Tafel extrapolation plot

Cyclic voltammetry and Tafel plots were conducted to understand the electrochemical performance of the electrode. The Tafel Extrapolation... 

It was shown above that the corrosion rate can be determined experimentally from the extrapolation of the linear portions of the polarization curves plotted in semilogarithmic space back to the corrosion potential. In order to perform Tafel extrapolation, it is necessary to polarize the electrode to large potentials on either side of the corrosion potential. It is also possible to determine corrosion rate experimentally using much smaller polarization from the corrosion potential, as is shown in this section. 

Figure 3.9 (a) and (b) Examples of metal CMP systems where potentiodynamic polarization plots (A) are convoluted by complex surface reactions, and are not suitable for straightforward determination of icon hy conventional Tafel extrapolation, (c) and (d) Analysis of low-overpotential anodic LSV data (scanned at 2 mV/s) to determine Rp for the systems considered in (a—b). The sohd hnes in (c) and (d) represent hnear fits to the data. The short horizontal dashed lines placed at the ends of the hnear fits mark the upper and lower bounds of the overpotentials used to choose these hnear regions. 

In this equation is the corrosion current density and rj the potential difference between the actual electrode potential and the free corrosion potential. The equation may be simplified for large values of t] and for small values of rj. For the first situation, a simple half-logarithmic relation results between In j and 1], and the corrosion rate /corr is calculated if the current density j is plotted versus 1] and the plot is extrapolated for a rj 0 Tafel extrapolation... 

Tafel coefficients 393 f, 402 f Tafel extrapolation 504 Tafel plots 14f,39ff tantalum... 

Binary Mg alloys. Krishnamurthy et al. (1986, 1988a-c) have extensively studied the corrosion behaviour of binary alloys with Ce, Nd and Y produced by conventional casting techniques and RSP, such as melt spinning and splat quenching. They have used polarization techniques to measure corrosion rates in 0.01 M NaCl solutions. A summary of their results is presented in table 6. The data for the Ce alloys are as published. However, the data for the Nd and Y alloys have been calculated using Tafel extrapolation and standard formulae (Shreir 1976) from the published polarization plots. 

Equation (1.37) is of the form n = a + b log / an empirical observation first reported by Tafel. Thus, a Tafel plot of rj vs loge/ giving a straight line at high overpotentials is indicative of quasi-reversible kinetics. The slope gives / and the intercept (obtained via the extrapolation back to n = 0) gives /0 see Figure 1.8. 

Figure 15.5 shows the net current density i as a curve defined by the sum of if and ir, which goes to zero when if = ir = io- This curve merges asymptotically with the two Tafel lines when substantial currents axe drawn in either direction, so that the intersection point of these lines, which defines E° and io, is obtainable experimentally by extrapolation of the linear (i.e., Tafel) portions of EMF versus log i plots. We can now define the overpotential 77 quantitatively. It is the excess electrical potential of the electrode relative to the reversible value E°, for a particular value of the... 

The fit to the Koutecky-Levich equation, Fig. 9, demonstrates that the anodic dissolution of Cu occurs under mass-transport control, and extrapolation of these fits to co 1/2 = 0 yields kinetically controlled currents, 7k, free from transport effects and appropriately used in Tafel plots. 

If this plot is extrapolated to do = 0.335 nm for a fully graphitic structure, the Tafel slope is exactly RT/F, for this carbon, at this temperature. This supports the belief that the Tafel slope is sensitive to the d0 lattice dimension of the carbon. For any carbon that is not fully graphitized, the observed Tafel slopes result from mixtures of contributions of the two types of surfaces, disordered and ordered. As the amount of disorder decreases, the Tafel slope more closely approaches the expected values for the basal structure of the carbon. 

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... 

The distance decay constant / (see below) in Miller et al. s original study was 0.9 per CH2, using ferricyanide and iron(IH) hexahydrate [44]. In a later study which accounted more thoroughly for double layer effects, 2 was determined to be 1 eV for kinetically facile redox probes such as ferricyanide, 1.3 eV for Ru-hexamine and 2.1 eV for iron(III) hexahydrate. With a better understanding of the redox probe behavior, f was found to be 1.08 + 0.20 per CH2 and independent of the redox couple and electrode potential [96]. Pre-exponential factors were also extracted from the Tafel plots. The edge-to-edge rate constants (extrapolated) are approximately 10 -10 s for all redox probes, which is reasonable for outer-sphere electron transfer. The pre-exponential factors are 5 x lO s [96]. 

This is the well-known Tafel equation, expressing overpotential as a linear function of the logarithm of the current density. An equation of this form has long been used to describe hydrogen and oxygen evolution at various electrodes. If the linear logarithmic plot of (14-21) is extrapolated back to zero overpotential, the cathodic component approaches the exchange current density y o. Thus log jo = —a/b. 

Fig. 36 Logjo versus log P02 plots for Pt cathode operating on oxygen and on air in contact with a Nation membrane [83-86], Extrapolations to the O2/H2O potential have been done from both the low current density/lowerTafel slope (60 mV/decade) branch and from the high current density/higher Tafel slope (120 mV/decade) branch [83-86],...

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