Crystal Stability of Diblock Copolymer Micelles in Solution

Overview & Synopsis

We investigate the relative stability of the disordered phase and of four crystal structures of micelles resulting from the self-assembly of AB diblock copolymers in semi-dilute solutions. Starting from the micelle-micelle pair distribution functions determined previously in the disordered fluid phase by Monte Carlo simulations of a coarse-grained model of diblock polymers, we extract effective pair potentials $v(r)$ between micelle centres of mass by a novel extrapolation/inversion technique. These $v(r)$ are used in extensive Monte Carlo simulations of micellar assemblies to determine the structures, mean-square displacements, and free energies of four ordered phases including FCC, BCC, diamond and the less common A15 crystals. For micelle densities close to melting, we predict the most stable structures to be FCC and A15, with the latter phase having the lowest free energy for micelles with small cores and large coronae, in agreement with a recent prediction for micelles forming in copolymer melts (G.M. Grason et al., Phys. Rev. Lett. 91, 058304 (2003)).