Integral equations Kirkwood definition

One of the important methods of developing a model for the potential energy of the liquid system is that based on integral equations. These include the Kirkwood integral equation, the Born-Green-Yvon equation, and the Omstein-Zernike equation. The last approach leads to the definition of the direct correlation function c(fi2). It is the approach which is most frequently used and is the one which is considered here. 

There is no limitation for the use of Kirkwood s superposition approximation (2.3.62) in the integral terms of equation (7.1.27) since there is a single defect in the recombination sphere of dissimilar defect. For example, a product a( r2 — f[ )piti(r2 f( t) in a line with definition (7.1.3) could be replaced by <7i,i(r2 rj <). Therefore, we have... 

In deriving (8.3.11) we took into account the fact that despite the reaction rate is still defined through the integral (4.1.19), its magnitude depends greatly on the equation for the correlation function for dissimilar particles. Making use of the definition of the functional (5.1.5), let us write down equation (8.3.8) (in usual dimensional units) modified by the Kirkwood... 

These equations can be expressed in terms of the chemical potentials of the salts when the usual definition of the chemical potentials of strong electrolytes is used. The transference numbers may be a function of x as well as the molality. Arguments which are not thermodynamic must be used to evaluate the integrals in such cases (see Kirkwood and Oppenheim [33]). One special type of cell to which either Equation (12.112) or Equation (12.113) applies is one in which a strong electrolyte is present in both solutions at concentrations that are large with respect to the concentrations of the other solutes. Such a cell, based on that represented in Equation (12.97), is... 

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