Ornstein–Zernike equation for the convex molecule fluids

Abstract

Pair distribution functions yield an important information on the structure of fluids. The general form of the Ornstein–Zernike equation which interrelates the total and direct correlation functions of molecular fluids, h(1, 2) and c(1, 2), respectively, is reformulated for systems of convex molecules. An expression is derived which makes it possible to determine the average correlation function as a sole function of the shortest surface–surface distance between hard cores of a pair of studied molecules. For both h and c, the shape effect is separated from the dependence of these functions on distance. As a result, the total correlation function can be determined from an expression, the convolution integral of which comprises the derivative of the cluster integral (related to the third virial coefficient) for three hard convex bodies. Preliminary results for the average correlation function, g^av( = h^av + 1), in the system of hard prolate spherocylinders with the reduced core length L = 0.4 and packing fraction y = 0.3142 are presented; values of g^av compare well with the corresponding simulation data.