Tilt ferroelectrics

Discotic and bowl-shaped molecules that form columnar phases, (a) Hexa-alkanoate [R=CH3-(CH2) -2C00-] of triphenylene (b) hexa-noyloxy-tribenzocyclononene, which forms a polar pyramidlc phase (c) l,2,5,6,8,9,12,13-octakis-((S)-2-heptyloxy) dlbenzo[e,l]pyrene, which has chiral therminal chains and forms tilted ferroelectric columnar liquid crystal. ... 

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. 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

Zareba et al. [165] described the crystal structure of the chiral 4-(l-methyl-heptyloxycarbonyl)-phenyl 4-heptyloxytolane-4 -carboxylate (C7-tolane) which shows monotropic antiferroelectric and ferroelectric phases. The single-crystal X-ray analysis of this compound shows that the crystal has a smectic-like layer structure composed of largely bent molecules where the chain of the chiral group is almost perpendicular (86°) to the core moiety. Within the layers, the molecules are tilted. The central tolane group of the molecule is roughly planar. 

Fig. 17a-c. Sketches of the molecular arrangements for the smectic structure with alternating layer-to-layer tilt a conventional and chevron smectic C layering in low molecular mass mesogens b ferroelectric hilayer chevron structures for achiral side-chain polymers c antiferroelectric hilayer chevron structures for achiral side-chain polymers. Arrows indicate the macroscopic polarization in the direction of the molecular tilt... 

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

Since P must remain normal to z and n, the polarization vector forms a helix, where P is everywhere normal to the helix axis. While locally a macroscopic dipole is present, globally this polarization averages to zero due to the presence of the SmC helix. Such a structure is sometimes termed a helical antiferroelectric. But, even with a helix of infinite pitch (i.e., no helix), which can happen in the SmC phase, bulk samples of SmC material still are not ferroelectric. A ferroelectric material must possess at least two degenerate states, or orientations of the polarization, which exist in distinct free-energy wells, and which can be interconverted by application of an electric field. In the case of a bulk SmC material with infinite pitch, all orientations of the director on the tilt cone are degenerate. In this case the polarization would simply line up parallel to an applied field oriented along any axis in the smectic layer plane, with no wells or barriers (and no hysteresis) associated with the reorientation of the polarization. While interesting, such behavior is not that of a true ferroelectric. 

It is now instructive to ask why the achiral calamitic SmC a (or SmC) is not antiferroelectric. Cladis and Brand propose a possible ferroelectric state of such a phase in which the tails on both sides of the core tilt in the same direction, with the cores along the layer normal. Empirically this type of conformational ferroelectric minimum on the free-energy hypersurface does not exist in known calamitic LCs. Another type of ferroelectric structure deriving from the SmCA is indicated in Figure 8.13. Suppose the calamitic molecules in the phase were able to bend in the middle to a collective free-energy minimum structure with C2v symmetry. In this ferroelectric state the polar axis is in the plane of the page. 

By our definition, the tilt plane is normal to the polarization in the ferroelectric state in the illustration in Figure 8.13 this is a vertical plane normal to the plane of the page. Since there is no tilt of the director projected onto this plane, the phase should be considered a type of SmA. We name this structure SmAPp (an untilted polar smectic the subscript F referring to a ferroelectric structure, in this case a ferroelectric state of an antiferroelectric phase). The antiferroelectric phase is therefore also an SmA denoted SmAPA (the subscript A for antiferroelectric). While this idea is certainly intriguing, no such antiferroelectric has yet been discovered. 

Apparently this switching mode is disfavored since, in fact, the chirality of the layers does not change upon switching to the ferroelectric state rather the layer interface clinicity changes. This occurs when the molecules in alternate layers simply precess about the tilt cone in a manner exactly analogous to antiferroelectric to ferroelectric switching in the chiral SmC phase. As shown in Figure 8.25, the ferroelectric state obtained from the ShiCsPa antiferroelectric phase is a ShiCaPf structure, an achiral macroscopic racemate with anticlinic layer interfaces. 

