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Disclination configurations of a nematic liquid crystal are studied within aself-consistent molecular field theory. The theory is based on a tensor orderparameter, and can accommodate anisotropic elastic energies without the knowndivergences in the Landau-de Gennes formulation. Our results agree with theasymptotic results of Dzyaloshinsky for the Frank-Oseen energy and far from thedefect core, but reveal biaxial order at intermediate distances from the core,crossing over to uniaxial, but isotropic configurations as the core isapproached. The elastic terms considered in our energy allow for separatecontrol of surface tension, anchoring, and elasticity contrast, and are used toanalyze recent results for lyotropic chromonic liquid crystals. The latterdisplay unusually large defect cores (on the order of tens of microns) whichcan be used for a quantitative comparison with the theory. Both $\pm 1/2$disclination configurations are well reproduced by our calculations. Elasticanisotropy is also shown to lead to qualitative changes in the disclinationpolarization, a quantity that is proportional to the active stress in models ofactive matter.

Anisotropic disclination cores in nematic liquid crystals modelled by a self consistent molecular field theory