Poisson-Bracket Approach to the Dynamics of Bent-Core Molecules

Details Poisson-Bracket Approach to the Dynamics of Bent-Core Molecules Poisson-Bracket Approach to the Dynamics of Bent-Core Molecules

2007-02-27

arxiv.org/abs/cond-mat/0702662v2

Phys. Rev. E 76 (2007) 011710

Physics

Condensed Matter

Soft Condensed Matter

16 pages, RevTeX, 1 figure

Scientific paper

10.1103/PhysRevE.76.011710

We generalize our previous work on the phase stability and hydrodynamic of polar liquid crystals possessing local uniaxial $C_{\infty v}$-symmetry to biaxial systems exhibiting local $C_{2v}$-symmetry. Our work is motivated by the recently discovered examples of thermotropic biaxial nematic liquid crystals comprising bent-core mesogens, whose molecular structure is characterized by a non-polar body axis $({\bf{n}})$ as well as a polar axis $({\bf{p}})$ along the bisector of the bent mesogenic core which is coincident with a large, transverse dipole moment. The free energy for this system differs from that of biaxial nematic liquid crystals in that it contains terms violating the ${\bf{p}}\to -{\bf{p}}$ symmetry. We show that, in spite of a general splay instability associated with these parity-odd terms, a uniform polarized biaxial state can be stable in a range of parameters. We then derive the hydrodynamic equations of the system, via the Poisson-bracket formalism, in the polarized state and comment on the structure of the corresponding linear hydrodynamic modes. In our Poisson-bracket derivation, we also compute the flow-alignment parameters along the three symmetry axes in terms of microscopic parameters associated with the molecular geometry of the constituent biaxial mesogens.

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