Spontaneous antiferroelectrics

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. 

Using this method, the M6R8/PM6R8 blend showed precisely the behavior expected for the achiral SmAPA structure. Specifically, the optical properties of the films were consistent with a biaxial smectic structure (i.e., two different refractive indices in the layer plane). The thickness of the films was quantized in units of one bilayer. Upon application of an electric field, it was seen that films with an even number of bilayers behaved in a nonpolar way, while films with an odd number of bilayers responded strongly to the field, showing that they must possess net spontaneous polarization. Note that the electric fields in this experiment are not strong enough to switch an antiferroelectric to a ferroelectric state. Reorientation of the polarization field (and director structure) of the polar film in the presence of a field can easily be seen, however. 

Figure 8.16 Illustration of symmetry of Soto Bustamante-Blinov achiral antiferroelectric smectic LC with finite number of layers. Such systems can be studied using DRLM technique with thin freely suspended smectic films, (a) With even number of bilayers, film has local C2 symmetry, and therefore no net electric polarization, (b) With odd number of bilayers, film has local Cnv symmetry and is therefore polar, with net spontaneous electric polarization in plane of layers.

It is interesting to point out here that with all of the theoretical speculation in the literature about polar order (both ferroelectric and antiferroelectric) in bilayer chevron smectics, and about reflection symmetry breaking by formation of a helical structure in a smectic with anticlinic layer interfaces, the first actual LC structure proven to exhibit spontaneous reflection symmetry breaking, the SmCP structure, was never, to our knowledge, suggested prior to its discovery. 

Note 7 When the tilt direction alternates from layer to layer, the smectic mesophase is antiferroelectric such mesophases do not possess spontaneous polarization. They can be turned into ferroelectric structures through the application of an electric field. 

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... 

The main features of the antiferroelectric switching in FLCPs are a third state, which shows an apparent tilt angle of zero, a less marked threshold between the three states when compared to the low molecular weight antiferroelectric liquid crystals, a hardly observed hysteresis, and an anomalous behavior of the spontaneous polarization with temperature (Fig. 24), which is not encoun-... 

Figure 6.14 Antiferroelectric behaviour schematic (a) parallel array of spontaneous polarisation dipoles characteristic of a ferroelectric crystal (b) antiparallel array of dipoles in an antiferroelectric crystal...

B], B2,..., B Unknown Series of achiral phases formed by banana- or bent-shape molecules. The phase symmetry reduces with suffix n. Manifest spontaneous brake of mirror symmetry and interesting ferroelectric and antiferroelectric properties... 

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. 

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... 

Fig. 13.16 Typical hysteresis-type dependence of the total (spontaneous and induced) polarization F as a function of the external field for a ferroelectric (dashed curve) and antiferroelectric (solid curve). Arrows show the direction of the field cycling...

A difference between ferro- and antiferroelectrics may also be discussed in terms of the soft elastic mode [3], In the infinite ferroelectric crystal, there is no spatial modulation of the spontaneous polarization (only dipole density is periodic). Therefore, at the transition from a paraelecttic to the ferroelectric phase, both the wavevector q for osciUatimis of imis responsible for polarization and the correspondent oscUlatimi frequency co = Kef tend to zero. We may say that the soft elastic mode in ferroelecttics condenses at q 0. In antiferroelectrics, the sign of the local polarization Pq alternates in space with wavevector qo = 2nl2l = n/l and the corresponding imi oscillation frequency is finite, m = Kqf = Kn ll. It means that in antiferroelectrics the soft mode condenses at a finite wavevector n/l and rather high frequency. As a result, in the temperature dependence of the dielectric permittivity at low frequencies, the Curie law at the phase transitimi between a paraelecttic and antiferroelectric phases is not well pronounced. 

Fig. 13.17 Field induced switching between the antiferroelectric structure left sketch) and two ferroelectric structures with opposite tilt and spontaneous polarization Pg. The directions of Pg coincides with the field Ex directions [22]...

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. 

Achiral smectic materials with anticUnic molecular packing are very rare [40] and their antiferroelectric properties have unequivocally been demonstrated only in 1996 [41]. The antiferroelectilc properties have been observed in mixtures of two achiral components, although no one of the two manifested this behaviour. In different mixtures of a rod like mesogenic compound (monomer) with the polymer comprised by chemically same rod-like mesogenic molecules a characteristic antiferroelectric hysteresis of the pyroelectric coefficient proportional to the spontaneous polarization value has been observed for an example see Fig. 13.27a. Upon application of a low voltage the response is linear, at a higher field a field-induced AF-F transition occurs. 

Fig. 13.29 Bent-shape molecules form polar smectic layers in the polar plane xz with polarization (a). Upon cooling, the molecules can spontaneously acquire a tilt forward or back within the tilt plane yz. The stack of the layers may be either synclinic SmCs or anticlinic SmCA (b). Additionally, depending on the direction of polarization P both the synclinic and anticlinic structure may have uniform (ferroelectric Pp) or alternating (antiferroelectric P ) distribution of polarization within the stack. In the field absence there are four stractures marked by symbols below. Note that the leftmost structure is chiral SmC and rightmost structure is also chiral because, for any pair of neighbours, the directions of the tilt and polarization change together leaving the same handedness of the vector triple. In the electric field, the phase transitions fixjm chiral SmCAPA <> chiral SmCsPp and from racemic SmCsPA to racemic SmCAPp structures are possible (shown by ark arrows)...

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