By combining the Nernst equation with the expressions for charge-transfer overpotential (ηCT) and diffusion overpotential (ηD), equations can be written for the total experimental polarization behav-ior, E(iex,ox) and E(iex,red), of a single half-cell reaction:
E = E′+ηCT+ηD (Eq 3.86)
Using the M↔ Mm+ + me reaction as an example, at positive over-potentials (net oxidation):
and at negative overpotentials (net reduction):
E = E +59
Similarly, and for reference and comparison, the following equations can be written for the total polarization behavior, E(iox) and E(ired), for the single half-cell reaction, for the oxidation reaction:
E = E +59
m log a + logi
i +59
mlog i
M Mo i
M ox,M
ox,M o,M
D,ox,M
m + β
D,ox,M−iox,M
(Eq 3.89)
and for the reduction reaction:
E = E +59
m log a logi
i
59
mlog i
M Mo
M red,M
red,M o,M
D,red
m + −β − ,M
D,red,M red,M
i −i
(Eq 3.90)
In Eq 3.88, it should be recalled that iex,red is a negative quantity; all other current densities in Eq 3.87 to 3.90 are positive quantities.
Curves representative of positive and negative overpotentials are shown in Fig. 3.15 for two electrodes. Electrode X,XX+has a more no-ble equilibrium potential, E′X, and is shown with a higher exchange
Fig. 3.15 Example of overpotential curves for two electrochemical reac-tions illustrating that the thermodynamic and kinetic parameters place each reaction in different regions of the range of potentials and log |iex|
current density, io,X, than the M,Mm+electrode with values of E′Mand io,M. The solid curves are plotted as a function of external current den-sity, iex, since this quantity can be measured experimentally and ex-presses the intensity or flux of ion transfer at the interface, which is the fundamentally correct basis for representing the characteristic behavior of the electrode. The significance of the linear portions of these curves and their extensions through the exchange current density for each elec-trode was previously discussed, and reference should be made to that discussion.
Polarization Behavior of the
Hydrogen-Ion and Oxygen Reduction Reactions
These reactions (2H++ 2e→ H2and O2+ 2H2O + 4e→ 4OH–), oc-curring either independently or simultaneously, are, in many respects, the two most important reactions supporting corrosion. Both reactions have been studied extensively as a function of the pH and the metal sur-face on which the reactions occur (Ref 3, 5, 6). The data on, and mecha-nisms for, the hydrogen evolution reaction are reasonably well estab-lished; in contrast, the oxygen reduction reaction is poorly understood, particularly with respect to the values of the exchange current density.
Also, in the potential range near +600 mV (SHE), electrode reactions involving hydrogen peroxide may make measurable contributions to the current density.
From polarization measurements on platinum and iron in 4% NaCl solution with the pH controlled by HCl additions, values of io,βred, and iD,red for the hydrogen reaction have been approximated and used to construct the idealized E versus log ired polarization curves shown in Fig. 3.16 (Ref 5). In constructing these curves, the equilibrium potential was calculated from E′ = –59 pH, io,H2 on Fe was taken to be 1 mA/m2 and independent of the pH, and the slope of the linear region (–βred) was taken to be –100 mV per log decade. From the diffusion coefficient of hydrogen ions, iD,red was calculated to be 6 × 104 mA/m2 at pH = 1.
These parameters lead, for example, at pH = 1, to a curve starting at the equilibrium potential E′ = –59 mV (SHE) and 1 mA/m2and ending as a vertical line at the limiting diffusion current density of 6 × 104mA/m2. The curves shift regularly with pH as shown. Corresponding to the ver-tical (diffusion control) sections of these curves, the interface hydro-gen-ion concentration approaches zero. As a consequence, when the po-tential decreases, a value is reached below which direct reduction of water is possible, H2O + e→ 1/2 H2+ OH–. This reaction is accompa-nied by further increases in current density as the potential is decreased.
