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Micelle formation in block copolymer/homopolymer blends: comparison of self-consistent field theory with experiment and scaling theory

We present a self-consistent field theory (SCFT) study of spherical micelle formation in a blend of poly(styrene-butadiene) diblocks and homopolystyrene. The micelle core radii, corona thicknesses and critical micelle concentrations are calculated as functions of the polymer molecular weights and the composition of the diblocks. Our results are compared with an earlier scaling theory and with X-ray scattering data. The agreement between self-consistent field theory and experiment for the micelle structure is sometimes quantitative and is generally more successful than scaling theory. For copolymers with relatively light core blocks, SCFT predictions for the critical micelle concentration improve over those of scaling theories by an order of magnitude. In the case of heavier core blocks, SCFT predicts the critical micelle concentration less well due to inaccuracies in the modelling of the bulk chemical potential. Overall, we find that SCFT gives a very good description of spherical micelle formation and hence demonstrate that a mean-field, equilibrium approach is valid for these systems.