Corrosion Tafel equation

As the corrosion rate, inclusive of local-cell corrosion, of a metal is related to electrode potential, usually by means of the Tafel equation and, of course, Faraday s second law of electrolysis, a necessary precursor to corrosion rate calculation is the assessment of electrode potential distribution on each metal in a system. In the absence of significant concentration variations in the electrolyte, a condition certainly satisfied in most practical sea-water systems, the exact prediction of electrode potential distribution at a given time involves the solution of the Laplace equation for the electrostatic potential (P) in the electrolyte at the position given by the three spatial coordinates (x, y, z). 

The rate at which corrosion occurs is expressed as the current density (A m" ), i.e. the ionic flux across the electrical double layer of the metal and at equilibrium, it is termed the exchange current density. The Tafel equation relates the exchange current density to the charge transfer overpotential. 

In the Tafel equations j8a and [lc are known as the anodic and cathodic Tafel constants. Tafel plots are useful in obtaining corrosion rates. Consider a sample of metal polarized 300 mV anodically and 300 mV cathodically from the corrosion potential Econ. The potential scan rate may be 0.1-1.0mV/s. The resulting current is plotted on a logarithmic scale. The plot is shown in Figure 1.24. The corrosion current icort is obtained from the... 

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,... 

We can calculate the corrosion potential and the corrosion current in a straightforward manner by writing the Tafel equation for the two partial reactions and solving for the potential at which the currents... 

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 ... 

In the range of electrode potential more positive (more anodic) than the pitting potential, the pitting corrosion occurs in the presence of chloride ions and the metal dissolution at a pit, initially hemispherical, proceeds through the mode of electropolishing, in which concentrated chloride salts in an occluded pit solution will control the pit dissolution. It is likely that the polishing mode of metal dissolution proceeds in the presence of a metal salt layer on the pit surface in the salt-saturated pit solution. It was experimentally found with stainless steels in acid solution [54] that the pit dissolution current density, pit, is an exponential function of the electrode potential, E (Tafel equation) ... 

The corrosion potential and corrosion current when there are no diffusion limitations or the rotating speed tends to infinity are calculated by solving the anodic and cathodic Tafel equations. Writing the Tafel equations for both the cathodic and anodic parts, we obtain ... 

Calculation of corrosion potential and corrosion current using the Tafel equation ... 

The Tafel equation gives a straight line in potential-log current density diagrams (Figure 4.3), which are normally used in the description of reaction rates related to corrosion. The diagram is sometimes called a Tafel diagram. 

Figure 3. Mixed potential diagram illustrating controls on the kinetics of corrosion at a pitted, oxide-covered metal. The potential range is from -700 to +300 mV/NHE. Arrows (B) corrosion current at the bottom of the pit, controlled by Fe Fe + (acid) and 2H - H2 (M) corrosion current at the mouth of the pit, controlled by the partial currents for Fe -> Fe2+ (passivated) and RX RH (Pit) corrosion current for the short-circuited pit, controlled by Fe Fe + (acid) and RX - RH. The three solid curves are generated using the Tafel equation and exchange current densities and Tafel slopes from reference (9). The dashed curve was measured at 5 mV s in pH 8.4 borate buffer, using methods described in reference (9).

The corrosion current can be calculated from the corrosion potential and the thermodynamic potential if the equation expressing polarization of the anode or cathode is known, and if the anode-cathode area ratio can be estimated. For corrosion of active metals in deaerated acids, for example, the surface of the metal is probably covered largely with adsorbed H atoms and can be assumed, therefore, to be mostly cathode. The thermodynamic potential is -0.059 pH, and if icon is sufficiently larger than io for 2 - e, the Tafel equation expresses... 

ASTM G 102, Practice for Calculation of Corrosion Rates and Related Information from Electrochemical Measurements— Corrosion rate equations and sample calculations are included. In this standard, corrosion rates are calculated from galvanic cell currents, polarization corrosion data (including Tafel extrapolations), and polarization resistance data. 

Corrosion on metals occurs at a reaction rate determined by opposing electrochemical reaction equilibria established between the metal and an electrolyte solution. As described earlier, one reaction is the anodic reaction, in which the metal is oxidized, releasing electrons from its surface. The other is the cathodic reaction, in which solution species like O2 or, or even the protective coatings and oxide films that cover the metal, are reduced, attracting electrons from the metal. In a corrosion system, the Tafel equations for both cathodic and anodic reactions can be combined into the Stern-Geary [33] equation. 

Figure 31.1 shows a classic electrochemically measured Tafel polarization diagram [33. The Tafel analysis is performed by extrapolating the linear portions of both cathodic and anodic curves on a log (current) versus potential plot to their point of intersection. This intersection point provides both the corrosion potential con and the corrosion current density for the system unperturbed. This is a very simple yet powerful technique for quantitatively characterizing a corrosion process. The Tafel equation can be simplified to provide Eq. (7) by approximation using a power series expansion. 

The December 2005 issue of the journal Corrosion" was dedicated to the 100 anniversary of the publication of tiie Tafel Equation. It contains mostly review articles, which can be useful for a deeper understanding of electrode kinetics. 

The use of the impedance technique in the study of polymer coated steel, has been thoroughly described elsewhere. The present paper compares this technique with that of harmonic analysis, originally proposed by Meszaros ). The authors have presented preliminary data using the latter technique(3) wherein the early stages of polymer breakdown have been studied. The current paper extends this work to polymers which have been immersed for a considerable period of time. The harmonic method gives information not available from the impedance technique in the Tafel slopes and the corrosion current are directly measurable. A brief summary of the harmonic method and the equations used are given below. 

From Eqs. (1222) and (12.23), it is clear that the corrosion current depends upon the exchange currents (i.e., available areas and exchange-current densities), Tafel slopes, and equilibrium potentials for both the metal-dissolution and electronation reactions. To obtain an explicit expression for the corrosion current [cf. Eq. (12.22)], one has first to solve Eqs. (12.22) and (12.23) for A0corr. If, however, simplifying assumptions are not made, the algebra becomes unwieldy and leads to highly cumbersome equations. 

The Tafel expressions for both the anodic and the cathodic reaction can be directly incorporated into a mixed potential model. In modeling terms, a Tafel relationship can be defined in terms of the Tafel slope (b), the equilibrium potential for the specific half-reaction ( e), and the exchange current density (70), where the latter can be easily expressed as a rate constant, k. An attempt to illustrate this is shown in Fig. 10 using the corrosion of Cu in neutral aerated chloride solutions as an example. The equilibrium potential is calculated from the Nernst equation e.g., for the 02 reduction reaction,... 

In this expression, bd and bc refer to the appropriate anodic and cathodic Tafel constants. Comparison of weight loss data collected as a function of exposure time determined from R , Rf from EIS, and gravimetric measurements of mild steel exposure to 0.5 M H2S04 are often within a factor of two. This suggests that use of Rn in the Stern-Geary equation may be appropriate for the estimation of corrosion rate (147-150). However, Rn measurements may underestimate corrosion rates. / p is often measured at effective frequencies of 1(T2 Hz or less in linear polarization or EIS measurements, while Rn is measured at 1 Hz or greater. An example of this is provided in Fig. 57, which shows the corrosion rate of carbon steel in 3% NaCl solution as a function of exposure time determined by EIS, linear polarization, noise resistance, and direct current measurement with a ZRA. Among these data, the corrosion rates determined by noise resistance are consistently the lowest. 

---