The direct reduction of water becomes the dominant reaction at higher potentials as the pH is increased; the data imply that this is the main re-duction reaction in deaerated water. The data also indicate, by
extrapo-lation to potentials near –100 mV (SHE), that is, E′ = –59 to –118 mV (SHE) at pH = 1–2, that iofor the direct reduction of water in acid solu-tion is on the order of 10–3mA/m2(Ref 5).
For reasons stated previously, it is considerably more difficult to con-struct illustrative polarization curves for the reduction of dissolved oxy-gen. Reasonable estimates of the exchange current densities, Tafel slopes, and diffusion rates have been used to construct the curves of Fig.
3.17 (Ref 3, 6). These curves, identified by letters, are described as fol-lows:
• Curves A, A′, A″ and B, B′, and B″: Conditions for the estimated solid curve, A, A′, A″: Platinum electrode, pH = 0.56 (1N H2SO4), PO
2= 0.2 atm (air). This curve is representative of reduction reac-tions in sulfuric acid saturated with air. The equilibrium potential is EO ,H
2
′ + = 1229 – 59 pH + 15 log PO
2 = 1184 mV (SHE), and the exchange current density is 10–2mA/m2. Because of the small solu-bility of oxygen in water (about 10 ppm), diffusion of oxygen to the interface becomes current limiting at about 103mA/m2. Diffusion controls the current between +500 and –35 mV (SHE). When the latter potential is reached, hydrogen can be evolved, and with a plat-inum electrode exhibiting io,H
2 on Pt = 104 mA/m2, a rapid in-crease in current along section A′ is observed. Additional dein-crease in potential results in charge-transfer polarization of the hydrogen reaction until diffusion control results in the region of limiting current density along A″. The dashed curve identified as B, B′, B″
Fig. 3.16 Cathodic polarization of the hydrogen reduction reaction on iron showing the effect of pH. Curve for platinum shows influ-ence of a metal with much higher exchange current density on the position of the hydrogen reduction curve. Source: Ref 5
represents the experimental measurements for a platinum electrode in 4% NaCl at pH = 1.1. Although these conditions differ slightly from those for the calculated curves, the agreement with the esti-mated curve (A, A′, A″) is reasonable. At lower potentials, –300 to –1000 mV (SHE), the experimental current density is higher than estimated because of turbulence created at the interface by hydro-gen evolution, thus bringing a greater concentration of hydrohydro-gen ions to the interface than would occur under stagnant conditions.
• Curves C, C′, C″ and D, D′, D″: Conditions for the estimated solid curve, C, C′, C″: Platinum electrode, pH = 7, PO2= 0.2 atm (air).
This curve is representative of the reduction reactions in water (pH = 7) saturated with air. The higher pH reduces the equilibrium potential to +800 mV (SHE), and io,O
2on Pt is estimated to be 4 × 10–5 mA/m2. On decreasing the potential, charge-transfer po-larization occurs along C, current-limiting diffusion popo-larization along C′, and reduction of water along C″. The dashed experimental curve, D, D′, D″, agrees well with the estimated solid curve.
• Curve E, E′, E″: Conditions: Platinum electrode, pH = 7, PO2= 10–4 atm. This curve is representative of partially deaerated water. The partial pressure of oxygen has been reduced from 0.2 to 10–4atm (10 ppm to about 5 ppb). Charge-transfer polarization occurs along E, oxygen diffusion limits the current density along E′, and direct reduction of water occurs along E″. The significance of this curve is
Fig. 3.17 Theoretical and experimental polarization curves for reduction of oxygen (O2+ 4H++ 4e→ 2H2O), hydrogen ion (2H++ 2e→ Η2), and water (2H2O + 2e→ H2+ OH–) on platinum. Curve A, A′, A″: Theo-retical curve for pH = 0.56, PO2= 0.2 atm; curve B, B′, B″: Experimental curve for pH = 1.1, PO2= 0.2 atm; curve C, C′, C″: Theoretical curve for pH = 7, PO2= 0.2 atm; curve D, D′, D″: Experimental curve for pH = 7, PO2= 0.2 atm;
curve E, E′, E″: Theoretical curve for pH = 7, PO2= 10–4atm
that the limiting current density has been decreased by a factor of 1000, from 103to 1 mA/m2.
