Non-Debye solvents

Onsager Theory for C(t) for Non-Debye Solvents. Generally solvents have more complex dielectric responses than described by the Debye equation (Eq. (18)). To obtain the time dependence of the reaction field R from Eqs. (12, (15), (16) and (7) an appropriate model for dielectric behavior of a specific liquid should be employed. One of the most common dielectric relaxation is given by the Debye-type form, which is applicable to normal alcohols. 

L. E. Fried and S. Mukamel, Solvation structure and the time-resolved Stokes shift in non-Debye solvents, J. Chem. Phys., 93 (1990) 932 16. 

McManis and Weaver [201] considered the consequences of non-Debye solvent relaxation upon the barrier-crossing dynamics of adiabatic electron-transfer processes using a formulation due to Hynes [200],... 

The use of calculated from T] according to Eq. (37), instead of Tl, in the correlation of In kg with the time of relaxation led to a single linear dependence valid for Debye and non-Debye solvents. Such behavior is illustrated by the plot prepared [169, 170] for the CoCq /Coc system in 12 solvents, including methanol, ethanol, propanol, and propylene carbonate, which also exhibits a non-Debye behavior [202]. This plot is shown in Fig. 7. 

An extended discussion of the behavior of redox system in non-Debye solvents has been given recently [169]. These problems were further discussed by Baranski et al. [188] in their work on the oxidation of ferrocene at a Pt microelectrode in several alcohols in the temperature range 190- 295 K. One should remember that the structure of such non-Debye solvents, which is related to the large-amplitude Tj relaxations, may be changed considerably [3] under the influence of ions, and also at the charged electrode surface. 

Also, when considering the systems in non-Debye solvents, the y parameter (Eq. (41)) should be changed [169] to... 

Such behavior may be due to solvation of the reactant by monomers in non-Debye solvents and to the lower local dielectric permittivity with respect to the bulk value. 

This short discussion shows that in the case of the non-Debye solvents further work is necessary on both the electrode kinetics and the dielectric relaxation behavior of the solvents in the presence of various electrolytes. There are also significant discrepancies between the results on the relaxation dynamics of these solvents reported by various authors (see [169]). 

Also, more attention should be paid to the study and analysis of electron-transfer reactions in non-Debye solvents which exhibit several relaxation times. Wider use of mixtures composed to two nonaqueous solvents of different Lewis basicity is advised. So far, such studies are rather limited (see, for instance, [227,305]). 

This is possible if the equivalent conductivity is proportional to the square root of the concentration Cq, i.e. if the Debye-Hiickel-Onsager law is obeyed. It is known that this square-root law is also obeyed for non-aqueous solvents as a good approximation, as long as the dielectric constant of the solvent is not less than e = 30. Figure 19 shows the equivalent conductivities as a function of Vm for three examples. If one bears in mind that, because of experimental difficulties, the accuracy of measurements in aqueous solutions is not attained, then the square root law is obeyed to a good approximation. 

Prins was bom and educated in The Netherlands receiving his doctorate from Leiden University in 1955. From 1955 until 1957 he was a research associate at the Department of Chemistry at Cornell University, with Peter Debye, working on the properties of non-ionic detergents in non-aqueous solvents. 

Considerable progress has been made in going beyond the simple Debye continuum model. Non-Debye relaxation solvents have been considered. Solvents with nonuniform dielectric properties, and translational diffusion have been analyzed. This is discussed in Section II. Furthermore, models which mimic microscopic solute/solvent structure (such as the linearized mean spherical approximation), but still allow for analytical evaluation have been extensively explored [38, 41-43], Finally, detailed molecular dynamics calculations have been made on the solvation of water [57, 58, 71]. 

A number of theoretical models for solvation dynamics that go beyond the simple Debye Onsager model have recently been developed. The simplest is an extension of Onsager model to include solvents with a non-Debye like (dielectric continuum and the probe can be represented by a spherical cavity. Newer theories allow for nonspherical probes [46], a nonuniform dielectric medium [45], a structured solvent represented by the mean spherical approximation [38-43], and other approaches (see below). Some of these are discussed in this section. Attempts are made where possible to emphasize the comparison between theory and experiment. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

The situation is more complex in the case of the so-called non-Debye liquids -the protic solvents. Due to their internal structure, these liquids exhibit a complicated dielectric relaxation behavior. This group of solvents comprises alcohols, formamide, propylene carbonate, and some other liquids. One should remember that in the In vs. In Tl analysis (Sec. 3.1.3), the rate constants measured in these solvents deviated from the values measured in aprotic solvents. 

With regard to dipolar liquids and thdr solutions in non-dipolar solvents, Piekara developed a complete theory of dipolar couplings calculating all three correlation factors Rcn, Pk, and Rs- These studies revealed that nitrobenzene molecules coalesce momentarily into antiparalld aggregates, which then tend to couple mutually into almost parallel pairs. Feterlin and Stuart performed a detailed study of the influence on Ae not orjly of Debye dipole couplings but moreover of anisotropy of the local Lorentz field. 

