Ordered phases of diblock copolymers in selective solvent

The authors propose a mean-field model to explore the equilibrium coupling between micelle aggregation and lattice choice in neutral copolymer and selective solvent mixtures. They find both thermotropic and lyotropic transitions from face-centered cubic to body-centered cubic ordered phases of spherical micelles, in agreement with experimental observations of these systems over a broad range of conditions. The stability of the nonclosed packed phase can be attributed to two physical mechanisms: the large entropy of lattice phonons near crystal melting and the preference of the intermicelle repulsions for the body-centered cubic structure when the lattice becomes sufficiently dense at higher solution concentrations. Both mechanisms are controlled by the decrease of micelle aggregation and subsequent increase of lattice density as solvent selectivity is reduced. These results shed new light on the relationship between micelle structure-"crewcut" or "hairy"-and long-range order in micelle solutions.