Renormalized one-loop theory of correlations in disordered diblock copolymers

Abstract

A renormalized one-loop (ROL) theory developed in previous work [P. Grzywacz, J. Qin, and D. C. Morse, Phys. Rev E. 76, 061802 (2007)] is used to calculate corrections to the random phase approximation (RPA) for the structure factor S(q) in disordered diblock copolymer melts. Predictions are given for the peak intensity S(q∗), peak position q∗, and single-chain statistics for symmetric and asymmetric copolymers as functions of χ(e)N, where χ(e) is an effective Flory-Huggins interaction parameter and N is the degree of polymerization. The ROL and Fredrickson-Helfand (FH) theories are found to yield asymptotically equivalent results for the dependence of the peak intensity S(q∗) upon χ(e)N for symmetric diblock copolymers in the limit of strong scattering, or large χ(e)N, but to yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of S(q∗) and a decrease of q∗ for large values of χ(e)N, relative to the RPA predictions, but an enhancement of S(q∗) and an increase in q∗ for small χ(e)N. The decrease in q∗ near the ODT is shown to be unrelated to any change in single-chain statistics, and to be a result of inter-molecular correlations. Conversely, the predicted increase in q∗ at small values of χ(e)N is a direct result of non-Gaussian single-chain statistics.