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We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic alignment, as a consequence of the elastic torques originating from their polar structure. The presence of intermediate -1/2 disclinations, however, turns this interaction from anti-aligning to aligning at scales that are smaller than the typical distance between like-sign defects. No long-range orientational order is observed. Strikingly, these effects are insensitive to material properties and qualitatively similar to what is found for defects in passive nematic liquid crystals., 6 pages, 4 figures

We develop polarized epifluorescence microscopy (PFM), a technique to qualitatively determine a director field, even when refraction effects are too strong to use optical polarized microscopy. We present the basic theory behind the technique and cover in detail the experimental setup. We validate PFM on the well-studied cases of a planar nematic cell, spherical nematic droplets, and a cylindrical capillary filled with nematic liquid crystal. Last, we use nematic capillary bridges to demonstrate that PFM can indeed provide measurements of the director field, even when refraction effects are large.

The presumed ground state of a nematic fluid confined in a cylindrical geometry with planar anchoring corresponds to that of an axial configuration, wherein the director, free of deformations, is along the long axis of the cylinder. However, upon confinement of lyotropic chromonic liquid crystals in cylindrical geometries, here we uncover a surprising ground state corresponding to a doubly twisted director configuration. The stability of this ground state, which involves significant director deformations, can be rationalized by the saddle-splay contribution to the free energy. We show that sufficient anisotropy in the elastic constants drives the transition from a deformation-free ground state to a doubly twisted structure, and results in spontaneous symmetry breaking with equal probability for either handedness. Enabled by the twist angle measurements of the spontaneous twist, we determine the saddle-splay elastic constant for chromonic liquid crystals for the first time., Chirality in molecular materials is commonly used to manipulate the polarization of light. Here, Nayani et al. observe the formation of doubly twisted structure in achiral chromonic liquid crystals when confined to a cylindrical capillary, which leads to spontaneous chiral breaking.

We stabilize nematic droplets with handles against surface-tension-driven instabilities using a yield-stress material as outer fluid and study the complex nematic textures and defect structures that result from the competition between topological constraints and the elasticity of the nematic liquid crystal. We uncover a surprisingly persistent twisted configuration of the nematic director inside the droplets when tangential anchoring is established at their boundaries, which we explain after considering the influence of saddle-splay on the elastic free energy. For toroidal droplets, we find that the saddle-splay energy screens the twisting energy resulting in a spontaneous breaking of mirror symmetry; the chiral twisted state persists for aspect ratios as large as ~20. For droplets with additional handles, we observe in experiments and computer simulations that there are two additional -1 surface defects per handle; these are located in regions with local saddle geometry to minimize the nematic distortions and hence the corresponding elastic free energy., Comment: 23 pages, 4 figures, PNAS (2013)