Critical Micelle Concentration of Multiblock Copolymers 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 micelles. This process has been examined in detail for diblock copolymers, but a similar level of understanding for multiblock copolymers is lacking. To this end, we present self-consistent field theory (SCFT) data for the CMC of swollen micelles at an intermediate segregation strength. Increasing the number of blocks at a constant block degree of polymerization decreases the CMC by orders of magnitude, with a nontrivial 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 copolymers, we developed a semiempirical relation that collapses the entire multiblock polymer CMC data set. Moreover, combining the CMC data with SCFT calculations of interfacial adsorption leads to predictions for the minimum achievable interfacial tension prior to micelle formation. These results set thermodynamic bounds for the use of multiblock compatibilizers.