Optimized cluster theory of structurally symmetric polymer blends

Abstract

The thermodynamic properties of model structurally symmetric polymer blends were calculated using a recently developed theory that is a generalization of the optimized cluster theories for atomic mixtures and single component molecular systems. Within this approach, cluster expansions for the Helmholtz free energy and pair correlation functions were developed for a mixture of polymer chains modeled using the interaction site formalism. A series of topological reductions was then performed to render an approximate expression for these quantities. The theory was previously shown to be equivalent to a set of diagrammatically proper integral equations. The critical temperature was determined to scale linearly with chain length in agreement with neutron scattering measurements and computer simulations. The critical temperature was also found to be suppressed with respect to the mean-field value due to composition fluctuations. The effective interaction parameter, χs, at the critical composition was well represented by the functional form, χs=A/T+B, where A and B are constants that depend on the chain length and total segment density. Deviations from random mixing were found to extend well beyond monomeric length scales and increased substantially as the critical temperature was approached.