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. We then make a parameter-free comparison of our results with an earlier scaling theory and X-ray scattering data. For the micelle core radii R, we find that SCFT reproduces the shape of the variation of R with different molecular parameters much more accurately compared to scaling theory, though, like scaling theory, it overestimates R by about 20-30%. For the corona thickness L, the accuracy of our SCFT results is at least as good as that of scaling theory. For copolymers with lighter 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, however, SCFT predicts the critical micelle concentration less well due to inaccuracies in the modeling of the bulk chemical potential. Overall, we find that SCFT gives a good description of spherical micelle formation and is generally more successful than scaling theory.