Published in Physical Review E, Volume 73, Issue 3, March 30, 2006, pages 031708.1-031708.8.
Copyright © 2006American Physical Society. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Physical Society. The following article appeared in Physical Review E and may be found at http://dx.doi.org/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∞v symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (D∞h) 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.