Selected experimental results for electron-transfer reactions

1996 ◽  
Author(s):  
Wolfgang Schmickler
Keyword(s):  
Electron Transfer ◽  
Transfer Coefficient ◽  
Outer Sphere ◽  
Chloride Ions ◽  
Transfer Reactions ◽  
Energy Of Activation ◽  
Trace Impurities ◽  
Electron Transfer Reactions ◽  
Temperature Range ◽  
Straight Line

Innumerable experiments have been performed on both inner- and outer-sphere electron-transfer reactions. We do not review them here, but present a few results that are directly relevant to the theoretical issues raised in the preceding chapters. The Butler-Volmer equation (5.10) predicts that for |η| > kT/e0 a plot of the logarithm of the current versus the applied potential (Tafel plot) should result in a straight line, whose slope is determined by the transfer coefficient α. Because of the dual role of the transfer coefficient (see Section 5.2), it is important to verify that the transfer coefficient obtained from a Tafel plot is independent of temperature. We shall see later that proton- and ion-transfer reactions often give straight lines in Tafel plots, too, but the apparent transfer coefficient obtained from these plots can depend on the temperature, indicating that these reactions do not obey the Butler-Volmer law. In order to test the temperature independence of the transfer coefficient, Curtiss et al. investigated the kinetics of the Fe2+/Fe3+ reaction on gold in a pressurized aqueous solution of perchloric acid over a temperature range from 25° to 75°C. In the absence of trace impurities of chloride ions, this reaction proceeds via an outer sphere mechanism with a low rate constant (k0 ≈ 10-5 cm s-1 at room temperature). Figure 8.1 shows the slope of their Tafel plots, d(lni)/dη, as a function of the inverse temperature 1/T. The Butler-Volmer equation predicts a straight line of slope αe0/k, which is indeed observed. Over the investigated temperature range both the transfer coefficient and the energy of activation are constant: α = 0.425 ± 0.01 and Eact = 0.59± 0.01 eV at equilibrium, confirming the validity of the Butler-Volmer equation in the region of low overpotentials, from which the Tafel slopes were obtained. The phenomenological derivation of the Butler-Volmer equation is based on a linear expansion of the Gibbs energy of activation with respect to the applied overpotential. At large overpotentials higher-order terms are expected to contribute, and a Tafel plot should no longer be linear.

Theoretical considerations of electron-transfer reactions

1996 ◽  
Author(s):  
Wolfgang Schmickler
Keyword(s):  
Electron Transfer ◽  
Outer Sphere ◽  
Transfer Reactions ◽  
Energy Of Activation ◽  
Reduced Form ◽  
Simple Derivation ◽  
Heavy Particles ◽  
Electron Transfer Reactions ◽  
Complex Processes ◽  
Outer Sphere Electron Transfer

Chemical and electrochemical reactions in condensed phases are generally quite complex processes; only outer-sphere electron-transfer reactions are sufficiently simple that we have reached a fair understanding of them in terms of microscopic concepts. In this chapter we give a simple derivation of a semiclassical theory of outer-sphere electron-transfer reactions, which was first systematically developed by Marcus and Hush in a series of papers. A more advanced treatment will be presented in Chapter 19. We begin with qualitative considerations. During the course of an outer-sphere electron-transfer reaction, the reactants get very close, up to a few Ångstroms, to the electrode surface. Electrons can tunnel over such a short distance, and the reaction would be very fast if nothing happened but the transfer of an electron. In fact, outer-sphere reactions are fast, but they have a measurable rate, and an energy of activation of typically 0.2 - 0.4 eV, since electron transfer is accompanied by reorganization processes of atoms and molecules that require thermal activation. While the reacting complex often has the same or similar structure in the oxidized and reduced form, metal-ligand bonds are typically shorter in the complex with the higher charge, which is also more strongly solvated. So the reaction is accompanied by a reorganization of both the complex, or inner sphere, and the solvation sheath, or outer sphere (see Fig. 6.1). These processes require an energy of activation and slow the reaction down. A natural question is: In which temporal order do the reorganization processes and the proper electron transfer take place? The answer is given by the Frank-Condon principle, which in this context, states: First the heavy particles of the inner and outer sphere must assume a suitable intermediate configuration, then the electron is exchanged isoenergetically, and finally the system relaxes to its new equilibrium configuration. A simple illustration is given in Fig. 6.2, where we have drawn potential energy surfaces for the reduced and the oxidized state as a function of two generalized reaction coordinates representing the positions of particles in the inner and outer sphere.

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