Stern-Geary equation

Linear polarisation measurement is based on the Stern-Geary equation . Ai... 

Combining equations 19.8 and 19.10 gives equation 19.3 the Stern Geary equation by simple algebra. However, Oldham and Mansfield point out that further differentiation of equation 19.9 gives... 

In the case of general corrosion, R can be used in the Stern-Geary equation to estimate corrosion rate ... 

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. 

This is the Stern-Geary equation, which shows that the corrosion rate can be determined by a small polarization from... 

It should be pointed out that the sum current, which can be measured in electrochemical experiments as the current between the counter and the working electrode, is not the corrosion current. The corrosion current Icon cannot be measured directly, and has to be determined by extrapolation from semilogarithmic plots of the polarization curve or from the slope of the polarization curve at Econ using the Stern-Geary equation. 

As mentioned in Chapter 1.3, the slope, d /di, at the zero-current potential is a measure of the polarization resistance, Rp. The corrosion can be determined from the polarization resistance using the Stern-Geary equation, if the Tafel slopes are known ... 

Recall that both Tafel slopes are positive in this form of the equation. The Stern-Geary equation is the basis for the linear polarization method in which the polarization resistance is determined typically by scanning the potential from a value slightly below the corrosion potential to one slightly above the corrosion potential. It is an extremely easy technique that has been put to considerable use in corrosion monitoring. The polarization resistance can be determined by a simple two-point measurement at values above... 

It should be noted that the Stern-Geary equation is dominated by the smaller of the Tafel slopes. Often in corrosion, the cathodic reaction is diffusion limited oxygen reduction, so be = 00. In that case, the corrosion rate is given by ... 

For the data in Fig. 6, the ohmic and polarization resistances can be determined to be about 0.3 and just under 100 cm, respectively. The value of Rp is slightly higher than that determined by linear polarization (Fig. 4) in a measurement that just preceded the EIS experiment on the same electrode. The double layer capacitance is seen to be 1/3000 SI cm = 333 pF cm . The polarization resistance determined by EIS can be used to determine the corrosion rate with the Stern-Geary equation, just as was described above for polarization resistance determined by linear polarization. EIS data provide no estimation of the Tafel slopes, which are required in the Stem-Geary equation. 

In linear polarization measurements, the current is measured at potentials between 10 and 20 mV in cathodic and anodic direction from the equihbrium potential. The dependence of current vs. potential in this potential range is hnear and the slope dE/dl represents the polarization resistance. The corrosion current is calculated using the Stern-Geary equation for known values of the anodic and cathodic Tafel slopes. 

Once Rp is known, the corrosion rate can be evaluated using the Stern-Geary equation. Polarization resistance and corrosion current are determined from the current measured close to the corrosion potential. Polarization resistance can be determined with minimum system perturbation with linear polarization resistance or by using EIS. Experimentally determined potential ranges that indicate expected iron corrosion intensity for different-measured corrosion potentials are shown in Fig. 12.3. 

The corrosion current density is given by Stern-Geary equation ... 

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

The Stern-Geary equation has been modified to minimize errors under particular conditions. Errors in Eq. (5.8) are especially significant 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). 

DERIVATION OF STERN-GEARY EQUATION FOR CALCULATING CORROSION RATES FROM POLARIZATION DATA OBTAINED AT LOW CURRENT DENSITIES... 

Equation (29.10) is the Stern-Geary equation. Should the cathodic reaction be controlled by concentration polarization, as occurs in corrosion reactions controlled by oxygen depolarization, the corrosion current equals the limiting diffusion current (Fig. 29.2). This situation is equivalent to a large or infinite value of Pc in (29.10). Under these conditions, (29.10) becomes... 

Differentiation of this expression leads to the Stern-Geary equation [17] ... 

This is perhaps the singly most important technique it arises from the Stern-Geary equation which describes a linear overpotential - current relationship in the vicinity (typically + 20 mV) of the corrosion potential where the linear polarization resistance is ... 

---