Statistical Theory of Biaxial Nematic and Cholesteric Phases

A statistical theory of biaxial nematic and cholesteric phases is presented. It is derived in the thermodynamic limit at small density and small distortions. The considered phases are composed of short rigid biaxial or less symmetric molecules. The expressions for various macroscopic parameters involve the one-particle distribution function and the potential energy of two-body short-range interactions. The cholesteric phase is regarded as a distorted form of the nematic phase. Exemplary calculations are shown for several systems of molecules interacting via Corner-type potential based on the Lennard-Jones 12-6 functional dependence. The temperature dependence of the order parameters, the elastic constants, the phase twists, the dielectric susceptibilities, and the flexoelectric coefficients are obtained. The flow properties and defects in nematics are also discussed.