Hydrodynamics of polar liquid crystals

Details Hydrodynamics of polar liquid crystals Hydrodynamics of polar liquid crystals

2005-10-25

arxiv.org/abs/cond-mat/0510652v2

Phys. Rev. E 73 (2006) 031708

Physics

Condensed Matter

Soft Condensed Matter

9 pages, corrected typos, added references, revised content, to appear in PRE

Scientific paper

10.1103/PhysRevE.73.031708

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local $C_{\infty v}$-symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals ($D_{\infty h}$) in that it contains terms violating the ${\bf{n}}\to -{\bf{n}}$ symmetry. First we show that these $\mathcal{Z}_2$-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.

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