Director polarization

The free energy density terms introduced so far are all used in the description of the smectic phases made by rod-like molecules, the electrostatic term (6) being characteristic for the ferroelectric liquid crystals made of chiral rod-like molecules. To describe phases made by bent-core molecules one has to add symmetry allowed terms which include the divergence of the polar director (polarization splay) and coupling of the polar director to the nematic director and the smectic layer normal ... 

Figure 15. The helical configuration of the director-polarization couple is unwound by a sufficiently strong electric field E. The increasing field induces a macroscopic polarization (which is thus not spontaneous) and finally polarizes the medium to saturation (all dipolar contributions lined up parallel to the field), as shown to the right.

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. 

Disclinations in tire nematic phase produce tire characteristic Schlieren texture, observed under tire microscope using crossed polars for samples between glass plates when tire director takes nonunifonn orientations parallel to tire plates. In thicker films of nematics, textures of dark flexible filaments are observed, whetlier in polarized light or not. This texture, in fact, gave rise to tire tenn nematic (from tire Greek for tliread ) [40]. The director fields... 

This transition is usually second order [18,19 and 20]. The SmC phase differs from the SmA phase by a tilt of the director with respect to the layers. Thus, an appropriate order parameter contains the polar (0) and azimuthal ((]i) angles of the director ... 

Fig. 17. Polymer dispersed Hquid crystal display (PDLC). (a) U < clear state, where U) is the threshold voltage of the ceU. and rij represent the indexes of refraction for light polarized parallel and perpendicular to the director of the Hquid crystal represents the index of refraction of the isotropic...

The classical scheme for dichroism measurements implies measuring absorbances (optical densities) for light electric vector parallel and perpendicular to the orientation of director of a planarly oriented nematic or smectic sample. This approach requires high quality polarizers and planarly oriented samples. The alternative technique [50, 53] utilizes a comparison of the absorbance in the isotropic phase (Dj) with that of a homeotropically oriented smectic phase (Dh). In this case, the apparent order parameter for each vibrational oscillator of interest S (related to a certain molecular fragment) may be calculated as S = l-(Dh/Di) (l/f), where / is the thermal correction factor. The angles of orientation of vibrational oscillators (0) with respect to the normal to the smectic layers may be determined according to the equation... 

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. 

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. 

Freely suspended films provide a perfect homeotropic alignment of smectic LCs since the layers always orient parallel to the LC/air interface.33 The director structure in such films can then be determined by analyzing the optical properties of plane-polarized light reflected from the surface of the films at a slightly oblique angle.34 The technique gains additional power when electrodes are added to the setup, allowing observation of the behavior of the films in the presence of an electric field parallel to the plane of the film.35... 

Using this method, the M6R8/PM6R8 blend showed precisely the behavior expected for the achiral SmAPA structure. Specifically, the optical properties of the films were consistent with a biaxial smectic structure (i.e., two different refractive indices in the layer plane). The thickness of the films was quantized in units of one bilayer. Upon application of an electric field, it was seen that films with an even number of bilayers behaved in a nonpolar way, while films with an odd number of bilayers responded strongly to the field, showing that they must possess net spontaneous polarization. Note that the electric fields in this experiment are not strong enough to switch an antiferroelectric to a ferroelectric state. Reorientation of the polarization field (and director structure) of the polar film in the presence of a field can easily be seen, however. 

Taken from the three spontaneous symmetry-breaking events leading to this layer structure [formation of layers with long-range orientational order of the director (Sm), tilt of the director from the layer normal (C), and polar orientation of the molecular arrows (P)], we term phases of this type SmCP. All of the complex textures and EO behavior of NOBOW in the B 2 phase can be understood in terms of various stacking modes of SmCP layers as shown in Figure 8.23. 

One of the key experimental results leading to the elucidation of this overall structural puzzle involved depolarized reflected light microscopy (DRLM) studies on NOBOW freely suspended films in the high-temperature SmCP phase.48 In the freely suspended films it appears that only one phase is observed, which is assumed to be the phase forming the majority domains in the EO cells. The DRLM experiment provides two key results. First, thin films of any layer number have a uniformly tilted optic axis, suggesting all of the layer interfaces are synclinic. Second, films of even-layer number are nonpolar, while films of odd-layer number are polar, with the polar axis oriented normal to the plane of the director tilt (lateral polarization). 

Application of an electric field to the SmCsPA phase then causes the system to switch to a ferroelectric state. This could occur in two ways. The molecules in every other layer could simply rotate about the director, leaving the layer clinicity the same but changing the chirality of alternate layers. This would require a locally diastereomeric transition structure where the polarization is not parallel to the layers. 

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. 

To prepare fr[Pg.520]

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