Salt Partitioning in Complex Coacervation of Symmetric Polyelectrolytes

We perform a general thermodynamic analysis for the salt partitioning behavior in the coexisting phases for symmetric mixtures of polycation and polyanion solutions. We find that salt partitioning is determined by the competition between two factors involving the ratio of the polyelectrolyte concentration in the coacervate phase to that in the supematant phase and the difference in the exchange excess chemical potential Delta mu(ex)-the excess chemical potential difference between PE segments and small ions-between the coexisting phases. The enrichment of salt ions in the coacervate phase predicted by the Voorn-Overbeek theory is shown to arise from its neglect of chain connectivity in the excess free energy which results in Delta mu(ex) = 0 under all conditions. We argue that chain connectivity in general leads to a finite value of Delta mu(ex) which decreases with increasing PE concentration. Explicit calculations using theories that include the chain connectivity correlations-a simple liquid-state theory and a renormalized Gaussian fluctuation theory-show nonmonotonic behavior of the salt-partitioning coefficient (the ratio of salt ion concentration in the coacervate phase to that in the supematant phase): it is larger than 1 at very low salt concentrations, reaches a minimum at some intermediate salt concentration, and approaches 1 at the critical point. This behavior is consistent with recent computer simulation and experimental results.