Phase separation in polyelectrolyte solutions. II. Interaction effects

The Voorn-Overbeek equations for complex coacervation were modified to include a term to account for a non-zero heat of mixing. The resulting equations were applied to an analysis of previously reported coacervation data on gelatin-gelatin systems. The (non-electrostatic) interaction parameter, χ₁₂, was evaluated from these data and was found to be a function of both the temperature and the initial mixing concentration. χ₁₂ was not proportional to T^-1. The electrostatic free energy term of the Voorn equation, in which (∂Fc/∂n₁) is a function of the polyion volume fraction, φ₂, to the 3/2 power, was not compatible with these data. A more general electrostatic term, f₁(σ,φ), was devised, evaluated and found to be a more nearly linear function of φ₂^I, the solute volume fraction in the dilute phase. The function f₁(σ,φ) was negative at low mixing concentrations and approached zero at high mixing concentrations. These data were interpreted as indicating the formation of stable aggregates of low configurational entropy in the original mixture. The coacervation is then driven by the gain in configurational entropy on the formation of the randomly mixed concentrated gelatin phase and the dilution of the non-random aggregate phase. The deviations from the Voorn-Overbeek equations can be considered as indicating a standard state entropy change when the polyions are mixed.