Salt partitioning in fully charged polyelectrolyte solutions: bulk thermodynamics and RPA

The formation of complex coacervates and salt partitioning for polyelectrolyte solutions are investigated through bulk thermodynamic and random-phase approximation (RPA) analyses. Our model system consists of fully charged hard sphere polyanions, counterions, uncharged components along with added hard sphere salt. A molecular equation of state is first formulated for those systems based on liquid state theory. Then, RPA analysis is performed via the Gaussian thread approach by taking the equation of state as effective local interactions and adding nonlocal interactions from long-ranged Coulomb potential. It is shown that the bulk thermodynamic calculation predicts salt partitioning between complex coacervate and supernatant phases in agreement with experiments, where the classical Voorn-Overbeek theory fails due to the absence of excluded volume and chain connectivity. We additionally probe the condition for microphase separation by using RPA. The effects of osmotic pressure on salt partitioning phenomena are also considered through both methods.