Abstract
We review the impact of tetrahedral order on the macroscopic dynamics of bent-core liquid crystals. We discuss tetrahedral order comparing with other types of orientational order, like nematic, polar nematic, polar smectic, and active polar order. In particular, we present hydrodynamic equations for phases, where only tetrahedral order exists or tetrahedral order is combined with nematic order. Among the latter we discriminate between three cases, where the nematic director (a) orients along a 4-fold, or (b) along a 3-fold symmetry axis of the tetrahedral structure. For the optically isotropic T_d phase, which only has tetrahedral order, we focus on the coupling of flow with e.g. temperature gradients and on the specific orientation behavior in external electric fields. For the transition to the nematic phase, electric fields lead to a temperature shift that is linear in the field strength. Electric fields induce nematic order, again linear in the field strength. If strong enough, electric fields can change the tetrahedral structure and symmetry leading to a polar phase. We briefly deal with the T phase that arises when tetrahedral order occurs in a system of chiral molecules. To case (a) belong (i) the non-polar, achiral, optically uniaxial D2d phase with ambidextrous helicity and with orientational frustration in external fields, (ii) the non-polar tetragonal S4 phase, (iii) the non-polar, orthorhombic D2 phase that is structurally chiral featuring ambidextrous chirality, (iv) the polar orthorhombic C2v phase, and (v) the polar monoclinic C2 phase. Case (b) results in a trigonal C3v phase that behaves like a biaxial polar nematic phase. Finally we discuss some experiments that show typical effects related to the existence of tetrahedral order.
Highlights
The quantitative macroscopic description of liquid crystals (LC) in terms of partial differential dynamic equations, free energy functionals, Ginzburg-Landau energies and the like, has been developed over the last 50 years [1,2,3,4]
We first recall the traditional types of orientational order, give some motivations why these are insufficient in the case of bent-core materials, and discuss tetrahedral order and and its interplay with other types of orientational order
The analysis presented in [35] includes a polar order parameter as well as third rank tensors of tetrahedral/octupolar type along with a discussion of possible isotropic–nematic phase transitions
Summary
The quantitative macroscopic description of liquid crystals (LC) in terms of partial differential dynamic equations, free energy functionals, Ginzburg-Landau energies and the like, has been developed over the last 50 years [1,2,3,4]. This is due to the existence of one (or more) preferred directions in the fluid, either due to rotational order (e.g., nematic LCs), or translational order (e.g., smectic and columnar LCs), or both (e.g., smectic C LCs). Thereby, the rotational and/or translational symmetry of isotropic liquids is spontaneously broken by the occurrence of ordered structures at an equilibrium phase transition. The latter can be obtained by changing some control parameters, like temperature, pressure, or concentration (in a mixture) leading to the distinction of thermotropic, barotropic, and lyotropic LCs, respectively
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