Smectic flexoelectrics

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. 

As noted earlier, the incorporation of chiral groups in the liquid crystal moieties can have the effect of inducing non-linear properties, which include thermochromism, ferroelectricity, antiferroelectricity, electrostriction, and flexoelectricity. In a now classical study, Hult [82] demonstrated that it was possible for supermolecular material 34 to exhibit two-state ferroelectric switching. The remarkable material he investigated, shown in Fig. 30, was found to exhibit two hitherto unclassified mesophases between the smectic... 

Finally note that the flexoelectric effect is also important in the smectic phase although the corresponding molecular theory is at a rudimentary stage. Recently a molecular model for the conventional and the so-called discrete flexoelectric effect in tilted smectic phases has been proposed... 

A.V. Emelyanenko and M.A. Osipov, Theoretical model for the discrete flexoelectric effect and a description for the sequence of intermediate smectic phases with increasing periodicity, Phys. Rev. E 68(5), 051703/1-16, (2003). doi 10.1103/PhysRevE.68.051703... 

Summarizing, experimental observations suggest that the giant (direct or converse) flexoelectricity of bent-core nematics is related to the polar smectic clusters occurring in them. In order to explore the exact mechanism for how clusters contribute to the flexoelectric response, further experimental and theoretical studies are needed. 

Non-standard EC has also been observed in bent-core nematics, where < 0, Ca < 0 is also realized and where flexoelectricity is strong. There is still no detailed theoretical description, which would have to include the strong frequency dependence of as well as the unusual viscosity and elastic properties these might indicate smectic cluster formations not only in the nematic but even in the isotropic phase. 

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 chapter is organized as follows The second section discusses the prototype polar smectics the ferroelectric liquid crystals. We discuss the structure of the ferroelectric phase, the theoretical explanation for it and we introduce the flexoelectric effect in chiral polar smectics. Next we introduce a new set of chiral polar smectics, the antiferroelectric liquid crystals, and we describe the structures of different phases found in these systems. We present the discrete theoretical modelling approach, which experimentally consistently describes the phases and their properties. Then we introduce the discrete form of the flexoelectric effect in these systems and show that without flexoelectricity no interactions of longer range would be significant and therefore no structures with longer periods than two layers would be stable. We discuss also a few phenomena that are related to the complexity of the structures, such as the existence of a longitudinal, i.e. parallel to the... 

The polarization in a specific tilted smectic layer formed of chiral liquid crystals always has two components, as already mentioned the piezoelectric and the flexoelectric components. The piezoelectric component is to a first approximation ... 

This chapter considers polarization in polar smectics in general and the flexoelectric polarization in polar smectics in particular. The existence of flexoelectric polarization has been known for a long time. The effects related to the phenomenon are more pronounced in systems formed of polar molecules including chiral polar smectics. Therefore it is not surprising that several important consequences of the flexoelectric phenomenon are present... 

In the most simple chiral polar tilted smectics, ferroelectric liquid crystals, the flexoelectric phenomenon influences the structure of the SmC phase only quantitatively. It affects the elastic and chiral couplings and consequently slightly changes the transition temperature to the tilted phase and the pitch of the helicoidal modulation. 

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. 

---