Colligative properties of polyelectrolyte solutions

The solution properties of polyelectrolytes are not well understood despite increasing theoretical and experimental effort, particularly during the last 10 years. Some of the current models for polyelectrolyte solutions are valid only at infinite dilution because they account only for long-range interactions. Nagvekar and Danner [M. Nagvekar, R.P. Danner, An Excess Gibbs Free Energy Model for Polyelectrolyte Solutions, Fluid Phase Equilibria 53 (1989) 219.] have developed an excess Gibbs free energy model for polyelectrolyte solutions. The key feature of the model is to express the excess Gibbs free energy as the sum of the contributions from long-range and short-range interactions. The `limiting lawsʹ of Manning [G.S. Manning, Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions. I. Colligative Properties, J. Chem. Phys. 51 (1969a) 924; G.S. Manning, Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions. II. Self-diffusion of Small Ions, J. Chem. Phys. 51 (1969b) 934.] were used to account for the long-range interactions while a local composition model of the Non-Random Two Liquid (NRTL) type was used for short-range interactions. In this work, we present the expressions for counterion activity coefficients and the motic coefficients in polyelectrolyte solutions with and without added salts at finite concentrations. Data for a number of polyelectrolyte systems with univalent and divalent counterions are analyzed using Nagvekarʹs proposed model. In the low concentration regime, the osmotic coefficient data are practically independent of concentration, and are in reasonable agreement with the Manning model. With increasing polyelectrolyte concentration, the osmotic coefficient data are a strong function of concentration, and the local composition model is shown to successfully represent the data.