Electron transfer process, frequency-dependent

Figure 3. Frequency-dependent conductivity [oM] for electron-transfer process.

Electron transfer processes, more generally transitions that involve charge reorganization in dielectric solvents, are thus shown to fall within the general category of shifted harmonic oscillator models for the thennal enviromnent that were discussed at length in Chapter 12. This is a result of linear dielectric response theory, which moreover implies that the dielectric response frequency a>s does not depend on the electronic charge distribution, namely on the electronic state. This rationalizes the result (16.59) of the dielectric theoiy of electron transfer, which is identical to the rate (12.69) obtained from what we now find to be an equivalent spin-boson model. 

Schlichthorl et al. [177] have used light modulated microwave reflectivity to derive the rates of interfacial electron transfer processes at the n-Si/electrolyte interface. In these measurements, the modulation frequency was constant, and the rate constants for charge transfer were derived from the potential dependent ARm response. Schlichthorl et al. [73] have extended the technique considerably by introducing frequency response analysis. The technique is therefore analogous to IMPS, although, as shown below, it provides additional information. 

Doom and Hupp have used preresonance Raman spectra in an analysis of the vibronic components which contribute to the intervalence absorption maximum of [(CN)5Ru -CN-Ru (NH3)5] and to the MLCT absorption maximum of [(bpy)Ru(NH3)4] ". These authors employ the time-dependent scattering approach of Heller to obtain the nuclear displacements of several vibrational modes coupled to the electronic transitions. They find in each case that several vibrational modes, spanning a wide range of frequencies, do contribute significantly to the photoinduced electron transfer processes. Hopkins and co-workers have used a two-color, ps Raman technique to investigate interligand electron transfer in Ru(II)-tn5-polypyridyl complexes, and they find vibrational relaxation of the electronically excited mole ule occurs within about 30 ps of excitation, after which interligand equilibration occurs more slowly than 5 x 10 s. 

The model s important prediction is that of the influence of each of branches of the longitudinal polarizi ion fluctuation spectrum on the electron-transfer probability. The high-frequency electronic branches. Equation (2c), which are responsible for the photoemission relaxation energies, exert only a minor influence on electron-transfer by virtue of a temperature-independent prefactor. The low-frequency branches. Equation (2a), contribute to the activation energy for the electron transfer process as well as to the temperature-dependent widths of photoemission lines via Equation (6b). The IR branches. Equation (2b), cause the apparent activation energies to increase with increas-... 

Instead of the quantity given by Eq. (15), the quantity given by Eq. (10) was treated as the activation energy of the process in the earlier papers on the quantum mechanical theory of electron transfer reactions. This difference between the results of the quantum mechanical theory of radiationless transitions and those obtained by the methods of nonequilibrium thermodynamics has also been noted in Ref. 9. The results of the quantum mechanical theory were obtained in the harmonic oscillator model, and Eqs. (9) and (10) are valid only if the vibrations of the oscillators are classical and their frequencies are unchanged in the course of the electron transition (i.e., (o k = w[). It might seem that, in this case, the energy of the transition and the free energy of the transition are equal to each other. However, we have to remember that for the solvent, the oscillators are the effective ones and the parameters of the system Hamiltonian related to the dielectric properties of the medium depend on the temperature. Therefore, the problem of the relationship between the results obtained by the two methods mentioned above deserves to be discussed. 

In the temperature interval of —70 to 0°C and in the low-frequency range, an unexpected dielectric relaxation process for polymers is detected. This process is observed clearly in the sample PPX with metal Cu nanoparticles. In sample PPX + Zn only traces of this process can be observed, and in the PPX + PbS as well as in pure PPX matrix the process completely vanishes. The amplitude of this process essentially decreases, when the frequency increases, and the maximum of dielectric losses have almost no temperature dependence [104]. This is a typical dielectric response for percolation behavior [105]. This process may relate to electron transfer between the metal nanoparticles through the polymer matrix. Data on electrical conductivity of metal containing PPX films (see above) show that at metal concentrations higher than 5 vol.% there is an essential probability for electron transfer from one particle to another and thus such particles become involved in the percolation process. The minor appearance of this peak in PPX + Zn can be explained by oxidation of Zn nanoparticles. 

---