Salting-Out and Salting-In of Polyelectrolyte Solutions: A Liquid-State Theory Study

We study the phase behavior of polyelectrolyte (PE) solutions with salt using a simple liquid-state (LS) theory. This LS theory accounts for hard-core excluded volume repulsion by the Boublik-Mansoori-Carnahan-Starling-Leland equation of state, electrostatic correlation by the mean-spherical approximation, and chain connectivity by the first-order thermodynamic perturbation theory. We predict a closed-loop binodal curve in the PE concentration-salt concentration phase diagram when the Bjerrum length is smaller than the critical Bjerrum length in salt-free PE solution. The phase-separated region shrinks with decreasing Bjerrum length, and disappears below a critical Bjerrum length. These results are qualitatively consistent with experiments, but cannot be captured by the Voorn-Overbeek theory. On the basis of the closed-loop binodal curve and the lever rule, we predict three scenarios of salting-out and salting-in phenomena with addition of monovalent salt into an initially salt-free PE solution. The Galvani potential-the electric potential difference between the coexisting phases-is found to depend nonmonotonically on the overall salt concentration in some PE concentration range, which is related to the partition of the co-ions in the coexisting phases. Free energy analysis suggests that phase separation is driven by a gain in the electrostatic energy, at the expense of a large translational entropy penalty, due to significant counterion accumulation in the PE-rich phase.