Debye solvents

In Debye solvents, x is tire longitudinal relaxation time. The prediction tliat solvent polarization dynamics would limit intramolecular electron transfer rates was stated tlieoretically [40] and observed experimentally [41]. 

Following the analysis of the previous section it has been shown that C(r) is given by Eq. (19) for a Debye solvent... 

According to Eq. (19), t, is the time scale for excited state solvation for a Debye solvent. In fact, it is the time scale for both excited state and ground solvation of dipolar solutes and ionic solutes, t, also plays a role in a broad range of reactive (Section III) and nonreactive charge transfer processes in solution. It is clearly worthwhile to establish a physical picture for this important variable. 

An Evaluation of the Debye-Onsager Model. The simplest treatment for solvation dynamics is the Debye-Onsager model which we reviewed in Section II.A. It assumes that the solvent (i) is well modeled as a uniform dielectric continuum and (ii) has a single relaxation time (i.e., the solvent is a Debye solvent ) td (Eq. (18)). The model predicts that C(t) should be a single... 

Ignoring the potential limitations of the dielectric data, we can evaluate the Debye-Onsager model for a number of apparently roughly Debye solvents, like propylene carbonate, the alkyl nitriles, the alkyl acetates, and other solvents. First of all, C( ) is often strongly nonmonoexponential, in contradiction to the theoretical prediction. Second, the observed average solvation time is often much different from xt. 

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. 

Fig. 4. Plot of AG /2.3 RT (25 °C) for metallocene electron self-exchange measurements [162] analyzed by means of the dielectric-continuum formula versus log rf for polar Debye solvents. PN, propionitrile for definition of the other solvents, see Table 1.

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]). 

Fig. 4.5 Plots of the in-phase, 6 , and out-of-phase, components of the dielectric permittivity of a hypothetical Debye solvent against the logarithm of frequency. The parameters assumed are 8in = 50, 8out =2, and tq = 20 ps.

The temperature dependence of the longitudinal relaxation time tl is also an important quantity. For a Debye solvent, tl is given by the relationship... 

Table 7.9 Reactant System Characteristic Frequencies in Selected Debye Solvents Estimated Using Equation (7.10.12) Together with the Solvent Molecule s Effective Moment of Inertia and the Reciprocal of the Longitudinal Relaxation Time...

As interaction between the two energy surfaces increases, the character of the reaction changes from diabatic to adiabatic. This interaction affects the shape of the cusp-shaped barrier associated with the transition state and thus the value of v. In the case of a simple Debye solvent the friction parameter is given by... 

The rate expression in Eq. (16.15) can be simplifled signiflcantly under a series of well-deflned approximations. In the short-time high-temperature approximation for a Debye solvent, the solvent dynamics is negligible on the time scale of the probability flux correlation function, leading to the following simpliflcation ... 

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. 

There have been other developments recently, particularly in the field of solvent dynamics, stimulated in part by the introduction of very fast (picosecond, femtosecond) experimental techniques for studying electron transfers, techniques which have now recently been applied to photosynthetic systems. In one approximation (Debye "solvent single exponential regime Xi/Xo small) the observed rate is given by... 

In a few cases, however, a more quantitative analysis can be undertaken whereby the desired solvent-dependent AG int values are obtained experimentally from optical ET reorganization energies for related binuclear systems. An example of this approach, involving self exchanges of metallocenium-metallocene (Cp2M ") redox couples in various polar Debye solvents is worth highlighting here since ET rate-solvent dependencies are observed that span the limits of nonadiabatic and adiabatic behavior [12]. For ferrocenium-ferrocene couples, the rate constants k gx (corrected for AG -solvent variations) are almost independent of the solvent dynamics, as... 

For a Debye solvent, is given by the solvation time x, defined as the integrated area of C,(0- We notice that is much shorter than Tj in BMI DCA", whereas they are nearly the same in acetonitrile. Also increases significantly as the ET barrier height decreases in the former, while it varies little in the latter. We understand these results as follows. 

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