Interpretation of Preferential Interaction Coefficients of Nonelectrolytes and of Electrolyte Ions in Terms of a Two-domain Model

For a three-component system consisting of solvent (1), polymer or polyelectrolyte (2J), and a nonelectrolyte or electrolyte solute (3), a two-domain description is developed to describe thermodynamic effects of interactions between solute components (2J) and (3). Equilibrium dialysis, which for an electrolyte solute produces the Donnan distribution of ions across a semipermeable membrane, provides a fundamental basis for this two-domain description whose applicability is not restricted, however, to systems where dialysis equilibrium is established. Explicit expressions are obtained for the solute-polymer preferential interaction coefficient gamma 3,2J (nonelectrolyte case) and for gamma +,2J and gamma -,2J, which are corresponding coefficients defined for single (univalent) cations and anions, respectively: gamma +,2J = magnitude of ZJ + gamma -,2J = 0.5(magnitude of ZJ + B-,2J + B+,2J) - B1,2Jm3/m1 Here B+,2J, B-,2J, and B1,2J are defined per mole of species J, respectively, as the number of moles of cation, anion, and water included within the local domains that surround isolated molecules of J; ZJ is the charge on J; m3 is the molal concentration of uniunivalent electrolyte, and m1 = 55.5 mol/kg for water. Incorporating this result into a general thermodynamic description(derived by us elsewhere) of the effects of the activity a+ of excess uniunivalent salt on an equilibrium involving two or more charged species J (each of which is dilute in comparison with the salt) yields:SaKobs bS/d a+ A(r+2J r 2j) A(B+2J B-2 2B12Jm3/m1)where KObS is an equilibrium quotient defined in terms of the molar concentrations of the participants, J, and A denotes astoichio metrically weighted combination of terms pertaining to the reactant(s) and product(s). The derivation presented here does not depend on any particular molecular model for salt-polyelectrolyte (or solute-polymer) interactions; it therefore generalizes our earlier (1978) derivation.