Field-Induced Effects and Dynamics

In the purely dielectric interaction picture (i.e., no current flow), the realignment or alignment of a cholesteric liqnid crystal in an applied electric or magnetic field, results from the system s tendency to minimize its total free energy. 

Clearly, the equilibrium configuration of the director axis depends on its initial orientation and the direction of the applied fields, as well as the signs of Ax and Ae. We will not delve into the varions possible cases as they all involve the same basic mechanism that is, the director axis tends to align parallel to the field for positive dielectric anisotropies, and normal to the field for negative dielectric anisotropies. 

In the case of positive dielectric anisotropies, the field-indnced reorientation process is analogous to that discussed for nematics (cf Sect. 3.6). In cholesterics, however, the reahgmnent of the director axis in the direction of the applied field will naturally affect the helical stmcture. 

This process can be described by the firee-energy minimization process. The total free energy of the system is given by 

upon minimization, yields the Euler equation  

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