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Milton Stern & Geary

One of the most useful equation behind most electrochemical techniques is without doubt the Stern Geary equation. The following are excerpts of the original papers that introduced this mathematical transform that led to the general usage of electrochemical principles in corrosion studies.

Electrochemical Polarization: I. A Theoretical Analysis of the Shape of Polarization Curves

by M. Stern and A. L. Geary (J. of the Electrochemical Society, Vol. 104, No. 1, 56-63, 1957)


At low overvoltage values, deviations from Tafel behavior for a noncorroding electrode are due primarily to the reverse reaction of the oxidation-reduction system, and at high overvoltages to concentration and/or resistance polarization. It is shown further that the practice of placing straight lines through a few experimental points is extremely hazardous, while the indiscriminate introduction of "breaks" is contrary to the electrode kinetics described.

Further complexities arising from a corroding electrode are described. In this instance, the forward and reverse reactions of both of the oxidation-reduction systems forming the corrosion couple must be considered. This representation of the local polarization diagram of a corroding metal is more fundamental than that used previously in the literature, and thus provides a clearer picture of the various factors which affect the corrosion rate and the shape of polarization curves.

A region of linear dependence of potential on applied current is described for a corroding electrode by treating it in a manner analogous to that for a noncorroding electrode. An equation is derived relating the slope of this linear region to the corrosion rate and Tafel slopes. This relation provides an important new experimental approach to the study of the electrochemistry of corroding metals since, in some instances, interfering reactions prevent determination of Tafel slopes at higher current densities.

Polarization measurements are an important research tool in investigations of a variety of electrochemical phenomena. Such measurements permit studies of the reaction mechanism and the kinetics of corrosion phenomena and metal deposition. In spite of their wide applicability and extensive use, considerable uncertainty in the interpretation of polarization measurements still exists. Some of the uncertainties include the proper method of plotting data and the correct interpretation of "breaks" in polarization curves. Abrupt changes in slope of overvoltage vs. log current have been given considerable significance in the past few years.


The picture of a mixed electrode presented in this paper could be made more extensive by including even a third oxidation reduction svstem. It is doubtful whether a detailed discussion of such a system would be of benefit at the present, but it will be included in a future publication. It is worth noting in passing, however, that the polarization curves would be even more complex than those discussed here. This analysis has illustrated several important concepts which are worth listing for emphasis.

  1. The representation of a corroding metal by polarization diagrams should be extended to include the reverse reactions of the various oxidation reduction systems which are operative.

  2. Deviations from Tafel behavior may be caused by local action currents, concentration polarization, and IR drop effects, and by a change in the predominant electrode reaction.

  3. An experimental polarization curve may show a linear dependence of potential on applied current for small amounts of polarization.

  4. An equation has been derived which relates the slope of the linear region of a polarization measurement to the corrosion rate and the Tafel slopes. This equation will prove valuable when interfering reactions prevent the determination of the Tafel constants at higher currents.

  5. The shape of an experimental electrochemical polarization curve, either cathodic or anodic, can be analyzed if sufficient data are obtained to permit an accurate description of the curve. Placing straight lines through four or five experimental points is hazardous, while the indiscriminate introduction of "breaks" is contrary to modern electrochemical concepts. Sufficient information concerning the system should be available to estimate whether concentration polarization or resistance drop effects have been included in the measurements.

Although this analysis contains only calculated polarization curves, a subsequent discussion will illustrate how experimental measurements comply with the electrode kinetics described.

The picture of a corroding metal presented here is consistent with the concept or theory of mixed potentials originally treated by Wagner and Traud and subsequently discussed by Petrocelli. The concept of discrete anodic and cathodic areas in electrochemical corrosion may be considered a special case of this theory. (back)

A Method For Determining Corrosion Rates From Linear Polarization Data

By Milton Stern (Corrosion, Vol. 14, No. 9, 1958, pages 440t-444t)


Corrosion testing by weight loss methods is generally a long, tedious affair which often does not produce completely satisfactory results. This is particularly true when the corrosion rate changes with time.
Several attempts to relate various electrochemical properties of a metal to corrosion rate have been described in the literature. Unfortunately, the techniques usually are more involved than weight-loss procedures and furthermore they may have no sound basis in theory. Recently, however, Skold and Larson' and Simmons' have described empirical observations which appear to have promise as a practical method for measuring instantaneous corrosion rates by electrochemical means. They showed that the slope of the linear portion of the polarization curve of iron can be related to its corrosion rate. The method has some foundation in theory and may have rather wide applicability to many systems.

