Spontaneous overcharging of macro-ion complexes

Oppositely charged macro-ions-one of which is flexible and carries a larger total charge than the other-are expected on an energetic basis to a;ssemble into neutral complexes which can aggregate due to attractive (e.g., van der Waals) interactions. We treat in this paper the counter-intuitive appearance of spontaneous overcharging in polyelectrolyte-colloid complexes, a phenomenon which has been observed in experiments and simulations involving flexible chains adsorbing on oppositely charged cores. We show that this overcharging can be accounted for in the Poisson-Boltzmann approximation; within this theory, overcharging is an entropic effect associated with release of the counterions of the highly charged polyelectrolyte chain as it "overwinds" onto the rigid colloidal particle. Increasing the rigidity of the polyelectrolyte chain leads eventually to underhanging of the complex.