Linear Tafel region

The central Tafel portions of Figure 7.12 haven t been discussed in much detail yet. We sometimes call these linear Tafel regions the potentials under kinetic control , since the magnitude ofl g, is a function of the rate constant of electron transfer (itself a Junction of the overpotential r)). 

Fig. IK The linear Tafel region as related to the ratio between i and...

A "small" perturbation in this context is one for which nrjF/vRT 1 or i/i 1. The linearity of the response allows easier and more rigorous mathematical treatment and is, therefore, often preferred. It is interesting to note that a linear response is also obtained when a small perturbation is applied to a system far away from equilibrium. To show this, we write the usual rate equation for an activation controlled process in the linear Tafel region (cf. Eq. 7F) namely ... 

Whereas the charge-injection method is a small-amplitude perturbation method in which measurement is conducted during open-circuit decay, we now discuss a different open-circuit measurement, in which the initial overpotential is high, in the linear Tafel region. The equations we need to solve are similar to Eqs. 9K and lOK, except that the value of the current in Eq. lOK is that corresponding to the linear Tafel region, namely... 

The quarter-wave potential used in Eq. 50K is equal to the polarographic half-wave potential and is therefore characteristic of the electroactive species in solution. If the reaction rate is slow and the transient is measured in the linear Tafel region, Eq. 42K must be used... 

Fig. 4L Variation of the peak potential for an anodic process with sweep rate over a wide range, covering both the reversible and the linear Tafel regions. The "critical" sweep rate v is the...

To obtain the stoichiometric number experimentally, it is necessary to measure i by two independent methods from extrapolation of the linear Tafel region to q = 0 and from micropolarization measurements. Equation 51F can then be used to calculate v, since the value of n is determined independently. Unless one considers a very complex system, both n and v are integers, and it is easy to distinguish experimentally among a small number of possible values of v. 

This is usually called the "totally irreversible case", but we consider the term to be misleading because, as seen in Fig. JL, the reaction can, in fact, be reversed. Referring to it as the "linear Tafel region" implies that the reaction occurs at high overpotentials, where the rate of the reverse reaction can be neglected. 

In the linear Tafel region the peak potential depends logarithmi-... 

The peak current density in the linear Tafel region is given by... 

Since (a/n) is usually smaller than unity, the peak current in the linear Tafel region is, as a rule, smaller than in the reversible region. The difference is not very large, however. For a = 0.5 and... 

Fig. lOL Calculated HE plots during linear potential sweep for mono-layer adsorption, as a function of sweep rate, for = 160 iClcm. The range of sweep rates and rate constants have been chosen so as to show both the reversible and the linear Tafel regions. The Y - axis is given in units of pseudocapacitance, = i/v. Reprinted with permission from Srinivasan and Gileadi, Electrochim. Acta, 11, 321, 1966). Copyright 1966, Pergamon Press. 

Consider now the current-potential behavior of a system close to E. Assuming that the two partial currents are in their respective linear Tafel region, we can write... 

The well-defined linear Tafel regions for the ORR on Pt(/zk/) can be used to extrapolate the current to the theoretical equilibrium potential to obtain the exchange current densities for the ORR on oxide -free Pt. At the same temperature, the exchange current density increases in the order... 

As a first approximation, one might expect that the composition of an electroplated alloy would be related to the current observed for each of the elements, when measured alone in the same solution at the same potential. Assume, for simplicity, that both metals are deposited at high negative overpotentials, within the linear Tafel region (where rj/h > 1). Then, one could write the... 

The two linear Tafel regions at Ni in methanolic HCl vary with r in a continuous and complementary way one has a slope that increases with T while the slope of the other simultaneously decreases with T (Fig. 4), so there is a singular temperature at which the Tafel relation is one line over the whole c.d. range. The directions of change of the slopes of the two Tafel lines at each temperature, other than at the singular temperature, correspond apparently to reaction mechanisms that are consecutive or parallel ). However, we believe, based on new data... 

In most of the simulated curves in Fig. 4 two linear regions in both the cathodic and anodic branches can be clearly seen that have slopes of 1391 and 11181 mV dec (at 298 K), whereas the quasi-equilibrium treatment would have predicted only a single linear Tafel region of slope 1391 mV dec for this mechanism. When the 1 2 ratio increases, varying from 10 (solid line) to... 

The existence of an ohmic potential drop during a potential measurement can alter the shape of the measured polarization curve. The current measured at a given potential is less than expected because the potential at the interface is less than what is intended. On a semilog plot, the ohmic potential drop causes the polarization curve to bend away from the linear Tafel region toward lower currents. 

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