Thermodynamics of polyelectrolyte solutions

The thermodynamics of polyelectrolyte solutions is also a strong function of ionic strength and charge density. Very large osmotic second virial coefficients are observed for highly charged macromolecules. The Flory theory of these solutions in presented in Section 10.3. 

Mandel, M. Statistical thermodynamics of polyelectrolyte solutions. In Selegny, E. (ed.) Polyelectrolytes, pp. 39-55. D. Reidel Publishing Company, Dordrecht (1974)... 

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. 

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. 

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... 

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

LA1 Lammertz, S., Pessoa Filho, P.A., and Maurer, G., Thermodynamics of aqueous solutions of polyelectrolytes Experimental results for the activity of water in aqueous solutions of some single synthetic polyelectrolytes, J. Chem. Eng. Data, 53, 1564, 2008. 

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. 

Subdivision of counterions into condensed and uncondensed populations according to the Manning/Oosawa depiction is not unique. For example, a hypothetical thermodynamically bound counterion population can be defined to account for the deviations of polyelectrolyte solutions from thermodynamic ideality (35) this population is not equal to the condensed population. One can also use different definitions of condensed. The inflection point in the radial ion distribution, the Bjerrum length, and the radial distance over which the electrostatic interaction energy decays to kT have all been employed as alternative criteria for defining a condensed fraction (50). 

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