Multi-step electrode reactions reaction rates

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. 

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. 

Note that many steps are involved in an EC reaction, such as the electron transfer reaction, transport of molecules from the bulk solution to the electrode surface and chemical reactions coupled to the electron transfer reaction. As with any multi step reaction, the rate of the overall reaction is generally determined by the rate of the slowest step (the rate-limiting step), and it is important to identify this step. In the analytical electrochemistry of dissolved species, the limiting step is typically the transport of molecules to the electrode surface through the solution. However, there are many instances where this is not the case and where the rate of the heterogeneous electron transfer reaction is important, for example in corrosion electrochemistry. 

Most electrode reactions encountered in the field of corrosion involve the transfer of more than one electron. Such reactions take place in steps, of which the slowest, called the rate-determining step, abbreviated RDS, determines the overall reaction rate. In simple cases, one can identify the rate-determining step by an analysis of the measured Tafel slopes. In the so-called quasi-equilibrium approach one assumes that with the exception of the rate-limiting step, all other steps are at equilibrium. This greatly simplifies the mathematical equations for the reaction rate. More realistic approaches require numerical simulation and shall not be discussed here. To illustrate the quasi equilibrium approach to the study of multi-step electrode reactions we shall look at proposed mechanisms for the dissolution of copper and of iron. 

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). 

---