Tafel-plot determination

Figure 6.4 Dependence of the apparent rate constants and the apparent intrinsic rate constant on the potential ( Tafel plots ), determined by fitting the experimental transients with (6.5).

Determine from this plot the Tafel slopes 6, and 6 by curve fitting using the theoretical curves calculated for various values of 6 and 6,.. Calculate from equation 19.14 using the Rp, value evaluated in Step 1 and the Tafel slopes determined in Step 3. 

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. ...

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. 

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. 

Thus for large amplitudes, the current is logarithmically related to overpotential as shown in Figure 2.17. Tafel plots (Fig. 2.17) are frequently employed by physical electrochemists to determine exchange currents and transfer coefficients. There are many other ways to obtain these parameters experimentally, but such numbers are rarely of interest to the analytical chemist. As we will see later, the rate of the heterogeneous electron transfer relative to other controlling factors (e.g., diffusion and coupled chemical reactions) is of critical importance to most experiments. 

Rational optimization of performance should be the main goal in development of any chemical sensor. In order to do that, we must have some quantitative tools of determination of key performance parameters. As we have seen already, for electrochemical sensors those parameters are the charge-transfer resistance and the double-layer capacitance. Particularly the former plays a critical role. Here we outline two approaches the Tafel plots, which are simple, inexpensive, but with limited applicability, and the Electrochemical Impedance Spectroscopy (EIS), based on the equivalent electrical circuit model, which is more universal, more accurate, and has a greater didactic value. 

The plot of log versus E-Eo is known as a Tafel plot (Fig. 5.5). The two branches intercept at log jo from which Rcl can be determined according to (5.23). The plot should be symmetrical about the vertical axis for a = 0.5, which can be determined from either slope. 

The -> polarization curves for irreversible and quasireversible systems are shown in Figure (a). The respective -> Tafel plots are presented in Figure (b). Tafel plots can be constructed only for electrochemically irreversible systems, and kinetic parameters can be determined only when irreversible kinetics prevails. A switching from reversible to irreversible behavior and vice versa may occur. It depends on the relative values of ks and the -> mass transport coefficient, km. If km ks irreversible behavior can be observed. An illustration of the reversibility-irreversibility problem can be found in the entry -> reversibility. 

The Tafel plot is presented in terms of the current density, while the quantity determined experimentally is the total current. An uncertainty in the real surface area of the electrode (which often exists, as... 

In a Tafel plot, the logarithm of the current is plotted against t], as illustrated in Figure 1. Note that the slope is equal to —ccnF/2.2RT and the intercept corresponds to logj o. From these values, k° can be determined with Eq. 11. Tafel plots are often employed in corrosion studies, since k° is usually small and the condition Co(0, t) Si Cq can be accomplished by simply stirring the solution. Deviations from the idealized Tafel behavior are seen at large t], where Cq(0,/) becomes significantly smaller than Cq. 

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]. 

As far as the chl.e.r. mechanism is concerned, the same, previously described, investigation has been performed and Figures 24 and 25 respectively report the polarization curve and the Tafel plot (currents normalized to the number of active sites at the electrode surface), for the case of a 1 M NaCl/3 M NaC104/0.01 M HCIO4 test solution. The measured Tafel slope has a value of 0.149 V, and the reaction order with respect to CP is about 0.7 the values of b and R both agree well with a Volmer-Heyrovsky mechanism [24], with a rate-determining electrochemical desorption, provided a value of about 0.7 is assumed for the coverage by the intermediate chlorine radicals [28] ... 

The slope of the plot of logarithm of current density versus potential, which characteristically is linear for an activation-controlled reaction, is defined as the Tafel slope. The Tafel slope determined in the exponential region of an i-V curve in HE solutions is about 60 mV/decade for p types and heavily doped n types of silicon samples as shown in Table 5.3. For lowly doped n-Si, since illumination is required... 

Kinetic data extracted from the foot of RDE dynamic polarization curves for 02 reduction yielded for pH < 11 linear log[i/(ilim — i)] versus E, or Tafel plots, with a slope of around 120 mV per decade, and thus consistent with the first electron transfer as being rate determining for the reduction of the CoPI-02 adduct. As expected for a reversible (Nerstian) two-electron redox couple, the Tafel slope at pH = 14, decreased to 30 mV per decade. It is interesting to note that an oxidized form of the closely related CoOEP displays extraordinary reversibility for the 02—H202 couple in solutions of pH < 1 [63]. 

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). 

The problem with redox reactions of this type is that their rate constants are usually too large for regular steady-state techniques to be reliably applied, a or p then have to be determined through the reaction order or by some method such as Faradaic rectification. Usually, such methods require evaluation of the double-layer behavior in order to make double-layer corrections. This is often an unsatisfactory business, especially when corrections would be required over a range of temperatures. We conclude that for this important class of electrochemical reactions more data for examination of b T) or a T) are required. However, for certain ionic redox reactions that are sufficiently slow, Weaver has been able to evaluate a as /( T) from Tafel plots over a range of 0.3 ... 

Tafel plots of E vs. log /, such as those shown in Figure 26.31, are often used to determine the rate of a corrosion process. For a corroding metal (anode) that is driven by a single kinetically controlled reduction reaction (such as hydrogen evolution from an acid-containing solution), one can write the following Tafel equations for cathodic proton reduction and anodic metal dissolution ... 

A rotating platinum disk electrode was used for gathering data for the calculation of the kinetic constants. Tafel plots (5) were developed (Figure 2), from which the heterogeneous rate constants, k , and the electron-transfer coefficients, a, were determined. In all determinations of kinetic parameters, a blank voltammogram, run under identical conditions, was subtracted from the data to remove current due to background reactions or charging of the double layer. 

Figure 2. Tafel plots of oxidation and reduction of iron at pH 3 in 0.1 m KCl determined at a rotating platinum disk electrode. Currents are extrapolated values for an infinite rate of rotation. Temperature = 298 1 K.

Table H. Heterogeneous electron-transfer kinetics at the platinum disk electrode at 298 K. All values determined from linear portions of Tafel plots at rates of rotation extrapolated to infinity. Reaction of Se and As too slow for observation...

Figure Bl.28.1. Schematic Tafel plot for the experimental determination of and a. 

All rate constants for this complex reaction have been determined from these measurements [163, 165]. H and Bi adlayers cause similar catalytic effects. Tafel plots obtained from rotating disk-ring measurements show slopes of —120 mV for Au/Pb and Au/Bi systems, while a slope of —55 mV vras found for Au/Tl. The —120 mV slope, as observed for bare... 

With the charge transfer coefficient determined from the Tafel plots (Figure 6. 8) and the concentration dependence of the exchange current densities, the following partial electrochemical reaction orders were determined... 

---