Primitive models of chemical association. III. Totally flexible sticky two-point model for multicomponent heteronuclear fixed-chain-length polymerization

Abstract

A multidensity integral-equation theory for polymerization into freely jointed hard-sphere homonuclear chain fluids proposed earlier [J. Chem. Phys. 106, 1940 (1997)] is extended to the case of multicomponent heteronuclear chain polymerization. The theory is based on the analytical solution of the polymer Percus–Yevick (PPY) approximation for the totally flexible sticky two-point (S2P) model of associating fluids. The model consists of an n-component mixture of hard spheres of different sizes with species 2,…,n−1 bearing two sticky sites A and B, randomly distributed on its surface, and species 1 and n with only one B and A site per particle, respectively. Due to some specific restrictions imposed on the possibility of forming bonds between particles of various species, the present version of the S2P model represents an associating fluid that is able to polymerize into a mixture of heteronuclear chain macromolecules. The structural properties of such a model are studied in the complete-association limit and compared with computer-simulation results for homonuclear hard-sphere chain mixtures, symmetrical diblock copolymers, alternating copolymers, and homonuclear hard-sphere chains in a hard-sphere solvent. Some results for the case of partial association are also presented. The PPY theory represents a quantitatively successful theory for the mixtures of short homonuclear chains and the short copolymer systems studied here. We also expect that the theory will prove to be of the same order of accuracy in investigating the case of partial association.