Description
DC Corrosion provides a modern set of tools for DC electrochemical corrosion testing within Gamry Framework™. It offers a unique combination of flexibility, power, and ease of use.
Electrochemical Basis of Corrosion
Nearly all metal corrosion occurs via electrochemical reactions at the interface between metal electrode and electrolyte. A thin film of moisture on a metal surface forms the electrolyte for atmospheric corrosion. Wet concrete is the electrolyte for reinforcing rod corrosion in bridges. Although most corrosion takes place in water, corrosion in non-aqueous systems is not uncommon.
Corrosion normally occurs at a rate determined by an equilibrium between opposing electrochemical reactions. The first is the anodic reaction, in which a metal is oxidized, releasing electrons into the metal. The other is the cathodic reaction, in which a solution species (often O2 or H+) is reduced, removing electrons from the metal. When these two reactions are in equilibrium, the flow of electrons from each reaction is balanced, and no net electron flow (electronic current) occurs. The two reactions can take place on one metal or on two dissimilar metals (or metal sites) that are electrically connected.
The following figure illustrates this process. The vertical axis is potential and the horizontal axis is the logarithm of absolute current. The theoretical current for the anodic and cathodic reactions are shown as straight lines. The curved line is the sum of the anodic and cathodic currents. When you sweep the potential of the metal, you measure the current. The sharp point in the curve results from the use of a logarithmic axis. It is actually the point where the current gets very small prior to changing sign.
Corrosion process showing anodic and cathodic current components.
The potential of the metal is the means by which the anodic and cathodic reactions are kept in balance. Refer to the previous figure. Notice that the current from each half-reaction depends on the electrochemical potential of the metal. Suppose the anodic reaction releases too many electrons into the metal. Excess electrons shift the potential of the metal more negative, which slows the anodic reaction and speeds up the cathodic reaction. This reaction, by Le Châtelier's Principle, counteracts the initial perturbation of the system.
In the DC Corrosion software, the equilibrium potential assumed by the metal in the absence of electrical connections to the metal is called the open-circuit potential, Eoc.
Corrosion Current
The value of either the anodic or cathodic current at Eoc is called the corrosion current, Icorr. If we could measure Icorr, we could use it to calculate the corrosion rate of the metal. Unfortunately, Icorr cannot be measured directly. However, it can be estimated using electrochemical techniques. In any real system Icorr and corrosion rate are a function of many system variables, including type of metal, solution composition, temperature, solution movement, metal history, and so on.
The above description of the corrosion process does not say anything about the state of the metal surface. In practice, many metals form an oxide layer on their surface as they corrode. If the oxide layer inhibits further corrosion, the metal is said to passivate. In some cases, local areas of the passive film break down, allowing significant metal corrosion to occur in a small area. This phenomenon is called pitting corrosion or just pitting.
Because corrosion occurs via electrochemical reactions, electrochemical techniques are ideal for the study of the corrosion processes. In electrochemical studies a metal sample a few cm² in surface area is used to model the metal in a corroding system. The metal sample is immersed in a solution typical of the metal's environment in the system being studied. Additional electrodes are immersed in the solution, and all the electrodes are connected to a device called a potentiostat. A potentiostat allows you to change the potential of the metal sample in a controlled manner.
With the exception of Open Circuit Potential vs Time and Galvanic Corrosion techniques, all of the DC Corrosion standard techniques use the potentiostat to perturb the equilibrium corrosion process. When the potential of a metal sample in solution is forced away from Eoc, we call it polarizing the sample. The response (current or voltage) of the metal sample is measured as it is polarized. The response is used to develop a model of the sample's corrosion behavior. Both controlled potential (potentiostatic) and controlled current (galvanostatic) polarization are useful. When the polarization is done potentiostatically, current is measured, and when it is done galvanostatically, potential is measured.
Suppose we use the potentiostat to force the potential of a metal anodically (towards positive potentials) from Eoc. In the previous figure, we are moving towards the top of the graph. This increases the rate of the anodic reaction and decrease the rate of the cathodic reaction. Because the anodic and cathodic reactions are no longer balanced, a net current flows from the electronic circuit into the metal sample. The sign of this current is positive by convention. The potentiostat accurately measures the current. If we take the potential far enough from Eoc, the current from the cathodic reaction is negligible, and the measured current is a measure of the anodic reaction alone. In the previous figure, notice that the curves for the cell current and the anodic current lie on top of each other at positive potentials. Conversely, at strongly negative potentials the cell current is dominated by the cathodic current.
