Thermodynamic Properties of Polyelectrolyte Solutions

of Chemistry, University of Ljubljana, Ljubljana, Yugoslavia 

During the last two decades the thermodynamic properties of numerous polyelectrolytes in aqueous solution have been investigated. Some research workers were more interested in natural, others again in synthetic polyelectrolytes with a variety of counter-ions. The thermodynamic behaviour of pure polyelectrolyte solutions and of their mixtures with simple electrolytes, was studied. It is impossible to give in one lecture a full account of the efforts in this direction. I shall, therefore, confine myself mainly to the work which has been done at this Department. 

Eric Selegny (ed.). Polyelectrolytes, 97-113. All Rights Reserved. Copyright 1974 by D. Reidel Publishing Company, Dordrecht-Holland 

V = number of ionic groups on polyion n = osmotic pressure 

To prove the applicability of this model to the interpretation of the results obtained with solutions of polystyrenesulphonates we have measured different thermodynamic properties related to different derivatives of the electrostatic free energy. 

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Oosawa, F. (1957). A simple theory of thermodynamic properties of polyelectrolyte solutions. Journal of Polymer Science, 23, 421-30. 

Coulombic, van der Waals, entropic and osmotic forces are coupled in a nontrivial way and give rise to important charge regulation in polyelectrolyte systems. The salt concentration is also an important factor to define the structure and thermodynamic properties of polyelectrolyte solutions. In weak polyelectrolytes the ionization equilibrium is also coupled to these interactions and thus the pKof ionizable groups depends on the organization of the interface and differs from that for the isolated molecule. 

Oppermann W, Wagner M. Determination of thermodynamic properties of polyelectrolyte solutions via analysis of the sedimentation equilibrium. Langmuir 1999 15 4089-4092. 

Many macromolecules in aqueous solution are polyelectrolytes. The remarkable changes in the conformation of linear polyelectrolytes as a function of concentration, ionic strength, and pH are discussed. The various theories of chain expansion are reviewed. The thermodynamic properties of polyelectrolyte solutions reveal dramatic behavior. The large increase in the reduced osmotic pressure, jr/c, as the solution is diluted is explained in terms of the entropy of the counterions. The strong dependence of the conformation of the chains with solution conditions also leads to large changes in the viscosity. The viscosity is also explained in terms of the coil size and the interactions of the chains. 

Feng Z, Liu HL, Hu Y (1996) Study on thermodynamic properties of polyelectrolyte solutions. Acta Chim Sinica 54 1076 1083... 

Thermodynamic properties of polyelectrolyte solutions are mostly determined by ionic distribution around the polyion skeleton. To explain thermodynamic properties, therefore, the rod-like model may be effective. It is assumed that the polyion is a rod of infinite length and has smeared charges distributed uniformly over the surfaces of the rod. That is, a real polyion chain consists of a series of discrete charges and each charge is surrounded by its own ionic atmosphere. If the radius of ionic atmosphere is... 

In the thermodynamic properties of polyelectrolyte solutions, it is always found that polyelectrolyte solutions are highly non-ideal. That is, the activity coefficient and osmotic pressure coefficient are much lower than unity. [1] Reasonable explanations on these phenomena are usually obtained by assuming that a part of counter-ions are bound on fixed charges. 

Theoretical considerations of the coulombic interactions of dissolved biopolymers have produced a complete picture of the distributions of counter and coions under the influence of the electrostatic charge on the macroion(56,57). The counterion condensation theory of Manning(56) has stimulated a great deal of activity in the study of dissolved macroions, especially because it provides a group of limiting laws describing the contribution of electrostatic effects to the thermodynamic and transport properties of polyelectrolyte solutions. Data... 

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. 

Table 4 Survey of literature data for thermodynamic properties of aqueous solutions of a single polyelectrolyte at around 300 K (without any other salt)...

Usually the acid-base properties of poly electrolyte are studied by potentiometric titrations. However it is well known, that understanding of polyelectrolyte properties in solution is based on the knowledge of the thermodynamic properties. Up to now, there is only a small number of microcalorimetry titrations of polyelectrolyte solutions published. Therefore we carried out potentiometric and microcalorimetric titrations of hydrochloric form of the linear and branched polyamines at 25°C and 65°C, to study the influence of the stmcture on the acid-base properties. 

It is the unique properties exhibited by polyelectrolytes that have led to their use in a variety of biomedical applications. Therefore, any discussion of polyelectrolytes as biomaterials should provide some insight into the properties of polyelectrolyte systems. In this section, an overview of polyelectrolyte properties will be presented, including polyelectrolyte solutions, gels, and complexes. The purpose of this section is not to provide an exhaustive review of polyelectrolyte thermodynamics but to provide background information for the ensuing discussion of biomedical applications of polyelectrolytes. 

Skerjanc J, Dolar D. Thermodynamic properties of a polyelectrolyte solution containing a mixture of counterions differing in charge. J Chem Phys 1989 91 6290-6294. 

The progress in this area of research is hampered by uncertainties in the current force fields, mixing rules, and other details of simulation protocols. In addition, some thermodynamic properties of solution like, the enthalpy or heat capacity of solution, caimot be simulated with sufficient accuracies to be tested against the experimental data for polyelectrolyte solutions. Further development of the force fields and methods to calculate solution thermodynamic parameters is needed to advance this area of science. 

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