DISTRIBUTION OF COUNTERIONS AROUND POLYIONS IN MIXED VALENCY COUNTERION SYSTEMS

The distribution of mono- and divalent counterions around polyions is discussed by use of the ionic activity coefficients of these ions calculated from the Poisson-Boltzmann equation appplied to rodlike polyion solutions. Our theoretical values of mean activity coefficients of simple salts are larger than the experimental values of Kwak et al. The calculated values assuming that the coion activity coefficient corrected for the salt term is 0.9-1.0 agree well with the experimental values in mixed valency counterion systems as well as in single counterion systems. Part of the “bound” divalent counterions become “free” by the addition of a large excess of monovalent counterions. For the case of an excess of monovalent salts on the binding of divalent counterions, the agreement between the experimental values by Krakauer and those calculated here is qualitatively satisfactory. Our calculated results are also compared with Manning's theory in mixed valency counterion systems. We conclude that the calculation based on the Poisson-Boltzmann equation for a rodlike model is better in treating mixed valency counterion systems than is Manning's theory. © 1979, American Chemical Society. All rights reserved.