Cholesteric 472 INDEX

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). 

Both with thermotropics and lyotropics, a large number of properties can be studied. For example, NMR can be used to obtain the order parameter of the cholesteric phase (2 ). Rheooptic studies (27) (for example, the variation of the refractive index under shear) describe the way cholesteric phase reorganizes to nematic after orientation by a strong shear. 

Other methods. In addition to the systems mentioned above, there are many others. Commonly encountered ones include optical methods in which the index-of-refraction variation is determined and, from this, the temperature and liquid-crystal or other contact thermographic methods in which the color of cholesteric liquid crystals or thermally sensitive materials are determined by the temperature. 

Fig. 4.1.4. Reflexion coefficient at normal incidence versus wavelength for a non-absorbing cholesteric (a) semi-infinite medium, b) film of thickness 25P, where P is the pitch. Curves are derived from the dynamical theory circles represent values computed from the exact theory ( 4.1.3) assuming that the medium external to the cholesteric (e.g., glass) has a refractive index 1.5. The parameters used in the calculations are n = 1.5, Sn = 0.07, X = nP = 0.5 /on. (After reference 21.)...

Figure 3. Schematic representation of the cholesteric liquid-crystalline structure of cellulosics P=Xjn where P represents the pitch, A the reflection wavelength, and n the mean refractive index of a sheet. P>0 for a right-handed twist, and P<0 for a left-handed twist.

For cholesteric liquid crystals, the wavelength of selective light reflection Xj is related to the pitch of the cholesteric helix P in the following manner Xj =nP, where n is the refractive index. It is evident that for a cholesteric mesophase with selective reflection of the... 

Many cellulose derivatives form lyotropic liquid crystals in suitable solvents and several thermotropic cellulose derivatives have been reported (1-3) Cellulosic liquid crystalline systems reported prior to early 1982 have been tabulated (1). Since then, some new substituted cellulosic derivatives which form thermotropic cholesteric phases have been prepared (4), and much effort has been devoted to investigating the previously-reported systems. Anisotropic solutions of cellulose acetate and triacetate in tri-fluoroacetic acid have attracted the attention of several groups. Chiroptical properties (5,6), refractive index (7), phase boundaries (8), nuclear magnetic resonance spectra (9,10) and differential scanning calorimetry (11,12) have been reported for this system. However, trifluoroacetic acid causes degradation of cellulosic polymers this calls into question some of the physical measurements on these mesophases, because time is required for the mesophase solutions to achieve their equilibrium order. Mixtures of trifluoroacetic acid with chlorinated solvents have been employed to minimize this problem (13), and anisotropic solutions of cellulose acetate and triacetate in other solvents have been examined (14,15). The mesophase formed by (hydroxypropyl)cellulose (HPC) in water (16) is stable and easy to handle, and has thus attracted further attention (10,11,17-19), as has the thermotropic mesophase of HPC (20). Detailed studies of mesophase formation and chain rigidity for HPC in dimethyl acetamide (21) and for the benzoic acid ester of HPC in acetone and benzene (22) have been published. Anisotropic solutions of methylol cellulose in dimethyl sulfoxide (23) and of cellulose in dimethyl acetamide/ LiCl (24) were reported. Cellulose tricarbanilate in methyl ethyl ketone forms a liquid crystalline solution (25) with optical properties which are quite distinct from those of previously reported cholesteric cellulosic mesophases (26). 

The semi-infinite structure is assumed, bordered at the front plane by a dielectric of the same refractive index as the average refractive index of the cholesteric . In such a case, we neglect the reflection from the front boundary. 

Let both the helical axis and the electric field are parallel to the normal z of a cholesteric liquid crystal layer of thickness d and >0. In the case of a very weak field the elastic forces tend to preserve the original stack-like arrangement of the cholesteric quasi-layers as shown in Fig. 12.15a. On the contrary, in a very strong field, the dielectric torque causes the local directors to be parallel to the cell normal, as shown in Fig. 12.15c. At intermediate fields, due to competition of the elastic and electric forces an undulation pattern appears pictured in Fig. 12.15b. Such a structure has two wavevectors, one along the z-axis (nld) and the other along the arbitrary direction x within the xy-plane. The periodicity of the director pattern results in periodicity in the distribution of the refractive index. Hence, a diffraction grating forms. Let us find a threshold field for this instability. 

Eigenmode 4 is also right-handed circularly polarized but propagates in the + z direction with the same refractive index. In the above calculation, the higher-order terms 8 / [8a (a + y/e) y/f and / [8a (a - v ) y ] are kept because they are important in calculating the optical rotatary power of the cholesteric hquid crystal. 

Outside the cholesteric cell, the medium is an isotropic medium with the refractive index rig. On top of the Ch film (incident side), there is incident hght and reflected light, and the actual Berreman vector is the sum of the Berreman vectors of the incident light and reflected light. From Equation (3.166) we know that for the incident Ught, the Berreman vector is... 

Cell thickness-dependence of the reflection of a cholesteric liquid crystal in the planar state. The pitch of the liquid crystal is P = 350 nm. The refractive indices of the liquid crystal are tig = 1 -7 and = 1.5. The liquid crystal is sandwiched between two glass plates with the refractive index = 1.6. The incident light is circularly polarized with the same helical handedness as the liquid crystal. Neglect the reflection from the glass-air interface. Use two methods to calculate the reflection spectrum of the liquid crystal with the following cell thicknesses P, 2P, 5P and lOP. The first method is the Berreman 4x4 method and the second method is using Equation (2.186). Compare the results from the two methods. 

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