Ion Association in Polyelectrolyte Solutions: Effects of Charge Correlations and Connectivity

Reversible counterion association equilibria in polyelectrolyte solutions is strongly affected by interactions between dissociated ionic species. Previous theories have treated this effect using the Debye-Hückel (DH) free energy, and frequently neglected correlations due to charge connectivity. We demonstrate that straightforward application of the DH free energy implies a reduction in the degree of ion association as charge concentration increases. This unphysical behavior is found to stem from improper regularization of the ion self-energy, an issue we remedy by introducing a smeared charge density. We then show that charge connectivity enhances the propensity for counterion binding along the polyions. The effects of connectivity on the demixing phase behavior of polyelectrolyte solutions are also discussed.