Renormalized One-loop Theory of Correlations in Disordered Diblock Copolymers

TL;DR

This paper develops a renormalized one-loop theory to improve predictions of the structure factor in disordered diblock copolymer melts, revealing new behaviors near the order-disorder transition and for asymmetric compositions.

Contribution

The paper introduces a renormalized one-loop theory that refines the random phase approximation for diblock copolymers, providing new insights into correlation effects and structure factor predictions.

Findings

ROL and FH theories are asymptotically equivalent at large χN for symmetric copolymers.

ROL predicts suppression of S(q*) and decrease of q* at large χN.

At small χN, ROL predicts enhancement of S(q*) and increase of q*.

Abstract

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 $\chi N$, where $\chi$ 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 $\chi N$ for symmetric diblock copolymers in the limit of strong scattering, or large $\chi N$, 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 $\chi N$, relative to the RPA predictions, but an enhancement of $S(q^{\star})$ and an increase in $q^{\star}$ for small $\chi N$ ($\chi N < 5$). 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 $\chi N$ is a result of non-Gaussian single-chain statistics.