Tilt plane, antiferroelectrics

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. 

The layer stacking is synclinic in the tilt plane and antiferroelectric in the polar plane. The phase composed of an infinite number of SmCP layers stacked in this way is termed SmCsP, where the subscripts S and A each refer a structural feature of the layer interfaces between adjacent pairs of layers. If two adjacent layers are tilted in the same direction, the interface is synclinic (subscript S) in the tilt plane. If two adjacent layers have antiparallel orientation of their polar axes, then the layer interface is said to be antiferroelectric (A) in the polar plane. 

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. 

A simple consideration of the synclinic banana phases in the context of the prior discovery of the Soto Bustamante-Blinov achiral antiferroelectric bilayer is illuminating. In Figure 8.28, the achiral antiferroelectric SmAPA bilayer structure is illustrated on the left. The layers are horizontal and normal to the plane of the page, and the tilt plane is vertical and normal to the plane... 

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 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. 

In the Ising model, all the molecules are in the tilt plane but, despite such a severe simplification, the electrooptic measurements and resonant X-ray scattering [29] have confirmed the sequence of ferro- ferri- and antiferroelectric phases. However, the same X-ray experiments clearly showed that the tilt planes in different layers are not at all parallel. Moreover, in frameworks of the Ising models the structure of the SmC o, phase could not be understood. Therefore, another approach has been developed. 

Fig. 13.22 Chiral antiferroelectric SmC A phase. Alternating tilt plane (a) and layer polarization (b) and the long-pitch helical structure (c). Note that the unit cell consisting of two layers rotates as a whole forming two geared helices of the same handedness. This type of rotation is controlled by molecular chirality inherent in all phases shown in Fig. 13.21...

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. 

As shown by the X-ray diffraction, polymer-monomer mixture consists of SmC bilayers. A bilayer is the principal unit cell having either non-polar C2h or polar C2v (b) S5mimetry. The former is incompatible with both ferroelectricity or antiferroelectricity, because such a structure has an inversion centre. On the contrary, in sketch (b) each bilayer is polar with Pq vector located in the tilt plane along the y-axis. In a stack of such layers the direction of Pq alternates and the stmcture (b) is antiferroelectiic in its ground state. Only strong electric field Ey causes the transition to the ferroelectric structure shown in sketch (c) as observed in experiment. Note that both the Pq and P = X Pq vectors are always lying in the tilt plane. 

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)...

In a stack of subsequent layers the tilt may be constant (synclinic structure) or alternating (anticlinic structure). Both synclinic and anticlinic multilayer stacks can further be subdivided into ferroelectric and antiferroelectric structures. The molecular projections (Mito the tilt plane 7y are shown in Fig. 13.29b. In ferroelectric (symbol F) phases spmitaneous polarization has the same direction in each layer (synclinic chiral SmCsPp and anticlinic achiral SmCAPp phases). In the antiferroelectric (symbol A) phases the direction of polarization alternates (achiral synclinic SmCsPA and chiral anticlinic SmCAPA phases). In fact we have a conglomerate of chiral and achiral phases both in either synclinic or anticlinic form. 

The so-called Px model is related to the polarizations existing at layer boundaries. The SmCj( phase has D2 symmetry with two C2-axes i.e., one at the middle of the layer and perpendicular to the molecular tilt plane Py) and one at the layer boundary parallel to the tilt plane (Px), as shown in Figure 9.15. Then, Px Px interaction between two adjacent layer boundaries stabilizes the antiferroelectric structure, if the fluctuation of Px is involved. Even in racemic compounds, Px always exists, though Py is zero. Thus, this model... 

It was the Harvard physicist Meyer who in 1974 first recognized that the symmetry properties of a chiral tilted smectic would allow a spontaneous polarization directed perpendicular to the tilt plane [61]. In collaboration with French chemists, he synthesized and studied the first such materials [62]. These were the first polar liquid crystals recognized and as such something strikingly new. As mentioned before, substances showing a smectic C phase had been synthesized accidentally several times before by other groups, but their very special polar character had never been surmised. Meyer called these liquid crystals ferroelectric. In his review from 1977 [43] he also discussed the possible name antiferroelectric, but came to the conclusion that ferroelectric was more appropriate. 

Quite recently, Prof. Fukuda has determined that the chiral alkyl chain makes a bent angle >54.7° (the magic angle) with the core axis and that the carbonyl group near the chiral center lies on the tilt plane in antiferroelectric SmCA on the basis of the polarized infrared spectroscopy. Jin, B. Ling, Z. Takanishi, Y. Ishikawa, K. Takezoe,... 

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. 

Fig. 9 Few possible combinations of tilt and polarization for B1 and Blrev phases. In B1 phase molecules are (a) not tilted or (b) tilted in the blocks. The tilt is denoted by one part of the molecule being thicker. This is a part that is tilted out of the paper plane. B lrev structures can be made of the deformed synclinic, antiferroelectric layers with the tilt in the defect region connecting the blocks (c) lower or (d) higher than in the block itself or from (e) the anticlinic antiferroelectric deformed layers or from (f) the synclinic layers where polarization alternates in the neighboring blocks of the same layer...

The situations where the molecular planes are tilted with respect to the layer normal (i.e., when m is not perpendicular to k) are shown in the upper row of Fig. 3.3. In the plane determined by the polarization P and the layer normal k (the polar plane) this tilt is illustrated by a nail at the end of the directors that is closer to the observer. Depending on whether the tilt directions are parallel or antiparallel we refer to synclinic (s) and anticlinic (a) structures. Combining these different situations with the Ferroelectric (F) and Antiferroelectric (A) layer polarizations we can... 

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