Primitive models of chemical association. IV. Polymer Percus–Yevick ideal-chain approximation for heteronuclear hard-sphere chain fluids

Abstract

We continue here our series of studies in which integral-equation theory is developed and used for the monomer-monomer correlation functions in a fluid of multicomponent freely jointed hard-sphere polymers. In this study our approach is based on Wertheim’s polymer Percus–Yevick (PPY) theory supplemented by the ideal-chain approximation; it can be regarded as a simplified version of Wertheim’s four-density PPY approximation for associating fluids considered in the complete-association limit. The numerical procedure of this simplified theory is much easier than that of the original Wertheim’s four-density PPY approximation, but the degree of accuracy is reduced. The theory can also be regarded as an extension of the PPY theory for the homonuclear polymer system proposed by Chang and Sandler [J. Chem. Phys. 102, 437 (1995)]. Their work is based upon a description of a system of hard-sphere monomers that associate into a polydisperse system of chains of prescribed mean length. Our theory instead directly describes a multicomponent system of associating monomers that form monodisperse chains of prescribed length upon complete association. An analytical solution of the PPY ideal-chain approximation for the general case of a multicomponent mixture of heteronuclear hard-sphere linear chain molecules is given. Its use is illustrated by numerical results for two models of copolymer fluids, a symmetrical diblock copolymer system, and an alternating copolymer system. The comparison with Monte Carlo simulations is given to gauge the accuracy of the theory. We find for the molecules we study here that predictions of our theory for heteronuclear chain systems have the same degree of accuracy as Chang and Sandler’s theory for homonuclear chain systems.