Ferrielectrics

Pb MnWO MnO dark shaded, WO light shaded, Pb spheres (Original data from 

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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. 

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. 

Fig. 30 Selected examples of chiral rod-like mesogens with one fluorinated chain (77° C) one enantiomer is shown as example (SmCA = antiferroelectric SmC phase SmC = ferroelectric SmC phase SmCpi = ferrielectric SmC phase SmCa = helical SmC phase SmI = chiral tilted low temperature phase) [197-199]...

Once the helical structure of the Sc phase is unwound, ferroelectricity is displayed (see Chapter 6 for the details). In recent years, many experimental studies have revealed that some liquid crystal compounds show new types of smectic phases with complex tilt and dipole order, such as the anti-ferroelectric smectic C phase, Sca phase, and the ferrielectric smectic C phase, Sc7 phase. For instance, in the Sca phase, the spontaneous polarization Ps is opposite for successive layers. It was found experimentally that the chiral So phase is in fact similar to the anti-ferroelectric Sca phase. 

Figure 54. Possible head-tail ordered herringbone structures for a complete commensurate CO monolayer on the basal plane of graphite only the projection on the surface plane is shown and the directions of the molecular dipole moments are indicated by arrows, (a) Ferrielectric stmcture with the net dipole perpendicular to the herringbone symmetry axis, (b) Ferrielectiic structure with the net dipole parallel to the herringbone symmetry axis, (c) An-tiferroelectric structure with no net dipole. The principal axes of the ellipses correspond to the 95% electronic charge density contour given in Table I. Note that each type of head-tail ordering can be combined with any of the six herringbone ground states from Fig. 6.

Initially the octyl to dodecyl compounds were prepared and these were found to exhibit relatively normal behavior, i.e. smectic A phases were found for the lower homologues with smectic and ferroelectric smectic C phases occurring for the higher members. However, when the tetradecyl homologue was examined in the polarizing transmitted light microscope, an iridescent helical mesophase was observed which upon cooling underwent a further phase transition to a ferroelectric smectic phase. In addition, this compound was also found to exhibit antiferroelectric and ferrielectric phases. 

These studies also showed two other interesting phenomena, firstly that certain members in the homologous series exhibit ferrielectric and antiferro-electric phases, and secondly for the materials that exhibit TGBA phases, a novel transition was found to occur in the isotropic liquid. The ferri- and anti-ferroelectric phases appear first for the n-undecyl homologue on ascending the series, and disappear once the chain length reaches sixteen carbon atoms in length. 

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. 

Figure 6.17 The polar dipole arrangement in the ferrielectric double perovskite Pb MnWO MnO di Orlandi et al. (2014)...

P.V. Dolganov, V.M. Zhilin, V.K. Dolganov and E.I. Kats, Ferrielectric smectic phase with a layer-by-layer change of the two-component order parameter, JETP Lett. 87(5), 253-257, (2008). doi 10.1134/S0021364008050068... 

Between crossed polars these defects appear as dark lines or brushes with curved or irregular shapes that correspond to extinction positions of the director and molecular long axes. Thus, the director can be either parallel or perpendicular to the polarizer and analyzer. The brushes tend to cover the specimen in rather a continuous way, indicating the liquid-like nature of the mesophase. The points where the brushes meet are called singularities in the texture (see Figure 3A). For nematic phases two forms of schlieren defect are found, one where two brushes meet at a point and one where four brushes meet. All tilted smectic phases (C, I, F, and ferrielectric C), except for the antiferroelectric phase, exhibit four brush singularities. Therefore, this provides a simple way of distinguishing between smectic and nematic phases. It should be noted that phases such as smectics A and B(hexatic) and crystal phases B(crystal), E, G, H, J, and K do not exhibit schlieren textures and so this narrows down the possibilities for phase identification. 

