Static Theory of Nematics

The static theory of nematic liquid crystals is introduced in this Chapter. Static continuum theory involves two major steps. The first step is to construct an energy based upon possible distortions of the director n, introduced in Chapter 1. The second step is to minimise this energy in some sense, and this leads to equilibrium equations involving n and its derivatives. The solutions of these differential equations yield possible equilibrium orientations for n it is these alignments of n that are the ultimate goal of static continuum theory since they indicate the director alignment within a sample of liquid crystal. The solutions with the least energy are interpreted as the physically relevant ones. 

Liquid crystals in confined geometries are known to be influenced by the orientation of the director at the boundaries. Section 2.6 introduces various ideas on boundary conditions and the concepts of strong and weak anchoring of the director at the boundaries. Finally, Section 2.7 gives a simplifying reformulation of 

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S. Chandrasekhar and N. V. Madhusudana, Molecular Statical Theory of Nematic Liquid Crystals, Acta Cryst., Vol. A27, p. 303 (1971). 

The static theory of nematic and cholesteric liquid crystals employs the unit vector field n, frequently referred to as the director, to describe the mean molecular alignment at a point x in a given sample volume V, Hence... 

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