Affinity interactions in counterion-polyelectrolyte systems: Competition between different counterions

Non-bonding, specific interactions between linear polyelectrolytes and diff erent species of counterions (of equal or different valence) are considered in the framework of the counterion condensation theory. It is assumed that these interactions are of short distance nature and that, within our theor etical approach, they apply only to the counterions territorially associate d (condensed) to the polyion, which are free to move within the condensatio n volume V-p around it. It is found that a simple additive term in the tota l free energy is sufficient to account for this interaction, resulting in a modulation of the polyelectrolytically determined population of territoria lly bound counterions. The distribution of free and condensed counterions a s well as its variation with the physicochemical variables of the solution can be readily calculated. Analysis of literature data on titrations of pol y(methacrylic acid) and dextran sulfate in aqueous solution with different species of monovalent and divalent counterions show that both polyanions ap pear to have a modest affinity free energy (of about RT) for Ca++ counterio ns when compared with Na+. On the other hand, polyion interactions with the Mg++/Na+ pair are well described by bare polyelectrolytic interactions.