The purpose of this discussion is (a) to describe the theoretical basis which makes the method attractive, (b) to define the conditions where the technique appears to be most applicable, and (c) to provide supporting evidence.

Description of the Method

It is often found experimentally that the initial portion of a polarization curve is linear so that potential plotted as a function of applied current or current density approximates a straight line. The slope of this straight line, DE/DI, has units of resistance and for convenience will be called the "polarization resistance." It is important to note that this is not a resistance in the usual sense. The nature of "polarization resistance" will be discussed in a later section.

Simmons, in a study of polar organic inhibitors in crude oil-salt water systems, found that a qualitative relation existed between DE/DI and the corrosion rate. He reported that all inhibitors which exhibit good weight-loss suppression give high values of "polarization resistance." The converse was also true. In addition, simultaneous measurement of DE/DI and weight change as a function of time showed that "polarization resistance" increases as inhibition proceeds reaching a maximum when the sample apparently stops corroding.

Skold and Larson' initially conducted polarization measurements to calculate corrosion rates from "breaks" in polarization curves by a method described by Schwerdtfeger and McDorman. This approach was abandoned for reasons described in heir paper. They found in their studies of steel and cast iron in natural waters that a linear relation existed between potential and applied cathodic and anodic current density at low values of applied current density. "Polarization resistance" was higher for samples having a low corrosion rate than for samples exhibiting high rates. Fortunately, their conditions were such as to give corrosion rates which varied over several orders of magnitude. A plot of corrosion rate versus "polarization resistance" on logarithmic scales gave a straight line with a negative slope. This empirical data was used to determine changes in corrosion rate with time for various systems.

General Features of the Method

"Polarization resistance," as used here, is not a resistance in the usual sense of the term. The linear dependence of potential on current only exists because the difference between two logarithmic functions of current approximates a linear function when the logarithmic functions are of the sane order of magnitude.

"Polarization resistance" measured by either anodic or cathodic polarization should be identical. This not only results from the derivation of Equation (1) and (8) but also is observed experimentally. Skold has confirmed this. but reports that the extent of the linear relation observed during anodic polarization is smaller than that observed during cathodic measurements.

The extent of the linear relation described by Equation (1) is dependent upon the beta values of the individual anodic and cathodic polarization curves. It is possible to analyze Equation (1) mathematically to show the amount of polarization which can occur for systems with various beta values while maintaining a linear relation within various error limits. To do this, it is necessary to assume that the anodic and cathodic beta values are equal. While this is not necessarily the case for many real systems, it provides a valuable guide in interpretation of experimental data.

In the region where current approximates a linear function of potential, the value e is the maximum deviation of potential from linearity at any current. For a reversible electrode, the corrosion current would be replaced by the exchange current and the known relation between potential and applied current in the linear region, it is possible to calculate the value of polarized potential below which a linear relation is expected within any given error.

The use of the "polarization resistance" for measuring corrosion rates has one particularly important advantage. The potential range investigated is close to the corrosion potential and the applied currents are generally smaller than the corrosion current. Thus, the nature of the-surface is not changed significantly, and the reactions which proceed during polarization are those which actually occur during the corrosion process. This is not necessarily the case when a corroding surface is markedly polarized, since under such conditions, the subsequent corrosion rate may be affected for some time after polarization has been discontinued.

The following is a list of situations where it appears that the use of linear polarization measurements can supply valuable information.

  1. Studies of the effect of environment variables on corrosion rate. These include changes in composition, velocity, and temperatures.
  2. Evaluation of inhibitors in controlling corrosion.
  3. Comparison of the corrosion rates of various alloys of similar composition in a given environment.
  4. Determination of changes in corrosion rate with time, including studies of underground structures as well as materials in aqueous solutions.
  5. It also may be possible to evaluate the condition of coatings in service which cannot be inspected by visual methods.

While the use of linear polarization data to determine corrosion rates cannot be considered a universal approach, there is sufficient basis in theory along with supporting evidence to believe that the technique can find a useful place in corrosion studies. (back)