The plot shows a distribution closely around a slope of unity indicated by the solid line in Figure 2 except for the alcohols and nitrobenzene. Such anomaly in alcohols is also reported for other chemical processes and time-dependent fluorescence stokes shifts and is attributed to their non-Debye multiple relaxation behavior " the shorter relaxation components, which are assigned to local motions such as the OH group reorientation, contribute the friction for the barrier crossing rather than the slower main relaxation component, which corresponds to the longitudinal dielectric relaxation time, tl, when one regards the solvent as a Debye dielectric medium. If one takes account of the multiple relaxation of the alcohols, the theoretical ket (or v,i) values inaease and approach to the trend of the other solvents. (See open circles in Figure 2.)... 

As I mention in another paper (p. loi), two outstanding types of polarization curve are obtained for polar substances dissolved in non-polar solvents. In the first type of curve Pg always diminishes as Cg increases. The second type is less simple it exhibits a maximum for Pg, usually when the concentration is low (such curves are chiefly exhibited by the lower alcohols) see figs, i and 2, p. 104. For the explanation we refer the reader to Debye s article in the Handbuch der Radiologic, More complicated Pg-curves, e.g. those with several maxima, will not be discussed here. 

The dipole moment of each of the compounds has been calculated from measurements of the dielectric constant of dilute solutions in a non-polar solvent, benzene, by the well known method given by Debye f. 

The solubility of the drug substance is attributable in large part to the polarity of the solvent, often expressed in terms of dipole moment, related to the dielectric constant. Solvents with high dielectric constants dissolve ionic compoimds (polar drugs) readily by virtue of ion-dipole interactions, whereas solvents with low dielectric constants dissolve hydrophobic substances (non-polar drugs) as a result of dipole or induced dipole interactions (Van der Waals, London, or Debye forces). This principle is illustrated in Fig. 1. The former is classified as polar solvents, with examples such as water and glycerin the latter are non-polar solvents, with example such as oils. Solvents with intermediate dielectric constants are classified as semipolar. The dielectric constants of some solvents are shown in Table 3. ... 

Other important physical chemical properties are polarity and dielectric constant. Water has a high dielectric constant (78.5 at STP), which would effectively mask ionic charges and lead to high solubility of ionic compounds. The dielectric constant of CO2 at 200 bar and 40°C is approximately 1.5, and CO2 is considered a very non polar solvent. As would be expected, polarity influences solubility for supercritical fluids. Carbon dioxide has a dipole moment of 0.0 Debye, while the value for NH3 is approximately 1.5. Therefore, C02 by itself is poorly suited for dissolving polar compounds. 

While by far the greater portion of the electrochemical studies on solutions have been made using water as solvent, researches have also been carried out in which the water has been replaced by other solvents, or mixtures of non-aqueous solvents with water. Until very recently such studies yielded little of value because of their scattered nature and, usually, lack of accuracy, to which was added a lack of an adequate theory for their interpretation. It will be shown in the following chapter that some headway has been made in the, difficult field of study of the thermodynamic properties of such solutions of electrolytes. The Debye-Hiickel theory is, if anything, more valuable in the interpretation of the results in this field than in that of aqueous solutions. 

In order to obtain activity coefficients or standard potentials from measurements on cells of the type shown in equation (1) it is necessary, as described in Chapters 8 and 10, to make some form of extrapolation. Furthermore in the test of the Debye-Huckel relations for these solutions it has been found that, because of the higher molecular weight of the non-aqueous solvents, the difference between the activity coefficient, f, and the rational coefficient, f, based on Raoult s law, cannot be neglected, even below a concentration of 0.1 normal, as it usually can with aqueous solutions. This difference was overlooked by the workers just mentioned, who found only partial agreement of their results with the Debye-Huckel theory. Their data have therefore been recomputed as follows. For the ethyl alcohol solutions, for instance, a reference solution with a molality, mu of 0.09501, was chosen. The relation... 

For self-exchange reactions of multiply charged complexes in non-aqueous solvents of low dielectric constant, Eqs (5.5)-(5.8) become numerically unstable because of runaway values of the Coulombic and Debye-Huckel terms, as noted... 

Table 5.3 shows that AV (calc) agrees with the experimentally observed to within the experimental uncertainty for the Debye solvents acetone and acetonitrile, and comes surprisingly close for methanol which, because intermolecular hydrogen-bonding contributes several frequencies to the apparent tl, is not considered to be a Debye liquid. Unfortunately, there are insufficient data for application of Eq. (5.23) to the Ru(hfac)3 electrode reaction in propylene carbonate, which is also regarded as a non-Debye liquid. In any event, the implication is that the fifty-percent rule applies to volumes of activation for electrode reactions but its effect is swamped by solvent dynamical contributions. 

From the macroscopic point of view, SCW is a non-polar solvent from a microscopic point of view, it is a molecule with a strong dipole of 1.85 Debye. Water in the supercritical state is able to react with different compounds. Therefore water is simidtaneously solvent and reactant in a variety of reactions. 

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