Kirkwood-Buff theory electrolytes

Behera, R. 1998. On the calculation of thermodynamic properties of electrolyte solutions from Kirkwood-Buff theory. Journal of Chemical Physics. 108, 3373. 

There are generally two ways to proceed in determining the equilibrium properties of a solution. The configurational averages can be carried out simultaneously over the solute and solvent species, or they may be carried out successively over the solvent, at fixed positions of the solute, and then over the coordinates of the solute species. The first method is due to Kirkwood and Buff (1951) and has been applied most successfully, until recently, to simple nonelectrolyte solutions and mixtures. The second is the McMillan-Mayer theory which has been more widely used in the study of electrolytes, polymers, and proteins. Our discussion of electrolytes will be in terms of the McMillan-Mayer (MM) formalism. For recent applications of the Kirkwood Buff theory see Perry et al. (1988). 

The Kirkwood-Buff (KB) theory is the most important theory of solutions. This chapter is therefore central to the entire book. We devote this chapter to derive the main results of this theory. We start with some general historical comments. Then we derive the main results, almost exactly as Kirkwood and Buff did, only more slowly and in more detail, adding occasionally a comment of clarification that was missing in the original publication. We first derive the results for any multicomponent system, and thereafter specialize to the case of two-components system. In section 4, we present the inversion of the KB theory, which has turned a potentially useful theory into an actually useful, general and powerful tool for investigating solutions on a molecular level. Three-component systems and some comments on the application of the KB theory to electrolyte solutions are discussed in the last sections. 

Ruckenstein and Shulgin (2002) used the Kirkwood-Buff fluctuation theory to obtain an expression for the salting out (of gases, but applicable to any non-electrolyte solute) in electrolyte solutions. The resulting expression can be re-written as ... 

The derived formalism is based on Kirkwood-Buff s fluctuation theory of nonelectrolyte mixtures [203], which defines exact relations between the microscopic details of the system and integrals over its microstructure characterized by the pair correlation functions. The formalism was successfully applied to study the microscopic mechanism of supercritical solubility enhancement in non-electrolyte solutions [41], to interpret gas solubility [184], solvation effects on the reaction kinetic rate [204], as well as other solvation effects [205]. 

An analogous approach to the solvation quantities derived for non-electrolyte systems [41,181], based on Kusalik and Patey s version of the Kirkwood-Buff fluctuation theory of mixtures [210], was developed recently [42] to make explicit contact not only between the solvation structure of individual ions and its corresponding macroscopic properties, but also between the individual ion s and the salt s properties without invoking any extrathermodynamic assumption [173,212]. 

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