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 within the framework of the counterion condensation theory of linear polyelectrolytes. The model allows for the proper identification of the kind of counterion association to a linear polyelectrolyte when it is in solution with two different types of counterions (of equal or different valences). Two extreme modes of counterion association to the polyelectrolyte are considered: loose territorial (classical condensation) and a covalent bonding at a specific site on the polyion. The model provides analytical expressions for 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 planning suitable experiments aimed at discriminating between the two types of counterion association proposed.