Helical ferroelectrics

In reality, a growth of the induced tilt at the phase transition is limited by two factors. In a strictly compensated non-helical ferroelectrics only term in expansion (13.10) is hmiting. In the most practical cases, the helix cannot be precisely compensated over the whole range of the smectic C phase and a hnite wavevector q, = IkIPq remains. Thus, in a more advanced theory, the space dependent, chiral terms must be added to expansion (13.10). They renormalize the transition temperature for the second time, and put a limit for the divergence of the induced tilt ... 

The deformed helical ferroelectric (DHF) effect. If the voltage applied to the smectic C phase is lower than the untwisting field value, the helix is not completely suppressed but only distorted (Fig. 14). For a square voltage, there will be an alternation between two deformed helical states, and optically it appears as switching of the refractive index ellipsoid [6,121). In contrast to ferroelectric switching, the response time for the DHF effect is independent of... 

Other more exotic types of calamitic liquid crystal molecules include those having chiral components. This molecular modification leads to the formation of chiral nematic phases in which the director adopts a natural helical twist which may range from sub-micron to macroscopic length scales. Chirality coupled with smectic ordering may also lead to the formation of ferroelectric phases [20]. 

When the mesogenic compounds are chiral (or when chiral molecules are added as dopants) chiral mesophases can be produced, characterized by helical ordering of the constituent molecules in the mesophase. The chiral nematic phase is also called cholesteric, taken from its first observation in a cholesteryl derivative more than one century ago. These chiral structures have reduced symmetry, which can lead to a variety of interesting physical properties such as thermocromism, ferroelectricity, and so on. 

Finally, ferroelectricity has been shown for columnar metallomesogens.35 Serrano and co-workers have shown that metal ft-diketonates, provided with chiral side chains (e.g., 32), form helical columns (vide supra), which can also be switched under an alternating electric field. 

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 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. 

PVDF is mainly obtained by radical polymerisation of 1,1-difluoroethylene head to tail is the preferred mode of linking between the monomer units, but according to the polymerisation conditions, head to head or tail to tail links may appear. The inversion percentage, which depends upon the polymerisation temperature (3.5% at 20°C, around 6% at 140°C), can be quantified by F or C NMR spectroscopy [30] or FTIR spectroscopy [31], and affects the crystallinity of the polymer and its physical properties. The latter have been extensively summarised by Lovinger [30]. Upon recrystallisation from the melted state, PVDF features a spherulitic structure with a crystalline phase representing 50% of the whole material [32]. Four different crystalline phases (a, jS, y, S) may be identified, but the a phase is the most common as it is the most stable from a thermodynamic point of view. Its helical structure is composed of two antiparallel chains. The other phases may be obtained, as shown by the conversion diagram (Fig. 7), by applying a mechanical or thermal stress or an electrical polarisation. The / phase owns ferroelectric, piezoelectric and pyroelectric properties. 

Deformed //clical Ferroelectrics (DHF)117 In a thicker cell (ca 5 pm) the surface stabilization no longer dominates and a helical structure is formed with the helix axis parallel to the glass plate. The external electrical d.c. field can influence and modulate the helix. 

Fig. 30 Selected examples of chiral rod-like mesogens with one fluorinated chain (77° C) one enantiomer is shown as example (SmCA = antiferroelectric SmC phase SmC = ferroelectric SmC phase SmCpi = ferrielectric SmC phase SmCa = helical SmC phase SmI = chiral tilted low temperature phase) [197-199]...

In a chiral smectic (Sc ) phase, the tilt angle is the same within a layer, but the tilt direction processes and traces a helical path through a stack of layers (Figure 43). It has been demonstrated that when such a helix is completely unwound, as in a surface stabilized ferroelectric liquid crystal cell, then changing the tilt of the molecules fi om +0 to —0 by alternating the direction of an applied field results in a substantial electro-optic effect, which has the features of veiy fast switching (%1 - lOps), high contrast and bistability [87]. The smectic A phase of chiral molecules may also exhibit an electro-optic effect, this arises due to molecular tilt fluctuations which transition is approached, which are combined with a... 

