Polymer reference interaction site model theory: New molecular closures for phase separating fluids and alloys

Abstract

The polymer reference interaction site model integral equationtheory when combined with known atomic‐like closure approximations is shown to be qualitatively inconsistent with classical mean field predictions for both long wavelength concentration fluctuations and the molecular weight dependence of the critical temperature of binary polymer blends. The fundamental error is shown to arise from the failure of atomic‐like closures to explicitly account for strong correlations between the segments on two interpenetrating polymer coils which are close in space but widely separated in chemical sequence. A family of new ‘‘molecular’’ closures are formulated which explicitly account for chemical‐bonding mediated correlations. These new closures are all qualitatively consistent with mean field scaling of the critical temperature with chain length. A detailed analytical derivation of the predictions of the new closures for thread‐like symmetric blends is carried out, and the influence of density and concentration fluctuations on the effective chi parameter, small angle neutron scattering profiles, and phase behavior are determined. Qualitative agreement with recent computer simulations is demonstrated. Generalization and/or application of the new molecular closures to treat strongly interacting fluids, soft repulsive force liquids, the liquid‐vapor transition, and polymer‐solvent demixing are also presented.