Renormalized one-loop theory of correlations in disordered diblock copolymers

A renormalized one-loop (ROL) theory developed in previous work [P. Grzywacz, J. Qin, and D. C. Morse, Phys. Rev E. 76, 061802 (2007)]10.1103/ PhysRevE.76.061802 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 X _eN, where X_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 X_eN for symmetric diblock copolymers in the limit of strong scattering, or large X_eN, 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 X_eN, relative to the RPA predictions, but an enhancement of S(q) and an increase in q for small X _eN. 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 X _eN is a direct result of non-Gaussian single-chain statistics.