Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Scott A. Furman et al.
MODELLING INHIBITOR RELEASE KINETICS IN
SELF REPAIRING SYSTEMS
Scott A. Furman*, Fiona H. Scholes, Anthony E. Hughes, Deborah Lau, Penny A. Corrigan,
Paul A. White, Tim H. Muster, Tim G. Harvey, Simon G. Hardin
CSIRO Manufacturing & Materials Technology
Private Bag 33, Clayton South MDC
Clayton 3169
Australia
Tel: +61 3 9545 2787
Fax: +61 3 9544 1128
Scott.Furman@csiro.au
www.cmmt.csiro.au
Aerospace primers use the dissolution of inorganic chromates, which act as corrosion inhibitors, to facilitate the
repair of defects in paint systems. Hence the paint and the underlying metal form a self repairing system.
Chromates prevent pitting corrosion of the underlying aluminium metal substrate and form Cr(III)-containing
surface species that further protect the exposed metal. The prevention of pitting corrosion in the aerospace
industry is crucial as it leads to potentially disastrous cracks in the metal when coupled with cyclic fatigue
loading. Diffusion of material through the primer’s polymer network is an important part of mass transport
processes within materials required in the design of self healing materials.
PITSIM is a computer model created to simulate the release of corrosion inhibitors from aerospace primers and
predict the pit initiation and growth inside defects through the coating system. In previous studies [1-5], the
release of chromate was found to have an unusual time release profile that followed t1/4 behaviour rather than the
expected Fickian t1/2 behaviour. PITSIM uses the chromate release profile to predict the chromate concentration
close to the metal surface (inside the paint defects) and predicts the electrochemical response to that
environment.
In this study, we use PITSIM to model the effect of different release profiles on the pitting behaviour inside paint
defects. This study demonstrates the usefulness of modelling in the design of new inhibitors and delivery
systems to achieve optimum repair performance.
1
Introduction
PITSIM [6-10] is a computer program which stochastically simulates the pitting corrosion of
aluminium alloys inside a defect in the overlying paint layer. The defect in the paint system
provides the external environment (containing salts, water, and other corrodents) direct access
to the metal surface. This paint defect is where pitting corrosion will initiate and PITSIM
simulates the various physicochemical processes that lead to corrosion. As shown in Figure
1, the paint layer contains a topcoat and primer layer over a thin conversion coating. The
primer contains a slightly soluble corrosion inhibitor (strontium chromate) which leaches out
of the primer and protects the aluminium metal. When the inhibitor concentration drops
below a critical value, pitting corrosion will initiate and propagate.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Scott A. Furman et al.
When subjected to cyclic fatigue loading during aircraft operation, these corrosion pits can
initiate cracks in the metal and the potential for serious mechanical failure increases [11-16].
For this reason, corrosion on aircraft is a high priority and represents a significant cost in their
ongoing maintenance.
Figure 1: Diagram of typical aerospace paint coating containing a defect
PITSIM was developed during the CPM (Corrosion Prediction Modelling) project which was
initiated in 1999 as part of a four year collaboration between BAE SYSTEMS (UK), BAE
SYSTEMS Australia, DSTO (Australia), and CSIRO (Australia). The aim of the CPM
project was to produce predictive corrosion tools that would ultimately lead to cost benefits in
the design, operation, and maintenance of aerospace structures. This is particularly relevant
to the management of aging aircraft which are being operated past their original design lives
[17-19].
PITSIM forms the heart of the damage module for the predictive corrosion tools by
simulating the response of the metallic aircraft surface to whatever microclimate the aircraft
experiences during its operation. However, validation of PITSIM on real aircraft would be
difficult as there is limited corrosion data containing enough detail for the simulations.
Therefore the industry standard neutral salt spray (NSS) test was used for validating PITSIM.
