Electrode kinetics multi-step reactions

As in the present state of the art the study of electrochemical kinetics is not confined to simple electrode reactions, recent developments of more complex cases will also be discussed. This concerns, in particular, mechanistic studies of multi-step reactions with both unstable and stable intermediates and adsorption processes. Each time, the most suitable methods for such studies will be selected for a discussion of the appropriate methodology and analysis procedure. 

In a staged multi-scale approach, the energetics and reaction rates obtained from these calculations can be used to develop coarse-grained models for simulating kinetics and thermodynamics of complex multi-step reactions on electrodes (for example see [25, 26, 27, 28, 29, 30]). Varying levels of complexity can be simulated on electrodes to introduce defects on electrode surfaces, composition of alloy electrodes, distribution of alloy electrode surfaces, particulate electrodes, etc. Monte Carlo methods can also be coupled with continuum transport/reaction models to correctly describe surfaces effects and provide accurate boundary conditions (for e.g. see Ref. [31]). In what follows, we briefly describe density functional theory calculations and kinetic Monte Carlo simulations to understand CO electro oxidation on Pt-based electrodes. 

This chapter discusses a staged multi-scale approach for understanding CO electrooxidation on Pt-based electrodes. In this approach, density functional theory (DFT) is used to obtain an atomistic view of reactions on Pt-based surfaces. Based on results from experiments and quantum chemistry calculations, a consistent coarse-grained lattice model is developed. Kinetic Monte Carlo (KMC) simulations are then used to study complex multi-step reaction kinetics on the electrode surfaces at much larger lengthscales and timescales compared to atomistic dimensions. These simulations are compared to experiments. We review KMC results on Pt and PtRu alloy surfaces. 

The oxygen/water half-cell reaction has been one of the most challenging electrode systems for decades. Despite enormous research, the detailed reaction mechanism of this complex multi-step process has remained elusive. Also elusive has been an electrode material and surface that significantly reduces the rate-determining kinetic activation barriers, and hence shows improvements in the catalytic activity compared to that of the single-noble-metal electrodes such as Pt or Au. 

The Frumkin epoch in electrochemistry [i-iii] commemorates the interplay of electrochemical kinetics and equilibrium interfacial phenomena. The most famous findings are the - Frumkin adsorption isotherm (1925) Frumkin s slow discharge theory (1933, see also - Frumkin correction), the rotating ring disk electrode (1959), and various aspects of surface thermodynamics related to the notion of the point of zero charge. His contributions to the theory of polarographic maxima, kinetics of multi-step electrode reactions, and corrosion science are also well-known. An important feature of the Frumkin school was the development of numerous original experimental techniques for certain problems. The Frumkin school also pioneered the experimental style of ultra-pure conditions in electrochemical experiments [i]. A list of publications of Frumkin until 1965 is available in [iv], and later publications are listed in [ii]. 

We shall not discuss here the mechanism of either of these reactions they were mentioned only to show the complexity of typical electrode reactions. It is evident then that the equations of electrode kinetics derived in Chapter E must be generalized to describe multi step electrode processes, which involve the transfer of several electrons. 

An example of the simplest (in the sense of the number of kinetic parameters) electrochemical reaction is reduction of silver ions (Ag+) from a dilute aqueous solution of a well soluble silver salt (e.g., nitrate) in the presence of excess of an indifferent salt (e.g., potassium nitrate) on a liquid silver-mercury alloy (also called amalgam) electrode. Besides the transfer of a single electron, only diffusion steps are involved in this process. The entire reaction can be very well modeled and the kinetic parameters are determined experimentally with high level of accuracy. The information gleaned while analyzing the mechanism of silver ion reduction can be used in elucidating more complex, multi-step, multiphase processes, such as the electrochemical reaction in a lithium-ion cell. 

This chapter is concerned with measurements of kinetic parameters of heterogeneous electron transfer (ET) processes (i.e., standard heterogeneous rate constant k° and transfer coefficient a) and homogeneous rate constants of coupled chemical reactions. A typical electrochemical process comprises at least three consecutive steps diffusion of the reactant to the electrode surface, heterogeneous ET, and diffusion of the product into the bulk solution. The overall kinetics of such a multi-step process is determined by its slow step whose rate can be measured experimentally. The principles of such measurements can be seen from the simplified equivalence circuit of an electrochemical cell (Figure 15.1). 

Many redox reactions at electrodes involve transfer of more than one electron. It is agreed that such processes usually involve several consecutive one-electron steps rather than a simultaneous multi-electron transfer. The kinetics of the overall reaction (and hence the current flowing) are complicated by such factors as the lifetimes of the transient intermediate species. 

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