Theory of Disperse Diblock Copolymers

Abstract

The equilibrium phase behavior of disperse diblock copolymers is studied using the self-consistent field theory. We first examine how dispersity affects the formation of complex spherical phases in conformationally asymmetric diblock copolymers. For disperse diblock copolymers with Poisson and Schulz-Zimm distributions, the Frank-Kasper σ phase appears at a lower degree of conformational asymmetry than what is predicted in monodisperse systems. We next present a general method of treating molecular weight distributions (MWDs) specified by a set of molecular weight fractions in numerical self-consistent field theory. The procedure is applied to MWDs with similar dispersity indices and different skewness obtained from experimental measurements. We find that consistent with experiments, the domain spacing and equilibrium morphology could vary with the skewness. Lastly, we investigate how the MWD shape characterized by the dispersity index and skewness affects the relative stability of complex spherical phases. The predicted set of complex phases could differ between MWDs with identical dispersity indices and different skewness. In particular, it is found that the formation of the C14 and C15 phases is favored for more positively-skewed distributions. Overall, the work underlines the importance of the MWD shape on the phase behavior of disperse diblock copolymers and the need of considering other statistical measures alongside the dispersity index, such as the skewness.