On surface biaxiality

Abstract

We propose the following: on the boundary of a nematic liquid crystal, the function which describes the molecular orientation is subject to a further symmetry condition, besides that reflecting apolarity. This additional symmetry delimits a class of biaxial states; within that class we study a model problem for a thin layer in which the anchoring energy prevails over the elastic energy in the presence of an electric field. We show that, when the anchoring and electric energies favour uniaxial states with optic axes at right angles, the equilibrium configuration migrates from one state to the other, traversing a whole family of biaxial states as the strength of the electric field increases.