Calamitic metallomesogens forming a chiral smectic C phase (SmC ) are ferroelectric materials. Due to the low symmetry of this phase when the helix is unwound (C2) the molecular dipoles are aUgned within the layers of the SmC phase, giving rise to ferroelectric order in the layers. Because the SmC phase has a helical structure, there is no net macroscopic dipole moment for the bulk phase. However, it is possible to unwind the helix by application of an external electric field or by surface anchoring in thin cells. Under such conditions, a well-aligned film of the ferroelectric liquid crystal can exhibit a net polarisation, called the spontaneous polarisation (Ps). Ferroelectric liquid crystals are of interest for display applications because the macroscopic polarisation can be switched very fast by an... 

The local symmetry group of the Sc phase is a C2 group and thus the Sc phase has helical electricity. The spontaneous polarization, Ps, is perpendicular to the layer normal and molecular axis. Due to its helical structure Ps changes its direction uniformly, evolving along the helical axis so that the Sc phase does not show a measurable ferroelectricity except in the unwinding of its helical structure. The Sc phase is one of the very important liquid crystal phases that has a prospective application in fast response display. The detailed structure of the Sc phase will be shown in Chapter 6. 

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. 

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. 

As this compound was one of the higher homologues in the series, and because we knew that the earlier homologues did not exhibit a chiral nematic phase, it was clear that the new phase also could not be a chiral nematic phase. In addition, it was clear from the formation of the defect structures seen in the microscope that the phase first formed from the isotropic liquid possessed a helix, see Plate 1, which had its heli-axis at right angles to the heli-axis in the lower temperature chiral ferroelectric smectic phase. This simple observation meant that if the phase was a lamellar smectic phase then the helix would have to be formed, inconceivably, in a direction parallel to the layers. Synthesis of the achiral variant confirmed that the phase formed first on cooling from the isotropic liquid was indeed a smectic A phase, and thus we immediately knew that we had found a smectic A phase where the helical macro structure formed in the planes of the layers, and thus the helix must... 

X-ray measurements on LC elastomers have shown [6-8] that the reversible transition between a chiral smectic C phase with and without a helical superstructure can be induced mechanically. The helix untwisted state corresponds in this case to a polar ferroelectric monodomain. The piezoelectricity arising from this deformation of the helical superstructure (which does not require a complete untwisting) has been demonstrated [9] for polymers cross-linked by polymerization of pendant acrylate groups (Figure 15). 

However, due to the helical structure of the SmC mesophase, no net spontaneous polarization results. Macroscopic nonvanishing polarization is only obtained when the helix is unwound. This requirement has been a severe limitation for the determination of Ps, and we had to wait until 1988 for the first observation of ferroelectric switching in a side chain SmC LCP [65]. Even now, the measurement of remains delicate and its reliability is directly connected to the quality of the uniform alignment achieved. 

Since the discovery of the first liquid crystalline material in 1888, helicity has proven to be one of the most fascinating topics in this field."" Several liquid crystalline phases with helical structure were reported, such as chlolesteric phase, blue phase, ferroelectric and antiferro-electric smectic phases, and helical smectic A phase. In most of these helical phases, at least a fraction of the constituent molecules have an asymmetric carbon, and it was long believed that chirality at a molecular level is a prerequisite to construct chiral architectures at the mesoscopic level. However, Watanabe et al. reported the first example of spontaneous helix formation in liquid crys-... 

The most studied chiral smectic phase is ferroelectric SmC phase [18], which is derived from Smectic C (SmC) phase. As shown in Fig. 5.2, the helical twist in SmC results from chiral organization of smectic layers as similar to the formation of N from nematic layers mentioned above. The molecules in each smectic layer... 

Fig. 5.2 Helical structure of SmC phase (a) and surface stabilized ferroelectric liquid crystals (SSFLC) (b and c)...

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