Crystal stability of diblock copolymer micelles in solution

Abstract

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 copolymers, 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 recent predictions for micelles forming in copolymer melts [G.M. Grason et al., Phys. Rev. Lett. 91, 058304 (2003)].

Keywords:

• diblock copolymers
• micelles
• self-aggregation
• effective potentials

Acknowledgements

JJM would like to thank the EACEA for support provided by an Erasmus Mundus Scholarship during his Master project, BC is supported by an EU Marie Curie Fellowship, and CP thanks Schlumberger Cambridge Research and the Royal Society of London for support during visits to Cambridge.

Notes

1. In order to perform the Fourier integrals in Equation (6), S _dat(k) was determined on a uniform grid by a cubic spline interpolation of the coarser grid of MC data.