Definición de aprendizaje

Errors in polarization resistance measurements are important in the accuracy of cor­

rosion monitoring probes and laboratory studies. A significant experimental error is the inclusion of ohmic resistance interferences in the potential measurements. Other errors come about by assuming that the polarization curve is linear up to a specified overvoltage, usually 10 mV, as described for corrosion monitoring probes in Section 5.4. A few of the more important factors affecting accuracy of polarization resistance measurements are discussed below. Errors attributable to transient, non-steady-state,

5.5 / Errors in Polarization Resistance Measurements 157

polarized potentials and unpolarized corrosion potentials, Ecorr, are discussed in Section 5.3. The interested reader is referred to Callow et al.,19 who have reviewed the considerable theoretical and experimental work devoted to the subject.

5.5.1 Ohmic Electrolyte Resistance

As described in Section 3.2.3, total overvoltage is the sum of activation, ea, concen­

tration, ec, and ohmic resistance, en, overvoltages. In conventional polarization mea­

surements, £q does not become significant until relatively high currents are reached.

Thus, ohmic resistance effects can often be neglected in polarization resistance mea­

surements because the ohmic resistance of the solution electrolyte is low compared to the polarization resistance. That is, the total resistance, R, measured by polariza­

tion resistance procedures is the sum of the polarization resistance, Rp, and the solu­

tion resistance, Rn,

R = Rp + Ra - (11)

Normally, R is identical to Rp because Rp » Rq. It is obvious from Equation (11), however, that a significant error will be present when R& becomes a significant frac­

tion of Rp. The error is non-conservative; a high R& results in an apparent corrosion rate which is lower than the real one. Therefore, accurate polarization measurements in low-conductivity solutions require that Ra be either reduced by supporting elec­

trolyte additions in the laboratory or compensated by any of the instrumental or pro­

cedural techniques described in Section 3.5.4. Fortunately, low-conductivity aque­

ous electrolytes of significant RQ are usually associated with low corrosion rates of high Rp, which are less affected by R&.

In some polarization resistance monitoring probes, the third electrode used as ref­

erence is positioned in close proximity to the working electrode to reduce RQ. A high-frequency, low-amplitude signal measures Rq, which is used to reduce the R measured by polarization in Equation (11) to the desired value of Rp.

5.5.2 Uncertain Tafel Constants

To obtain zcorr accurately from

Ae p ap c

” ~ 2 .3 < „ „ ( & + & ) ’

one must have reasonably accurate values for and f3c. However, numerator and denominator of Equation (8) contain both (5a and (5C, and as a consequence, zcorr is not very sensitive to the values selected for f5a and fic. Stem and Weisert12 suggested that experimental values range from 0.06 V to about 0.12 V, and pc values range from 0.06 V to infinity, the latter corresponding to diffusion control by a dissolved oxi­

dizer. Extreme values correspond to f3a = 0.06 V, = 0.06 V; and (3a = 0.12 V, pc = infinity. These values substituted into Equation (9) define two lines in Figure 5.3, which differ only in their intercepts on the Rp axis, in agreement with Equation (10). Virtually all of the experimental data fall within the error band defined by these

158 Ch. 5 / Polarization Methods to Measure Corrosion Rate

two lines on the graph. Furthermore, the line corresponding to Iftl = Iftl = 0.1 V lies between the two extremes, and the error resulting from using Iftl = Iftl = 0.1 V would not exceed a factor of 2 in any case. Hence, without any detailed knowl­

edge of the system whatever, one can obtain a reasonably good estimate of the cor­

rosion rate from polarization resistance measurements. Any more accurate estimates or measurements of f t and f t will reduce considerably the uncertainty of corrosion rates derived from Rp.

One should not confuse an error in corrosion rate with an error in Rp, which can be measured accurately and precisely. Thus, if relative values of corrosion rate are of greater interest than absolute values (which is often the case), the polarization resistance method becomes even more attractive. In the laboratory, the change in icorc with time or the kinetics of the corrosion process may be of more interest than the absolute value of i'corr. The same is true industrially. Often, a large change of corro­

sion rate in a process stream is far more important than the exact value of corrosion rate, especially if the corrosion rate is known within a factor of 2.

5.5.3 Nonlinearity of Polarization Curves

The polarization resistance is, thus, independent of the extent of linearity to be found in the polarization curve. However, the still-common practice of using the current at a single value of 10 mV overvoltage in corrosion monitoring probes leads to possi­

ble error, which has received considerable attention in the literature.

