### Abstract

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.

Original language | English (US) |
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Article number | 031708 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 73 |

Issue number | 3 |

DOIs | |

State | Published - 2006 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*73*(3), [031708]. https://doi.org/10.1103/PhysRevE.73.031708