Argentum Solutions, Inc.
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David C. Silverman |
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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:
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 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.
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. 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 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. 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. 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. 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. 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. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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David C. Silverman, Ph.D. - Primary Consultant |
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