Counterion condensation and phase separation in solutions of hydrophobic polyelectrolytes

We have developed a theory of counterion condensation in solutions of hydrophobic polyelectrolytes. In the framework of Oosawa’s two-zone model we demonstrate that solutions of necklaces can be unstable with respect to phase separation. This phase separation is triggered by the concentration-induced counterion condensation. For the range of parameters at which the polyelectrolyte solution is stable, we predict nonmonotonic dependence of the chain size on polymer concentration. This nonmonotonicity in the chain size manifests itself in the dramatic increase in solution viscosity at the crossover to concentrated polyelectrolyte solution. There is also a possibility of two peaks in the scattering function of qualitatively different physical nature observed in different concentration regimes. The scattering intensity at the peak position increases with polymer concentration in low concentration (necklace) regime and decreases with concentration in concentrated polyelectrolyte solutions.