Although some aspects of the in-service microclimate on aerospace structures could not be
explored by the NSS testing, such as variable chloride and pH levels, wet/dry cycles, and
variable temperature cycles, the NSS environment is sufficiently complex and corrosive to
validate the key components of the model. Some of these other aspects were studied
separately and found to be consistent with PITSIM’s predictions.
The model elements used in validation studies were 2024-T3 aluminium panels (1.6 mm 75
mm x 250 mm) coated with Alodine 1200 chromate conversion coating, PR143 chromateinhibited epoxy polyamide primer and FE102 topcoat. These panels contained artificial slots
in the paint system (to simulate defects) which were 20 mm long and varied in width from 0.2
mm to 4 mm. During NSS, small droplets formed on the surface of the panel from the
condensing salt fog. These would grow to form larger drops, as shown in Figure 2. As the
panels were placed at 21o to the vertical, the drops would eventually become large enough to
roll down the panels and fall off. These rolling drops scavenge other drops in their path and
leave a drop-free stripe down the panel (also shown in Figure 2).
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Scott A. Furman et al.
Thus the surface is continually washed with fresh brine solution and any inhibitor that has
leached into the drops is periodically removed.
Figure 2: Drops formed on test panels during NSS exposure. Clear area was formed by large drops rolling down
the surface
During the development and testing of PITSIM, it became very clear that the main factor
controlling the pitting corrosion was the availability of the corrosion inhibitor. The
probability of initiating a stable pit is directly related to the inhibitor concentration and only
when the inhibitor concentration drops below a critical value does the pitting probability
become significant. For the inhibitor studied here (strontium chromate) in 0.1 M NaCl, this
critical concentration is approximately 10-4 M. At this concentration the pitting probability is
approximately 10-4 pits/cm2/s but this increases to 10-2 pits/cm2/s when the inhibitor
concentration drops below 10-5 M.
In the validation study it was found that in the wider slots (>1 mm) the inhibitor did not have
a diffusional path from the cut edge of the primer to drops in the centre of the slot. As these
drops did not contain any inhibitor, pitting would initiate within the first few day of NSS
exposure. In the narrower slots (<1 mm), the inhibitor could diffuse into most drops covering
the slot. The time to initiate pits increased from 2 days for the 1 mm slot to 20 days for the
0.2 mm slot. As shown in Figure 3, PITSIM correctly predicted the time to produce pits in
the various slots. PITSIM also correctly predicted the number of pits per slot and the size of
the pits.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Scott A. Furman et al.
Figure 3: Comparison of simulations and experiments for the time taken to form pits in slots of various widths in
NSS
As the pitting behaviour is strongly linked to the inhibitor concentration, the inhibitor release
kinetics was studied [1-5] and found to be unusual in that it did not follow the expected
Fickian t1/2 profile. Instead, the release kinetics followed a t1/4 profile which produces a large
burst of inhibitor initially followed by ongoing slower release. In this study, the release
kinetics of the inhibitor is modified to investigate its effect on the pitting corrosion.
The immediate goal of this study was to find a release rate and kinetic profile that would
ensure protection against corrosion and provide the longest life possible for the aircraft.
However, as this modelling can indicate which release profiles provide the most benefit it can
help in designing new inhibitor systems. As most other self healing systems require the
release of some form of self healing agent, this approach can be used to optimize such
systems and assist in their design.
2
Computational details
The details of PITSIM have been previously described and will be summarized here. The
method is based on the original stochastic method developed by Gillespie [20-24] and has
been used in molecular reaction dynamics [25-27], nuclear reactions [28], molecular biology
[29-31], and surface reactions [32]. As pitting corrosion is stochastic in time, this method is
particularly well suited for its modelling.
The stochastic method takes all possible events and assigns a probability based on reaction
kinetics and similar information. A Monte Carlo procedure is used to select which event will
occur and a stochastic time step is incremented. The slot is modelled by dividing the region
into a number of smaller sub-volumes (similar to a finite difference approach) and modelling
the processes occurring in each sub-volume. Transfer of chemical species between the subvolumes accounts for diffusion and the probability of this is related to the diffusion
coefficient.
