Kinetically Limited Current Density

The case of mass transport limitation has been discussed before. This leads to a mass-transport-limited current density, independent of potential. But a limited current density could also be observed when the limitation is kinetic. This can happen when the metal ion exists in solution as a complex, although the electroactive species participating in the charge-transfer step is the free ion. An example of such a situation is the deposition of Cu from a solution containing copper pyrophosphate. A chemical step, the rate of which is independent of potential, is followed by an electrochemical step, as shown by the next two equations 

A limiting current was observed for this reaction, but its value was between one and two orders of magnitude lower than that calculated for mass transport limitation, indicating that it was due to the rate of release of Cu ions from the complex. Now the Faradaic resistance, defined as the partial derivative dr /dj approaches infinity at the limiting current density, and so does the Wagner number, leading to secondary current distribution and, hence, to uniform thickness of the deposit. 

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When anodic polarization is appreciable AE 0), the CD will tend toward the value and then remain unchanged when polarization increases further. Therefore, parameter i, as defined by Eq. (13.44), is a limiting CD arising from the limited rate of a homogeneous chemical reaction when Cj drops to a value of zero it is the kinetic limiting current density. 

Fig. 12.2 (a) Preparation of NOMGAs as metal-free catalysts for the ORR. (b) RDE voltammograms of the series of PDI-NOGMAs and Pt-C supported on GC electrodes at a rotation rate of 1,600 rpm. (c) Electrochemical activity given as the kinetic-limiting current density (/k) at 0.35 V for the PDI-NOGMAs supported on GC electrodes in comparison with that of a commercial Pt-C electrode (reproduced with permission [26])... 

Table 4. Kinetic limiting current densities j, in half-wave potentials, E,/2, at hemispherical microelectrodes of the radius a. Adapted according to [56]...

A plot ofagainst should yield a straight line whose slope is related to the number of electrons transferred in the reaction, and whose intercept is related to the kinetic current. This can be used in order to determine the kinetically limited current density of catalyst materials at various potentials (eliminating the effects of diffusion) and if desired, the number of electrons transferred which will provide indication of the mechanism of any given process. 

Term II represents the desorption of the adsorbed species from the reactive surface and decreases the surface coverage. Term III is the forward electrochemical ionization reaction responsible for current flow. From inspection of Eq. (4.62), in the case of an adsorption-limited reaction, the kinetic limiting current density should be the maximum possible adsorption rate where the surface coverage 6 becomes zero, or... 

The concentration of one of the components, and hence its limiting current density, is zero. In this case the Nemst equation is not applicable for the equilibrium potential therefore, we must use a kinetic equation that is written in terms of potential rather than polarization. When an oxidizing agent is not present in the solution Cy.ox = 0> oiily anodic currents are possible in the system, and these produce an oxidizing agent. It then follows from Eq. (6.32) that... 

The basic theory of mass transfer to a RHSE is similar to that of a RDE. In laminar flow, the limiting current densities on both electrodes are proportional to the square-root of rotational speed they differ only in the numerical values of a proportional constant in the mass transfer equations. Thus, the methods of application of a RHSE for electrochemical studies are identical to those of the RDE. The basic procedure involves a potential sweep measurement to determine a series of current density vs. electrode potential curves at various rotational speeds. The portion of the curves in the limiting current regime where the current is independent of the potential, may be used to determine the diffusivity or concentration of a diffusing ion in the electrolyte. The current-potential curves below the limiting current potentials are used for evaluating kinetic information of the electrode reaction. 

Potentiostatic current sources, which allow application of a controlled overpotential to the working electrode, are used widely by electrochemists in surface kinetic studies and find increasing use in limiting-current measurements. A decrease in the reactant concentration at the electrode is directly related to the concentration overpotential, rj0 (Eq. 6), which, in principle, can be established directly by means of a potentiostat. However, the controlled overpotential is made up of several contributions, as indicated in Section III,C, and hence, the concentration overpotential is by no means defined when a given overpotential is applied its fraction of the total overpotential varies with the current in a complicated way. Only if the surface overpotential and ohmic potential drop are known to be negligible at the limiting current density can one assume that the reactant concentration at the electrode is controlled by the applied potential according to Eq. (6). 

The mass-transport-limited current density for oxygen reduction is independent of the kinetic parameters for this reaction rather it depends on factors such as the concentration and the diffusion coefficient of oxygen in the medium. It depends oh the rate of flow of the liquid in a pipe or around a sailing ship or a structure immersed in a river. 

The electropolymerization kinetics have been studied by a few groups of investigators Beck et al. [78], Otero et al. [79], and Park et al. [73]. Beck et al. reported that the reaction limited current density, shows... 

Homogeneous chemical kinetics. A second important application of steady state measurements is in studies of chemical reactivity. Steady state measurements using electrodes of different radii can provide a powerful insight into the kinetics of homogeneous reactions where the limiting current density depends on the magnitude... 

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