Viscosity coefficients cholesterics

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. 

The force g normal to the layers will be associated with permeation effects. The idea of permeation was put forward originally by Helfrich to explain the very high viscosity coefficients of cholesteric and smectic liquid crystals at low shear rates (see figs. 4.5.1 and 5.3.7). In cholesterics, permeation falls conceptually within the framework of the Ericksen-Leslie theory > (see 4.5.1), but in the case of smectics, it invokes an entirely new mechanism reminiscent of the drift of charge carriers in the hopping model for electrical conduction (fig. 5.3.8). 

Fig. 9.9 Comparison of the dependencies of the viscosity coefficient on shear rate for the cholesteric and isotropic phases...

In the left part of the figure, the helical axis is parallel to the velocity gradient (shear) shown by two arrows. When cell thickness is less than the cholesteric pitch, d < Pq, and the rate of shear is small, then an effective viscosity is given by averaging two Miesowicz coefficients ... 

The physics of liquid crystals [97] indicate that the viscosity passes through a maximum at the point of tire transition from the isotropic to Ae LC state as a result of ordering of the object and cooperative orientation in flow for nematic systems and a large number of cholesteric systems. The existence of a maximum is usually found in flow of a liquid crystal with an uncontrollable orientation. If the coefficients corresponding to orientation of the macromolecules parallel to the direction of the velocity gradient (%) and parallel to the velocity vector (t] ) are separated out, then a more complex picture is obtained (Fig. 9.23). The maximum in the region of the nematic-isotropic phase transition for p-azoxyanisole is observed for the dependences 11(7) and A break is... 

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