condensed matter, soft condensed matter, statistical mechanics
Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local
C1v-symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (D1h) 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 Poissonbracket 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.
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