Arteleo Chemistry Journal

Polarization Methods

The polarization resistance (Rp) of a metal/electrolyte system and the pitting or breakdown potential (Eb) can be determined using at least two-electrode system. Subsequently, the rate of metal dissolution or corrosion rate is calculated using a function of the form icorr = f (/?, Rp) > ia. The methods are

• Linear Polarization (LP) as schematically shown in Figure 3.4 covers both anodic and cathodic portions of the potential E versus current density i curve for determining Rp.

• Tafel Extrapolation technique (TE) (Figure 3.2) takes into account the linear parts of the anodic and cathodic curves for determining Rp.

• Electrochemical Impedance Spectroscopy (EIS) as schematically shown in Figure 3.10 requires an alternating current (AC) and the output is a Nyquist plot for charge-transfer or diffusion control process, which can be used to determine Rp, which in turn, is inversely proportional to the corrosion current density icorr-

Standard or recommended experimental procedures for measurements of Rp can be found in the American Society for Testing Materials ASTM G-59 and ASTM G-106 testing methods, and ASTM G-5 is for anodic potentiodynamic studies, are included in the annual Book of ASTM Standards Vol. 03.02.

3.5.1 LINEAR POLARIZATION

First of all, using eq. (3.8) under anodic and cathodic polarization individually, the Tafel slopes are derived by letting exp ^ sj^2 > > exp [ - ( 1 Frl j for an anodic polarization analysis, where ia>> |ic| and Va >> Vc- On the other hand, exp j^2!^! << exp is for characterizing cathodic polarization when | ic| > > ¿aand jjc > > r/0 . Under these conditions, eq. (3.8) reduces to

Solving eqs. (3.25) for the overpotential yields

where 0a and /?c are known as Tafel slopes of the anodic and cathodic reactions, respectively. These slopes are defined by

Additionally, if a = 0.5, then 0a = ¡3C. Figure 3.4 shows a theoretical polarization curve for conducting polarization resistance measurements.

Figure 3.4 Schematic linear polarization curve.

Figure 3.4 Schematic linear polarization curve.

The linear polarization is confined to a small magnitude of the overpotentials Tja and r)c, respectively, using linear coordinates. This technique allows the determination of wr using a potential range of ±10 mV from the Ecorr [3]. Prior to determining wr, the polarization resistance Rp is estimated from the linear slope of the curve (Figure 3.4) as

The corresponding corrosion current density depends on kinetic parameters since ¿corr = / (0, Rp). Thus, the simple linear relation that defines the corrosion current density is of the form

where 0 = / (0a, 0C), and 0a and 0C are taken as positive kinetic parameters for determining icorr of a corroding or oxidizing metallic material. Notice that eq. (3.29) predicts that the corrosion current density is very sensitive to changes in the polarization resistance. In fact, the magnitude of the polarization resistance is mainly controlled by the corrosion current density [1,46]. Hence,

This constant 0 will be derived in the next section. In fact, this method requires knowledge of the Tafel anodic 0a and cathodic 0C slopes in order to calculate 0, and subsequently predict ¿COT.r using eq. (3.29). This wr expression is simple, but essential in corrosion measurements since icorr can be converted to corrosion rate in units of mm/y, which are more convenient for engineering purposes after 0 and Rp are determined, finally, the values of these slopes are 0a < 1 volt and 0C<1 volt, and 0 < 1 volt.

3.5.2 TAFEL EXTRAPOLATION

This method involves the determination of the Tafel slopes 0a and 0C as well as Ecorr and icorr from a single polarization curve as shown in Figure 3.2. This curve is known as the Stern diagram (non-linear polarization) based on eq. (3.22). The Evans diagram (linear polarization) is also included in order to show that both diagrams have a common Ecorr • icorr point. This figure illustrates a hypothetical electrochemical behavior of a metal m immersed in an electrolyte containing one type of oxidizer, such as H+ ions.

