One and two dimensional macroscopic aggregation of micelles occurs in the presence of multivalent counterions.

In the weak segregation limit, we investigate the surface-induced structures in the body-centered-cubic phase of diblock copolymers. Employing the Landau−Brazovskii mean field theory, we obtain the extent of surface-induced region as a function of temperature and surface field strength. At strong surface field strengthes, the lamellar and cylindrical characters are much more profound, and the surface-induced structure persists to a larger extent. A “phase diagram” of surface reconstructions is constructed, which describes the surface-induced structure. These results demonstrate that the coupling between the local average excess polymer concentration and the surface leads to lamella-like and cylinder-like structures close to the surface. Some of our theoretical results are in agreement with relevant experimental results. Our predictions about these interesting surface-induced structures should be observable in experiments under suitable conditions.

With mean-field dynamic density functional theory, we study the morphologies of sphere-forming diblock copolymers confined between two homogeneous surfaces. The effects of the film thickness and the surface field strength on the phase behavior of sphere-forming copolymer film are investigated. The morphologies deviating from the bulk sphere-forming structure are revealed, including cylinders oriented perpendicular to the surface, cylinders oriented parallel to the surface, perforated lamellae and lamellae by varying the film thickness, and surface field strength. We also construct the phase diagram of surface reconstruction, in which some interesting phase transitions are presented. Besides, we compare the present phase diagram with the relevant phase diagram of cylinder-forming block copolymer film.