In some cases, as we vary the potential, we first passivate the metal, then cause pitting corrosion. Analysis of a curve plotting the measured current versus time or potential may allow us to determine Icorr at Ecorr, the tendency for passivation to occur, or the potential range over which pitting will occur.
Quantitative Corrosion Theory
In the previous section, we pointed out that Icorr cannot be measured directly. In many cases you can estimate it from current-versus-voltage data. You can plot a logarithmic current-versus-potential curve over a range of about half a volt. The voltage scan is centered on Eoc. You then fit the measured data to a theoretical model of the corrosion process.
The model we use assumes that the rates of both the anodic and cathodic processes are controlled by the kinetics of the electron-transfer reaction at the metal surface. This is generally true for corrosion reactions. An electrochemical reaction under kinetic control obeys the following equation, the Tafel equation:
In this equation,
•I is the current resulting from the reaction,
•I0 is a reaction-dependent constant called the exchange current,
•E is the electrode potential,
•E0 is the equilibrium potential (constant for a given reaction),
•β is the reaction's Beta coefficient (constant for a given reaction); β has units of volts/decade.
The Tafel equation describes the behavior of one isolated reaction. But in a corrosion system, we have two opposing reactions.
The Tafel equations for both the anodic and cathodic reactions in a corrosion system can be combined to generate the Butler-Volmer equation seen below.
where
•I is the measured cell current in amperes,
•Icorr is the corrosion current in amperes,
•Ecorr is the corrosion potential in volts,
•βA is the anodic beta (Tafel) coefficient in volts/decade,
•βC is the cathodic beta (Tafel) coefficient in volts/decade.
What does the Butler-Volmer equation predict about the current-versus-voltage curve?
1.At Ecorr each exponential term equals one. The cell current is therefore zero, as you would expect.
2.Near Ecorr, both exponential terms contribute to the overall current.
3.Finally, as you get far from Ecorr, one exponential term predominates and the other term can be ignored. When this occurs, a plot of log(current) versus potential becomes a straight line.
In practice many corrosion systems are kinetically controlled and thus obey the Butler-Volmer Equation. A log(current)-versus-potential curve that is linear on both sides of Ecorr is indicative of kinetic control for the system being studied. However, there can be complications, such as:
•Concentration polarization, where the rate of a reaction is controlled by the rate at which reactants arrive at the metal surface. Often cathodic reactions show concentration polarization at higher currents when diffusion of oxygen or hydrogen ion is not fast enough to sustain the kinetically controlled rate.
•Oxide formation, which may lead to passivation, can alter the surface of the sample being tested. The original surface and the altered surface may have different values for the constants in the Butler-Volmer equation.
•Other effects that alter the surface, such as preferential dissolution of one component of an alloy, can also cause problems.
•A mixed control process, where more than one cathodic or anodic reaction occurs simultaneously, complicates the model. An example of mixed control is the simultaneous reduction of oxygen and hydrogen ion.
•Finally, potential drop as a result of cell current flowing through the resistance of your cell solution causes errors in the kinetic model. This last effect, if it is not too severe, may be correctable via iR-compensation in the potentiostat.
In most cases, complications like those listed above cause non-linearities in the Tafel plot. Use with caution the numbers that arise from a Tafel analysis on data that do not have a linear Tafel plot.
Classic Tafel analysis is performed by extrapolating the linear portions of a log(current)-versus-potential plot back to their intersection, see the figure below. The value of either current at the intersection is Icorr. Unfortunately, many real-world corrosion systems do not provide a sufficient linear region to permit accurate extrapolation. Most modern corrosion-test software performs a more sophisticated numerical fit to the Butler-Volmer equation. The measured data is fit to the Butler Volmer equation by adjusting the values of Ecorr, Icorr, βA, and βC. The curve-fitting method has the advantage that it does not require a fully-developed linear portion of the curve.
Classic Tafel analysis.
You can further simplify the Butler Volmer equation by restricting the potential to be close to Ecorr. The current-versus-voltage curve approximates then a straight line. The slope of this line has the units of resistance (Ω). The slope is called the Polarization Resistance, Rp. An Rp value can be combined with an estimate of the β coefficients to yield an estimate of the corrosion current.
