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All
My Impedance Spectra Look the Same!
This
complaint is very common.
"I’m an experienced polymer
chemist. I’m trying to use Electrochemical Impedance Spectroscopy (EIS) to predict
the corrosion resistant properties of paints. I’ve recorded many EIS spectra on
painted metal samples immersed in electrolyte. All (or most) of these spectra look the
same, regardless of the changes that I makes in my paint formulation. I obviously cannot
use the results to evaluate paint performance. What’s going on?"
There are two common causes for this
complaint.
- You have a very high quality paint that
gives very reproducible EIS spectra, or
- You are attempting to make measurements
that are beyond the capabilities of the potentiostat in your EIS system.
The second cause is more common. The
spectra look the same because you are measuring the characteristics of your
potentiostat,
not those of the paint.
The rest of this application note
describes the effects that a potentiostat can have on EIS measurements of coated metals.
Gamry Instrument potentiostats will be used as examples, but the discussion will apply to
EIS systems built around any potentiostat.
This note concludes with some specific
recommendations for getting meaningful EIS spectra on coating systems that are difficult
to measure.
Background
If you are not very
knowledgeable concerning electrochemical instrumentation, click
here. You will be taken to a
Primer on Potentiostats. This
Primer will introduce the
terminology used in talking about potentiostats and some potentiostat concepts that are
used in the remainder of this application note.
You will also need a basic
understanding of EIS to follow the discussion in this note. Experienced EIS users should
have no problems with the level of the discussion. If you are less experienced or you want
to brush up on your basics, click here
for a primer on EIS theory and practice.
Coating Capacitance
A capacitor is formed when a
non-conducting media, called the dielectric, separates two conducting plates. The value of
the capacitance depends on the size of the plates, the distance between the plates and the
properties of the dielectric. In the case of a coated metal immersed in electrolyte, the
metal is one plate, the coating is the dielectric, and the electrolyte is the second
plate.
The capacitance relationship is:
With,
C = the capacitance
e o = electrical permittivity
e r = relative electrical permittivity
(dielectric constant)
A = surface of one plate
d = distances between two plates
Whereas the electrical permittivity is
a physical constant, the relative electrical permittivity (dielectric
constant) depends on the material. Table 1
gives you a few useful er values.
Table 1
Typical Dielectric Constants
(relative electrical permittivity)
| Material |
er
|
| vacuum |
1
|
| water |
80.1 (20° C)
|
| organic coating |
2 - 7
|
Notice the large difference between the
dielectric constant of water and that of an organic coating. The capacitance of a
coated substrate changes as it absorbs water. EIS can be used to measure that change.
Notice that the capacitance of a
coating increases when the area of the coating increases and when the coating thickness
decreases.
Equivalent Circuit Model - Perfect Coating
A metal covered with an undamaged
coating generally has very high impedance. The equivalent circuit for this situation is in
Figure 1.
Figure 1
Purely Capacitive
Coating
The model includes a resistor (due to
electrolyte resistance) and the coating capacitance in series.
A Nyquist plot for this model is shown
in Figure 2. In making this plot, the following values were assigned:
R = 500 W
(realistic for a
poorly conductive solution)
C = 200 pF (realistic for a 1 cm2 sample, a 25 µM coating, and
er
= 6)
Fi = 0.1 Hz (lowest scan frequency -- a bit higher than typical)
Ff = 100 kHz (highest scan frequency)
Figure 2
Typical Nyquist Plot for
an Excellent Coating
The value of the capacitance cannot be
determined from the Nyquist plot. It can be determined by a curve fit or from an
examination of the data points. Notice that the intercept of the curve with the real axis
gives an estimate of the solution resistance.
The highest impedance on this graph is
close to 1010 W. This is close to the limit of measurement of many EIS
systems.
The same data are shown in a Bode plot
in Figure 3. Notice that the capacitance can be estimated from the graph but the solution
resistance value does not appear on the chart. Even at 100 kHz, the impedance of the
coating is higher than the solution resistance.
Figure 3
Typical Bode Plot for an
Excellent Coating
Equivalent Circuit Model – Real Coating
The impedance behavior of a purely
capacitive coating was discussed above. Most coatings degrade with time, resulting in more
complex behavior.
