Paper detail

A new light on the breaking of uniaxial symmetry in nematics

Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. For an arbitrary form of the bulk energy density, we show that energy minimizers among uniaxially symmetric configurations are usually not equilibrium configurations. It was known before that uniaxiality can sometimes be broken by energy minimizers. We prove here that this is always the case in one or two dimensions. Even more we prove that equilibrium configurations (not only minimizers) cannot be uniaxial in one or two dimensions (unless they are constant). Namely, uniaxial equilibrium configurations with at least one translational invariance direction must have a uniform director field. In the case of a hybrid nematic cell, or of a capillary with radial anchoring, our result implies that biaxial escape always occurs, and that it does so not only in the core of a defect: uniaxial order is destroyed in the whole cell.