The polarization curves in Fig. 3.17 were illustrative of the oxygen, hydrogen-ion, and water-reduction reactions on platinum. In general, platinum exhibits the highest values of exchange current densities, io, for these reactions of any of the metals. The lower values of exchange current density, particularly in the case of the oxygen reaction, may be due to the presence of oxide films, which are present on most metals.
The reactions then occur at the oxide/solution interface rather than at the metal surface. The calculated effect of reducing the exchange cur-rent density for the oxygen reaction in an environment of pH = 0.56 and PO
2 = 0.2 atm is illustrated in Fig. 3.18. The Tafel regions when the ex-change current density has values of 10–2, 10–3, 10–5, and 10–7mA/m2 are represented by the upper four curves. These curves merge into a common constant limiting diffusion current of 103mA/m2. At this cur-rent density, diffusion of dissolved oxygen to the interface is the limit-ing kinetic factor. The current density is constant over a range of poten-tials and depends only on the oxygen concentration, here corresponding to that established by PO
2= 0.2 atm or about 10 ppm dissolved oxygen.
This limiting current density is independent of the exchange current density. At potentials below –33 mV (SHE), hydrogen can be produced
Fig. 3.18 Illustration of the effect of exchange current density on the polar-ization curve for oxygen reduction in aerated environments of pH = 0.56 and PO2= 0.2 atm. Curves converge to the same diffusion limit and are identical when the hydrogen ion reduction is the dominant reaction.
by the reduction of hydrogen ions in this environment of pH = 0.56 (1 N). The Tafel region of the hydrogen ion polarization is shown as the dashed line starting at the exchange current density of 1 mA/m2. Below about –400 mV (SHE) the hydrogen reduction dominates the current density, and the total polarization curve deviates from that of oxygen diffusion control to hydrogen reduction under Tafel control to, finally, hydrogen diffusion control below –800 mV (SHE). It is emphasized that these curves for oxygen reduction cannot generally be measured experimentally at the high potentials on metals such as iron since anodic dissolution of the metal will contribute to the measured current density.
There are practical significances to the fact that the kinetics of the oxy-gen-reduction reaction are slow in the Tafel region (very small io) and that diffusion control occurs at relatively low current densities due to the small solubility of oxygen. In particular, corrosion processes that are supported by oxygen reduction in these potential ranges occur at rates less than those that would otherwise occur. The corrosion rates are further decreased if deposits form on the surface through which oxygen must diffuse to reach the metal surface. These deposits include thick corrosion product films, settling or adherent inert deposits, or deposits resulting from microbiological activity.
The reduction of ferric iron ions according to the reaction Fe3++ e→ Fe2+provides a strong cathodic reaction, which may cause the corrosion of a large number of metals and alloys. The reaction is of significance in both industrial environments and laboratory testing en-vironments. The influence results from the relatively high half-cell po-tential of the reaction, the kinetics being rapid near the half-cell poten-tial due to the relatively large exchange current density, and the high limiting current density under diffusion control (Ref 7). The standard half-cell potential is +770 mV (SHE), but the actual potential is usually higher since the Fe3+/Fe2+concentration ratio is generally much greater than unity, making the concentration-dependent term in the Nernst equation a positive quantity. These characteristics are illustrated by the cathodic polarization curves in Fig. 3.19 for reduction on platinum at concentrations of 100 and 10,000 ppm Fe3+. The curves were deter-mined under nitrogen deaerated conditions starting at the open-circuit potential and scanning in the negative direction. Stagnant conditions were maintained in the 100 ppm solution during initial polarization down to +400 mV (SHE). Diffusion control dominates in the range 600 to 400 mV (SHE). The limiting diffusion current density immediately increases on agitation by direct sparging of the nitrogen into the solu-tion, the increased interface velocity of the solution decreasing the dif-fusion boundary thickness. The current density increases again near –100 mV (SHE) due to hydrogen ion reduction, the hydrogen ions re-sulting from the hydrolysis of Fe3+and Fe2+ions to produce relatively low pH solutions. In the 10,000 ppm nitrogen-sparged solution, the
lim-iting diffusion current density is greater by a factor of about 100 as would be predicted from Eq 3.80. An increase in current density due to hydrogen ion reduction is not observed since at this higher concentra-tion, the ferric ion reduction dominates over hydrogen ion reduction.