For electrochemical systems containing several oxidizers, determining the corrosion point is more complex using the Evans diagram, but the Stern diagram would provided a similar polarization curve as shown in Figure 3.2, from which both Ecorr and easily determined by extrapolating the Tafel anodic and cathodic linear parts until they intersect as straight lines. Also included in Figure 3.2 are the exchange current densities, i0,n and i0,M> and their counterpart potentials, EQih and E0,m, for hydrogen evolution and metal oxidation, respectively. These potentials, E0,h and E0>m, are known as open-circuit potentials. Furthermore,the limiting current density iL for cathodic polarization is included as an additional information one can extract from a cathodic polarization curve. The latter term will be dealt with in Chapter 5.

Further analysis of Figure 3.2 yields the following summary:

The solid curve can be obtained statically or dynamically.

• This non-linear curve is divided into two parts. II E > Ecorr, the upper curve represents an anodic polarization behavior for oxidation of the metal M On the contrary, H E < Ecorr the lower curve is a cathodic polarization for hydrogen reduction as molecular gas (hydrogen evolution). Both polarization cases deviate from the electrochemical equilibrium potential (Ecorr) due to the generation of anodic and cathodic overpotentials, which are arbitrarily shown in Figure 3.2 as r)a and r?c, respectively.

• Both anodic and cathodic polarization curves exhibit small linear parts known as Tafel lines, which are used for determining the Tafel slopes (3a and /3C. These slopes can be determined using either the Evans or Stem diagram.

• Extrapolating the Tafel or Evans straight lines until they intersect define the Ecorr ■ Wr point.

• The disadvantage in using the Evans diagram is that the exchange current density (ia), the open-circuit potential E0 (no external circuit is applied), and the Tafel slopes for the metal and hydrogen have to be known quantities prior to determining the i^r • icoTT point.

• The advantage of the Stern diagram over the Evans diagram is that it can easily be obtained using the potentiodynamic polarization technique at a constant potential sweep (scan rate) and no prior knowledge of the above kinetics parameter is necessary for determining the Ecorr • i^r point. The resultant curve is known as a potentiodynamic polarization curve.

• In conclusion, Ecorr and icorr can be determined from an Evans diagram for an unpolarized metal since icorr — ia — —*c at E = Ecoor. On the other hand, if the metal is polarized, then the Stern diagram can be used for determining Ecorr, icorr, @a, and Pc. In addition, Ecorr is a reversible potential also known as a mixed potential. Further analysis of the polarization phenomenon requires use of the Ohm's law. Hence, the cell and the inner potentials are defined by, respectively

Rx = External resistance (Ohm = V / A) Ra = Solution resistance (Ohm = V / A) 4>s = Internal potential (V)

Solving eq. (3.31) for I yields

The current in eq. (3.33) strongly depends on the magnitude of the external resistance. A slight decrease in Rx increases the current I. Hence, if Rx —> 0, then I —► oo and I —> Owhen Rx —> oo. In addition, IRX —-> 0 as E —> 0.

With regard to eq. (3.32), <j>s can be neglected due to its small contribution to the cell potential. However, the electrolyte conductivity is of significance in determining the governing current expression. For instance, when IRx » IRa the electrolyte has a high conductivity and if IRx « IRa the electrolyte has a low conductivity. Hence, from eq. (3.33) the governing current expressions are

Nowadays, sophisticated instrumentation, such as a potentiostat/galvanostat is commercially available for conducting electrochemical experiments for characterizing the electrochemical behavior a metal or an alloy in a few minutes. Nevertheless, a polarization diagram or curve is a potential control technique. This curve can experimentally be obtained statically or dynamically. The latter approach requires a linear potential scan rate to be applied over a desired potential range in order to measure the current response.

On the other hand, a galvanostat can be used as the current control source for determining the potential response on a electrode surface. However, the potential control approach is common for characterizing electrochemical behavior of metallic materials. The potential can be applied uniformly or in a stepwise manner using a waveform. The former case generates a steady-state current response, while the latter provides a transient current response.

