Formation of block copolymer micelles in solution: A Monte Carlo study chain length dependence

Short block copolymers in a selective solvent (bad for A-block, good for B- Mock) are modeled by flexible bead-spring chains, where beads interact with short-range Morse potentials of variable strength. In particular, treating the strength EAA Of attraction between monomers of the A-block as a variab le, we study the mass distribution of the micelles that are formed under co nditions that correspond to the vicinity of the critical micelle concentrat ion (cmc). Choosing a composition f = N-A/N = (1)/(4) for the block copolym ers, we vary their chain length N from N = 4 to N = 32. Only such relativel y short chains can be used in thermal equilibrium, since the relaxation tim es of the system increase dramatically with increasing length. We show that in the regime of parameters accessible to our study, the number of chains per micelle is rather small and almost independent of chain length, implyin g that the core radius scales as N-A(1)/(3) in this regime. We compare our results with existing theoretical predictions and with experiments.