After a certain amount of time, water
penetrates into the coating and forms a new liquid/metal interface under the coating.
Corrosion phenomena can occur at this new interface.
The impedance of coated metals has been
very heavily studied. The interpretation of impedance data from failed coatings can be
very complicated. Only the simple equivalent circuit shown in Figure 4 will be discussed
here.
Even this simple model has been the
cause of some controversy in the literature. Most researchers agree that this model can be
used to evaluate the quality of a coating. However, they do not agree on the physical
processes that create the equivalent circuit elements. The discussion below is therefore
only one of several interpretations of this model.
Cc represents the
capacitance of the intact coating. Its value is much smaller than a typical double layer
capacitance. Its units are pF or nF, not µF. Rpo (pore resistance) is the
resistance of ion conducting paths that develop in the coating. These paths may not be
physical pores filled with electrolyte.
On the metal side of the pore, we
assume that an area of the coating has delaminated and a pocket filled with an electrolyte
solution has formed. This electrolyte solution can be very different from the bulk
solution outside of the coating. The interface between this pocket of solution and the
bare metal is modeled as a double layer capacity in parallel with a kinetically controlled
charge transfer reaction.
Figure 4
Equivalent Circuit for a
Damaged Coating
When you use EIS to test a coating, you
fit a data curve to this type of model. The fit estimates values for the model's
parameters, such as the pore resistance or the double layer capacitance. You then use
these parameters to evaluate the degree to which the coating has failed.
In order to show a realistic data
curve, we need to do this operation in reverse. Assume that we have a 10 cm2
sample of metal coated with a 12 µM film and that we have 5 delaminated areas. 1% of the
total metal area is delaminated. The pores in the film that access these delaminated areas
are represented as solution filled cylinders with a 30 µM diameter.
The parameters used to develop the
curves are shown below:
Cc = 4 nF Calculated for 10
cm2 area , er = 6 and 12 µM thickness
Rpo = 3400 W Calculated assuming k = 0.01 S/cm
Rs = 20 W Assumed
Cdl = 4 µF Calculated for 1% of 10 cm2 area and assuming 40 µF/cm2
Rct = 2500 W Calculated for 1% of 10 cm2 area using
Polarization Resistance at 1 mm/year and assumed constants
With these parameters, the Nyquist plot
for this model is shown in Figure 5. Notice that there are two well-defined time constants
in this plot.
Figure 5
Nyquist Plot for a
Damaged Coating
The Bode plot of the same data
is shown in Figure 6. The two time constants are visible but less pronounced on this plot.
The Bode plot does not go high enough
in frequency to measure the solution resistance. In practice this is not a problem,
because the solution resistance is a property of the test solution and the test cell
geometry, not a property of the coating. Therefore, it is usually not very interesting
when you are testing coatings.
Figure 6
Bode Plot for a
Damaged Coating
Problems in Measurement of Small Signals
Thick, high quality coatings
characteristically have almost infinite resistance and very low capacitance.
It is obvious that their high
resistance results in very small currents, especially at low frequencies where resistive
elements in the models dominate. On a more subtle level, their low capacitance results in
small AC currents. For example:
The impedance of a 10 nF capacitor at 1
kHz is 16 kW. With a 10 mV excitation at this frequency a
potentiostat measures 630 nA.
The impedance of a 10 pF capacitor
(often representative of a thick coating) at 1 kHz is 16 MW. With a 10 mV
excitation, the potentiostat has to measure 630 pA.
Basic physics and the realities of
electronics design and construction make it difficult to measure small currents. The
problem is especially severe for small AC currents at high frequencies. Click
here for
an in-depth technical discussion of these problems.
The result of these limitations is
discussed in the following sections.
EIS – Open Lead Experiment
There is a very simple test you can run
to test the limits of your potentiostat and its associated EIS system. Record an EIS
spectrum with no cell attached. We call this test the "Open
Lead Experiment". Click here
for detailed
instructions on how this measurement is made.
The EIS spectrum recorded in an Open
Lead Experiment using a Gamry Instruments’ PC4/300 with a 10 mV excitation voltage is
seen in Figure 7.