If we approximate the exponential terms in the Butler-Volmer equation with the first two terms of a power-series expansion and simplify, we get one form of the Stern-Geary equation:
In a Polarization Resistance experiment you record a current-versus-voltage curve as the cell voltage is swept over a small range near Eoc. A numerical fit of the curve yields a value for the Rp. Polarization Resistance data does not provide any information about the values for the β coefficients. Therefore, to use the Stern-Geary equation, you must provide β values. These can be obtained from separate Tafel-type experiments or estimated from your experience with the system you are testing.
Calculation of Corrosion Rate
When you fit corrosion data to a model, the numerical result is generally a corrosion current. We are interested in corrosion rates in more useful terms, such as a corrosion rate in millimeters per year. How is corrosion current used to generate a corrosion rate?
Assume an electrolytic dissolution reaction involving a chemical species, S:
You can relate current flow to mass via Faraday's Law.
where
•QS is the charge in coulombs resulting from the reaction of species S,
•n is the number of electrons transferred per molecule or atom of S,
•F is Faraday's constant = 96 485.34 coulombs/mole,
•MS is the number of moles of species S reacting.
A more useful form of Faraday’s Law requires the idea of equivalent weight. The equivalent weight (EWS) is the mass of species S that will react with one faraday of charge. For an atomic species, EW = AW/n (where AW is the atomic weight of the species). For a complex alloy that undergoes uniform dissolution, the equivalent weight is a weighted average of the equivalent weights of the alloy components. Mole fraction, not mass fraction, is used as the weighting factor. If the dissolution is not uniform, you may have to measure the corrosion products to calculate EW.
Substituting into Faraday’s Law we get:
where WS is the mass of species S that has reacted.
In cases where the corrosion occurs uniformly across a metal's surface, you can calculate the corrosion rate in units of distance per year. Be careful: this calculation underestimates the problem when localized corrosion occurs!
Conversion from a weight loss to a corrosion rate (CR) is straightforward. We need to know the density, d, and the sample area, A. Charge is given by Q = It, where t is the time in seconds and I is a current. We can substitute in the value of Faraday's constant. Modifying the previous equation,
where
•CR is the corrosion rate. Its units are given by the choice of K,
•Icorr is the corrosion current in amperes.
•K is constant that defines the units for the corrosion rate.
•EW is the equivalent weight in grams/equivalent
•d is the density in grams/cm³
•A is the area of the sample in cm².
The following table shows the value of K used in the corrosion rate equation for corrosion rates in the units of your choice.
Units for Corrosion Rate |
K |
Units |
|---|---|---|
mm/year (mmpy) |
3272 |
mm/(A cm year) |
µm/year |
3.272 · 106 |
µm/(A cm year) |
mils/year (Gamry default) (mpy) |
1.288 · 105 |
mils/(A cm year) |
See ASTM Standard G 102, Standard Practice for Calculation of Corrosion Rates and Related Information from Electrochemical Measurements, for further information. The standard can be obtained from ASTM, 1916 Race St., Philadelphia, Pennsylvania 19013-1187 (USA) www.astm.org.
Current and Voltage Convention in DC Corrosion
A current value of –1.2 mA can mean different things to people in different areas of electrochemistry. To a corrosion scientist it represents 1.2 mA of cathodic current. To an analytical electrochemist it represents 1.2 mA of anodic current.
In the DC Corrosion's standard techniques, we follow the corrosion convention for current:
•Positive currents are anodic, resulting in an oxidation at the metal specimen under test.
This convention is the same as the current convention used in other Gamry software packages such as Physical Electrochemistry and Electrochemical Impedance Spectroscopy.
Potentials can also be a source of confusion. Throughout Gamry's software, the equilibrium potential assumed by the metal in the absence of electrical connections to the metal is called the open-circuit potential, Eoc. We have reserved the term corrosion potential, Ecorr, for the potential at which no current flows, as determined by a numerical fit of current-versus-potential data. In an ideal case, the values for Eoc and Ecorr are identical. One reason the two voltages may differ in real systems is changes in the electrode surface during the scan. In DC Corrosion, all potentials are specified or reported as the potential of the working electrode with respect to either the reference electrode or the open-circuit potential. The former is always labeled as "vs Eref" and the latter is labeled as "vs Eoc".
