Flexoelectric effects cholesteric helix

Thus, the flexoelectric effect in cholesterics is as fast as the helix untwisting effect. By placing the sample between the cross polarizers and applying... 

Figure 37. An electric field E applied perpendicular to the helix axis of a cholesteric will turn the director an angle ) and thereby the optic axis by the same amount. The director tilt is coupled to the periodic splay—bend director pattern shown below, which is generated in all cnts perpendicular to the new optic axis. In this inverse flexoelectric effect, splay and bend will cooperate if and have the same sign. The relation between E and 0 is shown for a positive helical wave vector k (right-handed helix) and a positive average flexoelectric coefficient e= (Cs+ b)-When the sign ofE is reversed, the optic axis tilts in the opposite direction (0—>-0).

This effect is observed in a geometry where the cholesteric axis h is homogeneously oriented in the plane of the cell (along x) and an electric field is applied to the electrodes of a sandwich cell along the z axis [137,138]. In this case, the helical structure, even the ideal one, is incompatible with the planar boundary conditions, and splayed and bended regions form near the boundaries. Thus, according to Eq. (38), the flexoelectric polarization arises in those regions which can interact with the electric field. The distortion is very similar to that observed in the ferroelectric smectic C phase (see Fig. 24) for a so-called deformed helix ferroelectric effect [139]. 

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