Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known divergences in the Landau-de Gennes formulation. Our results agree with the asymptotic results of Dzyaloshinskii for the Frank-Oseen energy far from the defect core, but reveal biaxial order at intermediate distances from the core, crossing over to uniaxial but axisymmetric configurations as the core is approached. The elastic terms considered in our energy allow for the separate control of surface tension, anchoring, and elasticity contrast, and are used to analyze recent results for lyotropic chromonic liquid crystals. The latter display unusually large defect cores (on the order of tens of microns) which can be used for a quantitative comparison with the theory. Both ±1/2 disclination configurations are well reproduced by our calculations. Elastic anisotropy is also shown to lead to qualitative changes in the disclination polarization, a quantity that is proportional to the active stress in models of active matter.
Bibliographical noteFunding Information:
We thank Sergij Shiyanovskii for stimulating discussions, and him as well as the other authors of Ref. for sharing the raw data of the experiments with us. This research has been supported by the National Science Foundation under Grant No. DMR-1838977, and by the Minnesota Supercomputing Institute.
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