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A wander through the science of Ohm's and Kirchoff's Laws relating to Localised Corrosion Monitoring (LCM™) in passive metal and inhibited systems

There is a tendency to think that because corrosion is Electrochemistry it is not controlled by the same rules as for electrical circuits with combinations of resistors and capacitors. Monitoring of corrosion is typically thought of as some sort of black art that is best looked at using complex equations such as Fast Fourier Transforms that few people feel comfortable with and are typically not appropriate.

Kirchoff's current laws relating to the conservation of current in a circuit and the familiar Ohm's Law are very relevant to both general and localised corrosion monitoring, especially when combined with very standard school boy mathematics. It is primarily through trying to understand the processes that are going on in terms of electronic components and simple mathematics that we can attempt to apply the most appropriate monitoring technique. In turn, such knowledge combined with real testing data assists with inhibitor development or metal selection.


Randles Circuit

Consider the Randles circuit below. It is a familiar circuit that gives the impression that corrosion cells are largely based around Ohm's Law and that a linear response is obtained from a given DC polarisation.

Randles Circuit

Randles Circuit is fine and a good starting point, though it is not that useful for describing the processes that go on in localised corrosion monitoring, being a bit staid and static. It looks like something that is designed to be good enough for Electrochemists. Localised corrosion processes make corrosion dynamic and exciting, often with rapid changes in potential with corresponding bursts of current, or slow changes in potential lasting many hours and every case in-between. Components within the circuit are likely to change with time and voltage. In order to better understand localised corrosion and improve the method of monitoring, it is necessary to depart from the faithful Randles circuit and adopt something that includes the Anodic and Cathodic components of Rct, the galvanic influence of a localised corrosion site, solution resistance and components for resistive inhibitor films.

Let's consider a single electrode corroding happily in a solution at a stable potential. It is reasonable to assume that Rct, the charge transfer resistance, consists of anodic and cathodic parts.  Kirchoff's Law tells us about conservation of current. For corrosion to occur in these stable conditions, the corrosion current is impeded by the Cathodic charge transfer resistance, Rct cathodic, and the Anodic charge transfer resistance, Rct anodic. The total resistance to this process being Rct anodic + Rct cathodic. In stable conditions, the standard Rct = Rct anodic + Rct cathodic. The energy needed to drive the current through this chain of resistors being supplied from the corroding metal. The diagram below shows the replacement for Rct including a new component in the form of a battery which drives the general corrosion process. We will label this battery GCG for General Corrosion Generator, its energy comes from the corrosion process.

localised corrosion circuit

It is now easy to visualise current relating to general corrosion flowing in this replacement style circuit shown in figure 2. The circuit looks much more like an electronic circuit with resistors and a electro motive force to drive the current around the circuit. The circuit implies that in order to produce any current, it is necessary to convert metal to metal ions via Rct anodic. Any fluctuations in this current can be transmitted via the double layer capacitance or via Rct cathodic. Over time however, the same amount of current must flow through Rct anodic as Rct cathodic if the charge on Cdl does not change from the start of the test to the end of the test. Following the path of current through the Replacement Style circuit, it is apparent that the current has to enter the corrosive solution before passing back through Rct cathodic. There will be an element of solution resistance here, however for general corrosion, it is reasonable to think that anodic and cathodic reactions take place very close to each other, so the effect of solution resistance is going to be negligible.

The Randles circuit is often used as a model for tests that involve a polarisation using a Potentiostat or some other external device. This Replacement Style circuit can also be used in tests using an external current source such as a Potentiostat.

Powered randles circuit

The external power source is typically a Potentiostat. It is interesting to play a little with this circuit to see its limits. If the test electrode is polarised anodically, then as far as an individual metal molecule is concerned, we are increasing the energy drop for it to change into a metal ion and so promoting the anodic reaction. The same polarisation decreases the energy available to drive the cathodic reaction. The net result is the current tends to flow through Rct anodic and not Rct cathodic. We also know that the current response to an external polarisation is typically not linear. An increase in potential tends to give an exponential increase in current. This suggests that Rct anodic and Rct cathodic should be variable resistors. With polarisations in the anodic direction the value of Rct anodic decreases, whilst the value of Rct cathodic increases. Indeed due to this exponential current response to a polarisation, it does not take much of a polarisation before close to 100% of the current is flowing through Rct cathodic or Rct anodic depending on the polarisation direction. Thus Rct anodic and cathodic should be seen as variable resistors rather than fixed values.