Figure 7
Open Lead EIS Bode Plot
– PC4 with 10 mV Excitation
The open lead Bode plot looks
very much like a noisy spectrum for a parallel RC network. This shape is seen in the open
lead spectrum of every EIS systems that we have tested. The diagonal line in the magnitude
plot corresponds to a capacitor. The horizontal line at low frequency in the magnitude
plot is equivalent to a resistor.
The open lead spectrum is fairly
repeatable for a given hardware/software system. However, different potentiostats (with
the same model number) may show variations in the spectrum, especially in the low
frequency region. Differences of one half a decade in impedance are not uncommon.
You cannot measure impedances that lie
above the open lead spectrum. The EIS300/PC4 cannot measure 109
W at 10 kHz
since the system with no cell measures only 107 W at
this frequency.
The open lead spectrum is dependent on
a number of factors. Shielding and grounding, excitation amplitude and DC level are some
of the most important.
Accuracy
Contour Plot – PC4/300 Potentiostat
The results of the open lead experiment
and a few additional tests can be used to generate a very useful graph that we call the
"accuracy contour
plot". The accuracy of your impedance
measurements can be predicted from this graph. An accuracy contour map for the PC4
Potentiostat and the EIS300 EIS software can be seen in Figure 8.
Figure 8
Accuracy Contour Map
– EIS300/PC4 with 10 mV Excitation
This map applies when the EIS300
is operating with an PC4 Potentiostat in controlled potential mode. The AC excitation is
10 mV and a high quality faraday shield surrounds a cell isolated from earth ground.
On the contour map, each impedance
measurement is a single point, defined by the frequency and the measured impedance at that
frequency. Notice that the enclosed areas in the map are labeled with two numbers. They
are the maximum error in percent of reading and maximum phase error at any point in the
labeled region.
For example, at 100 mHz this system can
measure 109 W with errors of less than 1% in magnitude and
2° in phase. At 5x1010 W, still at 100 mHz, the errors can be larger - 10%
and 10° . Above 1011 W, the accuracy is unspecified, even though the
instrument may function.
Notice the diagonal boundary lines that
are labeled with equivalent capacitor values. You cannot measure a capacitor smaller than
30 pF, unless you are willing to accept errors of greater than 10% and 10° .
| NOTE:
Achieving these specifications in your experiment may require very careful shielding of
the cell and special cell design. |
The accuracy contour map
shown above only applies to isolated cells. It does not apply when the potentiostat is
used to make measurements on earth grounded "real world" systems such as highway
bridges or pipeline probes. All cells with a connection to earth ground will severely
degrade the system performance. Degradation of two orders of magnitude in impedance is
common. Click here to see the EIS300/PCI4
accuracy counter map measured with an earth grounded working electrode.
An accuracy contour map is valid for
only one excitation (AC) amplitude. The map in Figure 8 applies at a 10 mV excitation
amplitude. In most cases, increasing the amplitude shifts the limits on the map upwards.
At 100 mV excitation, the boundaries of the 10%, 10 degree region are 20 pF and 5x1011W. The
minimum capacitor limitation is almost independent of amplitude. The low frequency
resistance is a stronger function of excitation amplitude.
You may have noticed that the accuracy
contour map has additional diagonal lines in its lower right hand corner. This region is
generally not of interest in EIS on coatings, so it will not be discussed here. We hope to
write an application note describing the causes and consequences of this potentiostat
limitation at some point in the future. Contact us if you encounter this
limitation in your work.
Accuracy
Contour Map – Other EIS Systems
The accuracy contour map shown in
Figure 8 only apples to the Gamry Instruments EIS300 equipped with a
PCI4/300 Potentiostat
operated with 10 mV of excitation. If you have a different system, you need a different
map. Click here for a procedure that
allows you to estimate (or fully measure) the accuracy contour map for your EIS system.
If you don’t want to go to the
trouble of measuring the map, we can offer some guidelines. Older
potentiostats, such as
the Gamry Instruments PC3 or the Ametek PAR 273 will be worse than the PCI4 by one or two
decades in impedance. Their DC limit at 10% accuracy and 4 degrees of phase error will be
around 109 W and their capacitor limit will be at about 300
pF (or worse).
Note: Some EIS manufacturers quote
system performance with high excitation amplitudes and high error bands. Be careful, a
system may claim to measure 1012W, but the
manufacturer may not tell you that that measurement requires 5 volts of excitation and/or
allows 50% error.
