Kung William, Marchetti M Cristina
Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 1):011710. doi: 10.1103/PhysRevE.76.011710. Epub 2007 Jul 20.
We generalize our previous work on the phase stability and hydrodynamic of polar liquid crystals possessing local uniaxial C infinity v symmetry to biaxial systems exhibiting local C2v 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 (n) as well as a polar axis (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 p-->-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.
我们将之前关于具有局部单轴(C_{\infty v})对称性的极性液晶的相稳定性和流体动力学的工作推广到具有局部(C_{2v})对称性的双轴系统。我们的工作受到最近发现的由弯曲核液晶元组成的热致双轴向列型液晶实例的推动，其分子结构的特征是沿着弯曲液晶核的平分线存在一个非极体轴（(n)）以及一个极轴（(p)），该平分线与一个大的横向偶极矩重合。该系统的自由能与双轴向列型液晶的自由能不同，因为它包含违反(p \to -p)对称性的项。我们表明，尽管与这些宇称奇性项相关存在一般的展曲不稳定性，但在一定参数范围内均匀极化的双轴态可以是稳定的。然后，我们通过泊松括号形式在极化态下推导该系统的流体动力学方程，并对相应线性流体动力学模式的结构进行评论。在我们的泊松括号推导中，我们还根据与组成双轴液晶元的分子几何结构相关的微观参数计算了沿三个对称轴的流动排列参数。
