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Microscopic expressions for the elastic constants of binary liquid crystalline mixtures composed of short rigid uniaxial molecules are derived in the thermodynamic limit at small distorsions and a small density. Uniaxial and biaxial nematic phases are considered. The expressions involve the one-particle distribution functions and the potential energy of two-body short-range interactions. The theory is used to calculate the phase diagram of a mixture of rigid prolate and oblate molecules. The concentration dependence of the order parameters and the elastic constants are obtained. The possibility of phase separation is not investigated.

Elastic Constants of Binary Liquid Crystalline Mixtures