Counterion condensation in solutions of rigid polyelectrolytes

We present a simple theory to examine counter ion condensation in isotropic solutions of finite-length rigid polyelectrolytes. Electrostatic interactions are described by an extension of Debye-Huckel theory, in which a wavevector-dependent screening length takes into account the connectivity of the polyions. The counterions are divided into two classes, free and condensed, in chemical equilibrium. We demonstrate that trends in counterion condensation are affected by the polyion concentration, the polyion shape, and the solvent quality and that these trends in counterion condensation in turn affect the phase behavior and osmotic pressure of the polyelectrolyte solution.