Electron Transfer in Homogeneous Solutions

Marcus has developed his primarily classical theory for electron transfer reactions in homogeneous solutions. In the simplest type of reaction a single electron is transferred without breaking or forming bonds. A bimolecular exchange reaction is given by 

Here an electron is transferred from a donor molecule D to an acceptor molecule A. In addition it is useful to define self-exchange reactions of the components as given by 

The activated complex R is a non-equilibrium state, a small portion of which is formed by the fluctuation of the solvent environment. Fluctuations are essentially changes in the redox system configuration due to thermal motion. In the activated state the isoergonic electron transfer occurs to form P, the activated product complex which has the same nuclear configuration. P relaxes then to the equilibrium configuration P(). 

It should be emphasized here that the electron transfer in the activated state is a very fast process which occurs within a time interval of about 10 s. The relaxation times for the solvent and the reacting nuclei are much longer, typically 10 to 10 - s for vibrational motion and 10 to 10 s for rotational motion. Accordingly, it is a reasonable approximation that the positions of the nuclei are unchanged in the course of the electron transfer. This condition is called the Franck-Condon principle. It is well known from studies of absorption and emission of light by molecules. 

According to this transition state concept the corresponding electron transfer rate constant AgT is given by 

In the latter case (Eq. (6.2)), the reaction is isoergonic, that is, the free energy of the reaction is zero (AG = 0). The elementary electron transfer step occurs when 

Semiconductor Electrochemistry, Zweite Auflage. Rudiger Memming. 

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In fact, the surface may mediate the requisite chemistry of the initially formed radical cation so that different products can be observed from the same intermediate when generated photoelectrochemically or by other means. The radical cation of diphenyl-ethylene, for example, gives completely different products upon photoelectrochemical activation 2 than upon electrochemical oxidation at a metal electrode or by single electron transfer in homogeneous solution, Eq. (31) . Surface control of... 

III. FAST CHEMICAL REACTIONS TO INHIBIT BACK ELECTRON TRANSFER IN HOMOGENEOUS SOLUTION... 

The mechanism described above is also correct for electron transfer in homogeneous solution except that, instead of the reaction site being an electrode, it is the point where the two ions meet in the interior of the solution. In the equations for energy changes a factor of 2 relative to electrode reactions appears, since whole reactions rather than halfreactions are being considered. Theoretical and experimental comparisons between electrode reactions and redox reactions in solution have been made with satisfactory results3. 

Equations (8-l)-(8-4) represent a range of interfacial (bio)electrochemical electron transfer systems. Equations (8-l)-(8-4) emerge out of similar formalism for chemical and biological electron transfer in homogeneous solution such as illustrated in the chapter by Winkler and Gray. The analytical transparency of the formalism prompts some observations that illustrate the physical nature of interfacial (bio)electrochemical electronic transitions and at the same time some limitations ... 

Note that homogeneous electron transfer in the solution phase is negligible in the case of half-reactions involving gases, but that it may be very rapid for ionic redox systems. 

Phenylmethylphenacylsulfonium p-toluenesulfonate (PMPS), an onium salt, is known as a self-destructive electron acceptor which decomposes rapidly into phenylmethylsulfide and a phenacyl rachcal upon accepting an electron (59). When PMPS is added to an aqueous solution of ZnTPP-functionalized unimer micelles, the electron acceptor is localized on the anionic surface of the unimer micelle. The election transfer from the 2HnTPP triplet to PMPS produces a ZnTPP cation radical (ZnTPP ) and a phenacyl radical as transient species (Scheme 1), but reaction between these two transient species, which usually follows the photoinduced forward election transfer in homogeneous solutions, is prevented in the unimer micelle system because the ZnTPP " and phenacyl radical species are separated. Thus, the porphyrin cation radicals can be accumulated in the unimer micelle. 

This chapter attempts to survey the studies which have been made on the various electron transfer reactions, occurring between metal ions (of the same element) in homogeneous solution. These reactions include the types known as exchange reactions... 

Free radicals generally undergo one-electron transfer processes in homogeneous solution. Two-electron transfer processes, in which two radicals participate, are often highly exoergic. Typical examples are... 

ZnO (suspension) sensitizes the photoreduction of Ag" by xanthene dyes such as uranin and rhodamine B. In this reaction, ZnO plays the role of a medium to facilitate the efficient electron transfer from excited dye molecules to Ag" adsortei on the surface. The electron is transferred into the conduction band of ZnO and from there it reacts with Ag. In homogeneous solution, the transfer of an electron from the excited dye has little driving force as the potential of the Ag /Ag system is —1.8 V (Sect. 2.3). It seems that sufficient binding energy of the silver atom formed is available in the reduction of adsorbed Ag" ions, i.e. the redox potential of the silver couple is more positive under these circumstances. 

