COUNTERION ACCUMULATION IN ROD-LIKE POLY-ELECTROLYTE SOLUTIONS WITH ADDED SALT AND MANNING CONDENSATION THEORY

The Poisson-Boltzmann equation in the cylindrical cell model is solved numerically for charged polyelectrolyte solutions containing mono- or divalent counterions and monovalent coions. The results, which describe the ion distribution around the polyion, are compared with those derived from the Poisson-Boltzmann equations for salt-free solutions in the limit of infinite dilution and with the Manning counterion condensation theory. The general conclusion drawn not only supports further evidence that the Manning condensation theory can be deduced from the Poisson-Boltzmann equation but also suggests that counterion binding changes progressively from a free to condensed phase, as the polyion charge density parameter increases.