Critical Micelle Concentration of Multiblock Copolymer Micelles in Immiscible Homopolymer Blends

Above the critical micelle concentration (CMC), ternary mixtures of AB block copolymers in an immiscible A/B homopolymer blend produce swollen block copolymer micelles. This problem has been examined in detail for diblock copolymers, but a similar level of understanding for multiblock copolymers is lacking. We will present self-consistent field theory (SCFT) data for the CMC of swollen micelles at intermediate segregation. Increasing the number of blocks decreases the CMC by orders of magnitude, with a non-trivial effect emerging from the even/odd numbers of blocks owing to the entropy of bridge formation. Building on Leibler's theory for the CMC of diblock polymers, we developed a semi-empirical relation that collapses the entire multiblock polymer CMC data set. Moreover, we combined the CMC data with additional SCFT calculations of interfacial adsorption, to predict the maximum achievable reduction in interfacial tension prior to micelle formation. Implications of these results on multiblock compatibilizers will be discussed.