It is worthwhile to consider the role played by Cdl the double layer capacitor. Capacitors enable charge or energy to be stored and are also able to transmit current in situations where the current is changing with time. The capacitance of two parallel metal plates is inversely proportional to the distance between the plates. Thus the closer the two metal plates are together, the larger the value of capacitance. Double layer capacitors are at a molecular level with a molecular related distance between the charged particles, thus we can expect them to be willing to transmit dynamic currents easily and store significant charge. Indeed the energy that can be stored on Electrochemical capacitors is used in hybrid vehicles such as buses, in preference to batteries or much lower capacity standard capacitors. The point is that Cdl is capable of storing a significant charge. It may be the case that with changing potential, the capacity of Cdl also changes and like Rct anodic and cathodic is also variable. I don't think we need to concern ourselves with changes in the value of Cdl, other than it is capable of storing significant charge. For the sake of simplicity I will leave this as a fixed value.The diagram below shows the same circuit as above except with variable resistors.

Powered variable randles circuit

For cathodic polarisations, Rct cathodic tends towards an insulator and the effect of GCG becomes of less importance as the corrosion process is driven increasingly by the External Power Source. With this in mind the circuits can be simplified. Figure 6 shows how the circuit can be simplified for a cathodic polarisation. For an anodic polarisation, the component Rct cathodic needs to be replaced by Rct anodic.

Cathodic powered randles circuit

There are two main areas for monitoring localised corrosion, these are in passive metals such as stainless steel and inhibited systems. The mechanisms that start and stop the localised corrosion process in these two systems have subtle differences. It is therefore worthwhile to consider these two cases separately as they affect the way in which localised corrosion is monitored.


Localised Corrosion Monitoring in Passive Metal Systems

Consider now an electrode made of passive metal such as stainless steel undergoing a pitting event. The localised corrosion process is an accelerated form of corrosion that produces many more electrons and corresponding metal ions than areas that are just corroding generally. This supply of electrons is the same as if they were supplied by an external current source. We can thus replace the External Power Source with a Localised Corrosion Process.

Electrode rendles circuit

The External Power Source has now been replaced by a pitting event that has its own variable Rct anodic (pit) and Rct cathodic (pit). It also has its own power source labelled PCG for Pitting Current Generator. The power for PCG comes from the corrosion reaction of metal, such as Iron going from Fe to Fe2+ + 2e-. There are some differences however between electrons supplied by an external power source and a localised corrosion event, primarily to do with the influence of the cathodic reaction at the pit site.

In the above circuit Rct anodic (pit), PCG and Rct anodic become active when the switch is closed. It is worthwhile to consider the path of current during and after a pitting event. Localised events in passive metal systems may last just a fraction of a second to a few seconds and be of significant magnitude. In passive metal systems the current density per unit area at the localised site could be many millions of times larger than the background corrosion rate. To an external observer this is seen as a rapid drop in potential, typically followed by a slower increasing of potential towards the original rest potential. In Figure 7, when the switch is closed, current can follow four paths. We need to consider each route.

  • Route A: In a loop going back through Rct cathodic (pit).

  • Route B: In a loop through the solution resistance and then through Rct anodic.

  • Route C: In a loop through the solution resistance and then through Rct cathodic.

  • Route D: In a loop through the solution resistance and then through Cdl.

If the localised event is rapid, as is often the case with stainless metals, then it is unlikely that the cathodic reactions Rct cathodic (pit) and Rct cathodic will be able to consume the electrons produced by the pitting event fast enough. Rct anodic will tend to become much more resistive as the pitting event polarises the electrode in the cathodic direction. The vast majority of the current will tend to pass through the solution resistance and go straight through the double layer capacitance as if it were a short circuit. No charge is passed through this capacitance, it simply builds up charge in the form of electrons and charged ions. The state of charge of the double layer capacitor can typically be seen by an observer as a rapid decrease in potential. After the localised event, characterised by the opening of the switch, the charge remaining on Cdl is slowly consumed by the Cathodic Reaction Rct cathodic. Rct cathodic (pit) is now just a small part of Rct cathodic. This can be seen by an outside observer as a slow increase in potential.

