Čopar Simon, Dennis Mark R, Kamien Randall D, Žumer Slobodan
Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):050504. doi: 10.1103/PhysRevE.87.050504. Epub 2013 May 30.
Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame that can be extracted from the tensorial description of the nematic order vanishes in the uniaxial phase, we extend the nematic director to a full biaxial frame by making use of a singular value decomposition of the gradient of the director field instead. The degrees of freedom are unveiled in the form of quasidefects and the similarities and differences between the uniaxial and biaxial phase are analyzed by applying the algebraic rules of the quaternion group to the uniaxial phase.
单轴和双轴向列型液晶均由其结构单元的取向有序性定义。单轴向列型液晶仅使分子长轴取向，而双轴有序意味着沿三个轴的局部有序。由于双轴性的自然程度以及可从向列型有序的张量描述中提取的相关框架在单轴相中消失，我们通过利用指向矢场梯度的奇异值分解，将向列型指向矢扩展为完整的双轴框架。自由度以准缺陷的形式揭示，并通过将四元数群的代数规则应用于单轴相来分析单轴相和双轴相之间的异同。
