Phase Separation of Polyelectrolytes: The Effect of Charge Regulation

Complex coacervation, known as the liquid-liquid phase separation of solutions with oppositely charged polyelectrolytes, has attracted substantial interest in recent years. We study the effect of charge regulation (CR) mechanism on the complex coacervation, by including short-range interactions between the charged sites on the polymer chains, as well as an association-dissociation energy parameter in the CR mechanism. We investigate the phase diagrams of two CR models: (i)~the hopping CR model (HCR); and, (ii)~the asymmetric CR model (ACR). It is shown that during the phase separation, the polymers in the condensed phase are more charged than in the dilute phase, in accord with the Le Chatelier's principle. In addition, "secondary CR" effects also influence the change in the volume fraction of the two phases. The latter can cause the charge difference between the two phases to change non-monotonically as a function of the CR parameters. These predictions are subject to future experimental verifications.