Multiscale coarse graining of diblock copolymer self-assembly: from monomers to ordered micelles

Starting from a microscopic lattice model, we investigate clustering, micellization, and micelle ordering in semidilute solutions of AB diblock copolymers in a selective solvent. To bridge the gap in length scales, from monomers to ordered micellar structures, we implement a two-step coarse-graining strategy, whereby the AB copolymers are mapped onto ultrasoft dumbells with monomer-averaged effective interactions between the centers of mass of the blocks. Monte Carlo simulations of this coarse-grained model yield clear-cut evidence for self-assembly into micelles with a mean aggregation number n approximately 100 beyond a critical concentration. At a slightly higher concentration the micelles spontaneously undergo a disorder-order transition to a cubic phase. We determine the effective potential between these micelles from first principles.