INTEGRAL-EQUATIONS OF THE CORRELATION-FUNCTIONS FOR POLYMERIC LIQUIDS

The integral equations for intramolecular and intermolecular correlati on functions are derived for nonrigid polymeric (polyatomic) liquids b y the device of the Kirkwood charging parameters. These integral equat ions are cast into mean-field-type equations by using the potential el imination method, reported previously for dense simple fluids. Based o n the mean-field integral equations, we examine the superposition appr oximations for various levels of correlation. The present theory provi des a means to make systematic corrections for superposition approxima tions for correlation functions of various orders. Upon using the supe rposition approximations for the triplet correlation functions in the Kirkwood hierarchy and an assumption or another concerning the chargin g parameter dependence of the cavity functions, we derive a set of gen eralized Percus-Yevick and hypernetted chain integral equations for th e intramolecular and intermolecular pair correlation functions for bea ds (sites) of polymeric (polyatomic) liquids. This set of integral equ ations allows the intramolecular and intermolecular correlation functi ons to be determined self-consistently. The connection of this set of integral equations to the bead-bead (molecular) Ornstein-Zernike relat ion is pointed out. The integral equations for the intramolecular corr elation functions will be numerically solved for some properties of a single polymer chain in the infinite dilution limit in the sequel to t his paper.