On describing the equilibria in mixed solutions of polyelectrolytes and simple salts using the law of mass action

The validity of the law of mass action in its simplest form (using only the molar concentration) was examined for the case of the binding of counterions to polyions in mixed solutions of a polyelectrolyte and a simple + 1:− 1 salt at 25 °C. The study was made for a polyelectrolyte with a linear charge density ξ = 1.8 and monovalent counterions; both the counterions from the original polyelectrolyte as well as those from the added simple salt interact with the polyion only via Coulombic interactions (specific interactions are absent). For the given system, the apparent equilibrium constant for the binding of the counterions to the polyion was evaluated from the fraction of free counterions. The latter was calculated from the cell model of cylindrical symmetry for the studied polyelectrolyte in a salt-free solution and was confirmed experimentally. With the use of this apparent equilibrium constant, Ks-LMA, the fraction of free counterions f as well as the degree of charge neutralization of the polyion, θ, derived from f were evaluated in the concentration range of the polyelectrolyte's repeating units, cp, from 1·10− 7 to 1 monomol/dm3. These calculations were made for three different ratios of the concentration of the added simple salt, cs, and cp (cs/cp = 0, 1, and 4). Additionally, from the simple law of mass action the calculated values for f were also verified for the case of the titration of the linear polyelectrolyte (cp = 0.02 monomol/dm3) with the + 1:− 1 salt. In this latter case the results obtained from the simple law of mass action were compared with both the prediction of the cell model and the available experimental results. In all the studied cases the application of the simple law of mass action generally provided poor results; however, a significant improvement was obtained by including the term exp(− ϕ) in the equilibrium constant, ϕ being the dimensionless electrostatic potential at the surface of the polyion.