A systematic coarse-graining strategy for semi-dilute copolymer solutions: from monomers to micelles.

A systematic coarse-graining procedure is proposed for the description and simulation of AB diblock copolymers in selective solvents. Each block is represented by a small number, n(A) or n(B), of effective segments or blobs, containing a large number of microscopic monomers. n(A) and n(B) are unequivocally determined by imposing that blobs do not, on average, overlap, even if complete copolymer coils interpenetrate (semi-dilute regime). Ultra-soft effective interactions between blobs are determined by a rigorous inversion procedure in the low concentration limit. The methodology is applied to an athermal copolymer model where A blocks are ideal (theta solvent), B blocks self-avoiding (good solvent), while A and B blocks are mutually avoiding. The model leads to aggregation into polydisperse spherical micelles beyond a critical micellar concentration determined by Monte Carlo simulations for several size ratios f of the two blocks. The simulations also provide accurate estimates of the osmotic pressure and of the free energy of the copolymer solutions over a wide range of concentrations. The mean micellar aggregation numbers are found to be significantly lower than those predicted by an earlier, minimal two-blob representation (Capone et al 2009 J. Phys. Chem. B 113 3629).