Poisson-bracket approach to the dynamics of bent-core molecules

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.Comment: 16 pages, RevTeX, 1 figur

The solution of the puzzle of smectic-Q: The phase structure and the origin of spontaneous chirality

The so-called smectic-Q (SmQ) liquid crystal phase was discovered in 1983 in rod-like molecules, but its structure remain unclear in spite of numerous attempts to solve it. Herein, we report what we believe to be the solution: A unique bicontinuous phase that is non-cubic and is made up of orthogonal twisted columns with planar 4-way junctions. While SmQ had only been observed in chiral compounds, we show that this chiral phase forms also in achiral materials through spontaneous symmetry breaking. The results strongly support the idea of a helical substructure of bicontinuous phases and long-range homochirality being sustained by helicity-matching at network junctions. The model also explains the triangular shape of double-gyroid domains growing within a SmQ environment. SmQ-forming materials hold potential for applications such as circularly polarized light emitters that require no alignment or asymmetric synthesis