Field Untwisting of a Cholesteric Helix

Untwisting of a helix is observed only with positive dielectric anisotropy and only in a field perpendicular to the helical axis. The configuration in Fig. 6.6(b) conforms to this condition for Ae 0. In all other cases the effect is compound a rotation of the helical axis takes place first, and then the untwisting. 

FIGURE 6.14. Schematic representation of the untwisting of a cholesteric helix by a magnetic field. 

The process can be described within the framework of the elasticity theory of cholesterics. Let us start with (2.24) and with an initial helical distribution of the director. The free energy of cholesterics in an electric field is 

The function (f z) should satisfy the condition for minimum i.e., Euler s equation, 

This equation has already been encountered when discussing the Fredericks transition in nematics. Its solution may be expressed in terms of the elliptic function 

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