Temperature Dependence of the Pitch

The temperature dependence of the pitch can be described with Kimura and coworkers equation [Eq. (5)], and some general conclusions derived. For most systems, polar and steric interactions have to be considered, as for the left-handed twisted structure of CTC/DEME (Fig. 13) or for the right-handed one of 3C1-CTC-DEME (Fig. 14a). Here a break in the pitch versus the temperature curves can be detected, which 

Mono- and disubstituted glycols with alkyl groups 

Substituted glycols with alkyl/acetate groups  

Ethylene glycol monomethyl ether acetate EMMAc 

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By addition of each of several diesters of isosorbide, isomannide, and isoidide to a nematic phase, cholesteric phases can be produced. All compounds exhibit a large twisting power. In the cholesteric phase, helix inversion, large or small temperature-dependencies of the pitch, and broad blue phases were achieved.183... 

The values of (kA/D) and fi obtained from the temperature dependence of the pitch in the EDC-dioxane system show a linear change with the solvent composition in the same manner as the twisting power. For the EDC-m-cresol system which shows a quadratic variation of the twisting power with the solvent composition, a quadratic variation in kA/D and S is also observed. As S is related to the dielectric constant, the variation of the twisting power with solvent composition is related to the change of the dielectric constant with solvent composition in mixed solvents. A linear change of the dielectric constant will occur in the EDC-dioxane system, while a quadratic change will be expected in the EDC-m-cresol system. 

Dependence of pitch on temperature applications to thermography In most pure cholesteric materials, the pitch is a decreasing function of the temperature. An elementary picture of the temperature dependence of the pitch can be given in analogy with the theory of thermal expansion in crystals. " Assuming anharmonic angular oscillations of the molecules about the helical axis, the mean angle between successive layers... 

The strong temperature dependence of the pitch has practical applications in thermography, as was first demonstrated by Fergason. " " The material has to be so chosen that the pitch is of the order of the wavelength of visible light in the temperature range of interest. This is achieved by preparing suitable mixtures. Small variations of temperature... 

The local order in a cholesteric may be expected to be very weakly biaxial. The director fluctuations in a plane containing the helical axis are necessarily different from those in an orthogonal plane and result in a phase biaxiality . Further, there will be a contribution due to the molecular biaxiality as well. It turns out that the phase biaxiality plays a significant role in determining the temperature dependence of the pitch. Goossens has developed a general model taking this into account. The theory now involves four order parameters the pitch depends on all four of them and is temperature dependent. However, a comparison of the theory with experiment is possible only if the order parameters can be measured. 

Various models proposed may not account for all these experimental facts. The Keating [20] and Bottcher [21] evaluation does not account for such a variety of behavior. Goossens [22] proposed the chiral nematic structure as the result of an anisotropic dispersion energy between chiral mesogens, and predicts for thermotropic LCs a pitch that is essentially independent of temperature. Lin-Liu et al. [23] developed a theory that accounts for all the above-stated temperature effects. The temperature dependence of the pitch is determined by the shape and position of the intermolecular potential as a function of the intermolecular twist... 

The propagation of light perpendicular to the optical axis was studied in [21]. For a certain polarization of incident light, the cholesteric phase can be considered as a medium with a periodic gradient of the refractive index. The refractive index changes between and and the period is half of the pitch. The periodicity in the phase and amplitude causes a diffraction of polarized light. This diffraction was used for investigating the temperature-dependence of the pitch. 

Figure 14.12. (a) Temperature-dependence of the pitch for three different a-hydroxy carbon acids (see Figure 14.9) in identical host phases (CDEABr/decanol/water), after [51]. (b) Temperature-dependence of the pitch close to the chiral nematic/lamellar phase transition curve parameter host phase composition wt/wt chiral dopant tomatine. 

Figure 1. Temperature dependence of the pitch of a 1.75 1 by weight mixture of cholesteryl chloride (X = CC, CC) and cholesteryl myristate (X = CH3 COO-, CM) = 42°C.

Although experimentally the pitch dependence is difficult to measure, the temperature dependence of the apparent viscosity indeed was foimd to show oscillating behavior, which is due to the temperature dependence of the pitch. Details of the Leslie and other theories and of the relevant experiments are discussed in the book of Chandrasekhar. ... 

A large number of molecular-statistical theories and models, each of which explains cotain dependences, has been proposed for the theoretical explanation of the temperature dependences of the pitch. The most common dependence of the pitch of the cholestmc helix on the temperature was proposed in [2]. The angular dependence of the potential eno-gy of a chiral molecule in the next molecular field is written as... 

Using Eq. (7.6), it is possible to describe the different temperature dependences of the pitch by defining the relation between (pg and [6, 7,11]. When Uy (pg, the pitch is invCTsely proportional to the absolute temperature. If % and Uy are of the same order of magnitude, then the temperature coefficient of the pitch dPIdT is determined by the ratio of these parameters. 

We will first examine copolymers which form a cholesteric mesophase without elements of layered order. If the cholesteric structure is induced in the nematic mesophase by small amounts of cholesterol-containing units, then the character of the dependence of the pitch on the temperature will only be determined by the value of the angle of twisting of the molecules with respect to each other, and this, as shown, is greater the larger the order parameter S. As a consequence, the temperature dependence of the pitch should be detamined by the temperature dependence of the order parameter 5 in copolymers of nematogenic monomers with small amounts of cholesterol-containing units. 

A different temperature dependence of the pitch is observed for copolymers containing more than 30 mole % cholesterol units. As shown in the preceding... 

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