Specialized potentiostats optimized for
low current measurements have recently become available. Once such potentiostat is the
Gamry Instruments FAS2. It offers a DC limit of 1012 W at
10% accuracy and a capacitive limit of 16 pF. Click here
to see its accuracy contour map.
Good
Measurements Aren’t Easy
Careful experiment design is required
if you expect optimal performance from your EIS system. The following hints may prove
helpful.
Faraday Shield
A Faraday shield surrounding your cell
is mandatory for very low level measurements. It reduces both current noise picked up
directly on the working electrode and voltage noise picked up by the reference electrode.
A Faraday shield is a conductive
enclosure that surrounds the cell. The shield can be constructed from sheet metal, fine
mesh wire screen, or even conductive plastic. It must be continuous and completely
surround the cell. Don't forget the areas above and below the cell. All parts of the
shield must be electrically connected.
The shield must be electrically
connected to the potentiostat’s ground terminal.
Avoid External Noise Sources
Try to keep your system away from
electrical noise sources. Some of the worst are:
- Fluorescent lights
- Motors
- Radio transmitters
- Computers and computer monitors
Avoid AC powered or computerized
apparatus within your Faraday shield.
Cell Lead Length and Construction
Your cell leads must have a resistance
higher than that of the impedance you are trying to measure. If you use coaxial cable we
recommend a virgin Teflon dielectric. Long leads can severely degrade the AC response of
your potentiostat.
Lead Placement
Many coating tests involve cells with
capacitances so small that the capacitance between the potentiostat’s leads can
result in an error. Alligator clips can have 10 pF or more of mutual capacitance if they
are run alongside each other.
If you wish to avoid excessive
capacitance due to lead placement.
- Place the leads as far apart as
possible. Pay special attention to the working electrode lead.
- Have the leads approach the cell from
different directions.
- Remove alligator clips from the leads.
In extreme cases you can replace banana plugs and pin jacks with smaller connectors.
The cell leads must not be moved during
an experiment which measures small currents. Both microphonic and triboelectric effects
can create spurious results when the cell cables are moved.
Cell Construction
Make sure that your cell construction
does not limit your response. A cell where the resistance of the insulating material
between the electrodes is only 1010 W cannot be used to
measure 1012 W impedances. In general, glass and Teflon are
the preferred cell construction materials.
You also must worry about shunt
capacitance. Make the "inactive" portion of your electrodes as small as
possible. Avoid placing electrodes close together and parallel with each other.
How to Measure an Impossible System
What can you do if you are faced with a
sample that will produce data outside the defined regions of the accuracy contour map?
These suggestions may help.
AC amplitude
Larger AC amplitude may help you make
difficult measurements. As discussed above, increasing the amplitude can move the low
frequency limits in the accuracy contour map upwards. It has less effect on the minimum
capacitance.
One concern is that the electrical
field created by the excitation will cause failure in the paint. A five volt excitation
across a 25 micron coating creates a field of 200 kV/meter. Most bulk plastics (PVC is an
exception) claim dielectric strengths in excess of 12 MV/meter. Assuming coatings are one
tenth as good as bulk plastics, dielectric breakdown should not be a factor unless the
coating thickness is less than 5 microns.
Electrode Area
Electrode area is a critical
experimental parameter. In general, EIS measurements on coatings should use as large an
area as possible. Increasing the area has several beneficial effects:
- The capacitance of a point film is
directly proportional to the sample area. If one cm2 of a paint has an
unmeasureable capacitance (for example ten pF), 100 cm2 of the same film will
have a capacitance of one nF (easily measureable).
- If the paint has a uniform resistance,
the resistance of a sample is inversely proportional to the sample area. Make the sample
100 time bigger and the resistance falls by a factor of 100.
- Some paints have only a few, widely
separated, defects. Increasing the area increases the chance that a defect will be present
in the sample.
Get a Low Current Potentiostat
If the suggestions above are
impracticable, your only choice is get a potentiostat optimized for low current
measurement. Some newer potentiostat can measure capacitances as low as three pF and low
frequency resistances as high as 1013 W (with one
volt excitation). The Gamry Instruments FAS2
Femtostat offers this type of performance
at a very reasonable price.
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