INTEGRAL-EQUATIONS OF THE CORRELATION-FUNCTIONS FOR POLYMERIC LIQUIDS

The integral equations for intramolecular and intermolecular correlation functions are derived for nonrigid polymeric (polyatomic) liquids by the device of the Kirkwood charging parameters. These integral equations are cast into mean-field-type equations by using the potential elimination method, reported previously for dense simple fluids. Based on the mean-field integral equations, we examine the superposition approximations for various levels of correlation. The present theory provides a means to make systematic corrections for superposition approximations for correlation functions of various orders. Upon using the superposition approximations for the triplet correlation functions in the Kirkwood hierarchy and an assumption or another concerning the charging parameter dependence of the cavity functions, we derive a set of generalized Percus-Yevick and hypernetted chain integral equations for the intramolecular and intermolecular pair correlation functions for beads (sites) of polymeric (polyatomic) liquids. This set of integral equations allows the intramolecular and intermolecular correlation functions to be determined self-consistently. The connection of this set of integral equations to the bead-bead (molecular) Ornstein-Zernike relation is pointed out. The integral equations for the intramolecular correlation functions will be numerically solved for some properties of a single polymer chain in the infinite dilution limit in the sequel to this paper.