5. Main types of Liquid Crystals
Chiral molecules cause a twist in the nematic structure. Such a helical phase is called a cholesteric LC. Locally, the cholesterics are very similar to the nematic LCs. They consist of quasi-nematic layers, whose individual directors are turned by a fixed angle on proceeding from one layer to the next (Fig.11). The layers turned by an angle of 2π are equivalent; the distance between these two defines the pitch p of the helical structure.
The free energy density of distortions in cholesterics is given by
where qo = 2π/p corresponds to the intrinsic twist of the system.
In the nematics p can be thought as infinitely large, and, therefore, qo vanishes in
equation for nematics.
λmax = p·nave,
where nave is an average refractive index of the colesteric LC, nave2 = (ne2 + 2no2)/3.