Stability of the radial configuration in a nematic liquid crystal droplet with applied electric field

Abstract

We study in an analytical manner how the configuration of a radial nematic liquid crystal droplet behaves in the presence of an external constant electric field. Using the Landau expansion of the free energy, we showed that for the field greater than a critical value the radial structure is unstable against the formation of asymmetric hedgehog structure in which the singular point of the radial structure is shifted from the droplet center. In the present work we show that the phase transition from the symmetric to asymmetric hedgehog is of the second-order.