Image

Active Localised Corrosion

To date I have concentrated on localised corrosion in the initiation phase. There are other cases where a localised site remains active such as in a crevice. In this case the electronic circuit including a localised corrosion site should be re analysed. Normally we discount the effect of Rct cathodic (pit) as the pitting event is typically brief. However in an active system, Rct cathodic (pit) is constantly active. Thus not all the electrons produced by PCG will travel via Rct cathodic, some will go via Rct cathodic (pit). Rct cathodic (pit) does not have a protective passive film when the pit is active so it is likely to have a much lower resistance per unit area than Rct cathodic. The effect of Rct cathodic (pit) in a constantly active system has consequences that need to be considered when it comes to corrosion monitoring.


Methods of Monitoring Localised Corrosion in Passive Metal Systems

From the discussion there are a number of ways of monitoring localised corrosion in passive metal systems.

A localised event such as a pit, produces a typical potential signal which is observed as a rapid drop in potential followed by a slower recovery in potential. As previously discussed the rapid drop in potential is due to a burst of current from the pit site short circuiting itself via the double layer capacitance Cdl. This leaves behind a residual charge. The localised corrosion process may finish in a fraction of a second to a few seconds leaving the charge to slowly dissipate via the cathodic reaction Rct cathodic.

In order to monitor the metal loss caused by a localised corrosion event, it is necessary to know the quantity of charge associated with the event. Metal loss and charge are directly related. It is also useful to know the corrosion process for instance Fe may go to Fe2+ or Fe 3+ releasing either 2 or 3 electrons per atom of Fe.

The quantity of charge can be measured directly using a Zero Resistance Ammeter (ZRA) or indirectly using a Transient Calibration Method. Both methods are discussed.


Transient Calibration methods for use in Passive Metal Systems such as Stainless Steel

This technique monitors the potential of the test electrode with respect to time and periodically applies a calibrating polarisation.

The potential of the test electrode should be monitored with an electrode that is unlikely to produce potential signals of its own. Such an electrode may be a commercial reference electrode or a metal that is very resistant to localised corrosion such as Hastalloy.

There are two methods of calibrating the charge associated with a potential transient, these are by predicting the level of current produced by the localised site necessary to produce a transient of a specific magnitude, or calculating the quantity of current consumed by the cathodic reaction. This is really a form of measuring either the cause or the effect.

If via a Potentiostat, an identical polarisation is applied to the electrode as produced by a natural transient, then it is possible to replicate the current generated by the natural pit site. This being the anodic current produced by the pit site.

polarisation transient

It is not practical however to polarise the test electrode with a carbon copy of each and every transient detected. It is necessary to have easier methods.


Using a Rapid Cathodic Polarisation

If it is assumed that all localised events produce a sharp drop in potential caused by a burst of electrons produced by the localised event, then a rapid cathodic polarisation can be applied to the electrode to replicate this event. The amount of charge necessary to decrease the potential is monitored so that smaller naturally occurring transients can be calibrated based on the size of the potential drop. As the polarisation is rapid and in the order of 1 second, an assumption is made that all the charge applied is stored on Cdl and non is used up by the cathodic reaction. Many users will not like this approach as it is necessary to apply a large polarisation to the test electrode if naturally occurring transients are quite large.

Alternatively an assumption can be made that the capacitance of Cdl remains constant no matter how cathodically polarised it is. In this instance a small, but rapid polarisation can be applied, perhaps only in the order of 10mV. The charge necessary to polarise the electrode by this amount is monitored in the same way. Thus a 100mV naturally occurring transient will need to have produced 10 times more current. The value of Cdl may also be monitored by using a AC signal.

It is useful to also obtain a measure of the average general corrosion rate. Normally this has to be done using a slow LPR type polarisation, however with a small but rapid calibrating polarisation, the test electrode can be isolated after the polarisation and the potential monitored with respect to time. The potential rises slowly towards the original pre polarisation potential as the charge is consumed by the cathodic reaction, Rct cathodic. The area beneath the decay curve, V x Time is calculated and this value further divided by the Charge applied to give a value of Rp, the resistance to polarisation. Rp can be used in the normal way to calculate the general corrosion rate.