As this method involves a Monte Carlo procedure for the selection of which events to
execute, large sets of random numbers must be used.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Scott A. Furman et al.
Running the simulation with different sets of random numbers produces different results as
different events are selected at different times. In the original validation studies, 20 runs of
each case were averaged and the variability in the simulations matched the variability
observed in repeat experiments. For the simulations reported here, only 6 runs of each case
were performed on the 1 mm, 0.8 mm, and 0.2 mm slots. All other parameters were identical
to the original validation study except those related to altering the chromate release kinetics.
3
Results and discussion
Altering the parameters associated with inhibitor leaching in PITSIM allows the user to
change the loading of the inhibitor in the primer (expressed as mg/cm3), the kinetic profile
(ranging from t1 to t0.1) and the magnitude of the release rate for a given surface area of the
primer (expressed as mg/cm2/s). Changing the inhibitor loading is important as there is a
limited reservoir of inhibitor that can diffuse to a defect. Previous studies examined the size
of this depletion zone which contains inhibitor available for release. Inhibitor outside this
depletion zone cannot diffuse far enough through the primer to be released into the defect.
Changing both the magnitude of the release rate and the release kinetics affect not only how
fast the inhibitor is released but how quickly the inhibitor reservoir is depleted. These various
effects will be explored in the simulation reported here.
The general shape of the six release kinetics tested is shown in Figure 4. The linearly
increasing release profile corresponds to t1.0 behaviour while the sharp increase that almost
levels off is t0.1. Small changes in the exponent at these extremes have a large influence on
the shape of the profile while changes close to t1/2 (not shown) have little influence.
Figure 4: Different release kinetics for simulations
For the three different slot widths, the influence of changing the release kinetics is shown in
Figure 5. For both the 1 mm and 0.8 mm slots pits are produced within the first few days of
exposure to NSS regardless of the release kinetics. These pits form in water drops in the
middle of the slot which are not connected to the cut edge of the primer and therefore do not
contain any corrosion inhibitor. Altering the release kinetics therefore has no effect on the
pitting inside drops that are not diffusionally connected to the source of the inhibitor.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Scott A. Furman et al.
Figure 5: Effect of changing the release kinetics on the time to pitting in different slot widths
Pitting in the 0.2 mm slot is affected by the release kinetics as the drops span the width of the
slot and the inhibitor can diffuse to all areas of the metal surface covered with water. For the
tn release profiles with n≥0.9 there was no pitting observed even after 50 days of NSS. The
ongoing release of the inhibitor does not allow the inhibitor concentration inside the drops to
fall below 10-4 M and pitting does not occur.
For the tn release profiles with n≤0.25, pitting occurs after an average of 10-15 days of NSS.
As shown in Figure 6, the average inhibitor concentration in the water layer next to the
surface fluctuates around 10-4 M and pitting becomes more probable. The sudden decreases
in concentration occur when rolling drops clear the water out of the slot. Water continues to
condense on the surface and the inhibitor concentration builds back up as the primer releases
more inhibitor.
Figure 6: Average inhibitor concentration at surface for different simulations using release kinetics with n≤0.25
in 0.2 mm slot
During the periods where the average inhibitor concentration at the surface is much lower
than 10-4 M, the pitting probability increases significantly.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Scott A. Furman et al.
However, these periods are relatively brief and pits are not guaranteed to initiate as soon as
the concentration drops below 10-4 M. As shown in Figure 7, the results for the simulations
using profiles with n≤0.25 have a large variability. This is a reflection of the fluctuating
surface concentration and the stochastic nature of pitting.
