Rates of Heterogeneous Electron Transfer Reactions

Activation volume — As in case of homogeneous chemical reactions, also the rate of heterogeneous electron transfer reactions at electrode interfaces can depend on pressure. The activation volume AVZ involved in electrochemical reactions can be determined by studying the pressure dependence of the heterogeneous -> standard rate constant ks AVa = -RT j (p is the molar - gas constant, T absolute temperature, and P the pressure inside the electrochemical cell). If AI4 is smaller than zero, i.e., when the volume of the activated complex is smaller than the volume of the reactant molecule, an increase of pressure will enhance the reaction rate and the opposite holds true when A14 is larger than zero. Refs. [i] Swaddle TW, Tregloan PA (1999) Coord Chem Rev 187 255 [ii] Dolidze TD, Khoshtariya DE, Waldeck DH, Macyk J, van Eldik R (2003) JPhys Chem B 107 7172... 

Activation volume — As in case of homogeneous chemical reactions, also the rate of heterogeneous electron transfer reactions at electrode interfaces can depend on pressure. The activation volume AV involved in electrochemical reactions can be determined by studying the pressure dependence of the heterogeneous standard rate constant ks AV = R is the molar... 

Interfacial electron transfer is the critical process occurring in all electrochemical cells in which molecular species are oxidized or reduced. While transfer of an electron between an electrode and a solvated molecule or ion is conceptually a simple reaction, rates of heterogeneous electron transfer processes depend on a multitude of factors and can vary over many orders of magnitude. Since control of interfacial electron transfer rates is usually essential for successful operation of electrochemical devices, understanding the kinetics of these reactions has been and remains a challenging and technologically important goal. 

As shown by the cyclic voltammetric response in Fig. 10, the peak potential separation of the initial Mn(II,II) — Mn(II,III) electrode reaction is much larger than that of the other steps. This suggests significant inner-shell reorganization and a small rate of heterogenous electron transfer for oxidation of the fully reduced Mn(II,II) state. Similar kinetic sluggishness is observed for Mn(III)/Mn(II) electron-transfer reactions of some mononuclear complexes (see Sects 16.1.2 and 16.1.3). 

Attempts to develop a model for the digital simulation of the cyclic voltammetric behaviour of PVF films on platinum62 electrodes required inclusion of the following features (a) environmentally distinct oxidized and reduced sites within the film (b) interconversion of the above sites and interaction between them (c) rate of electrochemical reactions to depend on the rate of interconversion of redox sites, the rate of heterogeneous electron transfer between film and substrate, intrafilm electron transfer and the rate of diffusion of counter ions and (d) dependence on the nature of the supporting electrolyte and the spacing of electroactive groups within the film. 

The above analysis also shows that for almost all applications of fast CV employing V > 1 kV s , the quasi-reversible or irreversible nature of heterogeneous electron transfer reactions must be considered. In particular, this becomes important when fast CV is used in a kinetic analysis of fast homogeneous follow-up reactions. The extraction of the relevant rate constants is complicated by the mixed kinetic control of the electrode process and the chemical reaction. As a result, the number of parameters involved in the fitting procedures is increased considerably and with it the possibility of introducing errors. 

The electrochemical redox reaction of a substrate resulting from the heterogeneous electron transfer from the electrode to this substrate (cathodic reduction) or the opposite (anodic oxidation) is said to be electrochemically reversible if it occurs at the Nernstian redox potential without surtension (overpotential). This is the case if the heterogeneous electron transfer is fast, i.e. there must not be a significant structural change in the substrate upon electron transfer. Any structural change slows down the electron transfer. When the rate of heterogeneous electron transfer is within the time scale of the electrochemical experiment, the electrochemical process is fast (reversible). In the opposite case, it appears to be slow (electrochemically irreversible). Structural transformations are accompanied by a slow electron transfer (slow E), except if this transformation occms after electron transfer (EC mechanism). 

In general, electrochemical systems are heterogeneous and involve at least one (or both) of the fundamental processes - mass transport and an electron-transfer reaction. Moreover, electrochemical reactions involve charged species, so the rate of the electron-transfer reaction depends on the electric potential difference between the phases (e.g. between the electrode surface and the solution). The mass transport processes mainly include diffusion, conduction, and convection, and should be taken into account if the electron-transfer reaction properties are to be extracted from the experimental measurements. The proper control of the mass transport processes seems to be one of the main problems of high-temperature electrochemical studies. 

While a lowering of the temperature will lead to a lowering of the rate of following reactions it is important to note that this will also have an impact on the rate of heterogeneous electron transfer. The improved spectroscopic detection of intermediate species depends on their relative rates of formation and decay. While in the previous example cooling leads to improved detection of the intermediate species there are a number of instances where poorer SEC responses are obtained at lower temperature. 

The remaining sections of this chapter will be mostly concerned with reactions following mechanism I. In this case, the photocurrent magnitude is directly connected to the ratio between the rates of heterogeneous electron transfer and excited state decay. In addition, the effect of the Galvani potential difference on the photocurrent magnitude provides valuable information on the reactivity of the metalloporphyrin at the liquid/liquid boundary. 

In recent years, considerable attention has shifted to nanoscale electrodes (as already discussed in Chapter 15) and integrated systems. ° With this further downscaling, the intrinsic advantages of UMEs such as small ohmic drops and fast response times are further amplified. Mass transport also becomes so efficient that even fast electrochemical reactions become increasingly limited by the rate of heterogeneous electron transfer, allowing ultrafast electron-transfer kinetics to be studied. Furthermore, because the electrode size becomes comparable to the thickness of the electrical double layer and to the size of macromolecular analytes, new mass-transport phenomena have been predicted and new analytical applications can be considered, respectively. ... 

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