Electrode processes mass-transfer-controlled reactions

To develop any electrochemical process, a voltage should be applied between anodes and cathodes of the cell. This voltage is the addition of several contributions, such as the reversible cell voltage, the overvoltages, and the ohmic drops, that are related to the current in different ways. One of these contributions, the overvoltage, controls the rate of the transfer of electrons to the electrochemically active species through the electrode-electrolyte interface when there is no limitation in the availability of these active species on the interface (no mass-transfer control and no control by a preceding reaction). In this case, the relationship between the current that flows between the anodes and the cathodes of a cell and the overpotential is... 

The properties of the surface layers have a strong effect on the deposition process. The driving force of the electrochemical reaction is the potential difference over the electrochemical double layer. Adsorption of species can change this potential. For example, the additives used in electrodeposition adsorb in the Helmholtz layer. They can change the local potential difference, block active deposition sites, and so on. The thickness of the diffusion layer affects the mass-transfer rate to the electrode. The diffusion layer becomes thinner with increasing flow rate. When the diffusion layer is thicker than the electrode surface profile, local mass-transfer rates are not equal along the electrode surface. This means that under mass-transfer control, metal deposition on electrode surface peaks is faster than in the valleys and a rough deposit will result. 

The limiting current density is an important parameter for the analysis of mass transfer controlled electrochemical processes and represents the maximum possible reaction rate for a given bulk reactant concentration and fluid flow pattern. During anodic metal dissolution, a mass transfer limiting current does not exist because the surface concentration of the dissolving ion (e.g., Cu + when the anode is composed of copper metal) increases with increasing current density, eventually leading to salt precipitation that blocks the electrode surface. 

Galvanostatic and Potentiostatic Polarization Measurements. Electrode processes may be classified into two types reaction or charge-transfer controlled, and diffusion or mass-transfer controlled. The electrode processes in diaphragm and membrane chlor-alkali cells are charge-transfer controlled. On the other hand, the formation of sodium amalgam on a mercury cathode, is diffusion-controlled. 

Meanwhile, the anode and cathode reactions of Eqs. 8.1a and 8.1b are multi-component reaction systems. As mentioned regarding the ISA method, the anode and cathode reactions are mass-transfer control processes. Then the mass-transfer of each species would provide overpotential due to the species. To investigate the overpotential attributed to each species, the reaction gas addition method was attempted. This is very similar to the ISA except that a reactant gas is added to an electrode instead of an inert gas [41]. Figure 8.13 shows the voltage behaviors due to the addition of a reactant gas. Here, the subscript A denotes a reactant gas species. 

Over the years the original Evans diagrams have been modified by various workers who have replaced the linear E-I curves by curves that provide a more fundamental representation of the electrode kinetics of the anodic and cathodic processes constituting a corrosion reaction (see Fig. 1.26). This has been possible partly by the application of electrochemical theory and partly by the development of newer experimental techniques. Thus the cathodic curve is plotted so that it shows whether activation-controlled charge transfer (equation 1.70) or mass transfer (equation 1.74) is rate determining. In addition, the potentiostat (see Section 20.2) has provided... 

Transport Processes. The velocity of electrode reactions is controlled by the charge-transfer rate of the electrode process, or by the velocity of the approach of the reactants, to the reaction site. The movement or trausport of reactants to and from the reaction site at the electrode interface is a common feature of all electrode reactions. Transport of reactants and products occurs by diffusion, by migration under a potential field, and by convection. The complete description of transport requires a solution to the transport equations. A full account is given in texts and discussions on hydrodynamic flow. Molecular diffusion in electrolytes is relatively slow. Although the process can be accelerated by stirring, enhanced mass transfer... 

For an electrode reaction to be considered reversible, it is necessary to compare the rate of the charge transfer process and the rate of the mass transport of electroactive species. When the mass transport rate is slower than the charge transfer one, the electrode reaction is controlled by the transport rate and can be considered as electrochemically reversible in that the surface concentration fulfills the Nemst equation when a given potential is applied to the electrode. In Electrochemistry, knowledge of the behavior of reversible electrode processes is very important, since these can be used as a benchmark for more complex systems (see Chap. 5 in [1] and Sect. 1.8.4 for a detailed discussion). 

The study of the variation of the current response with time under potentiostatic control is chronoamperometry. In Section 5.4 the current resulting from a potential step from a value of the potential where there is no electrode reaction to one corresponding to the mass-transport-limited current was calculated for the simple system O + ne-— R, where only O or only R is initially present. This current is the faradaic current, If, since it is due only to a faradaic electrode process (only electron transfer). For a planar electrode it is expressed by the Cottrell equation4... 

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. 

With only a qualitative understanding of the experiments described in Section 5.1.1, we saw that we could predict the general shapes of the responses. However, we are ultimately interested in obtaining quantitative information about electrode processes from these current-time or current-potential curves, and doing so requires the creation of a theory that can predict, quantitatively, the response functions in terms of the experimental parameters of time, potential, concentration, mass-transfer coefficients, kinetic parameters, and so on. In general, a controlled-potential experiment carried out for the electrode reaction... 

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