Calculation of static correlations in a fluid of linear molecules

Recently, both X-ray and neutron diffraction data have been obtained for liquid crystalline materials. While these results contain information about the instantaneous correlations of molecular positions and orientations in such fluids, no relevant calculations are available to aid the interpretation of the data. In this paper a formalism which may be used to describe static, molecular correlations in isotropic or anisotropic fluids of linear molecules is developed. To obtain the theory, the direct and total correlation functions of two molecules are expanded as series of spherical harmonics the arguments of which describe the molecular orientations. A relation between the expansion coefficients of these series is obtained by making use of the Ornstein-Zernike equation. It is shown that this equation may be solved in the Percus-Yevick or Optimized-Random-Phase approximations by a variational technique. This technique is used to find the total correlation function in the Percus-Yevick approximation of hard, linear molecules of various length-breadth ratios at several fluid densities.