Ferroelectric Smectic C Phases

A vast array of covalent molecules have been synthesised over the years in the search for LCs that show the useful cholesteric and ferroelectric smectic C phases, often on a trial and error basis ignoring the interactions between the molecules. The idea that one could think of the interactions between the molecules as a kind of molecular recognition came from the careful analysis of the conformations of molecules in the layers [77,78]. The arguments are based on the symmetry limitations of the angle formed by the alkyl chain and the phenyl benzoate moiety in the molecules that were the subject of this study. A molecular recognition site within the phase was used as the basis for these speculations , which have actually proved rather successful. The actual interactions between molecules are usually weak, but the formation of layers of aromatic and aliphatic units in these mesophases gives rise to their unique properties. 

Further studies by Nishiyama et al. [34-45] showed that when taken in isolation, only one of the aromatic units within a supermolecular system has a propensity to exhibit liquid crystal phases, then the supermolecular material itself could be mesomorphic, see Fig. 5. For example, for the top molecular structure, 5 [45], in Fig. 5, only the biphenyl unit at the center of the structure supports mesophase formation, whereas the benzoate units are too isolated from the biphenyl moiety in order to affect mesomorphic behavior. The second material, 6 [45] has terminal phenyl units, which are only connected by aliphatic chains to the benzoate units. Thus in this case, the material has four aromatic units out of six which are not in positions that can enhance mesophase formation. However, the second material has similar transition temperatures and phase sequences to the first, i.e., both materials exhibit an unidentified smectic phase and a synclinic ferroelectric smectic C phase. If the third material, 7 [38], is examined, it can be seen that the mesogenic unit at the center of the supermolecule is an azobenzene unit which is more strongly supportive of mesophase behavior than the simple biphenyl moiety. Thus the clearing point is higher for this material in comparison to the other two. The attachment of the terminal phenyl unit is by a methylene spacer of odd parity, and as a consequence the smectic C phase has an anticlinic structure rather than synclinic. 

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. 

Similarly to the molecular engineering of calamitic molecules to produce ferroelectric smectic C phases [129], disk-like molecules with chiral peripheral chains tilted with respect to the columnar axis were predicted to lead to ferroelectric columnar mesophases [130]. Indeed, as it is the case with all flat disk-shaped mesogenic molecules, the tilt is mainly associated with the flat rigid aromatic cores of the molecules, the side-chains being in a disordered state around the columnar core. Thus, the nearest part of the chains from the cores makes an angle with the plane of the tilted aromatic part of the molecules. If the chiral centre and the dipole moment are located close to the core, then each column possesses a non-zero time averaged dipole moment, and therefore a spontaneous polarization. For reasons of symmetry, this polarization must be, on average, perpendicular to both the columnar axis and to the tilt direction in other words, the polarization is parallel to the axis about which the disk-shaped molecules rotate when they tilt as shown in Fig. 29. 

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. 

The interest in chiral dimers was stimulated to a large extent by the expectation that placing the chiral centre in the spacer, at least for even dimers, should increase its orientational order compared to that for a chiral centre located in a terminal chain and this in turn should result in an enhancement of the form chirality of the phase. This suggestion has still to be extensively investigated but the limited data available indicates that dimers having chiral spacers actually exhibit ferroelectric smectic C phases with low values of spontaneous polarisation [140]. 

Fig. 5.10.1. (a) Helicoidal structure of the ferroelectric smectic C phase, (b) a poled sample with the helix unwound by an electric field applied normal to the... 

Brehmer et al. [114] were the first to publish if, measurements for ferroelectric LC elastomer (Fig. 27). The plot was later widely reproduced [15,83,110]. It is difficult, however, to understand the absence of any pronounced changes in the if, value at the phase transition from the ferroelectric smectic C phase to the non-ferroelectric smectic A phase. On the other hand, we should note that Finkelmann and Eckert [116] recently reported for ferroelectric LC elastomers if,(7 ) curves similar to those shown in Fig. 24 for the coefficient if,. 

Only few data are available for other liquid crystal phases (apart from nematics). For example, the azimuthal anchoring energy was recently measured in the ferroelectric smectic C phase [75]. 

As mentioned above, the symmetry of the ferroelectric smectic C phase corresponds to the polar symmetry group C2, Fig. 7.1, so that when going along the -coordinate parallel to a helix axis and perpendicular to the smectic layers the director L and the polarization vector P, directed along the C2 axis, rotate such as... 

Figure 8.6. Temperature-dependence of tilt angle 0, spontaneous polarization P, and ratio PJO in the ferroelectric smectic-C phase of the compound DOBAMBC (from [37]).

Like the usual dielectrics, the ferroelectric smectic-C phase possesses contributions to its dielectric permittivity which are based on the deformation of molecular electron shells and the orientation of permanent molecular dipoles. The dielectric properties at low frequencies, however, are dominated by additional contributions, the Goldstone mode and the soft mode [43], which result from the presence of the spontaneous polarization P and the coupling between P and 9. 

Figure 6. Comparison of the local structures of the smectic C and the ferroelectric smectic C phases.

This effect is observed in a geometry where the cholesteric axis h is homogeneously oriented in the plane of the cell (along x) and an electric field is applied to the electrodes of a sandwich cell along the z axis [137,138]. In this case, the helical structure, even the ideal one, is incompatible with the planar boundary conditions, and splayed and bended regions form near the boundaries. Thus, according to Eq. (38), the flexoelectric polarization arises in those regions which can interact with the electric field. The distortion is very similar to that observed in the ferroelectric smectic C phase (see Fig. 24) for a so-called deformed helix ferroelectric effect [139]. 

In the absence of walls the dynamic behavior may be described, as in nematics, by adding a viscous torque to the elastic and electric ones. For the field-off state, the distortion decays with the nematic time constant (see Eq. (34), where K should be substituted for 22)- The time of the response to an electric field can only be calculated for the simplest case when jU=0, Te=7 / e sin 2 E -EI), where E is defined by Eq. (69). Thus, the response of the smectic C phase is sin 2 times slower than that of the nematic phase. However, in experiments the same substance often responds faster in the smectic C phase than in the nematic one [159-161]. This may be due to the smaller value of Yi when the motion of the director is confined by the cone surface. The same phenomenon has been observed for the ferroelectric smectic C phase [162]. The domain-wall motion makes the dynamics of switching more complicated the field-induced wall velocity has been calculated by Schiller et al. [70]. 

Concerning the same transition, an induced SmA-SmC transition was observed when an electric field was applied in a chiral compound at a temperature near the transition [136, 137], the SmA-SmC transition temperature increasing under an electric field (Fig. 18). This field-induced transition was attributed to the large spontaneous polarization and to the first order behavior of the transition. Further studies have shown that the first order transition between the polarized smectic A phase and the ferroelectric smectic C phase terminates at a critical point in the temperature-electric field plane [138, 139]. 

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