Helical chiral smectics

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... 

Fig. 7. Illustrating the structure of a chiral smectic C mesophase P = helical pitch)...

The role of supramolecular chemistry in materials is perhaps expressed most impressively in liquid crystals, in which slight variations of chiral content can lead to dramatic influences in the properties of the mesophases. The helical sense of these mesophases is determined not only by intrinsically chiral mesogens but also by the use of dopants which more often than not interact with achiral host LCs to generate chiral phases (Fig. 7). These phenomena are important both scientifically and technologically, most notably for the chiral smectic and cholesteric liquid crystal phases [68-71]. These materials—as small molecules and as polymers [72,73]—are useful because their order... 

Figure 2. Schematic representation of the cholesteric and chiral smectic C phase. The repeating distance along the helical axis (pitch) is between 200 nm to some pm.

First X-ray measurements show that the helical superstructure of the cholesteric and chiral smectic C phase can be untwisted by stretching the elastomer (5). High strains of 300% are necessary for this purpose (compared to 20% for the achiral elastomers). Nevertheless these results show that the chiral lc elastomers have the potential to act as mechano-optical couplers (cholesteric phase) or as piezo-elements (chiral smectic C phase) (5), because the mechanically induced change of the helical superstructure has to change the optical transmission or reflection properties or the spontaneous polarization. Both effects however have not yet been measured directly. 

In a chiral smectic (Sc ) phase, the tilt angle is the same within a layer, but the tilt direction processes and traces a helical path through a stack of layers (Figure 43). It has been demonstrated that when such a helix is completely unwound, as in a surface stabilized ferroelectric liquid crystal cell, then changing the tilt of the molecules fi om +0 to —0 by alternating the direction of an applied field results in a substantial electro-optic effect, which has the features of veiy fast switching (%1 - lOps), high contrast and bistability [87]. The smectic A phase of chiral molecules may also exhibit an electro-optic effect, this arises due to molecular tilt fluctuations which transition is approached, which are combined with a... 

Calamitic metallomesogens forming a chiral smectic C phase (SmC ) are ferroelectric materials. Due to the low symmetry of this phase when the helix is unwound (C2) the molecular dipoles are aUgned within the layers of the SmC phase, giving rise to ferroelectric order in the layers. Because the SmC phase has a helical structure, there is no net macroscopic dipole moment for the bulk phase. However, it is possible to unwind the helix by application of an external electric field or by surface anchoring in thin cells. Under such conditions, a well-aligned film of the ferroelectric liquid crystal can exhibit a net polarisation, called the spontaneous polarisation (Ps). Ferroelectric liquid crystals are of interest for display applications because the macroscopic polarisation can be switched very fast by an... 

Almost all the smectic phases, in which the molecules are arranged in layers and are tilted with respect to the layers, have counterpart chiral phases. The most important one of this class is the chiral smectic C phase — Sc phase. In these chiral liquid crystal phases, the molecules are tilted at a constant angle with respect to the layer normal but the tilt azimuthal rotates uniformly along the chiral axis and forms a helical structure. 

Fig. 5. Helical Structures of the chiral nematic and chiral smectic phases...

Fig. 33. a Concentric cylindrical twist walls separating different chiral smectic regions. Inside each region the layer surface adopts a helicoidal shape, b Each cylindrical twist wall is comparable to that found in a conventional TGB phase, a helical shape being given to the screw dislocations constituting them (after Gilli and Kamaye [43])... 

X-ray measurements on LC elastomers have shown [6-8] that the reversible transition between a chiral smectic C phase with and without a helical superstructure can be induced mechanically. The helix untwisted state corresponds in this case to a polar ferroelectric monodomain. The piezoelectricity arising from this deformation of the helical superstructure (which does not require a complete untwisting) has been demonstrated [9] for polymers cross-linked by polymerization of pendant acrylate groups (Figure 15). 

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.

Alam MZ, Yoshioka T, Ogata T, Nonaka T, Kurihara S. 2007. The influence of molecular structure on helical twisting power of chiral azobenzene compounds. Liq Cryst 470 63 70. Bahr C, Escher C, Fliegner D, Heppke G, Molsen H. 1991. Behavior of helical pitch in cholesteric and chiral smectic C phases. Ber Bunsen Ges 95(10) 1233 1237. 

