A theory of swollen hollow micelles of diblock copolymers in selective solvents

Micellization behavior of diblock copolymers in selective solvent near the critical micelle temperature (c.m.t.) is theoretically studied focusing our attention to that the core must be swollen with the solvent near c.m.t. Supposing a micellar solution of core–corona type spherical micelles with swollen hollow cores, we calculate the association number distribution and the micelle structure at equilibrium in terms of controlling parameters, i.e. intrinsic interfacial tensions (γ_eff0 and γ_AS0) for core/corona and core/solvent interfaces, and core-segment/solvent interaction parameter χ_AS. Infinitely-large micelle region (ILM-Region), where the micelle size is divergent, is found at smaller values of γ_AS0 and χ_AS other than micelle and unimer regions. In the micelle region near ILM-Region, the micelle size and the degree of swelling become extremely large as ILM-Region is approached, while the micelles become very compact far away from ILM-Region. By investigating the micellar behavior with increasing the association strength on a particular trace in the χ_AS−γ_eff0−γ_AS0 space, it is demonstrated that large swollen hollow micelles are easily formed near c.m.t., and then sharply change to be more compact micelles with decreasing solvent quality to core blocks. This is exactly similar to the so-called anomalous micellization experimentally observed near c.m.t.