Coupling chiral nematics

Other more exotic types of calamitic liquid crystal molecules include those having chiral components. This molecular modification leads to the formation of chiral nematic phases in which the director adopts a natural helical twist which may range from sub-micron to macroscopic length scales. Chirality coupled with smectic ordering may also lead to the formation of ferroelectric phases [20]. 

External field distortions in SmC and chiral SmC phases have been investigated [38], but the large number of elastic terms in the free-energy, and the coupling between the permanent polarization and electric fields for chiral phases considerably complicates the description. In the chiral smectic C phase a simple helix unwinding Fr6ede-ricksz transition can be detected for the c director. This is similar to the chiral nematic-nematic transition described by Eq. (83), and the result is identical for the SmC phase. Indeed it appears that at least in interactions with magnetic fields in the plane of the layers, SmC and SmC phases behave as two dimensional nematics [39]. 

For a chiral nematic with positive dielectric anisotropy and an electric field E orthogonal to the helix axis (z), then we observe a chiral nematic to unwound nematic transition for d >p. The analysis [132,139] of the unwinding mechanism is exactly the same as for the magnetic field case with the coupling -YiAxin H) replaced by - AnAe n E) in the free energy density expression. The equilibrium condition (see Eq. 127) or Euler s equation then becomes... 

Figure 37. Schematic diagram of a twisted nematic electrooptic cell for (a) zero voltage and (b) a voltage above threshold, V,h(TN). Note that some chiral nematic mesogens remain anchored in a planar arrangement on the alignment surface, which then provides the coupling for the field-off decay back to the twisted structure. The weak chiral nature prevents back flow.

---