Multistep electron transfers

In solid state materials, single-step electron transport between dopant species is well known. For example, electron-hole recombination accounts for luminescence in some materials [H]. Multistep hopping is also well known. Models for single and multistep transport are enjoying renewed interest in tlie context of DNA electron transfer [12, 13, 14 and 15]. Indeed, tliere are strong links between tire ET literature and tire literature of hopping conductivity in polymers [16]. 

In deriving the kinetics of activation-energy controlled charge transfer it was emphasised that a simple one-step electron-transfer process would be considered to eliminate the complications that arise in multistep reactions. The h.e.r. in acid solutions can be represented by the overall equation ... 

A multistep hopping mechanism explains not only the long distance hole transfer through DNA, it can also rationalize the electron transfer through reduced DNA as T. Carell and M.D. Sevilla demonstrate in this volume. 

An important aspect of hydrogen transfer equilibrium reactions is their application to a variety of oxidative transformations of alcohols to aldehydes and ketones using ruthenium catalysts.72 An extension of these studies is the aerobic oxidation of alcohols performed with a catalytic amount of hydrogen acceptor under 02 atmosphere by a multistep electron-transfer process.132-134... 

Figure 1. Schematic representation of the artificial photosynthetic reaction center by a monolayer assembly by A-S-D triad and antenna molecules for light harvesting (H), lateral energy migration and energy transfer, and charge separation across the membrane via multistep electron transfer (a) Side view of mono-layer assembly, (b) top view of a triad surrounded by H molecules, and (c) energy diagram for photo-electric conversion in a monolayer assembly.

Metal oxides possess multiple functional properties, such as acid-base, redox, electron transfer and transport, chemisorption by a and 71-bonding of hydrocarbons, O-insertion and H-abstract, etc. which make them very suitable in heterogeneous catalysis, particularly in allowing multistep transformations of hydrocarbons1-8 and other catalytic applications (NO, conversion, for example9,10). They are also widely used as supports for other active components (metal particles or other metal oxides), but it is known that they do not act often as a simple supports. Rather, they participate as co-catalysts in the reaction mechanism (in bifunctional catalysts, for example).11,12... 

V,/V-dimethylaniline, especially when those strong donors are paired with the relatively electron-poor MES derivative of the bis(arene)iron(ll) acceptor. As such, the dark reactions arise via essentially the same multistep mechanism as that for charge-transfer de-ligation, the difference arising from an adiabatic electron transfer (10) as the initial step that is thermally allowed when the driving force -AGET is sufficient to surmount... 

II. CONTROL OF MULTISTEP PHOTOINDUCED ELECTRON-TRANSFER SYSTEMS... 

Sc heme 1 Multistep photoinduced electron transfers in a natural photosynthetic system. 

In the presence of oxygen or in air-saturated solutions, 11 is the major product (Scheme 6.9) [56, 59]. The formation of the cycloadduct follows a multistep process that probably includes several inter- or intramolecular electron-transfer steps. Suggestions include the electron transfer to singlet oxygen as an important part of the mechanism [58]. One possible mechanism is shown in Scheme 6.9. Oxygen plays the role of both an electron- and a proton-acceptor. 

A key aspect of metal oxides is that they possess multiple functional properties acid-base, electron transfer and transport, chemisorption by a and 7i-bonding of hydrocarbons, O-insertion and H-abstraction, etc. This multi-functionality allows them to catalyze complex selective multistep transformations of hydrocarbons, as well as other catalytic reactions (NO,c conversion, for example). The control of the catalyst multi-functionality requires the ability to control not only the nanostructure, e.g. the nano-scale environment around the active site, " but also the nano-architecture, e.g. the 3D spatial organization of nano-entities. The active site is not the only relevant aspect for catalysis. The local area around the active site orients or assists the coordination of the reactants, and may induce sterical constrains on the transition state, and influences short-range transport (nano-scale level). Therefore, it plays a critical role in determining the reactivity and selectivity in multiple pathways of transformation. In addition, there are indications pointing out that the dynamics of adsorbed species, e.g. their mobility during the catalytic processes which is also an important factor determining the catalytic performances in complex surface reaction, " is influenced by the nanoarchitecture. 

One of the important applications of mono- and multimetallic clusters is to be used as catalysts [186]. Their catalytic properties depend on the nature of metal atoms accessible to the reactants at the surface. The possible control through the radiolytic synthesis of the alloying of various metals, all present at the surface, is therefore particularly important for the catalysis of multistep reactions. The role of the size is twofold. It governs the kinetics by the number of active sites, which increase with the specific area. However, the most crucial role is played by the cluster potential, which depends on the nuclearity and controls the thermodynamics, possibly with a threshold. For example, in the catalysis of electron transfer (Fig. 14), the cluster is able to efficiently relay electrons from a donor to an acceptor, provided the potential value is intermediate between those of the reactants [49]. Below or above these two thresholds, the transfer to or from the cluster, respectively, is thermodynamically inhibited and the cluster is unable to act as a relay. The optimum range is adjustable by the size [63]. 

The electron waiting-line problem is hence clear. In a particular multistep electron-transfer reaction, the step with the lowest servicing rate or conductivity produces the largest queue and, indeed, the total queue is virtually a simple multiple of the queue at the rds. In other words, in the steady state, all n steps proceed at the rate of the rate-determining step ir, [cf. Eq. (9.4)], and the total net current is... 

Equation (7.144) is the most general form of the Butler-Volmer equation it is valid for a multistep overall electrodic reaction in which there may be electron transfers in steps other than the rds and in which the rds may have to occur V times per occurrence of the overall reaction. This generalized equation is seen to be of the same form as the simple Butler-Volmer equation for a one-step, single-electron transfer reaction ... 

In comparing the general and the simple equations, it is seen that the transfer coefficients play the same role in a multistep, n-electron-transfer reaction as the symmetry factor does in one-step, one-electron transfer reaction, i.e., thea s determine how the input electrical energy (Ft)) affects the reaction rate. Table 15 shows the tabulation of values for y, r, v, y, and n, from which a and a have been evaluated. 

Also, in complex electrode reactions involving multistep proton and electron transfer steps, the electrochemical reaction order with respect to the H+ or HO may also vary with pH, indicating a change of mechanism with pH. In this respect, the use of schemes of squares outlined in Sect. 2.2 is very useful in the analysis of these complex kinetics [13]. 

The equations for multistep electron transfer according to the quasiequilibrium treatment can be derived on the basis of Parsons general and rigorous treatment [47]. For simplicity, mass transport limitations, double layer effects, ohmic overpotential, and specific adsorption or chemisorption are neglected in the present formalism. 

Identity (150) only holds if the same step remains rate-controlling over the wide range of potentials involved. As seen in Sect. 4.1, this condition is not very realistic in complex multistep electron transfer electrode reactions. 

A double electrode is clearly a convenient tool for the investigation of multistep processes. Its application to the study of multistep electron transfer is the subject of the next section. 

Double electrodes are invaluable in the elucidation of multistep electron transfers. Applications have been almost exclusively at the RRDE. 

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