TUTORIAL ON POLARIZATION RESISTANCE TECHNIQUE (Misnamed LINEAR POLARIZATION)

David C. Silverman

Table of Contents

Overview of TutorialSummary of Polarization Resistance TechniqueSources of Error

        Example (Nickel in Strong Acid)Example (Low Corrosion Rate Environment)

Overview of Tutorial

Predicting rates of general corrosion by electrochemical techniques is far easier than predicting the risk of localized attack such as crevice corrosion or pitting. The linear polarization technique or as it should be more properly called, the polarization resistance technique is one such technique for rapid estimates of general corrosion. The name "linear polarization" technique is actually a misnomer because it implies linearity at the corrosion potential. The inverse relationship between the polarization resistance (slope of the voltage versus current curve at the corrosion potential that this technique can estimate) and the corrosion current (corrosion rate) exists even though the curve itself is often not linear at the corrosion potential.

The methodology for generating the potentiodynamic sweep in the vicinity of the corrosion potential is adequately described in a number of references, one excellent example is ASTM G59 ”Standard Test Method for Conducting Potentiodynamic Polarization Resistance Measurements”. This standard test method developed using a laboratory round robin testing program provides a test circuit and a standard test protocol (430ss in sulfuric acid) useful for determining if the electrochemical equipment is functioning properly. The polarization resistance technique is very well established for routine use both for corrosion prediction and corrosion monitoring. During routine use, the realistic lower limit for corrosion rate estimation is about 0.001 mm/y (about 0.1 mpy) mostly because of limitations in estimating Tafel slopes. Under quiescent conditions and with no outside electrical or other interference, a maximum polarization resistance of about 106 ohm-cm2 has been suggested. Such values would translate to corrosion rates of about 10-4 mm/y or about 0.01 mpy. Sensors are available for on-line corrosion monitoring from several commercial suppliers.

This tutorial has several objectives: to provide a brief overview of the technique and data analysis to summarize the assumptions behind estimation of the corrosion rate from the

current vs. voltage (polarization resistance) plot

to summarize a number of the sources of error

to provide a simple example in the use of the technique

to provide an example in a very low corrosion rate environment that can cause offsets to the corrosion potential

Summary of Polarization Resistance Technique

Calculation of Corrosion Current

Excellent in-depth discussions are provided in F. Mansfeld, "The Polarization Resistance Technique for Measuring Corrosion Currents", in Advances in Corrosion Engineering and Technology (M. G. Fontana and R. H. Staehle, ed.), 6, ch. 3, Plenum Press, 1976 and more recently in J. R. Scully, "Polarization Resistance Method for Determination of Instantaneous Corrosion Rates", Corrosion, Vol.56, p. 199 (2000). Since such in-depth descriptions exist throughout the literature, only those portions pertinent to this tutorial are summarized below.

The overall technique requires the relationship between current measured versus voltage applied near the corrosion potential. Very often, the potential is scanned over a narrow voltage range centered on the corrosion potential, for example from -20 mV to +20 mV relative to the corrosion potential. The polarization resistance is determined from this curve as:

                             (1)

where Rp is the polarization resistance determined from the slope (derivative) of the voltage (V) versus current density (i) curve at the corrosion potential. An example of a methodology for generating the potentiodynamic sweep in the vicinity of the corrosion potential is described very adequately in ASTM G59 "Standard Test Method for Conducting Potentiodynamic Polarization Resistance Measurements". This standard provides a test circuit and standard solution useful for determining if the electrochemical equipment is functioning properly. 

The data are usually analyzed by assuming that the relationship between the current and voltage in the polarization curve is given by:

                                (2)

where icorr is the corrosion current density, V is the applied (assumed to be actual) voltage, Vcorr is the corrosion potential, and ba and bc are the anodic and cathodic Tafel slopes. The basis for this equation lies in the mixed potential theory proposed by Wagner and Traud in 1938. This paper (C. Wagner and W. Traud, "On the Interpretation of Corrosion Processes Through Superposition of Electrochemical Partial Processes and on the Potential of Mixed Electrodes, Z. Elektrochem. Ang. Physik. Chemie, Vol. 44, p. 391, 1938) has recently appeared in a translation by F. Mansfeld (F. Mansfeld, Corrosion, Vol. 62, p. 843, 2006). 