The equations used to convert from one form of potential to the other are:
iR-compensation in DC Corrosion
When you pass current between two electrodes in a conductive solution, there are always regions of different potentials in the solution. Much of the overall potential change occurs close to the surface of the electrodes. Here, the potential gradients are due to ionic concentration gradients set up near the metal surfaces. There is always a potential difference (a potential drop) caused by current flow through the resistance in the bulk of the solution.
In an electrochemical experiment, the potential that you wish to control or measure is the potential of a metal specimen (called the working electrode) versus a reference electrode. You are normally not interested in the potential drops caused by solution resistances.
The Gamry Instruments potentiostat, like all modern electrochemical instruments, can be set up as a three-electrode potentiostat. It measures and controls the potential difference between a non-current-carrying reference electrode and one of the two current-carrying electrodes (the working electrode). The potential drop near the other current carrying electrode (the counter electrode) typically does not matter when a three-electrode setup is used.
Careful placement of the reference electrode can compensate for some of the iR-drop resulting from the cell current, I, flowing through the solution resistance, R. You can think of the reference electrode as sampling the potential somewhere along the solution resistance. The closer it is to the working electrode, the closer you are to measuring a potential free from iR-errors. However, complete iR-compensation cannot be achieved in practice through placement of the reference electrode, because of the finite physical size of the electrode. The portion of the cell resistance that remains after placing the reference electrode is called the uncompensated resistance, Ru.
The DC Corrosion software uses current-interrupt IR-compensation to dynamically correct uncompensated resistance errors. In the current-interrupt technique, the cell current is periodically turned off for a short time. With no current through the solution resistance, its iR-drop disappears. The potential drops at the electrode surface remain constant on a short time-scale. The difference in potential with the current flowing and without is a measure of the uncompensated iR-drop.
The DC Corrosion software makes a current-interrupt measurement right after each data point is acquired. It actually takes three potential readings: E1 before the current is turned off, and E2 and E3 while it is off. See the figure below. Normally, the latter two are used to extrapolate the potential difference, ΔE, back to the exact moment when the current was interrupted. The timing of the interrupt depends on the cell current. The interrupt time is 40 µs on the higher current ranges. On lower current ranges, the interrupt lasts longer.
Current-interrupt potential versus Time.
The software has a second current-interrupt measurement mode that involves averaging of the two points on the decay curve. See the discussion of the Pstat.SetIruptMode() for more information.
In controlled-potential modes, the applied potential can be dynamically corrected for the measured iR-error in one of several ways. In the simplest of these, the IR error from the previous point is applied as a correction to the applied potential. For example, if an iR-free potential of 1 V is desired, and the measured iR-error is 0.2 V, the DC Corrosion software applies 1.2 V. The correction is always one point behind, because the iR-error from one point is applied to correct the applied potential for the next point. In addition to this common mode, the DC Corrosion software offers more complex feedback modes.
By default, the potential error measured via current-interrupt in controlled-potential mode is used to correct the applied potential. In the controlled-current modes, no correction is required. If iR-compensation is selected, the measured iR-error is subtracted from the measured potential. All reported potentials are therefore free from iR-error.
DSP sampling in DC Corrosion
All Gamry instruments have the ability to perform DSP sampling (super-sampling) during data acquisition. DSP sampling can decrease the noise component of the measurement.
By default, all DC Corrosion experiments use DSP sampling with a standard duty-cycle of 20%, or 0.20. This means that for a one-second sample period, data are acquired for 200 ms at a rate of 60 kHz. For this one-second sample period, the output point is made of an average of 12 000 samples. For custom experiments, you can change this duty-cycle by making an additional function call in the Explain script.
Literature
The following references are useful for learning more about the techniques that are available in DC Corrosion:
1.Denny A. Jones, Principles and Prevention of Corrosion, 2nd. ed., Prentice Hall, Upper Saddle River, NJ, 1995.
2.Herbert H. Uhlig and R. Winston Revie, Corrosion and Corrosion Control, 3rd. ed., John Wiley and Sons, New York, NY, 1985.
3.Electrochemical Techniques for Corrosion Engineering, R. Baboian, Ed., NACE, Houston, TX, 1986.
4.Corrosion Testing and Evaluation, STP 1000, R. Baboian and S.W. Dean, Eds. American Society for Testing and Materials, W. Conshohocken, PA, 1991.
5.Electrochemical Corrosion Testing, STP 727, F. Mansfeld and U. Bertocci, Eds., American Society for Testing and Materials, W. Conshohocken, PA, 1979.