Mean-field theory of binary mixtures of nematic liquid crystals consisting of biaxial molecules

Binary mixtures of liquid crystals whose constituent molecules are not cylindrically symmetric are considered. For a mixture consisting of biaxial molecules with ${\mathit{D}}_{2\mathit{h}}$ symmetry, two tensor order parameters are required to specify the orientational order of each component. Using mean-field theory, expressions for the free energy of the mixture and the orientational order parameters are obtained as functions of temperature. In the geometric-mean approximation, the parameters of the theory are ratios of anisotropic interaction strengths, which can be determined from measurements on the pure components. The theoretical predictions are compared with recent experimental results of ${}_{}{}^2{}_{}{}^{}\mathrm{NMR}$ measurements on the binary mixture of the liquid-crystal 2-fluorenyl-4’-tetradecyloxy-benzoate-${\mathit{d}}_9$ (${\mathrm{FLOC}}_{14}$) and p-xylene-${\mathit{d}}_{10}$ (p-Xy).