Hydrodynamics of polar liquid crystals

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local C v symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (Dh) in that it contains terms violating the n→-n symmetry. First we show that these Z2 -odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.