Reactions Controlled by the Rate of Electron Transfer

In this section we consider experiments in which the current is controlled by the rate of electron transfer (i.e., reactions with sufficiently fast mass transport). The current-potential relationship for such reactions is different from those discussed (above) for mass-transport-controlled reactions. 

Consider again the electron transfer reaction O + ne - R the actual electron transfer step involves transfer of the electron between the conduction band of the electrode and a molecular orbital of O or R (e.g., for a reduction, from the conduction band into an unoccupied orbital in O). The rate of the forward (reduction) reaction Vt is first-order in O  

When E = E°, no net current is flowing. This situation, however, is dynamic with continuous movement of charge carriers in both directions and with equal opposing anodic and cathodic current components. The absolute magnitude of these components at E° is the exchange current (i0), which is directly proportional to the standard rate constant  

The exchange current density for common redox couples (at room temperature) can range from 10 6pA/cm2 to A/cm2. The Butler-Volmer equation can be written in terms of the exchange current 

Equation (1.26) can be used for extracting information on z0 and a, which are important kinetic parameters. For sufficiently large overvoltages (rt 118mV/n), one of the exponential terms in Eq. (1.26) will be negligible compared with the other. For example, at large negative overpotentials, z c 4 and Eq. (1.26) becomes 

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Pai et al. (1983) measured hole mobilities of a series of bis(diethylamino)-substituted triphenylmethane derivatives doped into a PC and poly(styrene) (PS). The mobilities varied by four orders of magnitude, while the field dependencies varied from linear to quadratic. In all materials, the field dependencies decreased with increasing temperature. The temperature dependencies were described by an Arrhenius relationship with activation energies that decrease with increasing field. Pai et al. described the transport process as a field-driven chain of oxidation-reduction reactions in which the rate of electron transfer is controlled by the molecular substituents of the hopping sites. 

Oxidation and reduction processes are accompanied by the flow of electric charge through the interface metal-corrosive environment. In metals the charge carriers are electrons while in the corrosive environment charge flow is due to ions. Thus an active assessment of electrochemical corrosion processes can be achieved by assessing the electrical charge transfer process. In the reactions of corrosion that are controlled by the rate of charge transfer, the current - potential relationship can be described by the Butler-Vokner equation ... 

Cobalt(II) complexes of three water-soluble porphyrins are catalysts for the controlled potential electrolytic reduction of H O to Hi in aqueous acid solution. The porphyrin complexes were either directly adsorbed on glassy carbon, or were deposited as films using a variety of methods. Reduction to [Co(Por) was followed by a nucleophilic reaction with water to give the hydride intermediate. Hydrogen production then occurs either by attack of H on Co(Por)H, or by a disproportionation reaction requiring two Co(Por)H units. Although the overall I easibility of this process was demonstrated, practical problems including the rate of electron transfer still need to be overcome. " " ... 

Studies of electron transfer (ET) at micro-ITIES are scarce. Solomon and Bard first observed the ET between TCNQ (in DCE) and ferrocyanide (in water) at a micro-ITIES supported by micropipettes [5]. The pipette was used as a SECM probe for electrochemical imaging. The current was controlled by the rate of the bimolecular ET reaction at the micro-ITIES... 

Experimental data (Figure 4.2) for the dissociative electron transfer between radical anions and the carbon-halogen bond in alkyl halides indicates a linear relationship between log(k ) and Ed over a wide range of reaction rates [5, 9]. Very fast reactions become controlled by the rate of diffusion of two species towards each other, when every close encounter gives rise to electron transfer. A parabolic... 

When the above factors are put under control, the possibility of changing the ligand L in the pentacyano(L)ferrate complexes adds a further dimension for studying systematic reactivity changes, brought out by the controlled modification of the redox potentials of the Fe(II)-Fe(III) redox couples. In this way, the rates of electron transfer reactions between a series of [Fen(CN)5L]re complexes toward a common oxidant like [Coin(NH3)5(dmso)]3+ showed a variation in agreement with Marcus predictions for outer-sphere electron transfer processes, as demonstrated by linear plots of the rate constants versus the redox potentials (123). 

Radicals can be either reduced (to anions or organometallics) or oxidized to cations by formal single electron transfer (Scheme 11).50 Such redox reactions can be conducted either chemically or electro-chemically51 and the rates of electron transfer are usually analyzed by the Marcus theory and related treatments.50 These rates depend (in part) on the difference in reduction potential between the radical and the reductant (or oxidant). Thus a species such as an a-amino radical with high-lying singly occupied molecular orbital (SOMO) is more readily oxidized, while a species such as the malonyl radical with a low-lying SOMO is more readily reduced. The inherent difference in reduction potential of substituted radicals is an important control element in several kinds of reactions. 

The reaction kinetics is controlled by two factors ki (s-1) for the electron transfer between the nearest redox site and the electrode, and k2 (cm2 mol 1 s-1), for the electron transfer between the neighboring redox sites in a molecular wire. Here, the rate of electron transfer to the neighboring site in a polymer wire is assumed to be constant in a primary approximation. In the case of linear oligomer wires such as [nFeLi] and [ FeL2],... 

If the electron-transfer step in an electrode reaction is preceded by a chemical reaction that involves proton transfer, the polarographic current often will be a complex function of the concentration of the electroactive species, the hy-dronium ion concentration, and the rate constants for proton and electron transfer. Currents controlled by the rate of a chemical reaction are called kinetic currents and often are observed in the reduction of electroactive acids (e.g., pyruvic acid), in which the protonated form of the acid is more easily reduced than the anion. A polarogram of pyruvic acid in unbuffered solution exhibits two waves whose relative wave heights depend on the concentration of pyruvic acid and the solution pH.59... 

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