Tafel lines exchange current density

The sohd line in Figure 3 represents the potential vs the measured (or the appHed) current density. Measured or appHed current is the current actually measured in an external circuit ie, the amount of external current that must be appHed to the electrode in order to move the potential to each desired point. The corrosion potential and corrosion current density can also be deterrnined from the potential vs measured current behavior, which is referred to as polarization curve rather than an Evans diagram, by extrapolation of either or both the anodic or cathodic portion of the curve. This latter procedure does not require specific knowledge of the equiHbrium potentials, exchange current densities, and Tafel slope values of the specific reactions involved. Thus Evans diagrams, constmcted from information contained in the Hterature, and polarization curves, generated by experimentation, can be used to predict and analyze uniform and other forms of corrosion. Further treatment of these subjects can be found elsewhere (1—3,6,18). 

Fig, 1.24 Tafel lines for a single exchange process. The following should be noted (a) linear f-log I curves are obtained only at overpotentials greater than 0-052 V (at less than 0-052 V E vs. i is linear) b) the extrapolated anodic and cathodic -log / curves intersect at tg the equilibrium exchange current density and (c) /, and the anodic and cathodic current densities... 

The method permits the simultaneous determination of reaction order, m, and reaction rate constant, k, from the slope and the intercept of the straight line. The procedure can be repeated for various potential values below the limiting current plateau to yield k as a function of electrode potential. The exchange current density and the Tafel slope of the electrode reaction can be then evaluated from the k vs. potential curves. 

Return to the Fe dissolution experiment discussed above, altering the solution to contain 5 pM M Fe2+. In addition, allow hydrogen evolution to occur on the iron surface with an exchange current density of 1(T5 A/cm2, whereas the exchange current density for the iron reaction is 1CT6 A/cm2. Assume that both reactions have Tafel slopes of 100 mV/decade. These conditions are illustrated graphically in the Evans diagram, named in honor of its creator, U. R. Evans, shown in Fig. 25. The lines represent the reaction kinetics of the two reactions considered. 

Compare the form of these equations with the Tafel equation, eqn (1) the slope, b, of the Tafel line is thus (f T/( 1 - P)F) (anodic) and (RTj(PF) (cathodic). Note also that, when rj = 0, i = i0 and the exchange current density may be found from the intersection of the anodic and cathodic Tafel slopes (at tj = 0). This is one method of determining corrosion rates since,... 

Equations (5.21) and (5.22) are examples of Tafel equations in which the current is an exponential function of potential. The Tafel behavior is illustrated in Figure 5.5. The intersection of the extrapolated lines for anodic and cathodic currents yields the equilibrium potential and the exchange current density. 

Thus, the overpotential is logarithmically dependent on the current density. The parameter a and b are characteristics of electrochemical reactions and are readily obtained from a plot of t] vs. logf. The intercept of the straight line at t] = 0 gives the exchange current density and the slope can provide the transfer coefficient. Eq. (42) is commonly referred to as the Tafel equation. 

Tafel lines, A vs. In I(y), give constant slopes at small polarizations, but the theoretical values of the relative exchange current densities (from the ordinate) are dependent on y. For large polarizations, we need numerical solutions to Equations 16.59 or 16.62 with fixed values of r2, rx, j0, Db C°, and x- Figure 16.9 shows some of the results. 

The sign holds for anodic and cathodic overpotentials respectively. A plot of electrode potential versus the logarithm of current density is called the Tafel plot and the resulting straight line is the Tafel line" The linear part (5=2.3 RT/anF) is the Tafel slope that provides information about the mechanism of the reaction, and "a" provides information about the rate constant of the reaction. The intercept at r =0 gives the exchange current density... 

Tafel lines obtained on the metals Pt, Pd, Ir, Rh, and Au (Fig. 22) for the electroreduction of oxygen in acid solutions indicate that Au with no unpaired d electrons has a significantly lower exchange current density than other metals (10 amp cm" on Au as compared with 10 amp cm ) Rh and Ir, which are expected to have the same number of unpaired electrons, show essentially an identical current-potential behavior Pd and Pt with virtually the same number of unpaired electrons show the same Tafel behavior 90). 

One can determine the charge transfer coefficient from the slope of the Tafel lines and the exchange current density from an extrapolation to the Nemst potential E = Eq. 

An example is shown in Figure 6.16. The reciprocal current is plotted versus the reciprocal value of the rotation frequency of a rotating disc electrode. The currents taken from the extrapolation to 1/Vf = 0 (rotation frequency/ = 00) are represented versus the potential in Figure 6.17. The current-potential plot shows a current-potential curve in the sub-Tafel region. An approximate current-potential line is shown in Figure 6.17. An approximate value of the charge transfer resistance and of the exchange current density... 

Figure 15.4 illustrates the origin of the corrosion potential and also the principles of cathodic and anodic protection for a single oxidation reaction (M M ) and a single reduction reaction (H H2) occurring at the metal surface (the dashed lines represent the current-potential behavior of the reverse reactions and are not important to the present discussion). Because charge balance must be maintained, the potential is pinned at a value, Ecom where the cathodic current and the anodic current are equal (i.e., where the two curves intersect). This corrosion potential (Ecorr) is called a mixed potential, as it is determined by a mixture of two (sometimes more) electrochemical reactions. The anodic current (also the cathodic current, as they are equal) at this potential is the corrosion current (torr)- It is important to note that E orr and icorr are influenced by both the thermodynamics of the two reactions, manifested by the equilibrium potentials E(h+/h2) and E(m/m+)> and by the kinetics of the two reactions, manifested by the exchange current densities io(H+/h2) and o(m/m+)> and by the slopes of the two linear curves (the Tafel slopes). 

Equation (31) is valid for 6 and represents a Tafel equation with a correction term, which takes into account the lowering of concentration due to the rate control by diffusion and reaction, and the reverse reaction [44]. The slope and the extrapolation to / = 0 of the straight lines obtained from equation (31) allows the determination of the charge transfer coefficient, a, and the exchange current density, respectively, without diffusion and reaction rate control. 

V (N.H.E.) (1 N H2SO4) with a slope of RT/F. Above 0.9 V the slope rapidly increased until passivation occurred ( l.OV) with the current decreasing to negligible values. Extrapolation of the Tafel line to the calculated reversible potential gave an exchange current density of about 5 x 10 A/cm (geom). 

The extrapolation of an experimental polarization curve, measured from the Tafel region to the reversible potential, reveals the exchange current density (Figure 4.9). The reciprocal of the slopes of the straight lines yield the Tafel coefficients and P. ... 

We can determine experimentally by an extrapolation of either the anodic or cathodic Tafel line to the standard potential. A second method to obtain iP is based on the measurement of the exchange current density ... 

The exchange current density (given by the intersection between the anodic and cathodic Tafel lines) decreases as the thickness of the passive film changes from 1.7 to 2.7 nm. The behavior can be explained by the reduced probability of electron tunneling through the oxide barrier with increasing film thickness. 

Tafel equation, which tells us that in a certain current density range, overpotenital is linearly dependant on the logarithm of current density. The exchange current density can be obtained from the intercept at the current density axis. The slope of the line is called the Tafel slope. The higher the Tafel slope, the slower the reaction kinetics. 

---