MULTICOMPONENT HARD-SPHERE HETEROCHAIN FLUID - EQUATIONS OF STATE IN A CONTINUUM SPACE

Simple analytical equations of state have been derived for a mixture of heterochain molecules differing among themselves in both the chain length and primary structure. A model for a polymer chain has been constructed as a sequence of freely jointed tangent hard spheres, whose diameters are not necessarily identical. The statistical mechanical methods previously reported in the literature, namely, a polymeric analog of the Percus-Yevick approximation and the first-order thermodynamic perturbation theory (TPT) of polymerization, have been generalized. According to either of those approaches, the equation of state and residual thermodynamic potentials for the chain fluid are the sum of two terms of which one characterizes a system of disconnected monomers and the other one reflects the effect of monomer bonding in the chain. The specificity of the theories in question shows up in the representation of a second (bonding) term. The quantitative discrepancy in the predictive power of these theories tends to diminish with decreasing packing fraction of the system. As has been found, a version of perturbative theory recently developed by Freed for a homopolymer liquid and the TPT of polymerization lead to essentially the same result in their respective low-order approximations. The general results obtained have been exemplified by a binary copolymer-insolvent system. The copolymer primary structure has been accounted for in the thermodynamic formulas through a weight-average fraction of available chain unit diads, and the chain-length distribution, through a number-average degree of polymerization. Given the packing fraction, the only necessary molecular parameter in the derived expressions is the ratio of hard-sphere diameters for monomer units and the solvent molecules.