Cholesterics pitch

Analytical approaches to understanding the effect of molecular flexibility on orientational order have concentrated on both the isotropic-nematic and the nematic-smectic transition [61, 62] and mean field theory has shown that cholesteric pitch appears not to depend on the flexibility of the molecule [63]. 

Figure 6.1 Schematic representation for some different mesophases formed by calamitic meso-gens. P/2 is half of cholesteric pitch.

Figure 6.2 Discotic molecules in a (a) nematic state ND, (b) twisted nematic discotic state Np (P/2 is half of cholesteric pitch), (c) columnar state, ordered D0 and disordered Dd, (d) hexagonal ordered columnar state Dho two-dimensional packing arrays for columnar structures in (e) hexagonal, Colh rectangular, Colr oblique, Col0b.

Another technique widely used to measure the cholesteric pitch is based on the Bragg scattering of monochromatic light (obtained by a helium-neon laser) from fingerprint or planar textures of the cholesteric32 Its angular dependence is strictly related to the cholesteric pitch. 

A quantitative study of the cholesteric induction and of the chiral transfer from dopant to phase requires the definition of the helical twisting power 3. This quantity expresses the ability of a chiral dopant to twist a nematic phase and can be numerically expressed in Eq. (2) where p is the cholesteric pitch, c the dopant molar fraction, and r its enantiomeric excess its sign is taken to be positive or negative for right-handed (P), or left-handed (M) cholesterics, respectively. This relation holds for molar fractions <0.01-0.05 ... 

Werbowyj and Gray (79) examined the relationships between the cholesteric pitch and optical properties of HPC in water, CH3COOH and CH3OH. The reciproc pitch varied as the third power of the HPC concentration. Optical rotatory dispersion results show HPC has a right-handed superhelicoidal structure regardless of structure. As will be discussea below, a change in solvent can reverse the handedness of other cellulose derivatives. 

We have omitted discussing such interesting properties of liquid-crystal solutions as the Frank elastic constants, the Leslie viscosity coefficients, cholesteric pitch, textured structure (or defects), and rheo-optics. Some of them are reviewed in recent literature [8,167], but the level of their experimental and theoretical studies still remains largely qualitative. 

A cholesteric, or chiral nematic (N ) phase. This is a positionally disordered fluid in which the constituent molecules align on average their axes along a common direction called the nematic director. Being the DNA helices chiral, the orientational order develops an additional macro-helical superstructure with the twist axis perpendicular to the local director. The phase thus consists of local nematic layers continuously twisted with respect to each other, with periodicity p/2 (where p is the cholesteric pitch see Fig. 8a) [27,28]. For 150-bp helices, the N phase appears at a concentration around 150 mg/mL in 100 mM monovalent salt conditions. This LC phase is easily observed in polarized optical microscopy. Since the N pitch extends to tens of micrometers (that is, across... 

Schuster et al. reported that the photochromism of a fulgide could change the helical pitch length of a cholesteric liquid crystal. 27 They added an indolylfulgide 3 (5.2 % w/w) to a cholesteric liquid crystal composed of 4-cyano-4 -pentylbiphenyl 26 (5CB) and 1.35 % (w/w) of a chiral cyclic ether (R)- 27, prepared from (R)-binaphthol. The cholesteric pitch length could be changed reversibly between 30 and 42 pm, after UV and visible light irradiation, respectively. 

As an additional remark, the same research group designed a cholesteric network that acted as a humidity sensor, using a derivative of HPC esterified with acryloyl chloride to a low degree of substitution (0.22). The HPC acrylate hydrogel can change the cholesteric pitch, and thereby the reflective color changes with water uptake. 

Fig. 31 a Changes in the cholesteric pitch and ICD intensity of 32-HC1 versus the enantiomeric excess (% ee) of 80 (S rich) in concentrated (20wt%) and dilute (inset, lmgmlr1) water solutions, b Polarized optical micrographs of cholesteric liquid crystalline phases of 32-HC1 (20 wt%) in the presence of 0.001 equivalent of (S)-80 and 5% ee (S rich) of 80 (0.1 equivalent) in water. (Reprinted with permission from [151]. Copyright 2004 American Chemical Society)... 

Experimentally, the cholesteric structure parameters, i.e., pitch and handedness, can be derived from the optical properties of the phase and very specially from its so-called selective reflection. This most striking phenomenon is the reflection of one component of circular polarized radiation in a spectral interval around that wavelength which within the medium matches the cholesteric pitch, i.e. XrIh = i when n denotes the... 

In addition to the rigidity, steric effects and flexibility of side groups seems to Influence the formation and properties of cellulosic mesophases they allow (or not) the existence of a mesophase before crystallization, influence the temperature for onset of a mesophase, and contribute to the value of the cholesteric pitch. 

Microscopical Examination. Solutions were aged at 25 C. A portion of each cellulose solution was carefully placed between a microscope slide and a cover slip and then examined between the crossed polarizers of an Olympus microscope. Model BHSP. Cholesteric pitch sizes were measured from photomicrographs showing the characteristic fingerprint pattern (3). 

Plotting [0] against l/X gives a linear relationship as shown in Figure 12. The values for An were calculated from the slope and the cholesteric pitch and are shown in Table II. An (corrected for cellulose concentration) increased with increasing cellulose concentration and with decreasing NH4SCN content. 

The recent studies on the structure and properties of polypeptide liquid crystals, which are formed in solution as well as in the solid state, are reviewed in this article. Especially the cholesteric pitch and the cholesteric sense (right-handed or left-handed), which are characteristic factors of cholesteric liquid crystals, are discussed in detail in relation to the effects of temperature, concentration, and solvent. Further cholesteric liquid crystalline structure retained in cast fdms and thermotropic mesomorphic state in some copolypeptides are also discussed. 

Cholesteric liquid crystals are similar to smectic liquid crystals in that mesogenic molecules form layers. However, in the latter case molecules lie in two-dimensional layers with the long axes parallel to one another and perpendicular or at a uniform tilt angle to the plane of the layer. In the former molecules lie in a layer with one-dimensional nematic order and the direction of orientation of the molecules rotates by a small constant angle from one layer to the next. The displacement occurs about an axis of torsion, Z, which is normal to the planes. The distance between the two layers with molecular orientation differing by 360° is called the cholesteric pitch or simply the pitch. This model for the supermolecular structure in cholesteric liquid crystals was proposed by de Vries in 1951 long after cholesteric liquid crystals had been discovered. All of the optical features of the cholesteric liquid crystals can be explained with the structure proposed by de Vries and are described below. 

The temperature dependence of the cholesteric pitch in the polypeptide liquid crystals has been investigated in various solvents. The pitch P is related to the twisting angle (p between neighboring molecules separated by a distance d along the axis of torsion as follows. 

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