The influence of the substrate on which the Fe3+reduction is occur-ring is illustrated by the curves in Fig. 3.20. Cathodic polarization
Fig. 3.19 Cathodic polarization curves for 100 and 10,000 ppm Fe3+(as FeCl3) on platinum in nitrogen-deaerated solution. The increase in current density at 400 mV (SHE) is due to a velocity effect in introducing ni-trogen sparging into the solution. The limiting current density is increased by a factor of about 100 on increasing the concentration from 100 to 10,000 ppm.
The increase in current density near –100 mV (SHE) is due to hydrogen ion re-duction resulting from a decrease in pH due to Fe3+hydrolysis.
Fig. 3.20 Polarization curves for Fe3+reduction (Fe3++ e→ Fe2+) on plat-inum and on type 316 stainless steel, with aFe3+= 1 and aFe2+= 0.1 in chloride solution. The exchange current density is lower on the passive film of the stainless steel. The inflection in the curve near –200 mV (SHE) results from contribution to the current density due to hydrogen ion re-duction resulting from the hydrolysis of the Fe3+and Fe2+ions.
curves were determined using platinum and type 316 stainless steel sub-strates. The chloride solution in this case was 1.0 M in Fe3+and 0.1 M in Fe2+ions in which the equilibrium half-cell potential for the reaction, Fe3++ e = Fe2+, is +800 mV (SHE). That the open circuit potential, the potential prior to starting the downscan, is approximately this value in-dicates that the exchange current density for the reaction is relatively large. The continuous curvature of the polarization curve during the ini-tial downscan precludes detection of a linear Tafel region that could be extrapolated back to the equilibrium potential to give an exchange cur-rent density. An approximate value for the exchange curcur-rent density is obtained by assuming a Tafel slope of 100 mV per log decade, placing a line tangent to the experimental curve with this slope and extrapolating back to the open circuit potential, 800 mV (SHE). An exchange current density of approximately 104mA/m2is obtained for the Fe3+reduction on platinum. Extrapolation of the linear portion of the polarization curve for Fe3+on type 316 stainless steel to an open circuit potential in-dicates that the exchange current density is about 1 mA/m2. Thus, the kinetics of the Fe3+reduction is about 104greater on platinum than on stainless steel. However, the position of the polarization curve becomes independent of the substrate at potentials below 100 mV (SHE) since diffusion in the solution becomes the controlling factor independent of the substrate. Hydrolysis of Fe3+and Fe2+ions occurs, resulting in suffi-cient hydrogen ion concentration to allow the reduction of hydrogen ions to contribute to the current density below about –200 mV (SHE).
If the potential scan is positive to the open-circuit potential, the an-odic branch of the polarization corresponding to Fe2+→ Fe3++ e is measured. A short section of this branch is shown in Fig. 3.20. It is evident that the polarization quickly reaches diffusion control.
It is shown in the next chapter that nitrites can be used as passivating inhibitors for corrosion of iron in near-neutral solutions. Since the basis for accomplishing this is related to the polarization characteristics of the reduction of the nitrite ion, brief consideration is given here to the reaction and to the form of the experimentally determined polarization curve for this ion. The curve is shown in Fig. 3.21. Although several re-actions have been proposed for the reduction of this nitrite ion, the fol-lowing is considered here:
NO + 8H + 6e2– + →NH + 2H O4+ 2 (Eq 3.91) The curves in Fig. 3.21 apply to a platinum substrate in an environment of pH = 7, aNO
2
– = 0.01 and aNH
4
+= 10–5. The equilibrium potential cal-culated from the Nernst equation is 250 mV (SHE). The reduction branch of the curve shows a transition from Tafel control to diffusion control with a limiting diffusion current density of 103 mA/m2, fol-lowed at lower potentials by the reduction of water. An anodic branch
starting at the open-circuit potential is also shown but is not involved in the analysis of the inhibiting action of the nitrite ion.
