Phase behavior of polyelectrolyte solutions with salt

We have computed the phase diagrams of solutions of flexible polyelectrolyte chains with added simple electrolytes. The calculations are based on our recent theory [M. Muthukumar, Macromolecules 35, 9142 (2002)], which accounts for conformational fluctuations of chains, charge density correlations arising from dissolved ions, hydrophobic interaction between polymer backbone and solvent, and translational entropy of all species in the system. The theory is at the mean field level and recovers the results of the restricted primitive model with the Debye-Huckel description for solutions of simple electrolytes without any polymer chains and those of the Flory-Huggins and scaling theories for uncharged polymers in the absence of charges or electrolytes. In constructing the phase diagrams, the chemical potential of each of the species is maintained to be the same in the coexisting phases and at the same time each phase being electrically neutral (Donnan equilibrium). Comparisons are made with a more constrained situation where the chemical potentials of the independent components are maintained to be the same in the coexisting phases. Our calculations predict several rich phenomena. Even for the salt-free solutions, two critical phenomena (corresponding to the Flory-Huggins-type and the restricted-primitive-model-type critical points) are predicted. The coupling between these two leads to two critical end points and triple points. In the presence of salt, the valency of electrolyte ions is found to influence drastically the phase diagrams. Specifically, the predicted liquid-liquid phase transitions in certain temperature ranges is reminiscent of the re-entrant-precipitation phenomenon observed experimentally for polyelectrolytes condensed with trivalent salts.