Liquid Crystals

Chapter 4 - Cholesteric, Smectic, and Ferroelectric Liquid Crystals

4.1.   CHOLESTERIC LIQUID CRYSTALS

The physical properties of cholesteric liquid crystals are in almost all aspects similar
to nematics, except that the director axis assumes a helical form (Fig. 4.la) with a
finite pitch p = 2π/q0 . Figures 4.lb and 4.1c show two commonly occurring director
axis alignments: planar twisted and fingerprint, respectively. From this point of view,
we may regard nematics as a special case of cholesterics with p → ∞. Since the optical
property of the nematic, a uniaxial material, is integrally related to the director
axis, the helical arrangement of the latter in a cholesteric certainly introduces new
optical properties, particularly in the propagation and reflection of light from cholesteric
liquid crystal cells. In this section we summarize the main physical properties
associated with the helical structure.

4.1.1   Free Energies

Since the equilibrium configuration of a cholesteric liquid crystal is a helical structure
with a pitch wave vector q0 (q0 = 2π/p0), its elastic free energy will necessarily
reflect the presence of q0. The evolution of a cholesteric to a nematic liquid crystal
may be viewed as the “untwisting” of the helical structure (i.e., the twist deformation
energy is involved). This is indeed rigorously demonstrated in the Frank elastic theory,
1 where consideration of the absence of mirror symmetry in cholesterics results
in the addition of another factor to the twist deformation energy

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