Attempts were made to quantitatively treat the elementary process in electrode reactions since the 1920s by J. A. V. Butler (the transfer of a metal ion from the solution into a metal lattice) and by J. Horiuti and M. Polanyi (the reduction of the oxonium ion with formation of a hydrogen atom adsorbed on the electrode). In its initial form, the theory of the elementary process of electron transfer was presented by R. Gurney, J. B. E. Randles, and H. Gerischer. Fundamental work on electron transfer in polar media, namely, in a homogeneous redox reaction as well as in the elementary step in the electrode reaction was made by R. A. Marcus (Nobel Prize for Chemistry, 1992), R. R. Dogonadze, and V. G. Levich. 

Scheme 4. Possible reaction pathways for the hydrodimerization of acrylonitrile to adiponitrile. The asterisk indicates that electron transfer can be from the cathode or from [CH2CHCN] in homogeneous solution...

Electron transfer reactions of metal ion complexes in homogeneous solution are understood in considerable detail, in part because spectroscopic methods and other techniques can be used to monitor reactant, intermediate, and product concentrations. Unfavorable characteristics of oxide/water interfaces often restrict or complicate the application of these techniques as a result, fewer direct measurements have been made at oxide/water interfaces. Available evidence indicates that metal ion complexes and metal oxide surface sites share many chemical characteristics, but differ in several important respects. These similarities and differences are used in the following discussions to construct a molecular description of reductive dissolution reactions. 

Reductive dissolution occurs via (i) surface precursor complex formation between reductant molecules and oxide surface sites, (ii) electron transfer within this surface complex, and (iii) breakdown of the successor complex and release of dissolved metal ions. Surface speciation is important in determining rates of each of these contributing steps. Limited available evidence concerning rates and mechanism of surface chemical reactions and analogy to similar reactions in homogeneous solution both support this conclusion. 

An improved and direct correlation between the experimental rate constant and [obtained using Eq. (49)] is observed if v = /zd is used instead of v = 1/Tt, the solvent-dependent tunneling factor is utilized, and only AG (het) of Eq. (8) is used in Eq. (49) (see triangles in Fig. 18). Furthermore, the inverse of the longitudinal solvent relaxation time Xi is not necessarily the relevant one to use as the frequency factor v (see empty circles in Fig. 18). Similar conclusions were reached by Barbara and Jerzeba for the electron transfer reaction in homogeneous solutions. Barbara and Jerzeba measured the electron transfer time... 

The validity of an electroanalytical measurement is enhanced if it can be simulated mathematically within a reasonable model , that is, one comprising all of the necessary elements, both kinetic and thermodynamic, needed to describe the system studied. Within the chosen model, the simulation is performed by first deciding which of the possible parameters are indeed variables. Then, a series of mathematical equations are formulated in terms of time, current and potential, thereby allowing the other implicit variables (rate constants of heterogeneous electron-transfer or homogeneous reactions in solution) to be obtained. 

The behavior of the same azoxybenzene is studied in homogeneous conditions— when the dipotassium salt of cyclooctatetraene dianion (CgHgKj) acts as a dissolved electrode. In this case, the reduction of azoxybenzene stops at the very first stage, that is, after the transfer of one electron only (Todres et al. 1975). The initial one-electron reduction produces the azoxybenzene anion-radicals, which are not reduced further despite the presence of residual electron donor in the solution. The ESR method does not reveal these anion-radicals although one-electron oxidation by phenoxyl radicals quantitatively regenerates azoxybenzene and produces the corresponding potassium phenolate molecules in a quantitative yield. Treatment with water leads to a 100% yield of azobenzene (Scheme 2.14). 

Oxidative nitration, a process discovered by Kaplan and Shechter, is probably the most efficient and useful method available for the synthesis of em-dinitroaliphatic compounds from the corresponding nitroalkanes. The process, which is an electron-transfer substitution at saturated carbon, involves treatment of the nitronate salts of primary or secondary nitroalkanes with silver nitrate and an inorganic nitrite in neutral or alkali media. The reaction is believed ° °° to proceed through the addition complex (82) which collapses and leads to oxidative addition of nitrite anion to the nitronate and reduction of silver from Ag+ to Ag . Reactions proceed rapidly in homogeneous solution between 0 and 30 °C. 

Oxidation of carboxylate ions in homogeneous solution using some one-electron transfer agents gives in varying proportions the Kolbe dimer and the product from hydrogen atom abstraction from the solvent by the intermediate alkyl radical. Persulphate ion [109], hexachloco-osmate(v) [110] and the radical-cation from tris(4-bromophenyl)amine [111] all have been used to promote this reaction. 

A) Polyelectrolyte-Bound Electron Transfer Sensitizers in Homogeneous Solution... 

In the last two decades, much has been learned about fundamental aspects of electron transfer in organic and inorganic systems in homogeneous solution. More recendy, the attention of many laboratories has been attracted by the extraordinary potential applications of these fundamental concepts for building real devices which operate on a molecular level. 

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