Polarization smectic layers

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)...

We start with some elementary information about anisotropic intermolec-ular interactions in liquid crystals and molecular factors that influence the smectic behaviour. The various types of molecular models and commonly accepted concepts reproducing the smectic behaviour are evaluated. Then we discuss in more detail the breaking of head-to-tail inversion symmetry in smectic layers formed by polar and (or) sterically asymmetric molecules and formation of particular phases with one and two dimensional periodicity. We then proceed with the description of the structure and phase behaviour of terminally fluorinated and polyphilic mesogens and specific polar properties of the achiral chevron structures. Finally, different possibilities for bridging the gap between smectic and columnar phases are considered. 

These structures were firstly observed for terminally polar mesogens [11, 12]. However, recent experiments give clear evidence of the presence of smectic A layering [37, 38], re-entrant nematic behaviour [39], two-dimensional lattices [40, 41] and smectic layering with incommensurate periodicities [42] for non-polar sterically asymmetric LCs. 

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... 

Figure 8.6 Three-dimensional slice of C2 symmetrical SmC phase, showing tilt cone, polar axis (congruent with twofold symmetry axis), smectic layer planes, tilt plane, and polar plane.

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. 

Figure 8.20 Structure and phase sequence of prototypical bent-core mesogen NOBOW (8) are given, along with space-filling model showing one of many conformational minima obtained using MOPAC with AMI force field. With observation by Tokyo Tech group of polar EO switching for B2 smectic phases formed by mesogens of this type, banana LC field was bom. Achiral, polar C2v layer structure, with formation of macroscopic spontaneous helix in polarization field (and concomitant chiral symmetry breaking), was proposed to account for observed EO behavior.

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 ... 

The first term in (7) describes the coupling between the polarization splay and tilt of the molecules with respect to the smectic layer normal. This coupling is responsible for the chiral symmetry breakdown in phases where bent-core molecules are tilted with respect to the smectic layer normal [32, 36]. The second term in (7) stabilizes a finite polarization splay. The third term with positive parameter Knp describes the preferred orientation of the molecular tips in the direction perpendicular to the tilt plane (the plane defined by the nematic director and the smectic layer normal). However, if Knp is negative, this term prefers the molecular tips to lie in the tilt plane. The last term in (7) stabilizes some general orientation (a) of the polar director (see Fig. 7) which leads to a general tilt (SmCo) structure. 

Let us first consider the case where the preferred orientation of the polar director is perpendicular to the tilt plane (K > 0). The spatial variation of the layer normal and the nematic and polar directors is shown in Fig. 12. We see that regions of favorable splay (called blocks or layer fragments in Sect. 2) are intersected by regions of unfavorable splay (defects, walls). In the region of favorable splay the smectic layer is flat. In the defects regions the tilt angle decreases to reduce energy... 

Bent-core liquid crystals are especially interesting materials for basic research as in these systems the polar and tilt order are decoupled and polarization splay seems to be an inherent property of the system. Both effects lead to a variety of structures with unusual properties, e.g., formation of the 2D density modulated phases built of the smectic layers fragments. We have presented the current knowledge... 

We have also shown the existence of 2D phases due to more subtle electron density changes. In some cases additional peaks are observed in the XRD pattern, signifying a double layer periodicity in the system, which can be accounted for if a general orientation of the polar director is allowed. If the polar director is not perpendicular to the tilt plane there exists a component of polarization in the direction of the smectic layer normal (longitudinal polarization). By double layer periodicity the system escapes from the polar structure and in addition achieves better packing of the molecular cores and molecular tails. 

Finally, the difference of chirality enhancement in the N and SmC phases should be mentioned. As shown in Sect. 2.1, enhancement rate in SmC is about one order of magnitude larger than that in N. In the SmC chirality enhancement is attributed to two effects (1) the interaction between bent-core and chiral host molecules and (2) the coupling between ee, tilt, and spontaneous polarization. The latter effect is absent in the N phase and is an additional effect in SmC. Moreover, the chiral discrimination parameter AU is expected to be larger in SmC than in N because of a confined geometry, i.e., smectic layer. 

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