Distribution Function Theory of Nematic Liquid Crystals

The method of distribution functions—governed by Kirkwood integral equations—is applied to anisotropic fluids of the nematic type. It is shown how to obtain the self‐consistent‐field theory of Maier and Saupe (assuming their anisotropic dispersion force) with the help of some approximations. When the repulsive forces are included an additional term is present in $\ln {\rho }^{\text{(1)}}{\mathrm{(\theta )[\rho }}^{\text{(1)}}\mathrm{(\theta )\; \equiv }$ orientational distribution function]; estimating this term we conclude that the repulsive force cannot be neglected if $\text{l/d〉2}$ (l and d=molecular length and diameter) and the molecules are not too flexible. Also, the first few terms of Onsager's virial expansion for the free energy are derived.