Flexoelectricity versus electrostatics in polar nematic liquid crystals

Polar nematic liquid crystals have two special features, compared with conventional nematic liquid crystals. First, because of flexoelectricity, the combination of polar order and splay reduces the free energy. Second, because of electrostatics, any splay generates a bound charge density, which increases the free energy. To assess the competition between these two effects, we develop a theory that combines flexoelectricity and electrostatics. The theory predicts a phase diagram that includes ferroelectric, antiferroelectric, and conventional nematic phases.