Orientation chiral smectics

It is also possible that a membrane might have an even lower symmetry than a chiral smectic-C liquid crystal in particular, it might lose the twofold rotational symmetry. This would occur if the molecular tilt defines one orientation in the membrane plane and the direction of one-dimensional chains defines another orientation. In that case, the free energy would take a form similar to Eq. (5) but with additional elastic constants favoring curvature. The argument for tubule formation presented above would still apply, but it would become more mathematically complex because of the extra elastic constants. As an approximation, we can suppose that there is one principal direction of elastic anisotropy, with some slight perturbations about the ideal twofold symmetry. In that approximation, we can use the results presented above, with 4) representing the orientation of the principal elastic anisotropy. 

Blinov, L. M., Barberi, R., Kozlovsky, M. V., Lazarev, V. V., and de Santo, M. P. Optical anisotropy and four possible orientations of a nematic liquid crystal on the same film of a photochromic chiral smectic polymer. / Nonlinear Opt. Phys. Mat. 9, 1 (2000). 

Chiral lc-polymers can be prepared by a proper functionalization of lc-polymers with chiral and reactive groups. These elastomers are interesting, because they combine the mechanical orientability of achiral lc-elastomers with the properties of chiral lc-phases, e.g. the ferroelectric properties of the chiral smectic C phase. The synthesis of these elastomers was very complicated so far, but the use of lc-polymers, which are functionalized with hydroxyl-groups, has opened an easy access to these systems. Also photocrosslinkable chiral lc-polymers can be prepared via this route. 

Figure 14. Idealized presentation of the orientation process, which leads to piezoelectricity in chiral smectic C elastomers (only the mesogens are shown) [28], P macroscopic polarization). The deformed states with a partially unwound helix (left and right) are prepared from the ground state with a helical superstructure (middle) by mechanical forces. 0 and direction of the spontaneous polarization in and out of the plane of drawing, respectively.

Experimentally, piezoelectricity in cholesteric and chiral smectic C phases was reported for liquid-crystalline networks [140-147]. Multidomain lightly cross-linked systems were synthesized, then the orientation is obtained by mechanical strain [140] or by poling [147]. In other samples this orientation is performed prior to the crosslinking process [144, 146]. Macro-scopically oriented samples were subjected to either a static or a periodically varying strain. Open circuit voltages across the samples were measured that are linear functions of the applied strain [140-142, 144, 145],... 

Of these, the most important (and which, for simplicity, we shall consider exclusively) is the chiral smectic C, denoted smectic C. In this phase, like all smectics, partial translational ordering of the molecular centers of gravity is superimposed on the orientational ordering. In the case of smectic C, this translational order can be thought of as a mass density wave as follows ... 

As pointed out by Meyer [14], the reflection symmetry of smectic-C liquid crystals can be removed if the constiment molecules are chiral, and thus it becomes possible to have spontaneous polarization. This phase is called the chiral smectic-C or smectic-C, and its stmcture is shown in Figure 4.7. Within a layer, the structure is the same as in smectic-C. The liquid crystal director n is, however, no longer oriented unidirectionally in space but twists from layer to layer as in the cholesteric phase [15]. The symmetry group is C2. The two-fold rotational symmetry axis is perpendicular to both the layer normal a and the director n. Now it is possible to have spontaneous polarization along the two-fold rotational symmetry axis. 

Semmler, K., and Finkelmann, H Orientation of a chiral smectic C elastomer by mechanic fields, Polym. Adv. Techno ., 5, 231-235 (1994). 

This effect has been called the piezoelectric effect in many publications on liquid crystals, but there is good reason for giving it a different name. The piezoelectric effect corresponds to the occurrence of a charge on the surface of the crystal when there is a translational deformation, e.g., with compression or extension. The crystal in this case must be non-centrosymmetric. An effect of this type is also characteristic of polar liquid crystalline phases, e.g., of the chiral smectic C (Chapter 7). The effect, however, in which we are interested here is caused by flexion, a purely orientation deformation in a nematic liquid crystal. Consistent with this argument [1], we will call... 

In addition to thermotropic nematic liquid crystals, others such as chiral, smectic and lyotropic liquid crystals have been investigated and their dynamics and orienting properties studied. The structure of the tilted phase of a chiral liquid crystal has been investigated by means of the line-shape... 

This section pertains to reports on oriented molecules in which phases other than the usual thermotropic nematics have been used. Studies in chiral, smectic, columnar, lyotropic and polymeric liquid crystals as well as other unusual phases have been presented. The use of carbon-proton heteronuclear selective refocusing 2D NMR experiment designed for the spectral analysis of enantiomers dissolved in weakly ordering chiral liquid crystal solvents has been proposed." The method permits the extraction of carbon-proton residual dipolar couplings for each enantiomer from a complex or unresolved proton-coupled... 

The first chiral smectic C elastomer was synthesized by Zentel et al. in 1988 [13], [24]. The preparation of the network is similar to the synthesis of the cholesteric networks described above. The network was uniaxially stretched. An unwinding of the helicoidal superstructure is observed and an orientation of the director, as well as of the smectic layer normal roughly parallel to the stress axis occurs. A macroscopically uniform alignment of the sample was not observed as explained below. 

The viscous part of the stress tensor for the SmC and the ferroelectric chiral smectic (SmC ) phase agree with one another. The flow phenomena with a fixed director orientation discussed in the foregoing section can not be observed due to the inhomogeneous director orientation in the SmC phase. However, there is a large interest in rotational movements of the director in ferroelectric displays. 

This surface bistability is at the basis of chiral smectic C surface stabilized ferroelectric liquid crystal (SSFLC) devices [92]. As their name indicates, these devices are made of thin cells in which the walls, imposing the orientation of the molecules at the surfaces, unwind the spontaneous smectic C helix and stabilize two uniform configurations of the director in the cell. Switching between these two states can be done by applying an electric field. 

The combination of liquid crystalline chirality and surface polarization is also the origin of the so-called surface electroclinic effect in chiral smectic A phases if the smectic layers are oriented perpendicular to the surface, the surface electric field tilts the layer normal away from the surface molecular orientation [108-110] (Fig. 7). 

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