Tilt Chirality

The Helfrich-Prost model was extended in a pair of papers by Ou-Yang and Liu.181182 These authors draw an explicit analogy between tilted chiral lipid bilayers and cholesteric liquid crystals. The main significance of this analogy is that the two-dimensional membrane elastic constants of Eq. (5) can be interpreted in terms of the three-dimensional Frank constants of a liquid crystal. In particular, the kHp term that favors membrane twist in Eq. (5) corresponds to the term in the Frank free energy that favors a helical pitch in a cholesteric liquid crystal. Consistent with this analogy, the authors point out that the typical radius of lipid tubules and helical ribbons is similar to the typical pitch of cholesteric liquid crystals. In addition, they use the three-dimensional liquid crystal approach to derive the structure of helical ribbons in mathematical detail. Their results are consistent with the three conclusions from the Helfrich-Prost model outlined above. 

Tanaka, A., Hisaki, I., Tohnai, N. and Miyata, M. (2007) Supramolecular tilt-chirality derived from symmetric benzene molecules handedness of the 2 helical assembly. Chem. Asian J., 2, 230-238. 

The flexoelectric effect is a phenomenon where a space variation of the order parameter induces polarization. Chiral polar smectics are liquid crystals formed of chiral molecules and organized in layers. All phases in tilted chiral polar smectic liquid crystals have modulated structures and they are therefore good candidates for exhibiting the flexoelectric effect. The flexoelectric effect is less pronounced in the ferroelectric SmC phase and in the antiferroelectric SmC. The flexoelectric effect is more pronounced in more complex phases the three-layer SmCpu phase, the four-layer SmCFi2 phase and the six-layer SmCe a phase. 

In this chapter we consider several important aspects of the flexoelectric effect for chiral polar smectic liquid crystals and for the variety of phases. First, we discuss the reason for indirect interlayer interactions, which extend to more distant layers, and the lock-in to multi-layer structures. Second, although it was believed for a long time that polarization in tilted chiral smectics is always perpendicular to the tilt with the smectic layer normal, a component in the direction of the tilt may exist. And third, in multi-layer structures, the flexoelectricaUy induced polarization can be extremely large but is difficult to measure. 

The form chirahty of all of these chiral smectic mesophases takes the form of a helical stracture, but the helix manifests itself in a different way from the helix in the chiral nematic phase. In addition to being substantially the most commonly exhibited of the tilted chiral smectic phases, the chiral smectic C phase is by far the most important (least ordered and least viscous) in this category. The chiral smectic C phase is employed in the ferroelectric display device (see Chapter 13) but the helix must be unwound. 

Note that compound 8 exhibits a wide range of tilted chiral smectic phases and shows a chiral nematic phase at higher temperature. Despite possessing the S phase, compound... 

The symmetry requirements necessary for ferroelectricity in low-molecular mass compounds, which were discussed in Section 1.1.3, are valid for polymer mesophases too. If a tilted chiral smectic phase is stable after a polymerization process it must be ferroelectric. Following this idea, the first polymer liquid crystalline ferroelectric has been synthesized by Shibayev et al. [160]. Its spontaneous polarization did not differ very much from the precursor monomer [161]. After polyvinylidene fiuoride (PVF2)... 

Figure 11.2. The origin of pyroelectricity in tilted chiral columnar (and smectic) phases side view on disks (or rods) Y — polar group the column axis is vertical, the optical axis is tilted, and the vector of the macroscopic dipole is perpendicular to the plane of the paper. (Reprinted with permission from J. Mater. Chem. 5, 417 1995, The Royal Society of Chemistry [1].)...

J tilted chiral crystal J H tilted chiral crystal H G tilted chiral crystal G K tilted chiral crystal K... 

The reduced symmetry of chiral phases results in additional contributions to the low frequency permittivity. Tilted chiral phases such as smectic C, F and I lack a centre of symmetry, and it is possible for these materials to be ferroelectric. The resulting spontaneous polarization is directed along the C2 symmetry axis, and is perpendicular to the tilt plane it also depends di-... 

The local C2 symmetry in tilted chiral smectic layers leads to a polar inequivalence within the layers due to the chiral and polar nature of the individual molecules despite a considerable degree of molecular reorientation about the long axis (see Sec. 2 and 3 of this chapter) [19-22]. The consequence of this time-dependent alignment of the dipoles along the C2 axis is a spontaneous polarization (f s) parallel to the layer planes, which is averaged out macroscopically to... 

Illustration of the structure of the ferroelectric type arrangements and their deformation under electric fields of a tilted chiral columnar liquid crystal l,2,5,6,8,9,12,13-octakis-((S)-2-heptyloxy) dibenzo[e,l]pyrene that has chiral therminal chains and form tilted ferroelectric columnar liquid crystal (corresponding to the molecule of Figure 1.8c). 

Fig. 9.28 Six types of layer structures with different alignments of tilting (chirality) and polarity (see text)...

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