Stabilising the tetrahedral defect configuration in nematic shells

Monte Carlo simulations are used to investigate the director configurations and the arrangements of the disclination lines that form in nematic shells surrounding interior spherical and polyhedral particles. For nematic shells formed around an interior spherical particle, a tetrahedral arrangement of the disclination lines is observed but this arrangement is lost if the interior sphere is shifted from the centre. The simulations indicate that a narrower angular distribution is observed for interior tetrahedral particles and, for non-centrosymmetric shells, the distribution is significantly less broadened compared to similar spherical inclusions. Other shape polyhedral particles are shown to give disclination geometries of different symmetries.