Antiferroelectric interactions

Isozaki, T., Fujikawa, T., Takezoe, H., Fukuda, A., Hagiwara, T., Suzuki, Y., Kawamura, I. Competition between ferroelectric and antiferroelectric interactions stabilizing varieties of phases in binary mixtures of smectic liquid crystals. Jpn. J. Appl. Phys. 31, L1435-L1438 (1992)... 

The next question is why molecules switch collectively. The V-shaped switching occurs in the system where ferroelectric and antiferroelectric interactions compete and frustration between these structures takes place [99], [100]. Since such a frustrated system is very soft and the relaxation time becomes long, molecules change their steady-state orientation continuously under the surface constraint and varying field, resulting in the collective motion. 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

In the following sections, we shah demonstrate that the observed behavior of electro-optic activity with chromophore number density can be quantitatively explained in terms of intermolecular electrostatic interactions treated within a self-consistent framework. We shall consider such interactions at various levels to provide detailed insight into the role of both electronic and nuclear (molecular shape) interactions. Treatments at several levels of mathematical sophistication will be discussed and both analytical and numerical results will be presented. The theoretical approaches presented here also provide a bridge to the fast-developing area of ferro- and antiferroelectric liquid crystals [219-222]. Let us start with the simplest description of our system possible, namely, that of the Ising model [223,224]. This model is a simple two-state representation of the to-... 

Judging from purely energetic arguments the dipole moment of CO is expected to induce a head-tail ordered stmcture at very low temperatures in thermal equilibrium. A reasonable candidate stmcture for such a hypothetical fully ordered stmcture within the a-phase would be antiferroelectric with space group P2i3(7 ) (see, e.g.. Refs. 117 and 159). Based on a mean-field treatment of the dipole-dipole interactions the transition temperature to the fully ordered solid was estimated [230] to be smaller than 5 K. However, the nonvanishing residual entropy of 4.6 J/K mol reported in Ref. 76 has... 

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... 

In the previous section flexoelectric interactions were not considered in the free energy. We have also seen that only three of the structures found in antiferroelectric liquid crystals can be explained with the form of the free energy presented in the previous section. Let us first consider the discrete form of the flexoelectric effect and its influences on the theoretical description of the structures. We shall see that the flexoelectric effect is a source of indirect interactions between more distant layers and consequently the reason for all structures that cannot be expressed by the single phase difference. 

If there were only interactions described by negative ai, their structure would be synclinic ferroelectric. The basic period would consist of a single layer. For positive ai the structure would be antiferroelectric anticlinic (Fig. 5.6, first row). 

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. 

With increasing temperature the order of dipoles in each sublattice decreases and, at a certain temperature, a phase transition into the paraelectric phase occurs. It may be either second or first order transition. In the paraelectric phase local polarization Pq vanishes. The nature of the spontaneous polarization is similar in solid ferro- and antiferroelectrics. In both cases, the dipole-dipole interactions are dominant. For example, if dipoles are situated in the points of the body-centred cubic lattice, they preferably orient parallel to each other and such a structure is ferroelectric. However, the same dipoles placed into the points of a simple cubic... 

SmC A optically uniaxial antiferroelectric phase with period of 21 and zero spontaneous polarization P. It manifests Bragg diffraction and optical rotatoiy power (ORP). MV interactions prevail. The helical structure is shown in Fig. 13.22 it is similar to that of SmC, but the sign of helicity may be opposite. 

SmC a It is the most symmetric, antiferroelectric-type phase (P = 0) that borders SmA phase. It is helical but the helicity originates not from the molecular chirality but is due to specific NNN interactions. The pitch is short and incommensurate to the layer periodicity. In Fig. 13.21 the top view on the first five layers is shown and one may conclude that the helical pitch may be as short as 51, but it vary with temperature. Due to short helical pitch the phase does not show ORP. 

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