Kirkwood dielectric constant function

Figure 8-3. Plot of free energy of activation for the Menschutkin reaction EtjN + EtI Et4N + 1 against the Kirkwood dielectric constant function. Data are from Table 8-5, where the solvents are identified.

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. ... 

F = E + 47T//3). In fact, no Curie point can be observed with polar liquids as a function of l/T and the Debye theory is therefore not valid for our strongly polar mixtures. A much more refined theory than that of Debye, which is due to Kirkwood (1939), suffices to account for the general character of the dielectric constant of strongly polar liquids and its changes as a function of temperature. It is not the purpose of this article to give a full account of this theory. 

The effect of the medium on the rates and routes of liquid-phase oxidation reactions was investigated. The rate constants for chain propagation and termination upon dilution of methyl ethyl ketone with a nonpolar solvent—benzene— were shown to be consistent with the Kirkwood equation relating the constants for bimolecular reactions with the dielectric constant of the medium. The effect of solvents capable of forming hydrogen bonds with peroxy radicals appears to be more complicated. The rate constants for chain propagation and termination in aqueous methyl ethyl ketone solutions appear to be lower because of the lower reactivity of solvated R02. .. HOH radicals than of free RO radicals. The routes of oxidation reactions are a function of the competition between two R02 reaction routes. In the presence of water the reaction selectivity markedly increases, and acetic acid becomes the only oxidation product. 

It is expected that the excellence of a correlation should diminish as the correlated process and the model process are made increasingly different in their mechanistic character. Thus, we should not expect great generality from univariate correlations on the other hand, from the quality of the correlation we may be able to leam something about the correlated process. It is not surprising that the rate of one Menschutkin reaction is well correlated with the rate of another Menschutkin reaction, for their mechanisms should be very similar. The solvent effect data (8mAG ) in Table 8-10 are poorly correlated with the Kirkwood dielectric constant function, but a plot against Er (30) shows some improvement. - In this... 

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

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

In this section, we review some of the important formal results in the statistical mechanics of interaction site fluids. These results provide the basis for many of the approximate theories that will be described in Section III, and the calculation of correlation functions to describe the microscopic structure of fluids. We begin with a short review of the theory of the pair correlation function based upon cluster expansions. Although this material is featured in a number of other review articles, we have chosen to include a short account here so that the present article can be reasonably self-contained. Cluster expansion techniques have played an important part in the development of theories of interaction site fluids, and in order to fully grasp the significance of these developments, it is necessary to make contact with the results derived earlier for simple fluids. We will first describe the general cluster expansion theory for fluids, which is directly applicable to rigid nonspherical molecules by a simple addition of orientational coordinates. Next we will focus on the site-site correlation functions and describe the interaction site cluster expansion. After this, we review the calculation of thermodynamic properties from the correlation functions, and then we consider the calculation of the dielectric constant and the Kirkwood orientational correlation parameters. 

In a series of papers, H0ye and Stell have shown that the value of the dielectric constant and the associated Kirkwood G-factors can be related to the long-range behavior of the site-site correlation function The... 

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. 

The dielectric constant can be obtained from the rotational invariant coefficients of the pair correlation function. For example, following Fries et al., it can be evaluated using the Kirkwood g factor ... 

The first solvent property applied to correlate reactivity data was the static dielectric constant 8 (also termed e,) in the form of dielectric functions as suggested from elementary electrostatic theories as those by Bom (l/e), Kirkwood (e-l)/(2 fl), Clausius-Mosotti (e-l)/(8+2), and (8-l)/(e+l). A successM correlation is shown in Figure 13.1.1 for the rate of the 8 2 reaction of p-nitrofluorobenzene with... 

Visser al. related the diffusion coefficient to the solvent viscosity T (Figure 12). The solvent effect on is a combination of the influence on salt partition (Kp) and association (KJ. Both processes are influenced by the polarity of the solvent. An empirical relation, the Kirkwood function, describes the relation between polarity (dielectric constant 6 ) and extraction coefficient well. From Figure 13 it follows that a more polar membrane solvent promotes extraction. In general, polar solvents favor salt partition, but the tendency towards 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. 

It may be of some concern that the solvent dielectric properties are nowhere in evidence in this correlation, but that is the result of the solvents chosen. All have a value of the Kirkwood-Onsager (KO) parameter between 0.44 and 0.48. Only if data in solvents of very low dielectric constant are included (e.g. benzene, ether, THF, ethyl acetate) is there a contribution from the KO function [44] ... 

---