Mixed potential theory forms the basis for the Stern-Geary equation that is used in the polarization resistance technique M. Stern and A. L. Geary, "Electrochemical Polarization, A Theoretical Analysis of the Shape of the Polarization Curves", J. Electrochem. Soc., Vol. 104, p. 56, 1957). The corrosion current can be related to the Tafel slopes by:

                                                                    (3)

No assumptions are needed to derive equation (3) beyond those for validity of equation (2). The derivation of equation (3) is completely mathematical. The assumption of linearity between voltage and current is not needed (F. Mansfeld and K. B. Oldham, Corrosion Science, Vol. 11, p. 787 (1971)). Substituting equation (3) into equation (2) enables Tafel slopes and the polarization resistance to be extracted from a curve-fitting of equation (2) to the actual data.

As shown in this figure the polarization resistance Rp is the reciprocal of the slope of the polarization curve at the corrosion potential when plotted with current density on the ordinate and voltage on the abscissa. The polarization resistance is inversely proportional to the corrosion current density which can be transformed to a corrosion or penetration rate for uniform corrosion. From equation (3), the information that would be needed to estimate the corrosion rate are values of the two Tafel slopes and the polarization resistance, all measured at the corrosion potential. The value of the technique lies in the fact that in many instances, the method of making the measurement does not interfere with the quantities being measured as long as the 

polarization is in the vicinity of the corrosion potential (about ± 30 mV or less) and the measurement can be made very quickly, usually in a matter of minutes. An example of a violation of this condition is provided elsewhere in this tutorial. Notice also that in the above figure, the curve is not linear in the vicinity of the corrosion potential. In addition, a polarization curve is symmetrical in the vicinity of the corrosion potential only when the two Tafel slopes are equal. Obtaining a good estimate of the polarization resistance can sometimes be much easier than obtaining good estimates for the Tafel slopes. When that issue occurs one can still estimate the corrosion current (corrosion rate) by rewriting equation (3) as 

                                                                    (4)

and by assuming that B lies between about 10 and 30 mV (often about 15 to 25 mV).

Implicit Assumptions

Using equation (3) to quantify the corrosion process and estimate corrosion rates from a polarization curve such as that in the figure requires assumptions as summarized below.

1. The reaction rate (corrosion current) can be expressed as being proportional to the exponential of the voltage offset from the corrosion potential for one oxidation (anodic) and one reduction (cathodic) reaction. If this assumption is not fulfilled, equation (1) has to be modified to account for all of the reactions that affect corrosion. < modifications the of idea an provides (1971) 787 p. 11, Vol. Science, Corrosion Oldham, B. K. and Mansfeld>

2. Uncompensated resistance in the electrolyte is either absent or is much smaller than the polarization resistance. The resistance estimated by the polarization resistance technique contains all contributions to the total resistance. For example, most electrochemical systems involving charge transfer across an interface have both a polarization resistance Rp and an uncompensated solution resistance Rs. The polarization resistance as measured by this technique is equal to the sum of the actual polarization resistance and the uncompensated solution resistance,  

. The current interrupt technique can sometimes be used effectively to correct for the uncompensated resistance. Most modern potentiostats have that capability.

3. For the full form of equation (3) to be used, mass transfer cannot be the controlling or rate limiting step and both the anodic and cathodic reactions must be under activation control. Otherwise, the Tafel slope corresponding to the mass transfer controlled process is infinite. For example, if the process is under cathodic mass transfer control, the proportionality constant between Rp and icorr becomes ba/2.303. The technique can still, in principle, be used to estimate corrosion rates under these circumstances. In practice, a non-linear regression of the data versus the combined equations (2) and (3) should result in an extremely large Tafel slope for the sub-process under mass transfer control.

