Formation of a superlattice in mixtures of block copolymer micelles

The formation of a superlattice was observed in a binary solution mixture of diblock copolymer micelles. The larger micelles formed from polystyrene-$b$-polyisoprene (SI) diblocks had an overall radius of 29 nm, and the smaller micelles formed from polystyrene-$b$-polydimethylsiloxane (SD) diblocks had an overall radius of 16 nm. The radius ratio of the micelles was therefore 0.55. By indexing the peaks observed in the scattering pattern from the sample, the structure was assigned to the $Fm\bar {3}c$ space group. The structure is more commonly known in the literature as the binary AB$_{13}$ superlattice. The same lattice was again observed in a similar SI + SD system where the hydrodynamic radii of the bigger and the smaller micelles were 38 and 22 nm, respectively. In this system the size ratio of the micelles was 0.57. Similar to sterically stabilized colloidal hard spheres, the micelles were uncharged and hence the formation of the superlattice was driven solely by free volume entropy.