Entropic self-assembly of diblock copolymers into disordered and ordered micellar phases

We investigate the self-assembly of an athermal model of AB diblock copolymers into disordered and ordered micellar microphases. The original microscopic lattice model with ideal A strands and self-avoiding B strands is mapped onto a system of ultrasoft dumbbells, with monomer-averaged effective interactions between the centers of mass (CMs) of the two blocks. Extensive Monte Carlo simulations of this coarse-grained model are reported for several length ratios f = L(A)/(L(A) + L(B)) of the two strands of lengths L(A) and L(B). Clear-cut evidence is found for clustering and self-assembly into micelles with a mean aggregation number of n approximately equal 100 beyond a critical micellar concentration (cmc) in the semidilute regime. The cmc is found to decrease with increasing f, as predicted by an analytic calculation based on the random phase approximation. The initially disordered dispersion of polydisperse spherical micelles undergoes a disorder-order transition to a micellar crystal phase at higher copolymer concentrations. The effective pair potential between the micellar CMs is determined by inverting the measured CM-CM pair distribution function and is found to become steeper with increasing density.