Abstract
AbstractThe Poisson‐Boltzmann equation in the cylindrical cell model is solved numerically for charged polyelectrolyte solutions containing mono‐ or di‐valent counterions and mono‐valent coions. The results, which describe the ion distribution around the polyion, are compared with those derived from the Poisson‐Boltzmann equation for salt‐free solutions in the limit of infinite dilution and with the Manning counterion condensation theory. This approach generalizes the results of Le Bret and Zimm for the dependence of the condensation radius on the polyion concentration to polyelectrolyte solutions containing added salt and shows how counterion condensation occurs even at finite concentration. The general conclusion drawn not only supports further evidences 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.
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