Smectic-C Liquid Crystals

The finite tilt of the director axis from the layer normal (taken as the z axis) introduces a new degree of freedom, namely, a rotation aroimd the z axis, compared to the SmA phase. This rotation preserves the layer spacing and therefore does not require too much energy. Since du/dy and du/dx are equivalent to rotations around the x and y axes, respectively, we may express the free energy in Smectic-C (SmC) liquid crystals in terms of the rotation components  

Taking into account all the energy terms associated with director axis rotation, interlayer distortion, and possible coupling between them, the total free energy of the system is given by  

Here is the free energy assoeiated with direetor axis rotation withont ehange of layer spacing, is dne to layer distortions, and F is the cross term describing the conpling of these layer distortions and the fiee-rotation process. 

Field-Induced Director Axis Rotation in SmC Liquid Crystals 

In practical implementations or switching devices, the logical thing to do is to involve only one or a small munber of these distortions. If an external field is applied, the field-dependent terms [cf Eq. (4.5a) and (4.5b)] shonld be added to the total free-energy expression. The process of field-induced director axis distortion in SmC is analogous to the nematic case. For example, the first three terms on the right-hand side of Equation (4.70) correspond to the splay term in nematics  

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The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

The second issue concerns the anisotropy of the membrane. The models presented in this section all assume that the membrane has the symmetry of a chiral smectic-C liquid crystal, so that the only anisotropy in the membrane plane comes from the direction of the molecular tilt. With this assumption, the membrane has a twofold rotational symmetry about an axis in the membrane plane, perpendicular to the tilt direction. It is possible that a membrane... 

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. 

A very different model of tubules with tilt variations was developed by Selinger et al.132,186 Instead of thermal fluctuations, these authors consider the possibility of systematic modulations in the molecular tilt direction. The concept of systematic modulations in tubules is motivated by modulated structures in chiral liquid crystals. Bulk chiral liquid crystals form cholesteric phases, with a helical twist in the molecular director, and thin films of chiral smectic-C liquid crystals form striped phases, with periodic arrays of defect lines.176 To determine whether tubules can form analogous structures, these authors generalize the free-energy of Eq. (5) to consider the expression... 

To discuss the models in this section, we should mention two issues. First, the models assume the membrane is sufficiently soft that the tilt direction can vary with an energy cost that scales as (Vc(j)2. This is appropriate if the membrane is in a fluid phase like a smectic-C liquid crystal, with order in the tilt direction but not in the positions of the molecules. It is also appropriate if the membrane is in a tilted hexatic phase, with order in the orientations of the intermolecular bonds as well as the tilt. However, this assumption is not appropriate if the membrane is in a crystalline phase, because the tilt direction would be locked to the crystalline axes, and varying it would cost more energy than (V(f>)2. 

Chiralsil-val, 6 96-97 Chiral smectic C liquid crystals, 15 106-107 Chiral stationary phases, 6 79-82 Chiral supramolecular clusters, 24 61 Chiral synthons, 11 5 Chiral titanium complexes, 25 98—99 Chirobiotic phases, for chiral separations, 6 90-91... 

The existence of the layers and director tilt in the achiral smectic C liquid crystal phase are experimental facts. Given these, the maximum possible symmetry of the phase would be Ci, with a C2 axis normal to the tilt plane, and a a plane congruent with the tilt plane. In fact, there is no fundamental reason why a given C phase must possess either of these symmetry elements. But, breaking of either of the symmetry elements would afford polar symmetry, and no C phase has ever been shown to possess any property associated with polar symmetry (e.g. pyroelectricity). Therefore, we can say that all known C phases indeed possess the maximum possible symmetry consistent with the layers and tilt. 

Cowling SJ, Hall AW, Goodby JW (2005) Electro-optic response in a racemic smectic C liquid crystal. Adv Mater 17 1077-1080... 

Another example of a dispersion of SWCNTs in a multi-component antiferro-electric smectic-C liquid crystal mixture was shown by Lagerwall and Dabrowski et al. [497]. In this study, SWCNTs caused the appearance of a single-layer SmC phase between the SmA phase and the crystalline state in comparison to the non-doped sample exhibiting an SmA and two specific intermediate phases, an SmC p and an SmC Y phase. 

In a nematic liquid crystal, the molecules are aligned so that their long axes tend to point in the same direction but the ends are not aligned with one another. In smectic A and smectic C liquid crystals, the molecules maintain the long-axis alignment seen in nematic crystals, but in addition they pack into layers. 

