Analysis of Partitioning of Salt through Doping of Polyelectrolyte Complex Coacervates

Doping of salt ions within stoichiometric poly-electrolyte complex coacervates (PECs) is modeled with a theory that includes polymer ion pairing and counterion adsorption as equilibrium reactions along with Flory-Huggins free energy and electrostatic correlations that capture the effects of polyelectrolyte charge connectivity. The model shows at low salt concentration a region in which the salt content in the PEC depends linearly on the salt concentration in the (external) supernatant, consistent with the experimental observations of the Schlenoff group. We find that only in the limit of strong salt ion adsorption are all salt ions in the PEC bound to polyelectrolytes; for binding free energies up to several k(B)T per ion, a significant fraction of the salt ions in the PEC are free (or unbound), even at the lowest salt concentration. When the salt concentration in the supernatant is increased to higher values beyond this linear regime, the PEC strongly swells with water and free salt ions, similar to that observed experimentally. The model also predicts that the partitioning behavior of salt ions into the PEC is primarily governed by ion-specific effects, which manifest themselves in the strength of salt ion adsorption and polyelectrolyte ion-pairing, in agreement with observations of Schlenoff and co-workers. With an appropriate choice of parameters, the theory provides good agreement with experimental doping and phase behavior data in the literature.