confinement agrees with previous theoretical models [121].…”

“…On the experimental front, optical microscopy commonly provides information on quasi-2D samples, and in most cases, data merely reflect 2D projections of an underlying 3D system [56,115]. Renewed interest in the organization of rigid biopolymers as effective 2D systems (in bulk and under confinement) has led to new and interesting textures observed under strong confinement [116][117][118][119][120][121][122]. Simple simulation models reproduced the phenomenology observed in 2D [123][124][125][126].…”

Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement

“…The general importance of defects of liquid crystals is further fueled by the possibility to directly visualize the inherent orientational frustration on the macroscopic scale through the schlieren texture between two crossed polarizers 1 . Different orientational defect structures have therefore been explored a lot in the homogeneous nematic phase [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] with recent digressions to active systems [20][21][22] . Due to their simultaneous orientational and positional ordering, defects in the smectic phase naturally exhibit an even higher degree of complexity.…”

Surface, size and topological effects for some nematic equilibria on rectangular domains

“…A simple test is to check if Q ~ ∞ ( a 2 , b 2 ) ≠ 0 , which would demonstrate the loss of the WORS structure for a ≠ b . In Figure 1, we plot Q ~ ∞ on a square ( a = b = 1 ), which is simply the WORS (see also [32] where the authors report the WORS in an extended Osanger-type framework) and Q ~ ∞ on a rectangle ( a = 1 . 5 , b = 1 ) to illustrate the differences to the reader.…”