In the helical structure, the optical ellipsoid of the smectic C phase rotates together with the tilt plane. Like in cholesterics, we can imagine that helical turns form a stuck of equidistant quasi-layers that results in optical Bragg reflections in the visible range. Therefore, like cholesterics, smectic C liquid crystals are onedimensional photonic crystals. However, in the case of SmC, the distance between the reflecting layers is equal to the full pitch Pq and not to the half-pitch as in cholesterics, because at each half-pitch the molecules in the SmC are tilted in opposite directions. Hence, we have a situation physically different from that in cholesterics. 

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... 

The simplest phase corresponds to a compact triangular packing (still called hexagonal) of isotropic columns (see Fig. 9.3). The equivalent phases in smectic C liquid crystals are such that molecules are tilted relative to columns. A priori molecules may tilt towards the nearest or second nearest neighbour columns, or in any other direction. These three possibilities correspond to three distinct phases. Columns may also deform themselves into ellipses without molecules tilting relative to the columnar axis this is yet another phase. Columnar symmetry may also occur with local smectic order and an example is shown in Fig. 9.19 for long thin molecules with polar heads. All these phases have common elastic, hydrodynamic and topological properties. 

Smectic-C liquid crystals are similar to smectic-A liquid crystals except that the liquid crystal director is no longer perpendicular to the layer but tilted. For the convenience of symmetry discussion, let us introduce a unit vector a which is perpendicular to the layer. The symmetry group is C2h- The two-fold rotational symmetry is around the axis that is perpendicular to the na plane (which contains both n and a). This implies that there is no spontaneous polarization in the na plane. The reflection symmetry is about the ita plane, and therefore there is no spontaneous polarization perpendicular to the na plane either. This rules out the possibility of spontaneous polarization in smectic-C liquid crystals. 

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. 

Scheme 14.47 Novel fluorenol mesogens as chiral smectic C liquid crystals [164].

J.R. Bruckner, J.H. Porada, F. Knecht, C.F. Dietrich, M. Harjung, F. Giesselmann, Lyotropic chiral smectic C liquid crystal with polar electro-optic switching, 25th International Liquid Crystal Conference (CL-02.001), Dublin, Ireland, (2014)... 

Le Bamy, P, and Dubois, J. C., The chiral smectic C liquid crystal side chain polymers. in Side Chain Liquid Crystal Polymers (C. B. McArdle, ed.), Blackie, Glasgow, 1989, pp. 130-158. 

Beresnev, L., Chigrinov, V. G., Dergachev, D. I., Poshidaev, E. P., Funfschilling, J., and Schadt, M., Deformed helix ferroelectric liquid crystal display a new electrooptic mode in ferroelectric chiral. smectic C liquid crystals, Liq. Cry.st., 5, 1171-1177 (1989). 

What does the diffraction pattern from a smectic C liquid crystal look like If the sample is completely aligned with the normal to the layers along the z-axis, something called a monodomain sample, then there are two peaks at values for q of 2jt/d , where... 

Figure 2.8. (a) Smectic C liquid crystal (b) Resulting X-ray diffraction pattern. 

Another type of LCD uses a chiral smectic C Uquid crystal instead of a nematic liquid crystal. Chiral smectic C liquid crystals are ferroelectric, spontaneously developing an electric polarisation parallel to the smectic layers. In an tmdistorted chiral smectic C liquid crystal, the polarisation is at 90° to the normal to the layers and rotates around the normal as the director rotates aroimd a cone centred on the normal to the layers. However, if the chiral smectic C liquid crystal is placed between properly prepared pieces of glass separated by only several micrometres, it is possible to establish a texture in which the director is parallel to the glass surfaces and uniform throughout the hquid crystal. In this texture, the smectic planes are perpendicular to the glass surfaces and the... 

Broken focal conic fan texture and schlieren textme of the smectic C liquid crystal phase. 

Recently there was also considerable activity in the investigations of the SHG in nematic and cholesteric phases induced by an external electric field. Such experiments allow the high order molecular hyperpolarizabilities to be calculated. " The SHG was also observed in a ferroelectric (chiral smectic C ) liquid crystal. ... 

The present theory applies also to smectic-c liquid crystals in Rapini s iV-configuration. In this case, the following formal substitutions should be u ed ... 

Optically induced molecular reorientation in a smectic-C liquid crystal... 

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