Racemic structures, ferroelectrics

Sketch of the racemic and chiral structures of the SmCP phase of achiral banana-shape molecules in antiferroelectric (at E = 0) and ferroelectric (at E > Etj, 5 V/ om) states. Left column Racemic structure, in which the chirality alternates in the adjacent layers. The APE domains are synclinic with coexisting opposite tilt directions. Right column chiral structure, in which the adjacent layers have the same handedness, but domains of different chirality coexist. The shading illustrates the bent or tilted shape of the molecules (brighter parts are closer to the reader). R (L) is the chirality descriptor corresponding to right (left(-handed layer conformations. 

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. 

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)...

Nakata, M. Link, D. R. Araoka, F. Thisayukta, J. Takanishi, Y Ishikawa, K. Watan-abe, J. Takezoe, H. A racemic layer structure in a chiral bent-core ferroelectric liquid crystal. Liq. Cryst. 2001, 28, 1301-1308. 

The antiferroelectric SmC structure (see Fig. 17) can also occur in racemates [94] or in nonchiral compounds such as symmetric dimers [136, 137], nonsymmetric dimers [133], and main chain liquid crystal polymers [138], where its formation is driven by steric and/or conformational effects. Antiferroelectric ordering has been shown to increase the smectic order parameters in ferroelectric liquid crystals [94, 95]. 

The tilting of molecules in the B2 phase is clearly confirmed from the observation that the spherulites emerging from the isotropic phase show an electric field dependence of the position of the optical extinction lines (Fig. 9.26). Because of the tilting of banana molecules to the layer, chirality is spontaneously generated in addition to the polarity this fact sounds shocking but is so simple to be understood [132, 133]. If the molecule is rotated around their polar axis (the orientation of the bent in the molecules), which is akin to tilting the molecules in the layer, the rotation operation cannot be achieved by a simple translation (see Fig. 9.27). That is, these two states are in a mirror relation with left-handed and right-handed chirality. This is called the layer chirality. When the chirality couples with the polarity of the molecules, one would consider various smectic liquid crystal structures. There are two homochiral phases in which either (—) or (-I-) chiral molecules stack in the layers and a racemic phase in which layers are alternately stacked with layers of (—) and (-I-) chiral molecules. Each of those phases can be either ferroelectric or antiferroelectric, so that in total six different phases are present... 

Chirality can also be introduced when one or more chiral carbons are incorporated in the molecules, for example in the hydrocarbon terminal chains [67, 68], within the bent-core [69], or by addition of chiral dopants [6, 70], It was noted during the early research that the handedness of the homochiral structures is very sensitive to chiral dopants [6], or even on chiral surfaces [71]. On the other hand, it was observed that banana-smectics made of enantiomeric chiral molecules form synclinic - antiferroelectric [44] and anticlinic ferroelectric [67] domains. This combination of tilt and polar order implies that the phase is racemic, with a rigid alternation of right- and left-handed chiral layers. This shows that the molecular chirality has no or minor effect on deciding about anticlinic or synclinic packing (which is mainly determined by entropic reasons), but it can bias the otherwise degenerate tilt directions. 

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