Using a Slow Cathodic Polarisation

This technique measures the rate of the cathodic reaction at different levels of cathodic polarisation. It enables us to calibrate transients by calculating the charge consumed by the cathodic reaction. The charge associated with the pitting event can be measured by integrating the cathodic current over the Potential transient. This can be done by passing potential transients through a V / I calibration curve. The curve being produced by a slow cathodic polarisation that has only a limited charging element.

calibration curve

Such a cathodic polarisation can be speeded up by segmenting it into three stepwise polarisations of:

  • LPR magnitude to obtain the average general corrosion rate.

  • Half the amplitude of the maximum detected potential transient.

  • The amplitude of the maximum detected potential transient.

A small settling time can be applied after each polarisation in order to measure the reaction rate at each polarisation with only a limited contribution from Cdl charging. The Transient Calibration Curve is then made up of 3 straight lines connecting the points and the origin.


Transient measurement method using a Zero Resistance Ammeter (ZRA)

ZRA's offer an easy direct method of measuring the current associated with a localised event. Electrodes are constantly controlled via a ZRA without any feedback loop through a test solution. This makes the system very stable and able to cope with variations in solution conductivity. Though with passive metals, due to the speed of pitting events and the amplitude of the current produced, care should be taken to ensure that the current burst is correctly monitored. Typically the current burst due to a localised event on passive metals are missed due to low read rates or the use of sensitive current ranges that are unable to cope with a rapid high power current bursts. The resultant data can often be referred to as Current and Voltage Noise, having filtered out the signal of interest. Current data should be monitored at between 5 to 50 readings per second using a current range that is capable of measuring a sudden burst without need to change range.

Often people refer to the use of a ZRA as Current and Voltage Noise. For localised corrosion monitoring the potential data is not strictly necessary as the charge associated with a localised event is monitored directly from the current data. Potential data does have its uses however, in that it can indicate if the test electrodes have active localised corrosion without repassivating. In this case there may be a equal number of active sites on both electrodes producing a net zero or low galvanic current.

Potential data can assist in cases where localised sites are active, however we can not be sure of the level of that activity. Polarising the electrodes with a small polarisation will give a measure of average general corrosion rate. Normally this is done with a Potentiostat in the normal way. However when a ZRA is used, which is really a Potentiostat in disguise, a small polarisation can be used that offsets the potential between the two electrodes to get a measure of the average corrosion activity.


Localised Corrosion Monitoring with regards to Inhibited Systems

Typically the effect of a polarisation on a mild steel electrode will tend to give an exponential response for an increase in polarisation potential. For instance a 100 mV polarisation may give a 100 times greater current response than a 10mV polarisation would. However in inhibited mild steel systems, the inhibitor can cover the steel with a resistive film that tends to inhibited this exponential current response. For polarisations up to about 100mV, the cathodic current response can be seen as linear in inhibited systems. This has positive implications with regards to transient calibration in that a small LPR type polarisation can be used to calibrate transients that are many times larger in magnitude than the LPR polarisation with the minimum of interference to the cell.

It is worthwhile to revisit the electronic circuit suggested for pitting in passive metals. In this case however a resistive film dominates the flow of current through Rct anodic and Rct cathodic. The effect of the inhibitor film Rf is such that Rf + Rct anodic or Rf + Rct cathodic can be seen as equal to Rf with a double layer capacitance. Any DC current that manages to get through Rf easily finds a path through Rct anodic or Rct cathodic, the anodic and cathodic charge transfer resistances, as appropriate.

inhibited mild steel

In the circuit for inhibited mild steel, components are:-

  • Rs = Solution resistance

  • Rf = Inhibitor Film Resistance (also incorporates inconsequential charge transfer resistances)

  • Rct anodic (pit) = Anodic Charge Transfer Resistance at the pit site

  • Rct cathodic (pit) = Cathodic Charge Transfer Resistance at the Pit site

  • PCG = Pitting Current Generator

A pitting event can be seen as a localised breakdown in the inhibitor film. Once this film is broken at a localised site, the effect of metal loss by a corrosion process can be seen as a battery with an internal resistance, shown in the diagram above as Rct anodic (pit) and PCG. The effect of PCG may be further enhanced by the high state of potential of the test electrode prior to the pitting event. The current produced via the localised corrosion has three possible routes:-

  • Route A: Through Rs and Cdl.

