Electrode processes mass-transfer controlled process

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. 

Research and development efforts have been directed toward improved cell designs, theoretical electrochemical studies of magnesium cells, and improved cathode conditions. A stacked-type bipolar electrode cell has been operated on a lab scale (112). Electrochemical studies of the mechanism of magnesium ion reduction have determined that it is a two-electron reversible process that is mass-transfer controlled (113). A review of magnesium production is found in Reference 114. 

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... 

As general trend, it can be observed that for most of the studied phenolic compounds the anodic oxidation at BDD was very fast and, if the applied current density was sufficiently high, the kinetics of the process was under mass-transfer control and it was not appreciably dependent on the nature of the substituting groups in the aromatic ring, as it was reported at more usual electrode materials, like platinum (Torres et al. 2003). 

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. 

In (fl) we assumed a pure electron transfer controlled process at all potentials. As the electron transfer process becomes faster as a consequence of a more favourable electrode potential (eg more negative for a reduction), a situation will eventually arise where the electroactive material is unable to reach the electrode at a sufficiently fast rate. We then find that the current reaches a limiting value dependent upon the rate of mass transport. 

Copper salts are reasonably soluble over a wide pH range, but In and Ga salts only exhibit solubilities above ImM at pH < 3 for In and at pH < 1.5 for Ga (82). Rotating disk electrode experiments show that Cu deposits under mass transfer-controlled conditions on Mo, whereas In deposits under kinetic control at room temperature. There are a few reports on electrodeposition of Cu/In or In/Cu stacks for the realization of CIS semiconductor compounds [83, 84). One technologically interesting report from Penndorf et al. [83] describes the use of copper tape as both the substrate and source of Cu for the formation of CuInS2. Indium was electrode-posited on the copper tape in a roll-to-roU process with remarkably high current densities of 150-200 mAcm with the help of thiourea. CeU efficiencies of up to 6% were reported with this approach. 

Mass Transport. Probably the most iavestigated physical phenomenon ia an electrode process is mass transfer ia the form of a limiting current. A limiting current density is that which is controlled by reactant supply to the electrode surface and not the appHed electrode potential (42). For a simple analysis usiag the limiting current characteristics of various correlations for flow conditions ia a parallel plate cell, see Reference 43. 

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... 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

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). 

In this section, microdisc electrodes will be discussed since the disc is the most important geometry for microelectrodes (see Sect. 2.7). Note that discs are not uniformly accessible electrodes so the mass flux is not the same at different points of the electrode surface. For non-reversible processes, the applied potential controls the rate constant but not the surface concentrations, since these are defined by the local balance of electron transfer rates and mass transport rates at each point of the surface. This local balance is characteristic of a particular electrode geometry and will evolve along the voltammetric response. For this reason, it is difficult (if not impossible) to find analytical rigorous expressions for the current analogous to that presented above for spherical electrodes. To deal with this complex situation, different numerical or semi-analytical approaches have been followed [19-25]. The expression most employed for analyzing stationary responses at disc microelectrodes was derived by Oldham [20], and takes the following form when equal diffusion coefficients are assumed ... 

The curve shown in Fig. 3 cannot proceed indefinitely in either direction. In the cathodic direction, the deposition of copper ions proceeds from solution until the rate at which the ions are supplied to the electrode becomes limited by mass-transfer processes. In the anodic direction, copper atoms are oxidized to form soluble copper ions. While the supply of copper atoms from the surface is essentially unlimited, the solubility of product salts is finite. Local mass-transport conditions control the supply rate so a current is reached at which the solution supersaturates, and an insulating salt-film barrier is created. At that point the current drops to a low level further increase in the potential does not significantly increase the current density. A plot of the current density as a function of the potential is shown in Fig. 5 for the zinc electrode in alkaline electrolyte. The sharp drop in potential is clearly observed at -0.9 V versus the standard hydrogen electrode (SHE). At more positive potentials the current density remains at a low level, and the electrode is said to be passivated. 

This relationship holds for any electrochemical process that involves semiinfinite linear diffusion and is the basis for a variety of electrochemical methods (e.g., polarography, voltammetry, and controlled-potential electrolysis). Equation (3.6) is the basic relationship used for solid-electrode voltammetry with a preset initial potential on a plateau region of the current-voltage curve. Its application requires that the electrode configuration be such that semiinfinite linear diffusion is the controlling condition for the mass-transfer process. 

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... 

The very fast metal-metal ion electrode processes, for which the exchange current density is very high. At steady state the overall rates of those electrode processes are controlled by the rates of mass transfer of the electroactive components to and from the electrode-melt interface. 

It is assumed that all electrons transfers from the particle conduction band and surface states to the electrode take place under conditions where the current is mass transport controlled. The first order rate constant kg describes electron promotion either by thermal or photonic processes, and the rate constant k describes the loss of the electrons from the conduction band or surface states by a process which is first order in electron concentration. The validity of this assumption will be discussed later. There will be an equation similar to equation (71) for each value of m. If each equation is multiplied by its value of m and the engendered set of equations summed, it is possible to obtain the simple result that ... 

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