Chapter 3 Review Questions
1. Define E, E′, io,α, βox,βred, iox, ired, iex,ox, iex,red, iD,ox, and iD,red. 2. The following problem is designed to provide understanding of
Tafel plots for individual half-cell reactions and the form of experi-mental polarization curves to be expected based on the theory. As-sume that for a given metal, M,
Area: AM= 50 m2
Equilibrium half-cell potential: E′M= –500 mV (SHE) io,M= 1mA/m2
βox,M= 80 mV/log decade βred,M= 60 mV/log decade
(Recall that the equations for the polarization involve ratios of cur-rents or current densities, and therefore, the expressions are of the same form since the area factor cancels. Obviously, the numerical scale against which the plots are made will depend on the need to plot in terms of current or current density.)
a. On a copy of the 7-cycle semilog paper provided (Fig. 3.22), use coordinate ranges of –800 to –200 mV (SHE), and 10–1to 10+6mA. Plot the anodic Tafel line (EMversus log iox,M) us-ing Eq 3.47.
Fig. 3.21 Anodic and cathodic polarization curves for nitrite ion on platinum.
Assumed reduction reaction is aNO +8H 6e NH + 2H O
2– +
+4
+ → 2 .
Equilibrium half-cell potential corresponds to aNO = 0.1, aNH = 10–5 2–
+4 , and
pH = 7. Limiting current density is 103mA/m2.
b. Plot the cathodic Tafel line (EMversus log ired,M) using Eq 3.48.
c. Plot the polarization curves that should result from experimental measurements of the polarized potential, EM, versus log |Iex|.
Note that experimentally, EM is set and the resulting Iex mea-sured for potentiostatic polarization, and Iexis set and EM mea-sured in galvanostatic polarization. In either case, the external current must be the difference between the oxidation and reduc-tion components over the metal surface, Iex,M= Iox,M– Ired,M. Therefore, curves can be derived having the form of experimen-tal curves by plotting points representing the difference between the Tafel curves for progressively changed values of EM. The re-sulting Tafel and derived experimental curves should be similar to Fig. 3.11.)
3. From the following data for the polarization of iron, make a reason-able plot of the anodic polarization curve over the current density range from io,Feto iox,Fe= 10+4mA/m2.
io,Fe= 10–1mA/m2 β = +50 mV aFe2 += 10–6
Fig. 3.22 7-cycle semilog graph paper
4. From the following data for the polarization of the hydrogen evolu-tion reacevolu-tion on iron at a pH = 4, plot the cathodic polarizaevolu-tion curve from io,H
2 on Fe to iD,red,H
2: io,H
2 on Fe = 10 mA/m2 βred,H2 on Fe = 100 mV iD,red,H
2 = 10+4mA/m2
5. Plot the cathodic polarization curve for the hydrogen reaction on copper using the data in problem 4 but with a change in the value of the exchange current density to io,H
2 on Cu = 1 mA/m2. Why should the polarization curves for hydrogen evolution on copper and iron terminate at the same iD,redvalue?
References
1. J.Z. Tafel, Phys. Chem., Vol 50, 1905, p 641
2. J.O. Bockris and A.K.N. Reddy, Modern Electrochemistry, Vol 2, Plenum Press, 1973, p 632
3. K.J. Vetter, Electrochemical Kinetics, Academic Press, 1967, p 104–395
4. J.M. West, Electrodeposition and Corrosion Processes, D. Van Nostrand Co., New York, 1965, p 27–43
5. M. Stern, The Electrochemical Behavior, Including Hydrogen Overvoltage, of Iron in Acid Environments, J. Electrochem. Soc., Vol 102, 1955, p 609–616
6. J.P. Hoare, The Electrochemistry of Oxygen, John Wiley & Sons, 1968, p 117
7. A.C. Makrides, Kinetics of Redox Reactions on Passive Electrodes, J. Electrochem. Soc., Vol 111, 1964, p 392–399
CHAPTER