Tafel plots, linear

Fig. 2. Tafel plot, where and are both chosen to be 0.5 the temperature is 298.15 K. A iadicates the linear region (eq. 23) and B the Tafel (eq. 24).

Typical results, shown in Fig. 21(a), demonstrate that the rate constant for the reaction between TCNQ and aqueous Fe(CN)g increases with increasing driving force, promoted by decreasing [CIO4 as evidenced by the steeper Fe(CN)g concentration profiles. Moreover, the Tafel plot obtained for ET between Fe(CN)g and TCNQ is linear with an apparent measured a value of 0.31 0.02. In these studies, the concentration of reactant in the droplet phase was always at least 10 times the concentration of the reactant in the receptor phase, to ensure that depletion (and diffusional) effects within the droplet were negligible. 

Figure 1.8 A schematic representation or a Tafel plot of loge / vs. if. showing linearity at high overpotentials. At values of the overpotential < ryL, the current shows a linear dependence on...

A plot of logekt (obtained from the intercept) vs. the potential at which the measurements were obtained is a form of Tafel plot the plot should be linear, with slope fiF/RT and intercept k°. 

Let us now consider the charge state of the electrode. The emitter is positively biased. A p-type silicon electrode is therefore under forward conditions. If the logarithm of the current for a forward biased Schottky diode is plotted against the applied potential (Tafel plot) a linear dependency with 59 meV per current decade is observed for moderately doped Si. The same dependency of 1EB on VEB is observed at a silicon electrode in HF for current densities between OCP and the first current peak at JPS, as shown in Fig. 3.3 [Gal, Otl]. Note that the slope in Fig. 3.3 becomes less steep for highly doped substrates, which is also observed for highly doped Schottky diodes. This, and the fact that no electrons are detected at the collector, indicates that the emitter-base interface is under depletion. This interpretation is sup-... 

It is important to point out thatEq. (44) is a nonquadratic form of the rate equation and gives rise to linear Tafel plots the slopes of these plots depend strongly on the interfacial field parameter p (see Fig. 16). The... 

What is the cause of the non-linear portions of a Tafel plot ... 

Figure 7.12 Schematic Tafel plot of log / (as y ) against overpotential rj (as x ). The linear regions yield the Tafel slopes, from which the transfer coefficients a can be determined. The intersection between the two Tafel regions occurs on the y-axis at log /o. ...

A linear fit on a Tafel plot of overpotential versus the log of the current density yields the commonly reported Tafel slope... 

Equation 1.7 for the reduction of protons at a mercury surface in dilute sulphuric add is followed with a high degree of accuracy over the range -9 Tafel plot i.s shown in Figure 1.5. At large values of the overpotential, one reaction dominates and the polarization curve shows linear behaviour. At low values of the overpotential, both the forward and back reactions are important in determining the overall current density and the polarization curve is no longer linear. 

Equation 3.13 predicts a linear dependence of In / on E whose slope depends on the coefficient ana, while the ordinate at the origin depends on the electrochemical rate constant and the net amount of depolarizer deposited on the electrode. Accordingly, both the slope and the ordinate at the origin of Tafel plots become phase-dependent [133, 183]. Since the quantity of depolarizer varies from one... 

This equation again fits to a linear dependence of Ini on E. This means that the sample containing a mixture of X plus Y should give a linear Tafel plot. Remarkably, both the slope and the ordinate at the origin of that representation should be intermediate between those obtained for the X and Y components separately (Eq. 3.15). 

Fig. 3.11 Tafel plots for verdigris (A), atacamite (B), paratacamite (C), and cuprite (D) from linear scan voltammograms at sample-modified, paraffin-impregnated graphite electrodes immersed in 0.50 M potassium phosphate buffer (pH 7.0). Potential scan rate 50 mV/s...

Typical Tafel plots for different copper materials are shown in Fig. 3.11. In all cases, an excellent linearity was obtained for n i/ip) on E representations in terms of the correlation coefficient for linear fitting. Similar results were obtained for binary or ternary mixtures of such materials where highly overlapping peaks were recorded, both using linear potential scan and square-wave voltammetries. 

According to the previous treatment, linear Tafel plots of n i/ip) on E were obtained for samples providing from different regions of the helmet. As can be seen in Fig. 3.15, 2D diagrams using Tafel slope SL) and Tafel ordinates at the origin 00) yield a distribution of samples in three groups one formed by cuprite (CI-11), one formed by atacamite (CI-4, CI-6, CI-9), and one formed by a mixture of cuprite plus atacamite (C-12). 

This equation gives the i—V characteristics independent of 0. A linear Tafel plot with a slope of b = 2RT/F is obtained only if the second term on the right-hand side is negligible in comparison with the third. The deviations from this slope depend on the sweep rate and are minimal at small sweep rates. 

This equation has exactly the same form as the Tafel equation a linear Tafel plot does not necessarily imply a charge-transfer limited process. 

Figure 6 shows logarithmic plots of modulus j vs. 17 with data calculated from eqn. (80). Normalized linear Tafel plots are apparent from overpotentials of about 0.1 V. As is apparent from Fig. 6, at this value of overpotential the exponential due to the opposite reaction can be dropped in eqn. (80). 

Non-linear Tafel plots are predicted when A02 changes appreciably with electrode potential, that is at low ionic concentrations and close to the pzc (Fig. 3). 

A plot of In kf vs. potential (in fact, this is a Tafel plot) will be curved in the case of a linear mechanism with more than one rate-determining step. It is of the utmost importance to cover a large potential range. However, in the potential step method, l values exceeding ca. 200 s 1/2 cannot be determined and the accessible potential range is correspondingly limited. 

It is easy the recognize that a linear - Tafel plot can be obtained only in this case. This formalism can also... 

For redox processes, there is some evidence of Tafel slope curvature for certain processes under certain circumstances.228,229 These may be a partial result of double layer effects.196 In other cases experimental Tafel plots which are close to linear appear.177 230 The controversial question of P possibly varying with temperature231 232 will not be discussed here, although double layer effects196 may often be responsible. 

An example of the size of the impurity effects that may arise is shown in Fig. 1, which gives the electrode kinetics for the ferro-ferricyanide reaction on three different zinc oxide single crystals of varying conductivity. Each of the crystals was in excess of 99.999% pure. As can be seen, each crystal gives a linear Tafel plot under cathodic bias. However, the exchange currents, i.e, the extrapolations back to the reversible potential (+. 19 volts), differ by a factor of about 1000 and... 

In Fig. 2E we showed the i/T] relationship in both anodic and cathodic directions on a linear scale. In Fig. 3E the same data are shown on a semi-logarithmic plot (Tafel plot) as T] versus log i. A close look at this figure reveals several interesting points ... 

The Tafel plot is linear only at high values of the overpotential. 

The problem is aggravated when the reaction is fast, as shown in Fig. IK. To understand this figure we recall that a linear Tafel plot... 

Initially, the potential difference across the liquid-liquid interface has appeared to be concentrated in the diffuse double layer (Sec. 2.3). On this basis Koryta [6] concluded that the apparent charge transfer coefficient a is not related to the activation barrier and should have a value close to 0.5, as explained in Sec. 3.1.2. A numerical analysis based on Eq. (36) revealed however that, depending on the value of the parameter p (Eq. (37)), d can vary with the potential difference Aq0, i.e., Tafel plots should not be linear curves [60]. 

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