General weak segregation theory with an application to monodisperse semi-flexible diblock copolymers

Abstract

A general theory has been developed for a polydisperse semi-flexible multi-block copolymer melt. Using the Bawendi–Freed approach to model semi-flexible chains, an expression for the Landau free energy is derived in the weak segregation regime, which includes density and orientation order-parameters. The orientation order-parameter is described in the smectic phase and in more complicated structures, such as the hexagonal phase. The Landau free energy contains contributions of two kinds of interactions. The first kind is the Flory–Huggins interaction, which describes the incompatibility of chemically different blocks and may induce microphase separation. The second kind is the Maier–Saupe interaction, which may induce nematic ordering. In the framework of the weak segregation limit, the Landau theory allows us to predict phase structures in the melt as a function of the composition, persistence length, and the strength of the Flory–Huggins and Maier–Saupe interaction. The general theory is applied to a simple system of monodisperse semi-flexible diblock copolymers. In several phase diagrams, a number of possible phase structures are predicted, such as the bcc, hexagonal, smectic-A, smectic-C, and nematic phase. The influence of the Maier–Saupe interaction on the microphase structure is thoroughly discussed.