When Iftl ^ Iftl the curve is not symmetric around the origin, as shown in Figure 5.2d for f t = 30 mV and f t = 118 mV. These values of the Tafel constants, taken from Figure 5.1, are more typical for many anodic and cathodic Tafel constants in acid and saline aqueous solutions.

The errors that accrue from assumed linearity of 10 mV are summarized in Figure 5. II 20 as a function of f t and ft. There is no error when Iftl = Iftl = 120 mV. The error is maximized for the greatest difference between /? values, that is when one

= infinity (usually f t) while the other is 30 mV. It is notable that the errors are opposite in sign for assumed linearities, +10 mV anodic and -1 0 mV cathodic. Thus, when the polarized difference is measured in the two-electrode probe, the errors tend to cancel one another, and extended linearity and consequent reduced error may be observed in two-electrode measurements.18

5.5 / Errors in Polarization Resistance Measurements 159

Pc (mV) pc (mV)

(a) (b)

FIGURE 5.11 Errors in corrosion rate measurement due to assumed linearity of +10mV (anodic) and -10m V (cathodic) overvoltage for various values of (3a and /3C.

(From F. Mansfeld, Corrosion, Vol. 30, p. 92, 1974. Reprinted by permission, National Association of Corrosion Engineers.)

5.5.4 Competing Redox Reactions

The polarization resistance method measures the total oxidation occurring at the cor­

roding electrode. For most corroding metals, total oxidation is represented entirely by the anodic dissolution reaction of the corroding electrode, for example,

M —» M"+ + n e . (12)

However, this is not always true, as illustrated by the schematic polarization dia­

grams for passive alloy, M, in a solution containing a hypothetical redox system, Z2+/Z+, in Figure 5.12. In the usual case, (a), the corrosion potential £ Corr,i is estab­

lished several hundred millivolts active to the redox potential EZ²VZ+, and the corro­

sion rate zpassl is an order of magnitude or more greater than the exchange current density, z⁰,z²+/z+> for the redox reaction. As the passive surface film thickens, Case (b), the passive current density decreases (Section 4.5.2) to zpass2 near the exchange cur­

rent density, /⁰,z²+/z+> which is assumed constant for the purposes of this example.

Now the rate of oxidation, iz+ z2+> becomes significant compared to the passive cor­

rosion rate, /pass;2. The total rate of oxidation is given by the sum,

^'ox — ^pass,2 "I” ^Z+ Z2+- ( 1 3 )

The corrosion potential is established at £ conr>2 where total oxidation, iox, equals total reduction, z'red, which in this case equals iz2+ z +. That is,

J'ox - *red = JZ2+ Z+- ( 1 4 )

The polarization resistance method measures z'ox, and zz+ ^ Z2+ is a significant fraction of zpass. Considerable error may result if one assumes that z'ox = zpass.

When the passive corrosion rate, zpass, becomes quite low, Case (c), the total oxi­

dation rate, zox, is essentially equal to the rate of Z+ oxidation at the exchange

cur-160 Ch. 5 / Polarization Methods to Measure Corrosion Rate

rent density, i0. That is, iox = *0,z2+ z+- The corrosion potential draws very near to the redox potential, Ez2+/z+> until Econ,3 = £’z2+/z+- Polarization resistance essentially measures the exchange current density for the Z2+/Z+ redox system. In both cases, (b) and (c) of Figure 5.12, the corrosion rate is seriously overestimated by polariza­

tion resistance measurements.

Thus, parallel redox reactions can cause substantial errors in corrosion rates mea­

sured by polarization resistance. The possibility of this error can be detected with a platinum electrode in the same corrosive electrolyte. The redox potential is inde­

pendent of the surface on which it occurs (Section 3.1.2), and the highly catalytic

CURRENT DENSITY, (ARBITRARY UNITS)

FIGURE 5.12 Schematic polarization diagrams showing alloy M passivated by a redox system Z2+/Z+: (a) /pass » /0, z*/r. (b) /pass * k z*/r, (c) /pass « k

z*/r-5.6 / Other Methods to Determine Polarization Resistance 161

platinum surface readily assumes the potential of the major redox system present, with no competing oxidation currents due to corrosion. Thus, if the difference between the platinum redox potential and the specimen corrosion potential is quite low, a competing redox reaction is a strong possibility. Indig and Groot21 were the first to observe errors due to parallel redox reactions in an elevated-temperature autoclave system in which the stainless-steel corrosion potential was only 18 mV removed from the H+/H2 redox potential on platinum. They recommended that the potential difference should exceed 50 mV before the contribution from a parallel redox reaction can be neglected. Mansfeld and Oldham22 showed analytically that a difference as low as 20 mV can be tolerated.

5.6 Other M ethods to Determine