A continuum theory of disorder in nematic liquid crystals. I

Abstract

An alternative to the Maier-Saupe mean field theory of orientational order in nematics is suggested. It is a theory of disorder rather than order, analogous to the spin-wave theory of ferromagnetism. That is to say, the nematic is treated as a continuum with a perfectly aligned ground state, in which a spectrum of distortion modes involving splay, twist and bend are thermally excited with amplitudes determined by the Frank stiffness constants K 1 , K 2 and K 3 . It is argued that there cannot be more than 2 N independent modes, where N is the number of molecules, and a cut-off is applied to the spectrum accordingly, resembling the cut-off used in the Debye theory of solids. The theory is used to predict values for the con­ventional order parameter S 2 (= < P 2 (cos θ )>) and for higher order para­meters such as S 4 (= <P4(cos θ )>) in terms of K 1 , K 2 and K 3 , and the results agree adequately with experiment. Like the Maier-Saupe theory, the continuum theory suggests a minimum value for S 2 below which the nematic phase cannot be stable or even meta-stable. Refinements that might help to improve the agreement are discussed.