Theory of polyelectrolyte complexation-Complex coacervates are self-coacervates

The complexation of mixtures of cationic and anionic polymers to produce complex-coacervate phases is a subject of fundamental importance to colloid and polymer science as well as to applications including drug delivery, sensing technologies, and bio-inspired adhesives. Unfortunately the theoretical underpinnings of complex coacervation are widely misunderstood and conceptual mistakes have propagated in the literature. Here, a simple symmetric polyelectrolyte mixture model in the absence of salt is used to discuss the salient features of the phase diagram, including the location of the critical point, binodals, and spinodals. It is argued that charge compensation by dimerization in the dilute region renders the phase diagram of an oppositely charged polyelectrolyte mixture qualitatively and quantitatively similar to that of a single-component symmetric diblock polyampholyte solution, a system capable of self-coacervation. The theoretical predictions are verified using fully fluctuating field-theoretic simulations for corresponding polyelectrolyte and diblock polyampholyte models. These represent the first comprehensive, approximation-free phase diagrams for coacervate and self-coacervate systems to appear in the literature.