Renormalized One-loop Theory of Correlations in Disordered Diblock Copolymers

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.

16 pages, 13 figures, submitted to J. Chem. Phys

References in corpus (4)

• Intramolecular long-range correlations in polymer melts: The segmental size distribution and its moments
• Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts
• Intramolecular Form Factor in Dense Polymer Systems: Systematic Deviations from the Debye formula
• Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards' field theory

Cited by in corpus (2)

• Universality of Block Copolymer Melts
• Simple Calibration of Block Copolymer Melt Models