4. The corrosion potential does not lie close to the reversible potentials for the oxidation and reduction reactions. Being 25 mV or so from the reversible potential is often sufficient to allow equation (2) to be valid.

5. To estimate the rate of uniform corrosion from the polarization resistance, each reacting site across the entire electrode surface is assumed to function simultaneously as a cathode and an anode. The anodic and cathodic sub-reactions do not occur on different sites. This assumption is implicit in Mixed Potential Theory. In the extreme, if separated anodes and cathodes exist on the surface corrosion would be localized on the surface (e.g. pits) and the corrosion rate calculated using equations (2) and (3) would not be the rate of uniform corrosion. Note that the method might be used as a sensitive detector of such corrosion if such localized attack is severe. Success depends on how the experimental apparatus is used and resulting curve is analyzed. That application is beyond the scope of this discussion.

6. No additional electrochemical reactions are occurring to interfere with the current density versus voltage curve.

Assessing how well these assumptions are fulfilled requires some knowledge of the corrosion process. The polarization resistance technique like all electrochemical techniques cannot be used blindly. Fulfilling the above assumptions means that using the polarization resistance technique to estimate the corrosion rate is valid for that corrosion process. Many practical systems are often poorly characterized so assessing how well these criteria are fulfilled can be difficult. Some degree of imprecision must be associated with the estimated corrosion rate under these conditions. Additional sources of error can arise when the technique is applied in practice.

Sources of Error

Experimentally induced artifacts can sometimes cause significant errors even if the assumptions outlined in the section Summary of Polarization Resistance Technique underpinning the equations used to relate the current-voltage relationship to the corrosion rate are fulfilled. A number of these artifacts also influence potentiodynamic polarization scans. This section summarizes several of the more common issues:

inappropriate voltage scan rate uncompensated (solution) resistance

non-linearity in vicinity of corrosion potential when using a limited number of point

errors in Tafel slopes

varying corrosion potential

non-uniform current and potential distributions

Voltage Scan Rate

The rate at which the voltage is ramped can affect the slope of the polarization curve at the corrosion potential and, hence, the polarization resistance for the same reasons as discussed with respect to the potentiodynamic polarization scan. When one ramps the voltage in one direction (e.g. -20 mV to +20 mV relative to the corrosion potential) and then in the other direction (+20 mV to - 20 mV relative to the corrosion potential) the two curves should overlay each other. Otherwise, the slope of either curve may not represent the true slope. If the scan rate is too large, these curves will not overlap.

The problem may be understood by picturing the surface as a simple resistor in series with a parallel combination of a resistor and capacitor. The capacitor could represent the double layer capacitance and the resistor in parallel with it could represent the polarization resistance (inversely proportional to the corrosion rate). The series resistor would be the solution resistance. The goal is for the polarization scan rate to be slow enough so that the capacitor remains fully charged and the current/voltage relationship reflects only the interfacial corrosion process at every potential of the scan. If not, some of the current generated would reflect charging of the surface capacitance in addition to the corrosion process. The measured current would then tend to be greater than the current actually generated by the corrosion reactions. The scan would not represent the corrosion process alone.

The question becomes, what is that proper scan rate? Though no recognized method exists to estimate this scan rate because the capacitance and resistance could be functions of the applied voltage, the relationship between the modulus and the frequency in an electrochemical impedance spectrum could be used to create a conceptual method of

estimating if the chosen scan rate is reasonable (F. Mansfeld and M. Kendig, Corrosion, 37, 9(1981): p. 545). The conceptual approach uses the lowest breakpoint frequency (where the inverse of the phase angle passes through a maximum) of the impedance spectrum as the starting point. The premise is that the scan rate (rate of change of voltage) can be related to a frequency at every applied potential. That frequency must be low enough so that the impedance magnitude becomes independent of frequency. There the polarization or charge transfer resistance is being measured with no interference from surface capacitance. This figure shows these relationships.

