Current -potential mixed control

In those cases where i. (region A in Eig. 6.6), the real current density i essentially coincides with the kinetic current density i 4, and the electrode reaction is controlled kinetically. When 4 ik (region C), we practically have i 4, and the reaction is diffusion controiled. When 4 and 4 have comparable values, the electrode operates under mixed control (region B). The relative valnes of these current densities depend on the kinetic parameters and on the potential. 

It follows from the figures and also from an analysis of Eq. (6.40) that in the particular case being discussed, electrode operation is almost purely diffusion controlled at all potentials when flij>5. By convention, reactions of this type are called reversible (reactions thermodynamically in equilibrium). When this ratio is decreased, a region of mixed control arises at low current densities. When the ratio falls below 0.05, we are in a region of almost purely kinetic control. In the case of reactions for which the ratio has values of less than 0.02, the kinetic region is not restricted to low values of polarization but extends partly to high values of polarization. By convention, such reactions are called irreversible. We must remember... 

In a detailed rotating-disk electrode study of the characteristic currents were found to be under mixed control, showing kinetic as well as diffusional limitations [Ha3]. While for low HF concentrations (<1 M) kinetic limitations dominate, the regime of high HF concentrations (> 1 M) the currents become mainly diffusion controlled. However, none of the relevant currents (J1 to J4) obeys the Levich equation for any values of cF and pH studied [Etl, Ha3]. According to the Levich equation the electrochemical current at a rotating disk electrode is proportional to the square root of the rotation speed [Le6], Only for HF concentrations below 1 mol 1 1 and a fixed anodic potential of 2.2 V versus SCE the traditional Levich behavior has been reported [Cal 3]. 

In the galvanostatic electrolysis the potentials of the electrodes adapt automatically. To get an idea of the order of the emerging overpotential, we recorded the cathodic potential in relation to the current flow (Fig. 1) [5]. The declination of the exponential form indicates mixed control regime, i.e., the current is controlled by mass and electron transfer steps. 

It should be noted here that Eq. 30D can be used to correct for mass transport only when steady-state measurements are concerned, such as those obtained with the RDE. It is not applicable for polarography or for any other method in which the current varies with time. The reason is rather subtle when such methods are used, the activation controlled current and the diffusion controlled current depend differently on time. As a result, the dependence of measured current on time varies with potential in the region of mixed control, and a simple correction for diffusion limitation, following Eq. 30D is not valid. 

Metal deposition on the silicon surface may follow an instantaneous or a progressive nucleation process followed by a diffusion-limited growth of the nuclei. The growth of nuclei can be either kinetically limited, diffusion limited, or under a mixed control. The current transients measured by Oskam el at various potentials of... 

This raises some important possibilities, which have not escaped the attention of the electroplating community. For example, while metal deposition is conducted in fairly concentrated solutions of the metal being plated, and at current densities well below the mass-transport limit, additives acting as inhibitors for metal deposition are often introduced at concentrations that are several orders of magnitude lower, to ensure that their supply to the surface will be mass-transport limited. In this way, the tendency for increased rate of metal deposition on certain features on the surface, such as protrusions, will be moderated by the faster diffusion of the inhibitor to the very same areas. Furthermore, if deposition occurs in the region of mixed control, which is usually the case, it must be remembered that the relevant roughness factor is quite different for the charge-transfer and the mass-transport processes, and this may well be a function of current density, since the Faradaic resistance is inherently potential dependent. 

There are two types of problems in the analysis of electrocatalytic reactions with mixed control kinetics reactant adsorption and combined considerations of mass and charge transfer processes in the current vs. potential profiles. The dependence of the current density, j, with the overpotential, x, can be expressed under r values larger than 0.12 V (in absolute values) through the Tafel expression corrected by the mass transfer effects ... 

In a potential-step experiment, the potential of the working electrode is instantaneously stepped from a value where no reaction occurs to a value where the electrode reaction under investigation takes place and the current versus time (chronoamperometry) or the charge versus time (chronocoulometry) response is recorded. The transient obtained depends upon the potential applied and whether it is stepped into a diffusion control, in an electron transfer control or in a mixed control region. Under diffusion control the transient may be described by the Cottrell equation obtained by solving Tick s second law with the appropriate initial and boimdary conditions [1, 2, 3, 4, 5 and 6] ... 

