Fast Linear-in-Field Rotation of the Cholesteric Helix

1 Fast Linear-in-Field Rotation of the Cholesteric Helix 

This effect is observed in the geometry shown in Fig. 6.7(a) when 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 2 -axis [37, 81, 82]. In this case, the helical structure, even an ideal one, is incompatible with the planar boundary conditions and splayed and bended regions form near the boundaries. Thus, according to (3.19) the flexoelectric polarization arises in those regions which can interact with the electric field. 

In experiment, a deviation of the optical axis in the plane of a cell is observed. The sign and the magnitude of the deviation angle depend on the polarity and strength of the applied field, respectively. In the field-off state the helix is undistorted and the cell behaves like a uniaxial optical plate with the optical axis coincident with h. When the field is applied molecules leave the x, 2 -plane due to the flexoelectric deformation coming from the surface regions where the flexoelectric torque M = CfE (cf = d = 63) is developed. Now the optical axis does not coincide with the initial orientation of the helix h but forms an angle with respect to it, linearly dependent on E. The field-induced distortion of the helix is shown in Fig. 6.21 [81]. 

For director components parallel to the x, y-plane, = cos y , Uy = sin / , the free energy density of the system in an electric field is 

FIGURE 6.21. The pattern of the director rotation induced by an electric field applied perpendicular to the plane of the drawing [81]. Below components of the wave vector k of the distorted hehx. 

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