The break-point frequency, the point at which the inverse of the phase angle goes through a maximum and the impedance magnitude goes through its inflection point, can be calculated easily (F. Mansfeld, Corrosion, 37, 6(1981): p. 301) for the case of a surface that can be modeled as a parallel combination of a resistor (polarization resistance) and capacitor (double layer capacitance) in series with a resistor (uncompensated resistance). That frequency is about at the position of the middle arrowhead in the figure. This frequency is not the required frequency because the impedance magnitude is still increasing as frequency (scan rate) decreases. The frequency at which the impedance magnitude does not change, i.e. the frequency below which there is no capacitive contribution, is about an order of magnitude lower than the break-point frequency. The frequency can be converted to a scan rate by assuming that over some small voltage amplitude, e.g. ±5 mV, the voltage-current relationship is linear and the linear range corresponds to half of a sinusoidal wave.

The table below shows estimated maximum scan rates for several polarization resistances, solution resistances, and capacitances.

SolutionResistance(ohm-cm2)

PolarizationResistance(ohm-cm2)

SurfaceCapacitance

(µ farad-cm2)

MaximumScan Rate(mV-s-1)

10 103 100 5.1

10 104 100 0.51

10 105 100 0.05

10 106 100 0.005

100 103 100 6.3

100 104 100 0.51

100 105 100 0.05

100 106 100 0.005

10 103 20 25

10 104 20 2.5

10 105 20 0.25

10 106 20 0.025

100 103 20 50

100 104 20 2.6

100 105 20 0.25

100 106 20 0.025

The estimates are very conservative and are meant for illustrative purposes only. One possible way to overcome this issue is to operate the potentiostat at a very low scan rate for all materials, e.g. 0.1 mV/s as the polarization resistance limit for practical use of this technique is probably greater than 106ohm-cm2. Even at that scan rate, scanning over a cycle of 40 mV requires less than 5 minutes.

Sources of Error

Uncompensated Solution Resistance

The resistance calculated from

                                                                   (3)

is the sum of the actual polarization resistance and the uncompensated resistance between the sensing point of the reference electrode and the working electrode. The lower the conductivity of the solution, the greater is the uncompensated resistance and the greater is the chance of possible error in the estimated polarization resistance. The slope of the polarization curve at the corrosion potential as plotted in this figure would make the estimated Rp too large, the estimated corrosion rate too small. Often, the resistance estimated at high frequency (e.g. several thousand hertz) by electrochemical impedance spectroscopy can be used as the solution resistance. That number would be subtracted from the measured polarization resistance to provide the "true" polarization resistance.

This figure demonstrates how the unmeasured (uncompensated) voltage drop might vary with conductivity for different current densities (assuming that losses in wiring are minimal). The estimate was made by assuming a distance of 0.5 cm (5 mm) between the working electrode surface and the point in the solution sensed by the reference electrode. The resistance is approximately proportional to the distance between the electrode and the sensing point. In the absence of a voltage ramp, the actual voltage at the fluid side of the corroding electrode surface (relative to the reference electrode) would be the voltage set on the potentiostat minus the uncompensated voltage drop between the reference electrode

sensing point and the corroding electrode. Though this figure is provided for illustrative purposes only, it does show that the uncompensated voltage drop can be very large.

The effect that the uncompensated resistance can have on the effective potential (as opposed to the potential believed to be applied by the potentiostat) and the effective scan rate (as opposed to the scan rate believed to be applied by the potentiostat) has been analyzed mathematically and reported in the literature (F. Mansfeld, Corrosion, 38, 10(1982): p. 556 and K. Schwabe, W. Oelssner, and H. D. Suschke, Prot. Metals, 15(1979): p. 126). In summary, if the uncompensated voltage drop becomes significant, the applied potential can be much greater than the voltage that is actually affecting the corrosion processes. In addition, the applied scan rate can be much greater than the effective scan rate. More importantly, the differences will be a function of the magnitude of the current passed between the working and counter electrodes, becoming greater as the current increases.

