Renormalized one-loop theory of correlations in polymer blends

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 χ_a that is defined by applying the RPA to the small k limit of S (k). The predicted deviation of χ_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 χ_a N1, but negative (stabilizing) near the critical point. The positive correction to χ_a for low values of χ_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 χ_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.