Chemical bonding of divalent counterions to linear polyelectrolytes: Theoretical treatment within the counterion condensation theory

Chemical bonding of counterions to a linear polyelectrolyte is addressed wi thin the framework of the counterion condensation theory of linear polyelec trolytes. The model allows for the proper identification of the kind of cou nterion association to a linear polyelectrolyte when it is in solution with two different types of counterions (of equal or different valences). Two e xtreme modes of counterion association to the polyelectrolyte are considere d: loose territorial ("classical" condensation) and a covalent bonding at a specific site on the polyion. The model provides analytical expressions fo r calculating the fraction of counterions in each type of association. Any thermodynamic function of interest can also be readily computed through the appropriate function of the calculated excess Gibbs energy of the system. The concentrations of the different types of associated counterions, for a few particular solution conditions, are presented and discussed in order to provide tools not only for analyzing experimental results, but also for pl anning suitable experiments aimed at discriminating between the two types o f counterion association proposed.