Coexistence of Crew-Cut and Starlike Spherical Micelles Composed of Copolymers with an Annealed Polyelectrolyte Block

Abstract

The self-assembly of block copolymer A m B n into spherical micelles is analyzed using a numerical self-consistent-field theory. A is the hydrophilic annealed polyacid and B the hydrophobic part. The degree of polymerization for the polar moiety is fixed ( m = 100), whereas that of the tail is varied ( n = 100, 200, and 300). The charge in the annealed A block depends on both the pH and the added 1:1 electrolyte concentration φ s . Beyond the cmc, the diblock copolymers form either low aggregation number starlike or large aggregation number crew-cut micelles. A nonmonotonic behavior of the micellar properties as a function of φ s for fixed pH is found. For starlike micelles, the scaling of the aggregation number N agg with φ s is in fair agreement with analytical predictions, i.e., N agg ∼ φ s 0.7-0.9 . For the core radius, we find that R core ∼ φ s 0.24-0.3, and for the corona thickness T corona ∼ φ s -0.08 . For crew-cut micelles, the scaling exponents deviate significantly from analytical predictions. Upon increasing pH, a smooth transition from crew-cut to starlike micelles happens at high φ s . Interestingly, a coexistence between these two different micellar sizes is possible for relatively low values of φ s in a narrow pH range. The corresponding thermodynamics, phase diagram, and various structural properties are presented.