Renormalized One-loop Theory of Correlations in Disordered Diblock Copolymers

A renormalized one-loop theory (ROL) is used to calculate corrections to the random phase approximation (RPA) for the structure factor $\Sc(q)$ in disordered diblock copolymer melts. Predictions are given for the peak intensity $S(q^{\star})$, peak position $q^{\star}$, and single-chain statistics for symmetric and asymmetric copolymers as functions of $χN$, where $χ$ is the 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 $S(q^{\star})$ upon $χN$ for symmetric diblock copolymers in the limit of strong scattering, or large $χN$, but yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of $S(q^\star)$ and a decrease of $q^{\star}$ for large values of $χN$, relative to the RPA predictions, but an enhancement of $S(q^{\star})$ and an increase in $q^{\star}$ for small $χN$ ($χN < 5$). By separating intra- and inter-molecular contributions to $S^{-1}(q)$, we show that the decrease in $q^{\star}$ near the ODT is caused by the $q$ dependence of the intermolecular direct correlation function, and is unrelated to any change in single-chain statistics, but that the increase in $q^{\star}$ at small values of $χN$ is a result of non-Gaussian single-chain statistics.

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