Cholesteric helical structure

Because of its correlation with the selective reflection we refer to this feature as reflection Cotton effect or, in short, RCE (Korte and Schrader, 1981). All together, a positive RCE indicates a left-handed cholesteric helical structure also called M helix and, vice versa,a negative RCE indicates a right-handed P helix. The evaluation is summarized in Fig. 4.6-9. 

To obtain the tensor of the cholesteric helical structure one should imagine that the local tensor rotates in the laboratory co-ordinate system, or, alternatively, to introduce a rotating co-ordinate system. In the latter case, one should make transformation... 

For weak anchoring and 0 by analogy with a nematic (see Eq. 10.77), the free energy of the distortion includes the elastic term due to the bend-distortion (we assume K = Kn = K s) and the flexoelectric term with an average coefficient e. The second elastic term is due to the cholesteric helical structure (modulus K22). ... 

The most serious problem with respect to the DHF mode is that the helical structure is unwound and the alignment is deteriorated by applying an electric voltage larger than the saturated voltage. This is different from the cholesteric helical structure which is restored by cutting off the electric field. This phenomenon restricts applications, and, furthermore, is a critical problem from the viewpoint of product quality assurance. 

Under certain conditions, cellulose derivatives possessing the characteristics of cholesteric liquid crystals present cholesteric helical structures dissolution and transition from the cholesteric to the nematic phase [98]. When shear is over, the system is relaxed over a determined time and intense, shifting to a transition state, where the energy of deformation is minimal and the orientation ordering is maintained, causing the appearance of band structures. When the external field is removed, the shear-induced anisotropy is affected by the inevitable relaxation of the macromolecular chains. Structural relaxation after removal of the external field depends on the shear history and relaxation mechanism [99,100]. Moreover, literature suggests a possible competition between the order induced by shear and thermodynamically, and also a correlation between the viscosity peak and the appearance of the anisotropic phase at low shear rates [ 101,102]. 

FIGURE 5.51 The cholesteric phase of a liquid crystal. In this phase, sheets of parallel molecules are rotated relative to their neighbors and form a helical structure. 

Macroscopical helical structures formed by cholesteric liquid crystals have been used as chiral helical media for the asymmetric synthesis of helicenes. 

Several unique optical properties arise from helical structures of cholesteric liquid crystals. 

Electronic displays make use of the fact that the orientation of the molecules in liquid crystals changes in the presence of an electric field. This reorientation causes a change in their optical properties, making them opaque or transparent, and hence forming a pattern on a screen. Cholesteric liquid crystals are also of interest because the helical structure unwinds slightly as the temperature is changed. Because the twist of the helical structure affects the optical properties of the liquid crystal, these... 

According to the helical structure, the cholesteric phase (n ) is optically uniaxial negative, where the ordinary refractive index n0 nt is larger than the extraordinary... 

As is seen from Table 13, cholesteric copolymers display a maximum of selective light reflection ( w) in an IR- or a visible part of the spectrum. By varying the composition of a copolymer, it is possible to vary Xmax, in accordance with the stipulation max = nP, is proportional to the pitch P of the helical structure of a LC polymer (n — is the refractive index). The pitch of the helix in cholesteric copolymers is usually decreased, when the temperature is raised 105) (at temperatures above Tg), which is equally common for low-molecular cholesterics142) (Fig. 23a). The observed fact that the helix pitch for LC copolymers 2.1-2.3 (Table 13, Fig. 23b) is increased, is rather unusual but explicable within the theoretical views regarding vibrational movement of macromolecular fragments and their conformational mobility 60). 

Figure 2.3 Schematic representation of the periodical helical structures of the chiral nematic (cholesteric) phase. The pitch of the helix corresponds to the rotation of the director through 360°. There is no layered structure in a chiral nematic. N. phase.

Twisting a nematic structure around an axis perpendicular to the average orientation of the preferred molecular axes, one arrives at the molecular arrangement commonly called cholesteric (Kelker and Hatz, 1980). The twisted nematic phase is optically uniaxial, however with the axis perpendicular to the (rotating) director. Such a mesophase combines the basic properties of nematics with the implications of chirality The structure itself is chiral and as a consequence, a non-identical mirror image exists as it is shown schematically in Fig. 4.6-7. Besides the order parameters mentioned before, the essential characteristics of a cholesteric mesophase are the pitch, i.e., the period of the helical structure as measured along the twist axis, and its handedness, i.e., whether the phase is twisted clockwise or anticlockwise. 

Cholestogenic compounds (i.e. such which produce cholesteric phases) are optically active, i.e. their molecules are chiral under equivalent conditions the enantiomers form countercurrent, but otherwise identical helical structures. The close relationship of cholesteric and nematic phases is emphasized by the fact that a racemic mixture of cholestogenic compounds does not form a mesophase but a nematic one (Leclercq et al., 1969). A nematic phase can also be formed by mixtures of non-enantiomeric cholesto-gens which tend to form oppositely coiled structures on their own. However, the ratio... 

In Fig. 7 the optical rotatory dispersion (ORD) as well as the circular dichroism (CD) is shown for the right-handed cholesteric liquid crystal. A right-handed helical structure reflects right circularly polarized light and it shows positive optical rotation on the short wavelength side of the reflection band. 

In this liquid crystal phase, the molecules have non-symmetrical carbon atoms and thus lose mirror symmetry. Otherwise optically active molecules are doped into host nematogenic molecules to induce the chiral liquid crystals. The liquid crystals consisting of such molecules show a helical structure. The most important chiral liquid crystal is the cholesteric liquid crystals. As discussed in Section 1.2, the cholesteric liquid crystal was the first discovered liquid crystal and is an important member of the liquid crystal family. In some of the literature, it is denoted as the N phase, the chiral nematic liquid crystal. As a convention, the asterisk is used in the nomenclature of liquid crystals to mean the chiral phase. Cholesteric liquid crystals have beautiful and interesting optical properties, e.g., the selective reflection of circularly polarized light, significant optical rotation, circular dichroism, etc. 

Because of the spontaneously helical structure in the cholesteric liquid crystals, the second term in the integral must be revised to... 

As mentioned in Chapter 1, cholesteric liquid crystals have a helical structure. The helical structure results in unique optical properties, such as selective reflection, circular dichroism, drastic optical activity, and electro-optic effects. 

A lot of biological polymers exhibit cholesteric liquid crystal characteristics as pointed out first by Robinson et al. (1958). The notable examples are RNA and DNA. The well-known double helical structure, shown in Figure 6.25, makes them rod-like in conformation. 

Then the liquid crystalline monomers were polymerized under an ultraviolet irradiation. The system became a cholesteric gel. After heating the sample and removing the chiral molecules CB15, the helical structure remained. In Table 6.10, the cholesteric pitch P and reflective peak wavelength Amax are listed as a function of temperature at which polymerization occurs. The CB15 weighed 28% in the original mixture before the removal. 

Cholesterics (Fig. 2e) are considered a special case of the nematic structure where nematic planes are twisted from one layer to the next forming a helical structure, characterized by its pitch. These are frequently encountered in nature. We consider that the results obtained with nematics are valid for cholesterics. 

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