Kirkwood function

Some authors plot log k or AG against 1/e rather than against the Kirkwood function. Since 1/e is nearly linearly related to (e — 1)/(2e + 1), within the assumptions of a theory in which the solvent is treated as a continuum this substitution of variable is not serious. Another approach is to interpret the solvent dependence of the Hammett reaction constant p on a dielectric constant function. ... 

Density functions used earlier to interpret the relaxation data of polymers were the Cole-Cole function,70 the Fuoss-Kirkwood function,71 and the log 2) function.72 These functions, particularly the skewed log ( 2) distribution, were accounted for by 13C T, and n.O.e. data of some polymers, but the physical significance of the adjustable parameters has been questioned by some authors.68... 

FA of data matrices containing 35 physicochemical constants and empirical parameters of solvent polarity (c/ Chapter 7) for 85 solvents has been carried out by Svoboda et al. [140]. An orthogonal set of four parameters was extracted from these data, which could be correlated to solvent polarity as expressed by the Kirkwood function (fir — l)/(2fir + 1), to solvent polarizability as expressed by the refractive index function (rfi — + ), as well as to the solvent Lewis acidity and basicity. Thus,... 

A wide variety of different theoretical [e.g. Kirkwood function) and empirical cf. Chapter 7) parameters of solvent polarity have successfully been tested using multivariate statistical methods in order to model the solvent-induced changes in keto/enol equilibria [134],... 

Fig. 5-10. Correlation between lg(k/ko) [56] and the Kirkwood function (cr — l)/(2 r + 1) for the Menschutkin reaction between triethylamine and iodoethane at 40 °C in binary acetone/benzene and acetone/l,4-dioxane mixtures (rate constants relative to acetone as common standard solvent).

A comparison of Fig. 7-6 with Fig. 5-11 in Section 5.4.3 reveals some improvement of the poor correlation between g k/ka) and the Kirkwood function (fir — l)/(2er + 1). If FIBD solvents are included in the E-Y 7iQ)l g k/k(f correlation, two lines are obtained as in Fig. 5-12, one for non-HBD and one for HBD solvents. This demonstrates the utility of such correlations in discovering speeifie solute/solvent interactions such as hydrogen-bonding. 

The solvent effect on extraction constants is a combination of the influence on salt partition and association. Both processes are influenced by the polarity of the solvent [97]. The Kirkwood function describes the relation between polarity, , and extraction constant a more polar membrane solvent promotes extraction. In general, polar solvents favor salt partition, but the tendency toward complexation diminishes. Since the overall effect of solvent polarity on the extraction is positive, the polarity appears to affect the partition coefficient to a higher degree. 

Kirkwood function physico-chemical properties ( dielectric constant)... 

Based on the dielectric constant, the Kirkwood function is defined as ]Krrkwood and Westheimer, 1938 Reichardt, 1990]... 

Conductometric measurements were feasible down to 50 volume percent of THF, and the dissociation constants of lithium ion-pairs were determined from those data. The log Kdiss were shown to be linear with reciprocal of the appropriate dielectric constant - a relation commonly reported284) although not obvious. The solvating power of a medium is not determined uniquely by the bulk dielectric constant, D the more sophisticated Kirkwood function (D - l)/(2 D + l)329) could provide a better measure of that property. However, since the Kirkwood function is nearly linear with 1/D in the investigated range of dielectric constants, the discrimination between them is not practical. 

As another example, Reichardt (1988, p. 154) cites data from Huisgen and coworkers (Swieton et al 1983) for the cycloaddition of diphenylketene to n-butyl vinyl ether. Figure 2.3 shows a plot of the natural logarithm of the rate constant (relative to the slowest) versus the Kirkwood function. The slope corresponds to a dipole moment for the transition state of about 10 Debye (34x 10" Cm), larger than that of the product, indicating a considerable degree of charge separation. 

From the a-values, it is clear that the transport regime strongly depends on the solvent. The transport varies from purely diffusion limited to mainly kinetically limited. Both transport parameters and k have been correlated to the viscosity r and polarity e, (Kirkwood function) of the solvent, respectively. 

The diffusion coefficient correlates linearly with the viscosity T as was already shown in the case of a diffusion limited transport system (Figure 14). When using the empirical Kirkwood function, a linear relationship between k and obtained. Figure 15 shows that the use of a more polar solvent slows down the rate of decomplexation. Hence, the regime of the transport can be influenced by the solvent polarity. 

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