The most studied chiral smectic phase is ferroelectric SmC phase [18], which is derived from Smectic C (SmC) phase. As shown in Fig. 5.2, the helical twist in SmC results from chiral organization of smectic layers as similar to the formation of N from nematic layers mentioned above. The molecules in each smectic layer... 

Figure 5 Photomicrographs of liquid crystal textures seen in the polarizing microscope. (A) The Schlieren texture of a smectic I phase. (B) The focal conic texture of a chiral smectic C phase, which has a helical structure, forming at a transition from the liquid. The pitch of the helix shows up as parallel lines that are parallel to the molecule layers (each line corresponds to about a thousand molecular layers). The pitch lines reflect accurately the layer structure in the focal-conic domain. (A) Courtesy of JW Goodby, University of Hull, UK, with permission. (B) Reproduced with permission from Gordon and Breach, Switzerland.)...

More recently, it has been theoretically predicted by Brand [81] that elastomeric networks that have chiral nematic or smectic C mesophases should have piezoelectric properties. The non-centro-symmetric material responds to the deformation via a piezoelectric response. Following this prediction, both Finkelmann and Zental have reported the observation of piezoelectricity. In one case, a nematic network was converted to the cholesteric form with the addition of CB15, 2 -(2-methylbutyl)biphenyl-4-carbonitrile [82]. By producing a monodomain, it is possible to measure the electro-mechanical or piezoelectric response. Compression leads to a piezoelectric coefficient parallel to the helical axis. Elongation leads to the perpendicular piezoelectric response. As another example, a network with a chiral smectic C phase that possesses ferroelectric properties can also act as a piezoelectric element [83]. Larger values of this response might be observed if crosslinked in the Sc state. 

Fig. 4.36 Helical structure of the chiral smectic C phase Po is a pitch of the helix...

Like in the nematic phase, the textures of SmC reveal blurred Schlieren patterns with linear singularities of strength s = 1. The singularities of 5 = 1/2 are not observed due to the reduced symmetry (C2h) of the SmC phase. Chiral smectics C are periodic structures and the helical pitch can be measured under a microscope either from the Grandjean lines or as a distance between the lines indicating periodicity, like in Fig. 8.22 for the cholesteric phase. On the other hand, like in... 

The Goldstone mode in an achiral SmC tries to restore the symmetry of the smectic A phase Cooh —> Dooh by free rotation of the director along the conical surface with the smectic layer normal as a rotation axis. Thus, like chiral molecules convert a nematic into a cholesteric, they convert an achiral SmC into chiral SmC without any phase transition. In addition, mixing left (L)- and right (R)-handed additives results in a partial or complete compensation of the helical pitch both in cholesterics and chiral smectic C. For example, the L- and R- isomers of the same molecule taken in the equal amounts would give us a racemic mixture, that is achiral SmC without helicity and polarity. 

Due to low symmetry (C2) of the chiral smectic C phase, its theoretical description is very complicated. Even description of the achiral smectic C phase is not at all simple. In the chiral SmC phase two new aspects are very important, the spatially modulated (helical) structure and the presence of spontaneous polarisation. The strict theory of the SmA -SmC transition developed by Pikin [10] is based on consideration of the two-component order parameter, represented by the c-director whose projections ( 1, 2) = are combinations of the director compo-... 

FIGURE 3 Helically twisted liquid crystalline pha.ses (a) chiral nematic (chole.steric) (b) chiral smectic C. ... 

Zentel, R., Untwisting of the helical superstructure in the cholesteric and chiral smectic C phases of cross-linked liquid-crystalline polymers by strain, Liq. Crvst., 3, 531-536 (1988). 

The form chirahty of all of these chiral smectic mesophases takes the form of a helical stracture, but the helix manifests itself in a different way from the helix in the chiral nematic phase. In addition to being substantially the most commonly exhibited of the tilted chiral smectic phases, the chiral smectic C phase is by far the most important (least ordered and least viscous) in this category. The chiral smectic C phase is employed in the ferroelectric display device (see Chapter 13) but the helix must be unwound. 

The helical smectic A phase can form between the chiral smectic C phase and the isotropic phase [16a] or, alternatively, between the chiral nematic (cholesteric) phase and the isotropic phase [16bj. In the latter case, which was observed for a mixture of cholesteryl nonanoate (a homologue of (l.vii)) with p-nonyloxybenzoic acid, an interesting formal analogy exists between the smectic A phase and Abrikosov s flux lattice in type-II superconductors. 

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