  • Route B: Through Rs and Rf.

  • Route C: Through Rct cathodic pit.


Short Duration Transients

For transients of short duration, the easiest initial route for the current is via Cdl. Double layer capacitors are quite effective at storing charge and present an easy route for a rapidly changing current. Alternatively current, in the form of charged particles will diffuse their way through the inhibitor film to be consumed by a cathodic corrosion reaction at the metals surface. The final route for the charge is via the cathodic reaction at the pit site itself.

What probably actually happens is a combination of these events. For relatively short duration transients where the potential is constantly changing with time, current will pass through Cdl with relative ease promoting the rapid metal loss at the pit site. As the charge on the Cdl builds, this can be seen as a drop in potential of the electrode as a whole which will enhance cathodic reactions over the entire electrodes surface, including the localised site, and greatly reduce the rate of any anodic reactions. With passive metal systems a localised event may be finished within a fraction of a second, as the fresh metal surface rapidly forms a new passive film. In a system that depends on inhibitors there must be another process. If it is assumed that the inhibitor film is broken down and blow apart at a localised site, due in part perhaps to a bombardment of metal ions leaving the metal surface, then there needs to be a process that rebuilds this film to stop the localised corrosion process. This may be assisted by the enhanced cathodic reaction driven by the charge stored on the double layer capacitor. Positively charged particles may actively drag inhibitor molecules to the metals surface, where they may help to start rebuilding the inhibitor film, perhaps from the edges. This process will reduce the localised corrosion process still further. This may be seen as a gradual drop in potential as the rate of the Cathodic charge transfer is greater than the Anodic Charge transfer.  Eventually the film will be fully reinstated and any remaining charge on Cdl is consumed by the Cathodic reaction over the metals surface.


Short Duration Transients

pitting event

pitting event

There are two ways of monitoring Localised Corrosion caused by transients of a short duration.


Method 1

Potential is monitored with respect to time and occasionally a small LPR polarisation is applied to the cell. A transient detection routine looks for transients in the potential data. The LPR polarisation is used to convert the drop in potential into current using Ohm's Law.

Ohm's Law     Ip = dV / Rp

Ip = Pitting Current or anodic current at localised corrosion site.
dV = The change in voltage from the potential before the start of the transient
Rp = The polarisation resistance obtained from the LPR test.

This equation assumes that all the charge produced by the localised site, typically a pit, passes through the inhibitor film Rf as some stage, even if initially it is stored on Cdl. It discounts current generated by the pit site flowing back through the pit site itself. It is assumed however that this error is only small as the pit site surface metal may only be exposed without an inhibitor film for a brief period, whilst charge is building up on Cdl.  Once the potential has dropped, then the inhibitor film probably starts to rebuild itself at the pit site, thus only a small fraction of the current produced by the pit site travels via the pit site itself whilst there is no or little inhibitor film.


Method 2

Both Current and Voltage measurements are taken. The transient can be detected either by looking for Potential or Current transient. The technique assumes that half the current produced by the localised event passes over to the second electrode for consumption by the cathodic reaction. The same assumption is made as for method 1 in that it discounts current generated by the pit site flowing back through the pit site itself.

The technique is fine if the transient produced is by one small pit site that occurs on one electrode only. This is probably quite likely for a small transients lasting for a few minutes.

It is possible to get a reading of the general corrosion rate from a single transient. By integrating the area of the Potential Transient in units of Voltage x Time (VT) and dividing this by the charge passed, in units of Current x Time (IT), over the same period, the average general corrosion rate can be calculated from the polarisation resistance obtained Rp.

Using this strategy alone to work out the general corrosion rate is a risky one, as it depends on a localised corrosion event to occur. It may be the case that localised corrosion is simply active on both electrodes and no convenient transients can be detected. It is better to occasionally apply a polarisation to the galvanic couple to calculate the average corrosion rate.


