Renormalized one-loop theory of correlations in polymer blends

Abstract

The renormalized one-loop theory is a coarse-grained theory of corrections to the random phase approximation (RPA) theory of composition fluctuations. We present predictions of corrections to the RPA for the structure function S(k) and to the random walk model of single-chain statics in binary homopolymer blends. We consider an apparent interaction parameter chi(a) that is defined by applying the RPA to the small k limit of S(k). The predicted deviation of chi(a) from its long chain limit is proportional to N(-1/2), where N is the chain length. This deviation is positive (i.e., destabilizing) for weakly nonideal mixtures, with chi(a)N less than or approximately 1, but negative (stabilizing) near the critical point. The positive correction to chi(a) for low values of chi(a)N is a result of the fact that monomers in mixtures of shorter chains are slightly less strongly shielded from intermolecular contacts. The predicted depression in chi(a) near the critical point is a result of long-wavelength composition fluctuations. The one-loop theory predicts a shift in the critical temperature of O(N(-1/2)), which is much greater than the predicted O(N(-1)) width of the Ginzburg region. Chain dimensions are found to deviate slightly from those of a random walk even in a one-component melt and contract slightly as thermodynamic repulsion is increased. Predictions for S(k) and single-chain properties are compared to published lattice Monte Carlo simulations.