Statistical theory of elastic constants of biaxial nematic liquid crystals

Microscopic expressions for the elastic constants of liquid crystals composed of biaxial or uniaxial molecules are derived in the case of a weak anchoring, small distortions, and a small density. Both biaxial and uniaxial phases are considered. The expressions involve the one-particle distribution function and the potential energy of two-body short-range interactions. The theory was used to calculate the temperature dependence of the elastic constants for a system of rigid molecules similar to elipsoids with three different axes.