Long Duration Transients

Such transients can last for many hours. Localised Corrosion sites producing such transients may well be of a more considerable area than a short duration transient. Inhibitor film may be severely depleted on areas of the electrode surface for prolonged periods of time.

potential transient

The effects of long duration transients on the proposed electronic circuit should be considered.

inhibited mild steel

As this transient is of a long duration it is reasonable to expect Rf to change with time, perhaps as an operator adds more inhibitor due to a pitting alert.

For transients with a long duration the role of Cdl is less clear. It will still be able to store charge rapidly, however the quantity of charge it is willing to store will be much less than a transient that occurs over a short time period with more rapid rates of change of potential. Cdl requires a change in potential over a short time period for it to gain or loose charge. As the transients are of a long duration the rate of change of potential with respect to time tends to be lower. Cdl will still have a part to play though its role is less clear when looking at the long duration transient.Discounting Cdl, then during a localised corrosion or pitting event, current generated via the pit site can travel by one of two routes, either through Rf or back through the pit site itself Rct cathodic (pit). If this is a large pit, then an appreciable quantity of the current generated by the pit site may be consumed at the pit site itself. From a monitoring point of view this gives us a problem as it is difficult to take into account the magnitude of current flowing through Rct cathodic (pit).


Methods of Monitoring Metal Loss for transients with a Long Duration

Current and Voltage Method

The traditional form of localised corrosion monitoring will really struggle with long duration pitting events. A typical current and voltage snapshot only takes 1024 readings over a period of 17 minutes. 17 minutes of time may only represent 1% of the total duration of the pitting event. During this time the potential may remain constant and the galvanic current remain static. Some pit sites can be relatively broad in comparison to their depth. In this case there is nothing to stop a broad pit site locating itself evenly across the two segmented electrodes, further confusing the issue and reducing the level of galvanic current perhaps even to zero or something that varies around zero. This situation can also be seen as an active pit site on both galvanic electrodes.


Transient Detection and Calibration Method

The standard method of calibrating transients in inhibited systems is to use the value of LPR to convert the potential transient into current. This technique is fine for relatively short duration transients of a time interval that is shorter than the time between LPR polarisations, but not really suited for a transient that may last for several LPR cycles.

During a long duration transient, it is reasonable to expect Rf to change, perhaps as additional inhibitor is added to the system due to a pitting alert. The distribution of current flowing through Rf or Rct cathodic (pit) is also not known.

Having looked at some broad pit sites, it often looks as if they are made up clusters of smaller pits sites operating and overlapping in the same location and not a nice smooth single pit. This is helpful from a monitoring point of view as it suggests an element of inhibitor film is acting over the larger pit site, perhaps with a measure of reduced effectiveness. Smaller pitting events occurring within that site. This decreases the area where the cathodic reaction can easily occur at Rct cathodic (pit) and perhaps decreasing the overall value of Rf taking into account its possible semi effectiveness over the whole pit site. The net result is an increase in the percentage of cathodic current generated at the pit site travelling via the inhibitor film which due to its resistive nature appears to act as a dominating linear resistor.

It would seem reasonable therefore to segment a long duration transient into segments, each segment being calibrated by an adjacent LPR reading. This takes account of variations in inhibitor film resistance as a whole and at the whole pit site during the total time of the transient.

segmented calibration

The Ohm's law calculation is     I = dV / Rp

From this the charge of each of the sections 1 to 7 can be calculated and added to give the total charge and subsequent metal loss from the long duration transient.


General Discussion

The techniques discussed and in particular the circuits proposed can be used to assist with localised corrosion monitoring. Many of the techniques for monitoring transients are included within the LCM™ software supplied by ACM instruments using a range of tools. This range of tools is being expanded as required to cover peoples requirements. These tools enable raw data to be processed in a single step without complex human intervention.

Test cells need not be confined to electrodes of identical size or even the same material attached to the end of a probe. Having an idea of the processes and the electronic circuits involved with those processes, enables localised corrosion to be monitored in complex situations that would not normally be thought possible, such as in oil wells with intermittent conductivity or multiple electrode systems.

 
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