Figure 7: Variability in simulation results for release kinetics with n≤0.25 for 0.2 mm slot
Changing the loading of inhibitor in the primer has a more direct influence on the pitting
corrosion. Using the t1.0 release profile and keeping the same release rate, the loading was
dropped from 425 mg/cm to 50, 25 and 10 mg/cm3. The time to pitting in the 0.2 mm slot
was found to be a linear function of the loading, as shown in Figure 8. The explanation for
this is simple as with such low loading, the primer is completely depleted of inhibitor during
the simulation. Once the inhibitor is depleted, pitting is initiated within less than a day. By
extrapolating this line, it is estimated that the fully loaded primer would last over 200 days
before becoming depleted.
Figure 8: Effect of inhibitor loading in primer on the time to pitting
Changing the release rate is the final variable that can be changed to alter the release kinetics
of the inhibitor. Again, the t1.0 release profile was used and the release rate was varied over
two orders of magnitude.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Scott A. Furman et al.
The time taken to initiate pits in the 0.2 mm slot for the various release rates is shown in
Figure 9. At the lowest release rate of 2¯10-6 mg/cm2/s pits initiate within a few days and
indicates that there is not enough inhibitor to prevent corrosion. At the highest release rate of
2.5¯10-6 mg/cm2/s pits are not produced until at least 30 days (with an average to 80 days),
although in some cases it took as long as 115 days to for pits to initiate. At the slightly lower
release rate of 7.5¯10-5 mg/cm2/s, pits took about 30 days on average with a range of 4 to 47
days. At 2.5¯10-5 mg/cm2/s, five of the six simulations produced pits within a few days with
one outlier at 29 days.
Figure 9: Effect of release rate on time to pitting in 0.2 mm slot
The reason for this behaviour can be seen by looking at the average inhibitor concentration at
the surface, as shown in Figure 10. The concentrations fluctuate as the drops form and are
removed but with the higher release rates, the inhibitor concentration stays above 10-4 M. At
the lower release rates, the inhibitor concentration drops below the critical concentration more
frequently and pitting becomes more probable. It is clear that the two middle release rates are
only just sufficient to inhibit pitting corrosion. The release rate of 2.5¯10-5 mg/cm2/s is only
effective in 1/6 simulations and the 7.5¯10-5 mg/cm2/s release rate is effective in 5/6
simulations.
Figure 10: Average inhibitor concentration at surface for different release rates in 0.2 mm slot
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Scott A. Furman et al.
In most applications, protecting in 5/6 cases would not be considered effective and more
stringent testing would be required to ensure a much lower (eg: 1/1000) failure rate.
However, multiple runs of the stochastic software can generate such statistics to predict what
the optimum inhibitor release kinetics is to ensure complete protection. Increasing the release
kinetics to a level far above what would theoretically be safe would ensure protection but has
the disadvantage that the inhibitor will become depleted quicker.
4
Conclusions
The PITSIM software package has been used to study the effect of inhibitor release kinetics
on pitting corrosion. The release profile (tn), the release rate (mg/cm2/s), and the inhibitor
loading (mg/cm3) have been studied to evaluate their effect on preventing pitting. When the
release rate is high, release profiles with n≥0.9 protect until the inhibitor is depleted. Release
profiles with n≤0.25 protect while the surface concentration remains above the critical level
for the inhibitor. When the concentration drops below this critical level pitting becomes more
probable but is stochastic and the time to initiate pits is highly variable. Decreasing the
loading simply depletes the inhibitor quicker and pitting starts very soon after the inhibitor is
depleted. Changing the release rate over two orders of magnitude produced a transition from
very poor protection to sporadic protection to very good protection. This study demonstrates
the usefulness of stochastic modelling and will help to understand and design new self healing
systems which rely on releasing inhibitors.
ACKNOWLEDGEMENTS
The authors would like to thank the entire CPM team for numerous discussions and contributions. BAE
SYSTEMS is gratefully acknowledged for providing financial and technical support for part of this work through
the Corrosion Prediction Modelling project.
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18-20 April 2007, Noordwijk aan Zee, The Netherlands
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