Cholesteric order

Experimental evidence was reported for the existence of various additional phases a pre-cholesteric order in the form of a network of double-twisted cylinders, analogous to the thermotropic blue phases [27], a hexatic phase that replaces the hexagonal columnar in very long DNA fragments [31], and a structure with orthorhombic symmetry appearing in the transition to crystalline order [27]. 

Fig. 12.25. Structure of liquid crystalline polymers showing (a) nematic, (b) smectic, and (c) cholesteric orders.

Kimura, H. Hosino, M. Nakano, H. Statistical theory of cholesteric ordering in hard-rod fluids and liquid crystalline properties of polypeptide solutions. J. Phys. Soc. Jpn. 1982, 51 (5), 1584-1590. 

Osipov, M.A. Theory for cholesteric ordering in lyotropic liquid crystals. Nuovo Cimento della Societa Italiana di Fisica, D. Condensed Matter, Atomic. Molec. Chem. Phys. Fluids, Plasmas, Biophys. 1988, lOD (11), 1249-1262. 

Hibert and Solladie obtained 0.43% ee of ( + )-hexahelicene(21). More importantly, they found a measurable ee when the solvent pitch approaches infinity. These results indicate chat cholesteric order does influence the motions which lead from reactant to product (probably by affecting the equilibrium between the reactant conformations) but that oven nematic-like order, when combined with molecular asymmetry, can alter the balance between enantiomeric rate processes. Additionally, a part of the ee may arise from the partial circular polarization of the excitation light which results from selective reflection of one light component at the cholesteric surface. 

In each of the above experiments, the rotation of plane polarized light by the products allows very small enantiomeric excesses to be detected with excellent precision. In other cases, where the methods of detection are less precise, no Influence of cholesteric order on reaction dynamics is discernible (although they may be present)(23). 

In contrast, the very significant difference between activation parameters for pyrene-CA exclplex formation in cholesteric and Isotropic CM is compatible with the geometric requirements for exclplex formation the bulky exclplex must disturb cholesteric order, thus increasing the entropy of activation to displace ordered solvent molecules during exciplex formation, energy additional to that required in the isotropic phase must be infused. 

PBLG prepared via bacterial methods can form smectic liquid crystalline phases, while ordinary polydisperse PBLG exhibits nematic columnar, and cholesteric order in films and in solution. 

The concept of OP space helps us to analyze complicated configurations of the cholesteric order parameter even when these configurations are topologically trivial, i.e., equivalent to an undistorted cholesteric or nematic. 

Figure 22. The distribution of directors along circular cylinders, within a left-handed cholesteric phase the cylinder axis corresponds in (b) and (c) to the core of a screw dislocation, (a) The cholesteric order is perfect and the cylinder is cut along a generator, to be developed into a planar rectangle ABA B represented in (a ), the drawing corresponding to the external view of the cylinder.

In the storage effect/ on the other hand, a write mode is obtained below the dielectric relaxation frequency. This is a hydrodynamically produced turbulent flow that disturbs the (cholesteric) order. An erase mode is produced at high frequencies, where the ordered structure is restored by dielectric reorientation forces. 

Maret, G., Milas, M., and Rinaudo, M., 1981, Cholesteric order in aqueous solutions of the polysaccharide xanthan. Polymer Bull., 4 291. 

Figure 2.7. State diagram of a three-dimensional system, a - isotropic (I) state b - transition to the cholesteric ordering c - cholesteric (Ch) state d - transition to nematic ordering e - nematic (N) state - stable state, o - unstable state...

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