Association of ionized polymer micelles with oppositely charged polyelectrolytes

We consider the equilibrium structure of the complex formed by an ionized s tarlike polymer micelle with oppositely charged polyion. The charges on bot h the micelle and polyion are quenched, and the complex is immersed in a sa lt-free aqueous solution. Analytical and numerical self-consistent-field (S CF) models are employed to describe the properties of such a complex. Our f indings indicate that the micelle-polyion complex is essentially electroneu tral as a whole and that the polyion replaces almost all small counterions within the micelle corona. The structure of the complex is governed by the effective second and third virial coefficients of monomer-monomer interacti ons and is much more compact than original ionized micelle. Furthermore, th e structure of the complex is predicted to be insensitive to the molecular weight of the polyion. The effective virial coefficients can be mediated by variations in the solvent quality, the degree of ionization, and the incom patibility of the branches of the micelle and polyion. We derive the diagra m of the states of the complex and delineate the range of its thermodynamic stability. The results of numerical SCF calculations are in reasonable agr eement with the analytical predictions. It is also found that the detailed distribution of the polyion charge has only a minor effect on the overall s tructure of the complex.