On the local instability of radial hedgehog configurations in nematic liquid crystals under Landau-de Gennes free-energy models

We consider radial hedgehog equilibrium configurations of the tensor order parameter in spherical droplets of nematic liquid crystals modeled by free energies of Landau-de Gennes type. We show that such configurations must cease to be metastable 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 ∗Also affiliated with Chemical Physics Interdisciplinary Program, Liquid Crystal Institute, Kent State University, Kent, OH, USA. Electronic address: [email protected] †Electronic address: [email protected]