Sources of Error

Non-linearity in vicinity of corrosion potential

Sometimes, the slope of the voltage vs. current curve in the vicinity of the corrosion potential is assumed to be independent of applied potential. Devices exist which apply two voltages, one at -10 to -20 mV and the other at +10 to +20 mV, both relative to the corrosion potential. The voltage difference is divided by the current difference and the result is assumed to be the polarization resistance. Other devices exist which measure the current at discreet voltage increments and determine the curve by linear regression. This figure shows how a polarization curve might appear in the vicinity of the corrosion potential. In equation (3),

                                                                   (3)

the second derivative is not zero at the corrosion potential so curvature of the polarization curve might be expected at that point. The amount of curvature would depend on icorr which itself depends on the Tafel slopes and polarization resistance. Invoking the assumption of linearity where the curve is actually non-linear has been estimated to result in errors as high as 50% from this source alone. Such errors may be acceptable because corrosion rates estimated from mass loss can also be in error by 100%. During screening, rates differing by a factor of two or three may often be considered to be the same. Then, linearity may be assumed for simplicity. If more accuracy is needed, account should be taken of the full non-linearity in the polarization curve near the corrosion potential. Curve-fitting by non-linear regression of the data against an equation such as

                                              (2)

is a reasonable way to extract the polarization resistance. Packages in common spreadsheets can be used for this purpose.

Sources of Error

Errors in Tafel Slopes

A plethora of methods exist for estimating the corrosion current (polarization resistance) and Tafel slopes that do not assume linearity in the relationship between voltage and current. A number of these methods have been developed which tend to use a regression against the actual polarization curve to calculate the Tafel slopes and the polarization resistance followed by calculation of the corrosion current. Differences between actual and calculated Tafel slopes can cause large errors in estimated corrosion currents (corrosion rates). Regression techniques can sometimes lead to non-unique solutions by locating a local and not a global minimum in the response surface. Care must be used when trying to extract the corrosion rates from the polarization curve. One simple technique useful during screening is to assume that the corrosion current is equal to the reciprocal of the polarization resistance multiplied by, for example, 0.025V as discussed in the section Summary of Polarization Resistance Technique in this tutorial.

Sources of Error

Varying Corrosion Potential

The corrosion potential is the potential of a corroding surface in an electrolyte relative to a reference electrode measured under open circuit conditions. This potential is created by all of the electrochemical reactions occurring on the corroding surface. One of the requirements of the polarization resistance technique is that the electrochemical reactions must be at steady state or at least constant during the measurement. Such a condition is identified by a constant corrosion potential. If the corrosion potential is varying, the current-voltage relationship defining the polarization curve may not reflect the same corrosion phenomena at all points of the curve. One large error source often overlooked is not waiting long enough for the corrosion potential to be at steady state before initiating a polarization resistance scan. For example, a corrosion potential varying at the rate of 0.1 mV/s translates to a 40 mV variation over 400 seconds. When a polarization resistance scan is generated from -20 mV to +20 mV relative to the starting corrosion potential at 0.1 mV/s, the scan takes 400 seconds. In this case, the corrosion potential would vary as much as the scan potential.

An additional source of error could occur when the slight polarization required by this technique upsets the electrochemical processes enough so that the generated curve does not pass through the point (0,0). That is, an applied current is observed at 0 volts relative to the original corrosion potential. This phenomenon seems to be more prevalent in more passive systems or when corrosion rates are very low. The example in the section Example (Low Corrosion Rate Environment) in this tutorial suggests how this issue might be handled to obtain a reasonable curve fit. But, corrosion rates estimated from mass loss and polarization resistance, both at steady state, might still be expected to differ.

