Gibbs energy polyelectrolytes, aqueous solutions

Abstract This chapter reviews the thermodynamic properties of aqueous solutions of polyelectrolytes, concentrating on properties that are related to phase equilibrium phenomena. The most essential phenomena as well as methods to describe such phenomena are discussed from an applied thermodynamics point of view. Therefore, the experimental findings concentrate on the vapor liquid phase equilibrium phenomena, and the thermodynamic models are restricted to expressions for the Gibbs energy of aqueous solutions of polyelectrolytes. 

There are many well-established models for the Gibbs energy of nonelectrolyte solutions and also several methods to describe conventional polymer solutions. However, the state of the art for modeling thermodynamic properties of aqueous solutions of polyelectrolytes is far less elaborated. This is partly due to the particular features of such solutions but is also caused by insufficiencies in the knowledge of the parameters that characterize a polyelectrolyte, for example, the polydisper-sity and the different stmctures (primary, secondary etc.) of the polyelectrolytes. The development and testing of thermodynamic models has always been based on reliable experimental data for solutions for which all components are well characterized. Such characterization is particularly scarce for biopolymers and biopolyelectrolytes. Furthermore, such polymers are generally more complex than synthetic polymers. Therefore, the present contribution is restricted to a discussion of the thermodynamic properties of aqueous solutions of synthetic polyelectrolytes that consist of only two different repeating units that are statistically distributed. Furthermore, it is restricted to systems where sufficient information on the polyelectrolyte s polydispersity is available. 

As an example, we discuss here an aqueous solution of one polyelectrolyte P and one strong electrolyte S (=Mv Xv ), where P and S share a common counterion X. Some of the counterions that originate from the polyelectrolyte are assumed to be located in a small volume Vp around the polyelectrolyte backbone (the phenomenon is called counterion condensation ). The polyelectrolyte, condensed counterions, free counterions, free coions, and water contribute to the Gibbs energy of the solution ... 

The aqueous phase contains free (or dissolved ) counterions. These ions are either dissociated from the polyelectrolyte or result from the dissolution of the salt S. Their contribution to the Gibbs energy of the solution is ... 

Keywords Aqueous solutions Counterion condensation Excess Gibbs energy Osmotic coefficient Polyelectrolytes Salt effects Thermodynamics Vapor liquid equilibrium... 

When a neutral salt S is dissolved in the aqueous polyelectrolyte solution there is also a contribution to the Gibbs energy of the aqueous solution by the other ions, here called coions. When vcoi is the stoichiometric coefficient of that coion in S, following the same ideas as explained before for the free counterions, that contribution is ... 

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