Biaxial liquid crystals cholesteric

The applicability of homotopic theory becomes much less obvious for liquid crystal phases with more complicated order parameters such as biaxial nematics and cholesterics, which are both locally defined by three directors forming a tripod. This gives rise to a description of the line singularities in terms of the quaternion group, Q. This is particularly interesting because the quaternion group Q is non-Abelian, a property that... 

Fig. 4.27 Helical stricture of the ellipsoid of dielectric permittivity for a cholesteric liquid crystal (a very weak biaxiality is determined by component 5e3)...

Finally, we can write the tensors of the orientational order parameter Qy in the rotating frame for locally uniaxial and biaxial cholesteric liquid crystal (ChLC) Uniaxial ChLC ... 

We can also consider the general case of a biaxial cholesteric liquid crystal where fio(0) and yW2(2) are independent. Introducing two new parameters n and 6 defined by... 

As the chirality k increases, both the ratio /ao(0)//A2(2) and the parameter fi of the cholesteric phase at the transition temperature decrease. The difference between the transition temperatures of the biaxial and uniaxial cholesteric liquid crystal is... 

For a pure biaxial cholesteric liquid crystal, (1) calculate the isotropic-cholesteric phase transition temperature, (2) calculate the order parameter as a function of reduced temperature. 

Figure 5-15. Fingerprint texture of a low molar mass liquid crystal with 10% (left) and 80% (right) biaxial cholesteric polymer. Figure reprinted from H. Ogawa, E. Stibal-Fischer, and H. Finkelmann, Macromol. Chem. Phys. 205, 593 (2004) with permission from Wiley-VCH...

Conoscopy provides an extremely sensitive method with which to determine the degree of biaxiality. By the early 1990 s, conoscopic measurements had already indicated the presence of phase biaxiality in a nematic side-on liquid crystalline side-chain polymer [9]. However, the method s sensitivity is also its weak point because surface effects may induce optical biaxiality in an actual uniaxial system. For this reason, deuterium NMR was used to confirm phase biaxiality in a liquid crystalline polymer system similar to the one investigated with conoscopy by Leube [11-13]. Due to the fairly high viscosity of the polymeric samples, the tilt experiment, employed by Yu and Saupe to show phase biaxiality in a lyotropic liquid crystal [4], was used. The results obtained in this way are in good agreement with observations of optical textures in a biaxial cholesteric copolymer [16], where phase biaxiality disturbs the smooth optical periodicity of the cholesteric phase structure. 

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