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

TL;DR

This paper extends the Poisson-bracket formalism to analyze the phase stability and hydrodynamics of polarized biaxial liquid crystals with bent-core molecules, revealing conditions for stable polarized states and deriving related hydrodynamic equations.

Contribution

It introduces a generalized Poisson-bracket approach for biaxial bent-core liquid crystals, accounting for parity-odd terms and stability conditions, and computes flow-alignment parameters from molecular geometry.

Findings

Stable polarized biaxial states are possible despite splay instabilities.

Hydrodynamic equations for the polarized state are derived.

Flow-alignment parameters are expressed in terms of molecular geometry.

Abstract

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.