Polyelectrolyte complex coacervation: Effects of concentration asymmetry

Using a simple liquid-state theory, we study the phase behaviors of concentration-asymmetric mixtures of polycation and polyanion solutions. We construct a three-dimensional (3D) phase diagram in terms of the concentrations of the three independent charged components: polycation, polyanion, and small cation (ρ -ρ -ρ ₊), for a given Bjerrum length. This phase diagram yields rich and complex phase-separation scenarios. To illustrate, we sequentially examine the following three systems that are directly relevant to experiments: a symmetric mixture, an asymmetric mixture with one type of small ions, and an asymmetric mixture with both types of small ions. We re-express the information in the 3D phase diagram using three experimentally more easily controllable parameters-the asymmetry factor r, the initial extra-salt concentration ρ , and the initial polyelectrolyte (PE) concentration ρ of both solutions prior to mixing. We construct three reduced phase diagrams in the ρ -r, r-ρ , and ρ -ρ planes, respectively, and examine the evolution of the volume fraction of the coexisting phases, concentration of the PE and small-ion species in each phase, and the Galvani potential Ψ , as functions of these experimental controlling parameters. We rationalize our findings in terms of the key thermodynamic factors, namely, the translational entropy of the small ions, the electrostatic correlation energy, and the requirement for charge neutrality.