Equilibrium theory of polymer liquids: Linear chains

An equilibrium theory of polymer melts, developed previously by us for polymer rings, is generalized to include linear polymer chains. This theory is based on the reference interaction site model (RISM) integral equation approach developed by Chandler and co-workers for molecular liquids. We are able to construct a tractable formalism for the high polymer problem by employing the fact that a polymer molecule in a melt is ideal. This leads to a set of coupled, nonlinear integral equations for the intermolecular radial distribution functions. A simple optimized perturbative scheme is developed for long linear chains based on the relative unimportance of end effects. To lowest order, the theory reduces to a single nonlinear integral equation. Chain end corrections to the site-averaged intermolecular correlation functions vanish according to N−2, where N is the degree of polymerization. Numerical techniques were used to compute the radial distribution function and structure factor for hard core linear Gaussian chains of 16 000 units over a range of densities. Calculation of higher order corrections for end effects is possible with our formalism.