Lubensky T C, Radzihovsky Leo
Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19174, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Sep;66(3 Pt 1):031704. doi: 10.1103/PhysRevE.66.031704. Epub 2002 Sep 11.
We study phases and phase transitions that can take place in the recently discovered bow-shaped or bent-core liquid-crystal molecules. We show that to completely characterize phases exhibited by such bent-core molecules a third-rank tensor T(ijk) order parameter is necessary in addition to the vector and the nematic (second-rank) tensor order parameters. We present an exhaustive list of possible liquid phases, characterizing them by their space-symmetry group and order parameters, and catalog the universality classes of the corresponding phase transitions that we expect to take place in such bent-core molecular liquid crystals. In addition to the conventional liquid-crystal phases such as the nematic phase, we predict the existence of other liquid phases, including the spontaneously chiral nematic (N(T)+2)() and chiral polar (V(T)+2)() phases, the orientationally ordered but optically isotropic tetrahedratic T phase, and a nematic N(T) phase with D(2d) symmetry that is neither uniaxial nor biaxial. Interestingly, the isotropic-tetrahedratic transition is continuous in mean-field theory, but is likely driven first order by thermal fluctuations. We conclude with a discussion of smectic analogs of these phases and their experimental signatures.
我们研究了最近发现的弓形或弯曲核液晶分子中可能发生的相和相变。我们表明，为了完全表征此类弯曲核分子所呈现的相，除了矢量和向列（二阶）张量序参量外，还需要一个三阶张量(T_{(ijk)})序参量。我们给出了可能的液相的详尽列表，通过它们的空间对称群和序参量对其进行表征，并对我们预期在此类弯曲核分子液晶中发生的相应相变的普适类进行编目。除了诸如向列相之类的传统液晶相之外，我们预测还存在其他液相，包括自发手性向列相((N_{(T)} + 2)^)和手性极性相((V_{(T)} + 2)^)、取向有序但光学各向同性的四面体相(T)，以及具有(D_{2d})对称性的既非单轴也非双轴的向列相(N_{(T)})。有趣的是，在平均场理论中，各向同性 - 四面体转变是连续的，但可能由热涨落驱动为一级相变。我们最后讨论了这些相的近晶类似物及其实验特征。