SmC C2 X T(2) Optically active chiral analogy of SmC phase showing macroscopic periodicity with twist axis perpendicular to smectic layers. Quasi-long-range positional order along the layer normal and two-dimensional liquid-like structure within the layer plane. Single layers of the same symmetry may form diffcaent phases in the bulk ferroelectric (SmC ), antiferroelectric (SmCA ) and ferrielectric (SmCy ). 

Fig. 13.15 Schematic structure of a ferroelectric (a), an antiferroelectric (b) and a ferrielectric (c). Note that period of each structure is different /, 21 cuid 3/, respectively...

In some crystals the location of dipole moments can even be more complicated. For example, in Fig. 13.15c, one layer with the dipoles looking down alternates with two layers where the dipoles are looking up. Therefore we have three-layer periodicity 3/ with two antiparallel layers and one extra polar layer. Such a structure may be considered as a mixture of the ferroelectric and antiferroelectric structures and is called ferrielectric. In case (c), the ferroelectric fraction is one part per period, qp = 1/3 and the spontaneous polarization is finite, Pg = (l/3)Po. For pure antiferroelectric phase qp = 0/2 and for pure ferroelectric one qp = 1/1 = 1. More generally, for different ferrielectric structures qp = nim, where m is the number of layers in the unit cell (period) and m is the ferroelectric layer fracture per unit cell, both being integers. Then, for both n and m oc, nim 1, the difference between n and m become smaller and smaller and the so-called Devil s staircase forms. 

Here, ferrielectric SmC /r/i and SmC /r/2 phases replace SmC y and SmC p phases. Further on we shall repeatedly refer to this phase sequence. 

Then, for paraelectric SmA phase both = 0 and = 0, for ferroelectric SmC phase 0 but = 0 as discussed in Section 13.1, for antiferroelectric SmC A phase = 0 but f 0, and for ferrielectric phases SmC F/ both 0 and AP 7 0. Now the Landau expansion of the free energy in the vicinity of transitions between the paraelectric, ferroelectric and antiferroelectric phases will operate with two order parameters and both coefficients at the terms in the free energy are considered to be dependent on temperatiue ... 

The two polarizations Pp and Pap may be taken as secondary order parameters coupled with the genuine order parameters. As a result, depending of the model, the theory predicts transitions from the smectic A phase into either the synclinic ferroelectric phase at temperature Tp or into an anticlinic antiferroelectric phase at Tap- One intermediate ferrielectric phase is also predicted that has a tilt plane in the i + 1 layer turned through some angle

tilt plane in the i layer. The models based on the two order parameters are of continuous nature (9 may take any values) and, although conceptually are very important, caimot explain a variety of intermediate phases and their basic properties. 

SmC f/i biaxial ferrielectric phase with 31 periodicity and finite P. It manifests ORP, which may change sign at a certain temperature. 

SmC f uniaxial antiferroelectric phase with4Z periodicity and zero P. However, on account of chirality the phase acquires small P and ferrielectric properties. 

As we know, chiral tilted mesophases, manifest ferroelectric (C, F, 1 and other less symmetric phases), antiferroelectric (SmCA, SmC ) and ferrielectric (SmC/7/ ) properties. These properties owe to a tilt of elongated chiral molecules, and polar ordering of the molecular short axes (and transverse dipole moments) perpendicular to the tilt plane. The head-to-tail symmetry n = n is conserved. The Ps vector lies in the plane of a smectic layer perpendicularly to the tilt plane. Such materials belong to improper ferro-, ferri and antiferroeiectrics. 

NHit)2S0it (LB Number 39A-1). This crystal is ferroelectric below — 49.5°C. The dielectric constant is practically independent of temperature above the Curie point (Fig. 4.5-68). The spontaneous polarization changes its sign at about — 190°C (Fig. 4.5-69), suggesting a ferrielectric mechanism for the spontaneous polarization. 

C. The phase exhibiting the triple hysteresis loop is called ferrielectric by several authors. 

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