Further interpretation of the polarization curves can be extended using Pour-baix graphical work depicted in Figure 3.5 for pure iron (Fe). The resultant plots represent the functions E = f(i) and E vs. f [log(i)] for an electrolyte containing CFe+2 = 0.01 g/l = 1.79a;10-4 mol/l = 1.49xl0~7 mol/cm3 at pH = 0. Additionally, the reactions depicted in Figure 3.5 and some related kinetic parameters are listed in Table 3.2 for convenience. One important observation is that both anodic and cathodic Tafel slopes, /?„ and @c, respectively are equal numerically and consequently, Figure 3.5b has an inflection point at(wr,-Ecorr)-This electrochemical situation is mathematically predicted and discussed in the next section using a current density function for a mixed-potential system.

Figure 3.5 Corrosion of iron (0.01 g/1) with hydrogen evolution at pH — 0 [46].

Table 3.2 Kinetic parameters for Iron (O.Olg//) and hydrogen reactions at pH = 0 [46].

Parameters	Fe = Fe+2 + 2e~	2 H+ + 2e~ = H2
E° (VsHE)	-0.50	0
%o (A/crnz)		1.41x10"°
0a {V)	+0.328	+0.123
0c (V )	-0.328	-0.123

In fact, Figure 3.5 compares both linear and extrapolation results for iron. The interpretation of this figure is based on complete activation control in the absence of diffusion and external current [46]. Thus, it can be deduced from this figure that

• the net current density (inet =ia ~ ic) is zero at equilibrium, but the corrosion current density is icorr = 0.1622 mA/crn2 at the corrosion potential,

• The polarization curves are reversible in nature; however, if irreversibility occurs, the heavy line in Figure 3.5a would follow the vertical axis at a potential range E0,c < E < E0<a when inet — 0.

• The open-circuit potentials, Eaji and E0ipe, can be estimated using the Nernst equation.

One important fact is that the solution must be continuously stirred to keep a uniform concentration of the species in solution; otherwise, the concentration at the electrodes become uneven and the open-circuit potential ECipe increases during oxidation and ECih decreases during reduction. At equilibrium, the overpotential becomes r) = E — Ea = 0 since the applied potential and the applied current density are E = Ea,and i = ia, respectively. However, if i > i0,Fe, the iron reaction is irreversible because it corrodes by liberating electrons.

Combining the Pourbaix diagram and the polarization curves for iron in water at pH = 7 yields interesting information on the electrochemical state as shown in Figure 3.6, which includes the hydrogen and oxygen lines for comparison [46]. Observe the correspondence of potential between both diagrams. For instance, the potential at point A, indicates that corrosion occurs along line CP, but at point B the potential suggests that passivation occurs and iron is protected anodically. Point P is a transitional potential at the critical current density. Any slight change in potential iron passivates at E > Ep or corrodes at E < Ep. Also, If E < Ec Pourbaix predicts immunity, but the polarization curve indicates that corrosion is possible.

Furthermore, the advantage of the Pourbaix diagram as shown in Figure 3.6a is that it predicts the electrochemical state for immunity, corrosion, and passivation, and it is related to the polarization curve shown in Figure 3.6b. However, only the polarization curve predicts the corrosion rate through the current density iCOrr for metal oxidation and the passivation rate through the passive current density for metallic cation reduction to form an oxide protective film on the electrode surface. The passivation phenomenon is discussed in details in Chapter 6.

Figure 3.6 Comparison of Pourbaix diagram and polarization curve for iron in water at pH = 7 and P = 101 kPa [46].

Figure 3.6 Comparison of Pourbaix diagram and polarization curve for iron in water at pH = 7 and P = 101 kPa [46].

Q 7 pH 14 O log i a) Pourbaix Diagram b) Polarization Curve

Q 7 pH 14 O log i a) Pourbaix Diagram b) Polarization Curve

0 0