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Instability of radial hedgehog configurations in nematic liquid crystals under Landau–de Gennes free-energy models
Phys. Rev. E 59, 563 – Published 1 January, 1999
DOI: https://doi.org/10.1103/PhysRevE.59.563
Abstract
We consider radial hedgehog equilibrium configurations of the tensor order parameter in spherical droplets of nematic liquid crystals modeled by free energies of the Landau–de Gennes type. We show that such configurations must become unstable at sufficiently low temperatures in droplets of sufficiently large radii for all but a very limited range of elastic-constant ratios, which are very near the limit where the elastic-energy terms in the model cease to be positive definite. The analysis is complicated by the fact that no analytical solution is available for the hedgehog configuration. Nevertheless, using a combination of analytical bounds and numerical computation, we are able to construct a perturbation to which we can show that the spherically symmetric ground state becomes unstable.
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