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.
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Figure 11. Structure of cholesteric liquid crystals (vibration of molecules represents thermal fluctuations of the director): p is pitch; n is director; χ is helical axis direction |
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.
Although the nematics and cholesterics are similar in their basic structures,
the optical properties of the cholesterics is significantly different due to the
strong twisting. In a certain spectral range, cholesteric phases show a selective
reflection of the circularly polarized light of the same handedness.
The maximum of this reflection is at the wavelength λmax
λmax = p·nave,
where nave is an average refractive index of the colesteric LC, nave2 = (ne2 + 2no2)/3.
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Nematics
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Smectic LCs