Total current density potential dependence

The potential dependence of the partial current densities and of the total current density is shown in Figure 6.1. 

Figure 6.1 Potential dependence of the partial current densities, Eqs. (6.8) and (6.9), and of the total current density (Eq. (6.11)). The dashed, straight line represents the region of linear relation between current and potential.

The authors found in their study of the partial current of Ni and Mo that the partial current of Ni deposition increases with the total current with increasing negative potential but has only a marginal dependence on the rotation rate. The molybdenum content of the deposit is independent of the total current density but increases with the rotation rate (diffusion limitation). 

As we have seen in Section 3.2.1, the expression for current density of an electrochemical reaction contains a mass transfer and a kinetic element, as shown in Eq. (3.147). Steady state polarization curves and preparative runs are needed to provide information, respectively, on the dependence of total current densities and of partial current densities on electrode potential... 

Further Observations on the Technique of Steady-State Electrochemical Kinetic Measurements 1. In potentiostatic measurements, the appropriate interval of potential between each measurement depends on the total range of potential variation. It may be between 10 and 50 mV and can be automated and computer controlled (Buck and Kang, 1994). It is helpful to observe a series of steady-state currents at, say, 20 potentials taken from least cathodic to most cathodic, and the same series taken from most cathodic to the least cathodic. The two sets of current densities should be equal at each of the chosen constant potentials. In practice, with reactions involving electrocatalysis, a degree of disagreement up to 25% in the current density at constant potential is to be tolerated. 

Figure 15. Comparison of decomposition data with numerical data for the dependence of dimensionless potential O0 with the total dimensionless current density/, ok = 0.5 y = 10.0, s = 1.0 y= 10.0, s = 0.1 and y= 50.0, s = 0.1 (from left to right). Solid line v2 = 1.0, numerical result dotted line v2 = 0.1, o numerical result.

The problem, in the view of the present authors, is that the partial current density for deposition of, say, nickel is determined from the total amount of nickel deposited per unit time. However, in a solution containing Ni , Mo04 , NH3 and Cit , there can be as many as nine different species from which nickel could be deposited (six complexes with 1-6 molecules of NH3, two with citrate, and one adsorbed mixed-metal complex). The reversible potential for deposition of nickel is, in principle, different for each complex (depending on the stability constants). Hence, although all these parallel paths occur at the same applied potential, the overpotential is different for each of them. Moreover, there is no basis to assume that the exchange current densities or the Tafel slopes would be the same. If the observed Tafel plot would, nevertheless, be linear over at least two decades of current density, it could be argued that one of these parallel paths for deposition of nickel happens to be predominant. However, in the work quoted here, the apparent linearity of the Tafel plots extends only over a factor of about three in current density, namely over half a decade (cf.. Fig. 4a in Ref. 97). 

V/hen only activation overpotentials are important, the obtained current distribution is called the secondary distribution. The potential difference across the interface depends on the local current density. Therefore, the solution near the electrodes is no longer an equi-potential surface. Since higher current densities involve larger overpotentials (passivation excluded), the activation overpotentials will tend to make the current distribution more uniform. Also the total current will decrease. This can easily be understood by means of fig. 1.16. 

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