CALCULATION OF CORROSION RATES FROM POLARIZATION DATA

5.8 CALCULATION OF CORROSION RATES FROM POLARIZATION DATA

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, there- fore, to be mostly cathode. The thermodynamic potential is − 0.059 pH, and if i corr

2 H 2 − e − , the Tafel equation expresses cathodic polarization behavior. Then,

is suffi ciently larger than i 0 for H + →

i corr φ

corr =− . 0 059 pH + β log

from which i corr and the equivalent corrosion rate can be calculated. Stern [4] showed that calculated corrosion rates for iron, using (5.7) and employing empiri-

cal values for β and i 0 , were in excellent agreement with observed rates. Typical values are given in Table 5.2 .

T A B L E 5.2. Comparison of Calculated and Observed Corrosion Currents for Pure Iron in Various Deaerated Acids [4]

Solution

0 i corr i μ A/cm ( 2 ) (volts, S.H.E.)

φ Hcorr + 0.059pH

(V)

μ A/cm ( 2 )

Calculated Observed 0.1 M Citric acid

10.4 11.5 pH = 2.06 0.1 M Malic acid

1.2 1.2 pH = 2.24 4% NaCl + HCl pH = 1

0.10 10.5 11.1 pH = 2

72 KINETICS: POL ARIZATION AND CORROSION R ATES

Subsequently, Stern and Geary [8] derived the very important and useful equation, now known as the Stern – Geary equation,

I appl ⎛ ββ c a ⎞

I corr =

I = ⎛ c a corr ⎞

23 . R ⎝ ββ c + a ⎠

where β c and β a refer to Tafel constants for the cathodic and anodic reactions, respectively, and I appl Δ φ is the polarization slope (the reciprocal of the polariza- / tion resistance, R = Δ φ/I appl ) in the region near the corrosion potential, for which the change of potential, Δ φ , with I appl is essentially linear (for derivation, see the Appendix, Section 29.2 ). Under conditions of slight polarization, for which Δ φ is not more than about 10 mV, the anode – cathode area ratio, which need not be known, remains essentially constant and conditions otherwise at the surface of the corroding metal are largely undisturbed.

If corrosion is controlled by concentration polarization at the cathode, as when oxygen depolarization is controlling, Equation (5.8) simplifi es to

I a I appl corr = (5.9)

Although values of β are relatively well known for H + discharge, they are not as generally available for other electrode reactions. Stern showed, however, that the

majority of reported β values are between 0.06 and 0.12 V. If β c is known to be

0.06 V, for example, and β a is between 0.06 and 0.12 V, the calculated corrosion current is within at least 20% of the correct value. Under other assumptions, the corrosion rate can be calculated to at least a factor of 2.

The general validity of Eqs. (5.8) and (5.9) is shown by data summarized in Fig. 5.10 . The observed corrosion current, corresponding to data on corrosion of nickel in HCl and on corrosion of steels and cast iron in acids and in natural waters, extends over six orders of magnitude. Some exchange current densities

for Fe 3+ → Fe 2+ − e − on passive surfaces are included because the same principle applies in calculating i 0 for a noncorroding electrode as in calculating I corr for a corroding electrode. Also, straight lines are shown representing values calculated on the basis of several assumed β values within which most of the empirical data lie. Equations (5.7) , (5.8) , and (5.9) have been widely used with considerable success for determining the corrosion rates of various metals in aqueous environ- ments at ambient and elevated temperatures.

The linear polarization method has obvious advantages in calculating instan- taneous corrosion rates for many metals in a wide variety of environments and under various conditions of velocity and temperature. It can also be used to

ANODE– C ATHODE AREA R ATIO

Figure 5.10. Relation between polarization slope at low applied current densities and observed corrosion or exchange current densities [9] . ( Copyright ASTM INTERNATIONAL. Reprinted with permission. )

evaluate inhibitors and protective coatings, as well as for detecting changes of corrosion rate with time. A correction is required if an IR drop is involved in the measurement.

The Stern – Geary equation has been modifi ed to minimize errors under par- ticular conditions. Errors in Eq. (5.8) are especially signifi cant in systems in which the corrosion potential is close to one of the reversible potentials — that is, is outside the Tafel region. Mansfeld and Oldham [10] have developed a set of equations that provides less error than Eq. (5.8) when this situation applies (see Appendix, Section 29.2 ).