Tilt chiral smectics

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)... 

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... 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

Fig. 10. The chiral smectic Chquid crystal stmcture. The director, n, rotates about the normal to the smectic layers, keeping the tilt angle. A, constant.

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

The second issue concerns the anisotropy of the membrane. The models presented in this section all assume that the membrane has the symmetry of a chiral smectic-C liquid crystal, so that the only anisotropy in the membrane plane comes from the direction of the molecular tilt. With this assumption, the membrane has a twofold rotational symmetry about an axis in the membrane plane, perpendicular to the tilt direction. It is possible that a membrane... 

It is also possible that a membrane might have an even lower symmetry than a chiral smectic-C liquid crystal in particular, it might lose the twofold rotational symmetry. This would occur if the molecular tilt defines one orientation in the membrane plane and the direction of one-dimensional chains defines another orientation. In that case, the free energy would take a form similar to Eq. (5) but with additional elastic constants favoring curvature. The argument for tubule formation presented above would still apply, but it would become more mathematically complex because of the extra elastic constants. As an approximation, we can suppose that there is one principal direction of elastic anisotropy, with some slight perturbations about the ideal twofold symmetry. In that approximation, we can use the results presented above, with 4) representing the orientation of the principal elastic anisotropy. 

A very different model of tubules with tilt variations was developed by Selinger et al.132,186 Instead of thermal fluctuations, these authors consider the possibility of systematic modulations in the molecular tilt direction. The concept of systematic modulations in tubules is motivated by modulated structures in chiral liquid crystals. Bulk chiral liquid crystals form cholesteric phases, with a helical twist in the molecular director, and thin films of chiral smectic-C liquid crystals form striped phases, with periodic arrays of defect lines.176 To determine whether tubules can form analogous structures, these authors generalize the free-energy of Eq. (5) to consider the expression... 

Note 4 The tilt direction varies in a random manner from layer to layer in conventional smectic C mesophases. However it can alternate from layer to layer, as in an antiferro-electric chiral smectic C mesophase (see Definition 5.9, Note 7) and in the smectic C mesophase formed by certain liquid crystal dimers with an odd-number of carbon atoms in the spacers. The recommended symbol for this type of mesophase is SmCa. 

Note 4 Locally, the structure of the chiral smectic C mesophase is essentially the same as that of the achiral smectic C mesophase except that there is a precession of the tilt direction about a single axis. It has the symmetry C2 in the Schoenflies notation. 

Note 1 Two forms of TGBC mesophase are possible in one form the director within the layer is tilted and rotates coherently through the layers in a block as in a chiral smectic C mesophase, while in the other form the director within a block is simply tilted with respect to the layer normal as in a smectic C mesophase. 

SmB SmC SmC SmCA SmCPA SmCPp SmCo, SmIA SmX UCST XRD Smectic B phase Smectic C phase (synclinic tilted smectic C phase) Chiral (synclinic tilted) smectic C phase Chiral anticlinic tilted (antiferroelectric switching) SmC phase Antiferroelectric switching polar smectic C phase Ferroelectric switching polar smectic C phase Chiral smectic C alpha phase Chiral antiferroelectric switching smectic I phase Smectic phase with unknown structure Upper critical solution temperature X-ray diffraction... 

Miyachi K, Matsushima J, Ishikawa K, Takezoe H, Fukuda A (1995) Spontaneous polarization parallel to the tilt plane in the antiferroelectric chiral smectic-CA phase of liquid-crystals as observed by polarized infrared-spectroscopy. Phys Rev E 52 R2153-R2156... 

In a chiral smectic (Sc ) phase, the tilt angle is the same within a layer, but the tilt direction processes and traces a helical path through a stack of layers (Figure 43). It has been demonstrated that when such a helix is completely unwound, as in a surface stabilized ferroelectric liquid crystal cell, then changing the tilt of the molecules fi om +0 to —0 by alternating the direction of an applied field results in a substantial electro-optic effect, which has the features of veiy fast switching (%1 - lOps), high contrast and bistability [87]. The smectic A phase of chiral molecules may also exhibit an electro-optic effect, this arises due to molecular tilt fluctuations which transition is approached, which are combined with a... 

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. 

The structure of the smectic A phase when it is composed of optically active material (i.e., smectic A ) remains the same as that for the achiral phase. The molecules are arranged in diffuse disordered layers, and there is no long-range periodic order. However, because of the molecular chirality, the environmental symmetry is reduced to [10]. As a consequence, when an electric field is applied to a chiral smectic A= phase there will be a coupling of the electroclinic susceptibility to the field and the long axes of the molecules will tilt with respect to the layer planes. The tilt angle, for relatively low applied fields, varies linearly with the field. This linear electrooptic phenomenon is called the electroclinic effect. 

On the other hand, it has been shown on LMWLCs that the well-known SmC, where the molecules are tilted with respect to the layer normal, is no longer the only possibility to obtain a fluid biaxial phase [63], As a consequence, a strict determination of the chiral smectic phase structure requires not only a careful analysis of the X-ray diagrams obtained on powder as well as on aligned samples, but also a study of the electrooptic response, which allows discrimination between the ferroelectric, the antiferro-electric, and the ferrielectric behavior. 

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 more complex chiral polar smectics, antiferroelectric liquid crystals, there are many consequences of the flexoelectric effect. It influences interlayer interactions and causes indirect interactions between more distant layers to appear and become important. The phenomenon is the reason for the appearance of commensurate structures that extend up to six layers. In addition, longitudinal polarization, i.e. the polarization that has a component parallel to the tilt, exists in more complex structures such as the SmCpi2, the SmC jj and the SmC phases. Unfortunately it seems that flexoelectric polarization cannot be detected separately from other phenomena by simple means. A way of measuring the flexoelectric contribution in tilted polar smectics still seems to be an open question. 

C.C. Huang, S. Dumrongrattana, G. Nounesis, J.J. Stofko and P.A. Arimilli, Heat-capacity, tilt-angle, and polarization measurements near the smectic-A-chiral-smectic-C transition of one liquid-crystal compound, Phys. Rev. A 35(3), 1460-1463, (1987). doi 10.1103/PhysRevA.35.1460... 

Fig. 4.34 Structure of a single monolayer of chiral smectic C. Rotation axis C2 is polar axis. Chiral molecules are tilted through angle 1 the director n forms with layer normal h...

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