Theory of bent-core liquid-crystal phases and phase transitions

Abstract

We study phases and phase transitions that can take place in the newly discovered banana (bowshaped 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 novel liquid phases, including the spontaneously chiral nematic (NT +2) * and chiral polar (VT +2) * phases, the orientationally-ordered but optically isotropic tetrahedratic T phase, and a novel nematic NT 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.

Computer Simulations of Biaxial Nematics

“…Even for this GB model, the N u phase disappeared for an intermediate 170 degrees apex angle. Interestingly, close to the nematic-smectic phase transition a spontaneous chirality symmetry breaking [136] was reported [133,134,137] to produce organisations related to those predicted by Lubensky and Radzihovsky [4], or observed by Görtz and Goodby [19]. The presence of a central transverse dipole [135] suppresses the N u phase to give transitions from isotropic to smectic phases, and this is at variance with results from atomistic simulations (see later on).…”

“…For instance, bentcore mesogens can form an extremely rich class of LC and their proper characterisation also requires third rank tensors [4]. Another counterexample is that of ferroelectric phases where also first rank order parameters are relevant [60,61].…”

“…However, it should be pointed out that neither theory nor simulations have yielded a specific molecular design but rather have provided reassurance on the N b not being a priori forbidden. The N b phase was not the only "missing link" in the class of thermotropic LC organisations, and as a side comment we also quote the ferroelectric nematic among the elusive phases predicted by theory [4] and computer simulations [5] which is yet an open challenge on the experimental ground. As we shall discuss later, part of the elusivity of N b may be due to the fact that many of the molecular features that favour a biaxial arrangement of the molecules in the fluid nematic also favour their packing in the competing smectic or crystalline biaxial phases.…”

Phase ordering of zig-zag and bow-shaped hard needles in two dimensions

“…29,30 The good agreement between hard-core models and some experiments suggests that entropy alone can suffice to drive the formation of ordered structures. 31 High-aspect ratio molecules with a bent core 32,33 or a banana shape 34,35 assemble in an even richer set of morphologies, including biaxial nematic, 36,37 fan-shaped texture, 38 and nematic with splay-bend deformation or conical twist-bend helix. 39 From the technological viewpoint these structures are quite interesting.…”

Metallomesogens: Retrospectives and Perspectives

“…Свойства этих мезофаз объясняются образованием молекулярных агрегатов с тетра-эдрической структурной организацией (рис. 3), и они рассматривались как первый случай наблюдения ранее теоретически предсказанных типов мезофаз [130][131][132], названных тетра-эдрическими нематическими и тетраэдрическими смектическими мезофазами.…”