Integral equation for the angular distribution function of an anisotropic fluid taking account of short-range order in a quasichemical approximation

An integral equation for the one-particle angular distribution function of nonspherical molecules is formulated on the basis of the thermodynamically closed system of equations obtained earlier for the occupation numbers of a multicomponent mixture of molecules with internal degrees of freedom. It is shown that this equation goes over into a known equation of Vlasov-Onsager type for large coordination numbers (for strongly elongated molecules), and yields a known rigorous result which does not contain a phase transition into the anisotropic state in the one-dimensional case. The criterion for such a transition is formulated in the form of an eigenvalue problem for the kernel of the equation obtained. In the case of single-axis molecules, an explicit expression is given for its kernel which takes account of the anisotropy in both the attraction and repulsion as well as the finite compressibility of the substance. For a binary liquid-crystal mixture, an equation is obtained in explicit analytic form within the framework of the XYZ-model for the transition line of an isotropic fluid (IF) into a nematic liquid crystal (NLC), which agrees with experiment for individual NLC. Formulas are hence obtained for a computation of the parameters of the interaction anisotropy in terms of the IF-NLC transition line parameters, and also specific results for para-azoxyanisole (PAA). © 1978 Plenum Publishing Corporation.