Steady-state process current densities

Figure 16 shows the steady-state limiting current density, ilim, for the oxygen reduction reaction (ORR) on pure Al, pure Cu, and an intermetallic compound phase in Al alloy 2024-T3 whose stoichiometry is Al20Cu2(Mn,Fe)3 after exposure to a sulfate-chloride solution for 2 hours (43). The steady-state values for the Cu-bearing materials match the predictions of the Levich equation, while those for Al do not. Reactions that are controlled by mass transport in the solution phase should be independent of electrode material type. Clearly, this is not the case for Al, which suggests that some other process is rate controlling. 

The classification of methods for studying electrode kinetics is based on the criterion of whether the electrical potential or the current density is controlled. The other variable, which is then a function of time, is determined by the electrode process. Obviously, for a steady-state process, these two quantities are interdependent and further classification is unnecessary. Techniques employing a small periodic perturbation of the system by current or potential oscillations with a small amplitude will be classified separately. 

The etch rate of anodic oxide can be determined by methods similar to those for thermal oxide or deposited oxides. It may also be estimated from the anodic current of the oxidized electrode. The anodic i-V curve of a silicon electrode typically shows a passivation-like peak above which the dissolution occurs through a two-step process the formation of oxide film followed by the chemical dissolution of the oxide. The steady-state anodic current measured at an anodic potential above the peak potential indicates the dissolution rate of the anodic oxide. Thus, the passivation current, /p, listed in Table 5.5 can be used for estimation of the etch rate of the oxide film formed at the anodic potentials. (A current density of 1 mA/cm corresponds to a silicon etch rate of 3.1A/S or to a silicon oxide etch rate of about 7 A/s.) For example, in 1% HF solution, ip is 5mA/cm, and thus the etch rale of the oxide film formed at a potential anodic of the first current peak is about 35 A/s. hi 2M KOH solution at room temperature, ip == 0.002mA/cm equivalent to an etch rate of about 0.014 A/s. These numbers appear to be in general agreement with the data in Table 4.1. 

To deal with problems concerning non-steady-state processes, the function F i, t) in the Eq. (3.33) should be specified. When the current density is controlled, that is, when the system is perturbed by the specified signal i t), the usual equations obtained for simple (noncomplex) systems can be used with... 

In steady-state measurements at current densities such as to cause surface-concentration changes, the measuring time should be longer than the time needed to set up steady concentration gradients. Microelectrodes or cells with strong convection of the electrolyte are used to accelerate these processes. In 1937, B. V. Ershler used for this purpose a thin-layer electrode, a smooth platinum electrode in a narrow cell, contacting a thin electrolyte layer. 

Electrode processes are often studied under steady-state conditions, for example at a rotating disk electrode or at a ultramicroelectrode. Polarog-raphy with dropping electrode where average currents during the droptime are often measured shows similar features as steady-state methods. The distribution of the concentrations of the oxidized and reduced forms at the surface of the electrode under steady-state conditions is shown in Fig. 5.12. For the current density we have (cf. Eq. (2.7.13))... 

Here F is the Faraday constant C = concentration of dissolved O2, in air-saturated water C = 2.7 x 10-7 mol cm 3 (C will be appreciably less in relatively concentrated heated solutions) the diffusion coefficient D = 2 x 10-5 cm2/s t is the time (s) r is the radius (cm). Figure 16 shows various plots of zm(02) vs. log t for various values of the microdisk electrode radius r. For large values of r, the transport of O2 to the surface follows a linear type of profile for finite times in the absence of stirring. In the case of small values of r, however, steady-state type diffusion conditions apply at shorter times due to the nonplanar nature of the diffusion process involved. Thus, the partial current density for O2 reduction in electroless deposition will tend to be more governed by kinetic factors at small features, while it will tend to be determined by the diffusion layer thickness in the case of large features. 

Steady-state Current Overpotential Behaviour - For a simple single charge-transfer process equation (2.28) describes the closed-circuit behaviour. At low overpotentials, the current and overpotential are linearly related and the exchange current density can be evaluated from the gradient (see equation... 

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. 

Rather slow electrode processes (especially in the case of gas electrodes) which have low exchange current densities. At steady state, the overall rates are generally determined by the rates of charge transfer and/or of secondary chemical reactions at the electrode-melt interface. 

This section shows that in order to separate klr and kTec it is necessary to carry out non-steady-state measurements. A simple example of a non steady-state measurement is switching the illumination on and off. The photogenerated flux of holes, g, towards the surface feeds into three processes surface charge storage, interfacial electron transfer and recombination. The magnitudes of the corresponding components of the total current density can be written in terms of the surface hole charge Qs ... 

In an earlier study we had reported the XPS analysis of tungsten oxides formed during anodic polarization experiments. It was determined that even at high applied potentials, the oxide thickness values are less than the mean free path of electrons in the oxides (generally assumed to be between 30 to 50 A ). Clearly the oxide growth in tungsten is a slow process. However, despite the relatively small thickness vsilues, the steady state current density during anodic polarization is restricted to a few tens of microamperes. 

Steady-state polarization curves, such as that presented in Figure 5.4(a), provide a means of identifying such important electrochemical parameters as exchange current densities, Tafel slopes, and diffusion coefficients. The influence of exchange current density and Tafel slopes on the steady-state current density can be seen in equations (5.17) and (5.18), and the influence of mass transfer and diffusivities on the current density is described in Section 5.3.3. Steady-state measmements, however, cannot provide information on the RC time constants of the electrochemical process. Such properties must be identified by using transient measurements. 

In the quasi-steady-state approximation, which is also known as the step method [9], it is assumed that the rate of variation in the WP shape, that is, the anodic dissolution rate, is small compared with the rates of transfer processes in the gap therefore, for calculating the distribution of the current density, the WP surface can be considered as being immobile. This approximation can be used at not very high current densities. At very high current densities, ignoring the WP surface motion during anodic dissolution and the hydrodynamic flow induced by this motion causes a considerable error in the calculated distribution of current density [33]. 

Though, in recent years, the solutions of the ECM problems with moving boundaries, which account for the dependence of current efficiency on the current density, have been obtained [42], it is difficult to solve the ECM problem with a moving boundary taking into account the physicochemical processes on the electrodes and in the IEG. Therefore, the approximate methods reducing the initial problem to the problem in the region with fixed boundaries were developed. The most popular approximate methods are the quasi-steady-state and local, onedimensional approximation methods. 

The transfer processes in the gap within the quasi-steady-state approximation are calculated similarly for both the direct and inverse problems. To simplify the calculation of transfer processes in the gap, the boundary-layer approximation is commonly used. According to this approximation, the current density is calculated separately in the bulk gap and in the near-electrode diffusion layers, and their congruence is provided via the boundary conditions. The transfer processes in the... 

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