Micelles of diblock copolymers with charged and neutral blocks: Scaling and mean-field lattice approaches

Polymer micelles composed of block copolymers with one charged and one neutral block in aqueous salt free solution are analyzed by scaling and mean-field lattice theory. We study the micellar structure as a function of the length of the both blocks and the fractional charge of the hydrophilic block. The diagram of the different regimes of the behavior of the equilibrium micellar sizes is constructed. The distribution of the counterions in the system is examined using the scaling and the mean-field approaches. The numerical mean-field results are found to be consistent with three scaling regimes:  a quasineutral at small fractional charge, the “Pincus” regime where the Coulomb interaction in the corona is unscreened since the counterions are located outside the corona region, and an osmotic regime where the Coulomb interactions are screened by counterions located in the corona region.