A Molecular Thermodynamic Model of Complexation in Mixtures of Oppositely Charged Polyelectrolytes with Explicit Account of Charge Association/Dissociation

Into an extended Voorn-Overbeek (EVO) free energy model of polyelectrolyte (PE) complexation and phase behavior, we incorporate three classes of short-ranged electrostatic effects, namely counterion association dissociation, cross-chain ion pairing (IP), and charge regulation by treating each as a reversible chemical reaction leading to a corresponding law of mass action in a self-consistent fashion. The importance of each reaction is controlled by a corresponding chemistry dependent standard free energy input parameter. Our model also accounts for Born (or ion solvation) energy using a linear mixing rule for the effective dielectric constant. In monophasic systems, the proposed model can qualitatively explain the observed shifts in acidity and basicity observed in potentiometric titration of weak PEs in the presence of salt and oppositely charged PEs in accordance with Le Chatelier's principle. We demonstrate how a competition between counterion condensation (CC) and IP alone can explain the complex coacervation of strongly charged PEs as well as the existence of a critical salt concentration. Binodal diagrams predicted in our model are also affected by long-ranged electrostatics and are most sensitive to IP strength both for weak and strong PEs. The extent of IP increases in the dense phase at the expense of reduced CC upon coacervation consistent with counter release view of complex coacervation. We compare binodal diagrams predicted by our model against experimental data for both weakly and strongly dissociating polyions pairs and find a plausible parameter set that leads to an acceptable and partial agreement with experiments in the two cases, respectively.