Both tilt domains in the green stripe texture switch to the same ferroelectric state in this process, thus causing the stripes to disappear. The anticlinic structure is SmA-like in the sense that the average optic axis is along the layer... 

Application of a field to the ShiCaPa phase causes switching by precession of the director around the tilt cone in alternate layers, to give a ferroelectric ShiCsPf state with uniform tilt. In this case, there can be no domains of opposite tilt since such domains would necessarily have their polarization opposing the applied field. This leads to a uniform SmC-like texture with a green birefringence color. The extinction brushes in the cylindrical focal conic rotate counterclockwise when the net tilt rotates clockwise, as indicated in Figure 8.25. As anticipated, the chiral rotation of the brushes is a direct manifestation of the chirality of the phase. Elsewhere in the sample there must be ShiCaPa domains of opposite handedness, which would possess the opposite sense of tilt for the same sign of the applied field. 

As can be easily seen by inspection of these illustrations of the SuiCsPa and ShiCsPf phases, while the director tilt in the tilt plane is synclinic for both, the layer interfaces have a different character when observed in projection in the bow plane. The antiferroelectric diastereomer has synclinic character at the layer interfaces, while the ferroelectric diastereomer is anticlinic in the bow plane. This suggests a very simple reason for the tendency toward antiferroelectric bananas, this being basically the same as the tendency toward ferroelectric calamitic smectics preference for synclinic layer interfaces. 

From this discussion the clear similarity between the SmAPA and SmCsPA structures is easily seen. In addition, the suggestion of Brand et al.29 that a bilayer smectic with all anticlinic layer interfaces (the SmAPF) would produce an achiral ferroelectric smectic follows directly. The unanticipated tilt of the director in the tilt plane, leading to a chiral layer structure, seems to be a general response of the bent-core mesogens to the spontaneous nonpolar symmetry breaking occurring in these rigid dimer structures. 

Figure 8.29 Illustration showing how all-anticlinic bilayer smectic should be ferroelectric is given. In case of covalent dimers (bent-core mesogens), equilibrium tilt of director combined with anti clinic layer interfaces in bow plane provides SmCsPF ferroelectric banana structure.

Figure 8.35 Illustration of bistable ferroelectric EO switching observed for blue focal conic domains of MHOBOW. SmCsPF structure can be assigned for these domains. In this phase director structure in all layers is oriented identically. This structure and corresponding extinction bmsh orientation for cylindrical focal conic are illustrated at bottom of figure for two bistable ferroelectric states. Note that for material with 30° tilt angle, such as MHOBOW, two ferroelectric states look very similar in still photos. In fact, two states result from large rotation of extinction brushes through 60°, as can be easily seen when observing switching in motion.

Ferroelectric mesophase that appears through the breaking of symmetry in a tilted smectic mesophase by the introduction of molecular chirality and, hence, mesophase chirality. 

Note 1 When the numbers of layers with opposite tilt directions are not the same, the smectic mesophase has ferroelectric properties. 

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. 

Chiral molecules which form smectic liquid crystals are often capable of forming structures in which the electric dipoles associated with the molecules all point approximately in the same direction in a particular region but in which this direction rotates as one moves in a direction normal to the smectic planes. Such materials are rather misleadingly referred to as ferroelectric liquid crystals. The mechanism responsible for this effect is illustrated in Figure 7.3. The molecules tilt into a smectic-C phase due to their structure as illustrated. Dipoles associated with the molecules are supposed to point in a direction normal to the page. Thus, if the molecules all have the same handedness the dipoles all point in he same direction. This description is an oversimplification as the molecules rotate about their long axes but point preferentially in the manner indicated. This phenomenon has been successfully applied to... 

Figure 7.3. Schematic diagram to illustrate the mechanism of ferroelectric liquid crystals. It is supposed that the molecules have a structure which encourages a tilt as in (a). It is further supposed that (in this simple illustration) there exists an electric dipole at right angles to the molecular axis which points out of the paper in (a), , and into the paper in (6), . It is supposed that the configuration shown in (a) represents the lower energy state.

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