Refinements of the above volume diffusion concept have been made by a model that includes a contribution of surface-diffusion processes to the dissolution reaction of the more active component at subcritical potentials. By adjustment of different parameters, this model allows for the calculation of current-time transients and concentration-depth profiles of the alloy components [102]. In addition to this, mixed control of the dissolution rate of the more active component by both charge transfer and volume diffusion has been discussed. This case is particularly interesting for short polarization times. The analysis yields, for example, the concentration-depth profile and the surface concentration of the more noble component, c, in dependency on the product ky/(t/D), where is a kinetic factor, t is the polarization time, and D is the interdiffusion coefficient. Moreover, it predicts the occurrence of different time domains in the dissolution current transients [109]. 

Figure 3.6a depicts the linear scan voltammograms (LSVs) of the ORR on 20 % Pd/C without ethylene glycol at co = 400, 800, 1,200 and 1,600 rpm. The LSVs show a clear dependence of the ORR current densities with potential and rotation rate. The ORR on the Pd electrocatalyst seems to be under kinetic and mixed control in the potential scanned, not reaching a well defined limiting current. Levich-Koutecky plots 1/j vs. at different potentials corresponding to the experimen-... 

When defining the overall current-potential curve in general cases, which are sometimes called mixed control or quasi-reversible systems, first one needs to write the equation for the current, based on general rate laws involving the interfacial concentrations ... 

F ure 4.30 Kouteki-Levich plot for reduction of Fe(CN)6 to Fe(CN) on a 0.385 cm platinum rotating disk electrode rmder mixed control in 0.5M K2SO4, at 28 °C. The reciprocal of the measured current is shown as a function of (0 for three potentials [12]. 

For many electrode processes of interest, the rates of electron transfer, and of any coupled chemical reactions, are high compared with that of steady state mass transport. Therefore during any steady state experiment, Nernstian equilibrium is maintained at the electrode and no kinetic or mechanistic information may be obtained from current or potential measurements. Apart from in a few areas of study, most notably in the field of corrosion, steady state measurements are not therefore widely used by electrochemists. For the majority of electrode processes it is only possible to determine kinetic parameters if the Nernstian equilibrium is disturbed by increasing the rate of mass transport. In this way the process is forced into a mixed control region where the rates of mass transport and of the electrode reaction are comparable. The current, or potential, is then measured as a function of the rate of mass transport, and the data are, then either extrapolated or curve fitted to obtain the desired kinetic parameters. There are basically three different ways in which the rate of mass transport may be enhanced, and these are now discussed. 

This last point, which has been ignored until now, in fact imposes limitations on all transient techniques. Essentially, in addition to the faradaic current flowing in response to a potential perturbation, there is also a current due to the charging of the electrochemical double-layer capacitance (for more details see Chapter 5). In chronoamperometry this manifests itself as a sharp spike in the current at short times, which totally masks the faradaic current. The duration of the double layer charging spike depends upon the cell configuration, but might typically by a few hundred microseconds. Since It=o cannot be measured directly it is necessary to resort to an extrapolation procedure to obtain its value, and whilst direct extrapolation of an /Vs t transient is occasionally possible, a linear extrapolation is always preferable. In order to see how this should be done we must first solve Pick s 2nd Law for a potential step experiment under the conditions of mixed control. The differential equations to be solved are... 

The appropriate procedure for the extrapolation of the / — co data to co = < may be deduced from the following argument, again based ontheNernst diffusion layer model. The current at any potential in the region of mixed control is given both by the kinetic equation... 

The basic setup controls the potential, but no information is returned from the experiment. A potentiostat system allows monitoring the actual potential, recording the cell current, and mixing different input signal such as potential steps, sweeps, sinusoidal signals, and dc levels. Figure 2 shows some concepts. 

The schematic indicating the potential region where OPCD occurs is shown in Fig. 2 using the example of CoFe alloy. The schematic considers electrodeposition process from the solution which is at standard conditions (P°, Cqq2+ = Cpg2+ = 1 mol). In order to obtain desired composition of CoFe (50 50) alloy, the concentrations of Co and Fe ions in the solution have to be appropriately adjusted together with the potential (overpotential) or current at which the alloy deposition occurs. Typical approach towards the solution and deposition potential (current) design involves experiments where the concentration of more noble metal, Co, is such that C(-q2+ < Cp 2+, so that Co deposition occurs under mixed control for a... 

---