Krichevskii parameter

The ratio of properties in Equation 9.24 is called the Krichevskii function, and identified at the solvent critical point as the Krichevskii parameter (Levelt Sengers 1991). The first EST correlation for partial molar volumes of gases in liquids was done by Brelvi (Brelvi and O Connell 1975c), using characteristic properties for his correlation of the reduced bulk modulus (Brelvi and O Connell 1972). Recent work (Ellegaard, Abildskov, and O Connell 2011) has used the form of Equation 9.4 for partial molar volumes of gases in ILs. The comparisons with data for these systems seem not to be as successful as for their compressibilities and phase equilibria, for reasons that are not apparent. 

DILUTE NEAR-CRITICAL. MIXTURES KRICHEVSKII PARAMETER... 

Near but below the solvent critical point, the infinite-dilution distribution coefficient or K factor of a solute between the two phases is determined by the Krichevskii parameter and the densities of the pure-solvent liquid and vapor phases ... 

The origin of local solvent density enhancements in a compressible SCF can be understood from two different viewpoints. The more recently proposed viewpoint [10,12] ties the existence of local density enhancements directly to the presence of the solvent s critical, correlated density fluctuations, while the more common viewpoint bases the existence of local density enhancements upon the attractiveness of the solute-solvent interaction potential and the compressibility of the fluid [2,10,17,22,23,29-32]. These two viewpoints are described below. (Note that the effect of local density enhancements can also be understood within a purely thermodynamic framework through the Krichevskii parameter, lirrix- Q dP/dx)v r where x is the solute mole fraction. See Refs. [27], [28] and [33].)... 

According to Krichevskii (1967) this derivative is well behaved at the critical point of the solvent, and its value can be calculated from the derivatives (dp dT)l x and (3773x)cri taken along the critical line of the mixture and along the coexistence curve of the pure solvent. Thus, both the fluctuation theory (Equation 2.11) and the classical thermodynamics (Equation 2.90) predict that the divergence of VI is determined by the solvent s compressibility, while their sign and amplitude depends on the solute-solvent interactions described by the integral Cu or the Krichevskii parameter (dp dx)%. 

Femandez-Prini and Japas (1994) analyzed the effect of the intermolecular parameters upon V. They showed that the sign of VI changes with solvent density, and at low density becomes more negative for bigger solutes. On the other hand, the limiting expression of the Krichevskii parameter for low density is Japas et al. (1998). 

The generalized Krichevskii parameter or its equivalent, the direct correlation function integral, Cu, is well behaved in the critical region, as shown in Figure 2.18, and on this is based Equation (2.85) (O Connell et al., 1996), which was used to fit the standard partial molar volume of nonelectrolytes all over the density range. 

Values for the Krichevskii parameters of dilute solutions have been reported by many investigators, primarily for dilute aqueous solutions,but also... 

Krichevskii s parameter at the solvent s critical point, a finite quantity that plays a central role in the asymptotic behavior of the solubility coefficients [186]. In fact, at constant temperature and solvent density, the presence of a noble gas solute induces a local density depletion with a corresponding increase in over both that... 

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