Tilted chiral phases

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-... 

Chirality (or a lack of mirror symmetry) plays an important role in the LC field. Molecular chirality, due to one or more chiral carbon site(s), can lead to a reduction in the phase symmetry, and yield a large variety of novel mesophases that possess unique structures and optical properties. One important consequence of chirality is polar order when molecules contain lateral electric dipoles. Electric polarization is obtained in tilted smectic phases. The reduced symmetry in the phase yields an in-layer polarization and the tilt sense of each layer can change synclinically (chiral SmC ) or anticlinically (SmC)) to form a helical superstructure perpendicular to the layer planes. Hence helical distributions of the molecules in the superstructure can result in a ferro- (SmC ), antiferro- (SmC)), and ferri-electric phases. Other chiral subphases (e.g., Q) can also exist. In the SmC) phase, the directions of the tilt alternate from one layer to the next, and the in-plane spontaneous polarization reverses by 180° between two neighbouring layers. The structures of the C a and C phases are less certain. The ferrielectric C shows two interdigitated helices as in the SmC) phase, but here the molecules are rotated by an angle different from 180° w.r.t. the helix axis between two neighbouring layers. 

The enhanced chirality by doping SmC with BSMs can be explained qualitatively in the same way as in the N phase. However, the situation is more complicated in SmC because of spontaneous polarization and flexoelectric effect, and (3) must be replaced by an equation including such effects. Actually, the contribution of flexoelectric effect has been discussed by Gorecka et al. [4]. The other important effect is caused by the fact that the BSMs are in the tilted smectic phase. As mentioned above, the tilt of BSMs induces chirality as observed in the B2 phase. 

Fig. 8 Definition of layer chirality in the bent-core tilted smectic phase...

As mentioned in the introduction, chiral compounds can exhibit chiral mesophases and these are important due to the important physical properties that they may exhibit, including thermochroism, ferroelectric and electroclinic effects [15], In 1975, Meyer predicted the existence of a spontaneous polarization (Pg) in chiral, tilted smectic phases [86], and the existence of such polar order within a liquid crystal phase has important implications both scientifically and industrially [19]. The asymmetry associated with the chirality may also produce a beneficial lowering of transition temperatures. 

Almost all the smectic phases, in which the molecules are arranged in layers and are tilted with respect to the layers, have counterpart chiral phases. The most important one of this class is the chiral smectic C phase — Sc phase. In these chiral liquid crystal phases, the molecules are tilted at a constant angle with respect to the layer normal but the tilt azimuthal rotates uniformly along the chiral axis and forms a helical structure. 

As the difference in the transition temperatures between the chiral and racemic forms of the same compound is found to be only of the order of 1 °C, it is clear that the transition is driven by intermolecular forces responsible for the tilted smectic phase and not by the dipole-dipole... 

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. 

Let us first consider a fictitious material, which has a tilted SmC phase, whose molecules are chiral but not polar. Let us also keep in mind that such a material does not exist in reality. There exist materials, which at a certain, well-defined temperature, exhibit a sign reversal of their polarization. At exactly the temperature of the polarization reversal the polarization does not exist due to several reasons the average of the coexistent chiral conformations is not polar or the hindrance of the rotation is such that the polarization coincides with one of the two axes x and z) or both. But this is not the case for a wider temperature range. The molecule itself always has some polarization because of its structural asymmetry. 

If the mesogens are chiral, a twisted nematic, suprarmolecular, cholesteric (twisted) phase can form [51, 52]. The achiral nonlinear mesogens can also form chiral supramolecular arrangements in tilted smectic phases. 

Year 1975 has been marked off by an outstanding publication of R. Meyer and his French co-workers [4]. As has been discussed in Section 4.9, chirality of molecules removes the mirror symmetry of any phase. The idea of Meyer was to apply this principle to the SmC phase by making it chiral. He believed that if chiral molecules formed a tilted smectic phase, its point group symmetry would reduce from to C2... 

FELCD Ferroelectric liquid crystal device a device exploiting the ferroelectric property of chiral tilted smectic phases (especially smectic C ). 

One of the disadvantages of the LCD display is that the response time is slow (approximately 50 (jls) and the liquid-crystal phase is too symmetric to allow vector order. To overcome this problem, tilted smectic phases with ferroelectric properties (polarisation can be reversed by an electric field) can be used, providing that the liquid crystal is chiral. One such ferroelectric liquid crystal is... 

In conclusion, this work shows that a lamellar, lilted, fluid phase exists in lyotropic liquid crystals and that it exhibits characteristic chirality effects, namely helicity and spontaneous electrical polarization, known Irom the thermotropic ferroelectric SmC phase. These results contribute significantly to a better understanding of lyotropic liquid crystals and bridge a substantial gap between the two fields of liquid crystal research. In accordance with the established nomenclature of lyotropic and thermotropic liquid crystals, the novel phase is suggested to be denoted as the lamellar L, phase, where the index a denotes a tilted fluid phase and the superscript indicates that molecules are chiral. 

There is one more, rather polymer-specific possibility for combining a tilted smectic matrix and a chiral dopant, namely copolymerization. Thus, a nonchiral methacrylate monomer inducing a tilted smectic phase was copolymerized with a chiral comonomer that forms a smectic A homopolymer only [77], The resulting copolymers ... 

Ferroelectricity can also be observed in other chiral tilted smectic phases of FLCPs such as smectic F, smectic I, and smectic H (Fig. 21). Those smectic phases are more ordered and therefore more viscous, so the switching processes are hindered. Nevertheless, these phases of FLCPs show such ferroelectric behavior as pyro- and piezoelectric effects [28,30,77,106]. 

Dielectric relaxation spectroscopy can monitor molecular and collective modes for motion of liquid crystalline molecules. In ferrolectric liquid crystals based on chiral tilted smectic phases the complex dielectric permittivity e has, in addition to molecular orientational modes, two contributions from the director fluctuations. 

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... 

Figure 7 The four possible arrangements of bent-core mesogens in a tilted, lamellar phase after Reddy and Tschierscke. The nomenclature [2] is subscripted s is synclinic, while that subscripted a is anticlinic—referring to the relative tilt from layer to layer. P implies that the phase is polar and subscript A is antiferroelectric and F is ferroelectric. As indicated, SmCaPA and SmCgPp are chiral, while clearly SmCsPp and SmCaPp are ferroelectric.

The sense of the pitch of the chiral smectic C mesophase is controlled by the same molecular factors as that of the cholesteric phase. If a chiral nematic forms a tilted smectic phase (C, H, I ) on cooling, either directly or through an intermediate smectic A phase, the smectic phase has the same sense of rotation as the chiral nematic phase. 

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