Phase Separation of Polyelectrolyte Solutions

Abstract

It is shown theoretically that phase separation may arise in solutions of polyelectrolytes due to electrostatic interactions alone. Two models are considered thermodynamically. In both models the free energy is represented as the sum of an entropy of mixing term and an electrostatic free energy term, while the van der Waals attractions are neglected. In the one model, electrically charged rigid cylindrical rods are in solution with an equivalent amount of counterions but without additional electrolyte. The free electrical energy, in this case, is given by the expression of Lifson and Katchalsky. In the other model the solution contains two types of macroions of opposite charge. The macroions are flexible coils carrying a number of univalent charges, the charge density being sufficiently low. The electrical free energy in this case may be approximated by the Debye-Huckel expression. For both models, it is shown that the decrease in the electrical free energy in a phase separation can, at given temperature and pressure, more than compensate for the increase in the entropy of mixing term. The effects of polymer concentration, dielectric constant, charge density, and salt content follow directly from the thermodynamic treatment of the models.