Sources of Error

Non-Uniform Current and Potential Distributions

The Wagner number W is useful for qualitatively predicting if a current distribution is uniform or non-uniform. The parameter W is dimensionless and is given by

                                                                   (5)

where κ is the conductivity, L is a characteristic length, V is the voltage, and i is the current density. The derivative is a partial derivative. This number can be considered as the ratio of the resistance to electron transfer across the interface to the resistance of the solution. For practical purposes, equation (5) can be represented by

                                                                   (6)

where Rp is the polarization resistance and RΩ is the uncompensated solution resistance. One rule-of-thumb proposed is that if W is less than 0.1, the current distribution is likely to be non-uniform unless precautions are taken to ensure that the cell geometry is ideally symmetric. The solution resistance would be the dominant factor. In this case, the voltage must be corrected for IR drops. The reference "The Measurement and Correction of Electrolyte Resistance in Electrochemical Tests", ASTM STP 1056, L. L. Scribner and S. R. Taylor (eds.), 1990. provides a significant amount of information on the measurement of and correction for the uncompensated resistance.

Sources of Error

Example of Use of the Technique (Nickel in Strong Acid)

The polarization resistance method was used to estimate the corrosion rate of nickel in strongly acidic phosphoric/phosphorous acid solutions, the total acid content being 50 wt%. The procedure was to scan the potential between -20 mV and +20 mV at 0.1 mV/s after about 1 hour, after about 4 hours, and finally after 24 hours of exposure. The corrosion potential was stable during the generation of replicates at each time period. In several solutions, the potential did change by about 50 mV over the 24 hour period. The requirement of a stable corrosion potential was met fairly well under all conditions.

This figure shows a plot of typical polarization curve, the data points being the measured points and the curve being the result of curve-fitting by non-linear regression the equations

                                           (2)

and

                                                                   (3)

The symbols are explained in the section entitled Summary of Polarization Resistance Technique in this tutorial. Note that the measured points have curvature even at the corrosion potential. A more detailed discussion is provided in Silverman, D. C., "Practical Corrosion Prediction Using Electrochemical Techniques", Uhlig's Corrosion Handbook,

2nd ed., ch. 68, p. 1179 (2000)     (1800k).

The following table shows the calculated Tafel slopes and the corrosion rates estimated from the regression analysis and from mass loss. The Tafel slopes and polarization resistance values were averaged across the runs over the 24 hour period because the corrosion rate did not change over that period. The error shown is the standard deviation. 

Solution Tafel Slopeba

Tafel Slopeba

PolarizationResistance

Corrosion Ratemm/year

# (mV) (mV) (ohm-cm2 CorrosionCurrent Mass Loss

1 47(+/-25) 65(+/-24) 83(+/-15) 1.6 1.8

2 62(+/-16) 82(+/-20) 116(+/-18) 1.6 1.6

3 50(+/-10) 54(+/-9) 24(+/-5) 5.0 22

4 59(+/-9) 44(+/-10) 16(+/-5) 7.3 30

The difference between corrosion rates in the last two cases touches on several artifacts which can contribute to errors. First, the solution resistance was about 1 to 2 ohm-cm2 as measured by electrochemical impedance spectroscopy at 5000 Hz. The error introduced by ignoring solution resistance is very small in the first two cases but may account for at least 10% of the value in the last two. Second, though the standard deviation in the measurement of the polarization resistance is only about 20% of the average value, the difference between the extremes in the polarization resistance (measurement + standard deviation) - (measurement - standard deviation) ) is about 100% for those two cases. Seemingly small errors in relatively small polarization resistance values can lead to large errors in estimated corrosion rates. Third, the corrosion potential for those two cases was about -250 mV (SCE), close to the reversible potential for hydrogen under these extremely acidic conditions. Hydrogen evolution in the form of bubbles was observed further suggesting that the corrosion potential might have been close to the reversible potential for the hydrogen evolution reaction in this system. Such proximity could have led to errors in the calculated values because the assumption behind the Butler-Volmer equation that only one irreversible anodic and one irreversible cathodic reaction are present may have been violated.

