Polarization chirality

Berkovitch-Yellin, Z., Addadi, L., Idelson, M., Leiserowitz, L., and Lahav, M. Absolute configuration of chiral polar crystals. Nature London) 296, 27-34 (1982). 

The use of silica gel impregnated with chiral polar selector, such as D-galacturonic acid, (-i-)-tartaric acid, ( )-brucine, L-aspartic acid, or a complex of copper(II) with L-proIine, should also be mentioned. 

Shibata T., Yamamoto J., Matsumoto N., Jonekubo S., Osanai S. and Soai K. (1998) Amplification of a slight enantiomeric imbalance in molecules based on as5mmetric autocatalysis. The first correlations between high enantiomeric enrichment in a chiral molecule and chirality polarizing light,... 

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 last term gives the electrostatic contribution to the free energy. The coefficient e is afways positive and the pofarization is never the reason for the phase transition in chiral polar liquid crystals. The polarization P is an improper order parameter and appears only when the proper order parameter - the tilt - is non-zero. 

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. 

More than 700 pollutants have been reported in water, and these include substances that are both inorganic and organic in origin. Microbial populations are also contributing to the pollution of water resources to some extent. Water is a uiuversal solvent for most polar organic compounds and so the presence of chiral pollutants in water is a common phenomenon. Therefore, almost every type of chiral polar pollutant is found in the various water bodies, as reported in the literature [5-7,18]. The main water bodies contaminated by chiral pollutants are the oceans, rivers, lakes and ground water. In view of these points, the contamination of various kinds of water bodies is discussed in what follows. 

The occurrence of a net dipole moment in tilted columnar (and smectic) phases can be most conveniently visualized and explained with a schematic molecule that consists of a rigid disk- (or rod-) shaped core, elongated flexible chains attached in two (or one) long direction(s), and chiral polar groups at the chain-core junctions (Figure 11.2). If the core and chains are of the same thickness, the optical axis of the molecules will tend to align along the column axis (or the layer normal). But if the core and chain are of different thicknesses, the formation of a kink between core and chain is favored. If the (e.g., acyloxy) chains are thicker than the (e.g., condensed aromatic) core, space is more efficiently used and the void between cores is reduced, if the cores (but not the chains) are tilted toward the column axis (or the layer normal). Thus the optical axis tilts, and a kink forms between the core and... 

---