Directors ferroelectrics

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. 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

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]. 

He is a recognized expert in solid state and materials chemistry and environmental chemistry. He has active programs in solid state f-element chemistry and nanomaterials science. His current research interests include heavy metal detection and remediation in aqueous environments, ferroelectric nanomaterials, actinide and rare-earth metal sohd slate chemistry, and nuclear non-proliferation. He currently maintains a collaboration in nuclear materials with Los Alamos National Laboratory and a collaboration in peaceful materials science development with the Russian Federal Nuclear Center - VNIIEF, Sarov, Russia, U.S. State Department projects. He has published over 100 peer-reviewed journal articles, book chapters, and reviews, while presenting over 130 international and national invited lectures on his area of chemistry. Dr. Dorhout currently serves as Vice Provost for Graduate Studies and Assistant Vice President for research. He has also served as the Interim Executive Director for the Office of International Programs and as Associate Dean for Research and Graduate Education for the College of Natural Sciences at Colorado State University. 

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. 

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. 

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. 

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. 

From this discussion the clear similarity between the SmAPA and SmCsPA structures is easily seen. In addition, the suggestion of Brand et al.29 that a bilayer smectic with all anticlinic layer interfaces (the SmAPF) would produce an achiral ferroelectric smectic follows directly. The unanticipated tilt of the director in the tilt plane, leading to a chiral layer structure, seems to be a general response of the bent-core mesogens to the spontaneous nonpolar symmetry breaking occurring in these rigid dimer structures. 

Figure 8.29 Illustration showing how all-anticlinic bilayer smectic should be ferroelectric is given. In case of covalent dimers (bent-core mesogens), equilibrium tilt of director combined with anti clinic layer interfaces in bow plane provides SmCsPF ferroelectric banana structure.

Figure 8.35 Illustration of bistable ferroelectric EO switching observed for blue focal conic domains of MHOBOW. SmCsPF structure can be assigned for these domains. In this phase director structure in all layers is oriented identically. This structure and corresponding extinction bmsh orientation for cylindrical focal conic are illustrated at bottom of figure for two bistable ferroelectric states. Note that for material with 30° tilt angle, such as MHOBOW, two ferroelectric states look very similar in still photos. In fact, two states result from large rotation of extinction brushes through 60°, as can be easily seen when observing switching in motion.

The experimental observations could be consistently explained if the general tilt structure (SmCo) inside the layers is assumed. For most bent-core smectics the polar vector is perpendicular to the tilt plane, defined by the layer normal and averaged long axis direction, just as polarization in the ferroelectric rod-like liquid crystalline systems. However, since in the bent-core liquid crystals the polar order is decoupled from the tilt order, the polar director can in general have any direction in space thus it can also have a non-zero component along the layer normal. This can be achieved by a combination of tilting (rotation around the polar director) and leaning (rotation around the direction perpendicular to the polar director) of... 

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 ... 

Ferroelectric switching is the most likely process encountered in FLCPs. A solution of the equation of motion of the SmC director, when the dielectric anisotropy is supposed to be negligible, leads to the introduction of a switching time r which is related to the rotational viscosity y and the spontaneous polarization by the following rela-... 

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... 

Smectic elastomers, due to their layered structure, exhibit distinct anisotropic mechanical properties and mechanical deformation processes that are parallel or perpendicular to the normal orientation of the smectic layer. Such elastomers are important due to their optical and ferroelectric properties. Networks with a macroscopic uniformly ordered direction and a conical distribution of the smectic layer normal with respect to the normal smetic direction are mechanically deformed by uniaxial and shear deformations. Under uniaxial deformations two processes were observed [53] parallel to the direction of the mechanical field directly couples to the smectic tilt angle and perpendicular to the director while a reorientation process takes place. This process is reversible for shear deformation perpendicular and irreversible by applying the shear force parallel to the smetic direction. This is illustrated in Fig. 2.14. 

We can answer the last question if consider a constraction of the so-called surface stabilised ferroelectric liquid crystal cell or simply SSFLC ceU [9]. Such SSFLC cell is only few micrometers thin and, due to anchoring of the director at the surfaces, the intrinsic helical stmcture of the SmC is unwound by boundaries but a high value of the spontaneous polarisation is conserved. The cell is con-stracted in a way to realise two stable states of the smectic C liquid crystal using its interaction with the surfaces of electrodes, see Fig. 13.6a. First of all, in the SSFLC cell, the so-called bookshelf geometry is assumed the smectic layers are vertical (like books) with their normal h parallel the z-axis. Then the director is free to rotate along the conical surface about the h axis as shown in Fig. 13.6b (Goldstone mode). It is important that, to have a bistability, the director should be properly... 

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