Example in a Low Corrosion Rate Environment(Aluminum and Magnesium with Cocoyl Glutamate)

Estimating polarization resistances from polarization resitance scans for passive alloys exhibiting low corrosion rates can have some unique issues. Reasonable estimates can be obtained as long as account is taken of their influence on the generated curve. This example is extracted from D. C. Silverman and T. K. Hirzel, "Divergent Effects of N-Acyl Glutamates on Corrosion of Aluminum and Magnesium Alloys", Corrosion, Vol. 58, p.99

(2002) 1     (227k).

Cocoyl glutamate was discovered to prevent staining of magnesium and aluminum alloys under alkaline conditions. The question was how this staining was being prevented, corrosion inhibition vs. removal of corrosion products (e.g. some corrosion acceleration). Solutions of various concentrations of cocoyl glutamate were formulated at a pH of 9.5. Corrosion of aluminum 7075-T6 and magnesium AZ31B were measured in these solutions by generating polarization resistance curves as a function of time over 24 hours and exposing these alloys to the test environments for 30 days to obtain corrosion rates by mass loss.

The polarization resistance curves were analyzed by non-linear regression of the equations (2) and (3) against the data.

                                            (2)

and

                                                                   (3)

The symbols are explained in the section entitled Summary of Polarization Resistance Technique in this tutorial.

This figure shows the plot of 1/Rp versus time for magnesium and this figure shows the same plot for aluminum. Triethanolamine was used as a control because it is present in many metalworking fluids and is thought to provide corrosion inhibition to at least steel. When Tafel slopes are difficult to estimate, the reciprocal of the polarization resistance can often be used to represent the corrosion rate for screening purposes. The inherent assumption was that the Tafel slopes did not change as a function of conditions, an assumption thought to be reasonable in this study. 

Corrosion rates were estimated by assuming a reasonable value of "B" in 

                                                                    (4)

The estimate was made in this case assuming a value of 0.025V for both aluminum and magnesium. The corrosion rate of magnesium was estimated to be in the range of 0.5 to 1 mpy (0.01 to 0.02 mm/y). The corrosion rate of aluminum was estimated to be less than 0.1 mpy (<0.0025 mm/y). Mass loss results suggested somewhat higher corrosion rates for magnesium in the range of 2 to 3 mpy. The aluminum corrosion rates from mass loss were less than 0.1 mpy (<0.0025 mm/y). The results suggested that the cleaning of magnesium was by removal of stains by corrosion of discoloration products while the cleaning of aluminum was through relatively complete passivation of aluminum. Further discussion of the reasons for this conclusion can be found in D. C. Silverman and T. K. Hirzel, "Divergent Effects of N-Acyl Glutamates on Corrosion of

Aluminum and Magnesium Alloys", Corrosion, Vol. 58, p.99 (2002) 1     (227k).

Note that the agreement of corrosion rates for magnesium between techniques is good but not great. Assuming that the choice of 0.025V is within a factor of two of the actual value, the discussion elsewhere in this tutorial suggests that the discrepancy could be an artifact of the procedure for generating and analyzing the polarization resistance scans especially for alloys exhibiting very low corrosion rates. This figure shows a typical scan for magnesium and this figure shows a typical scan for aluminum, both generated after 24 hours of exposure. At that time, the corrosion potential measured as an open circuit potential was stable, changing at less than 1 mV per hour for either alloy.

The abscissa for each plot is the voltage relative to that voltage registering as zero current on the polarization resistance scan not as the voltage relative to the open circuit potential measured prior to starting the scan. The reason is that equation (2) is derived from the fact that no current is applied at the corrosion potential. To use equation (2) to estimate polarization resistance and Tafel slopes requires that when V=Vcorr, iapplied = 0. The fact that Vcorr,true measured at open circuit and Vcorr,apparent as estimated from polarization resistance plots are slightly different means that polarization to -20 mV relative to Vcorr,true upset the corrosion process enough that it could not recover during generation of the scan. The process being examined electrochemically is slightly different from the process existing under open circuit potential even under the low polarization required by this technique. This artifact does not negate the usefulness of the polarization resistance technique. It does indicate that care is required when interpreting results especially for more passive alloy-environment systems.