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Electrochemical Impedance Spectroscopy Part 1: Polarization Resistance: Familiar parameter measured in a new way June 6, 2008 1
Electrochemical Impedance Spectroscopy
Part 1: Polarization Resistance:Familiar parameter measured in a new way
June 6, 2008
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Copyright © M. L. Taylor `
Objective
• The purpose of this lecture series is to generate a set of notes on Impedance Spectroscopy which are easy to use yet powerful enough that a researcher will be able to decide whether or not to pursue the technique more in depth.
• All figures are drawn by Matthew Taylor of the Georgia Institute of Technology, except where noted.
• This work may be used for any purpose, so long as reproduced figures are attributed to the author.
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Copyright © M. L. Taylor `
What is Electrochemical Impedance Spectroscopy?
• Electrochemical reactions are those that involve electron transfer.
• Corrosion Scientists are primarily interested in this type of phenomena.
• Impedance is a measure of resistance to response to an outside stimulus, such as a fluctuation in potential, and has both real and imaginary parts
• A Spectrum of data is collected by collecting measured impedances at individual frequencies and combined to form a spectrum of data.
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Copyright © M. L. Taylor `
Why would I want to use EIS? (I have DC)
• DC methods drive the system from equilibrium
• Reaction parameters are time-dependent and may be altered during DC. Observing the system tends to change it.
• There is more data avaliable (Rp as opposed to Rp+Rs can be measured)
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Excitation System Response
E I
E I
E
E E
log(I)
I E
DC Technique Input Output
Potentiostatic / Pulsed Potential
Cyclic Voltammetry
Potentiodynamic Scan
Galvanostatic/Pulsed Current
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Copyright © M. L. Taylor `
Introduction of the Equivalent Circuit
• Describe a system in terms of impedance
• not a model, but an analog
• Possible to describe a variety of systems
• acoustics
• electrochemical charge transfer reactions
• fluids in a container
• mechanical materials systems
• Practically any system has an impedance associated with it
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Analogous Systems
M
F
C Rm
M
Rm
Cm
F
Mechanical Electrical
Mass Inductor
Spring Capacitor
Normal Force Electrical Potential
Dashpot Resistor
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Copyright © M. L. Taylor `
Polarization Resistance
• Useful for predicting a corrosion rate under steady-state conditions
• Commonly determined from Taefel slopes on the potentiodynamic scan
• Our model circuit / system for consideration
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Copyright © M. L. Taylor `
DC determination of Polarization Resistance
• Measure Rp (Polarization Resistance) by scanning potential away from Ecorr
• In DC, the circuit describing the corroding surface (for a simple case) is nothing but a resistor. The Impedance being measured is entirely real.
• From Ohm’s law, we apply an overpotential and measure the current change, deriving Rp
• Any capacitance in the system may not be measured, as a capacitor acts as an open circuit under DC conditions!
• The solution Resistance is measured as a part of Rp and must be accounted for.
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Inet =!
Rp
Rp
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Copyright © M. L. Taylor `
AC Determination of Polarization Resistance
• Impedance has real and imaginary components, both of which depend on the AC frequency.
• Solution resistance is measured separately from polarization resistance
• Capacitance of the ionic double layer may be measured
• Measured by applying a small amplitude AC signal over a range of appropriate frequencies
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Rp
Rs
Soluion BulkIonic
Double LayerMetal
(conductor)
Cdl
Figure: Randles Cell
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Copyright © M. L. Taylor `
Simple Passive Circuit Elements
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ZRi (!) = RiRi
ZCi (!) = ! j
!C
Cdl
Element Impedance Symbol
Resistor
Capacitor
j =!"1Note:
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Copyright © M. L. Taylor `
Rules for Circuit Analysis
• Impedances in series add directly
• Impedances in parallel add inversely
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Z1
Z2 Zseries = Z1 + Z2
Z1
Z2
Zparallel =1
1Z1
+ 1Z2
Combination Circuit Equation
Series
Parallel
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Copyright © M. L. Taylor `
Impedance of the Randles Cell
• consider the capacitor and Rp in parallel
• A little complicated, but we can multiply by the complex conjugate to of the bottom to seperate real and imaginary (multiplied by j) terms.
• Adding Rs and then Separating into Z’ (real) and Z’’ (imaginary), we have:
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Rp
Rs
Cdl
Zp =1
1Rp
+ 1!j
!Cdl
Zp =Rp
1 + !2CR2p
! j!CdlR2
p
1 + !2C2dlR
2p
Z !! = !!CdlR2
p
1 + !2C2dlR
2p
Z ! = Rs +Rp
1 + !2CR2p
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Copyright © M. L. Taylor `
Continued
• Z’ and Z’’ are related to |Z| by the pythagorean theorem, and to ϕ by the tangent function
• Plotting |Z| versus frequency yields a plot, from which graphical extraction of analog parameters may be performed. Along with ϕ vs. f, this is known as a Bode Plot.
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|Z| =!
Z !2 + Z !!2! = tan!1
!Z ""
Z "
"Z = Z ! + jZ !!
log(f), hz
|Z|,
! RP
RS
f = 2!"
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Copyright © M. L. Taylor `
Graphical Evaluation of the Randles Cell
• The high frequency intercept is equivalent to the solution resistance, Rs
• The low frequency intercept is equivalent to the polarization resistance plus the solution resistance
• Capacitance may be determined
• ωmax is the frequency where -Z’’ is at its maximum
• This geometrical - mathematical technique can be applied to any combination of RC circuits.
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!max =1
RpCdl.
Z', Real Impedance, !
-Z'',
Im
agin
ary
Im
pedance, !
Low Freq
uency
High
Freq
uenc
y
"max
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Copyright © M. L. Taylor `
Reading• Book Chapters
• Mansfeld, Florian Analytical Methods in Corrosion Science and Engineering (2005) Ch. 13 pp. 463-506
• Books
• Cottis et al. Corrosion Testing Made Easy: Electrochemical Impedance and Noise. (1999)
• Barsoukov and J.R. MacDonald, Impedance Spectroscopy: Theory, Experiment, and Applications. (2005) pp. 608
• Baboian. Electrochemical Techniques for Corrosion Engineering. (1986)
• Peer Reviewed Papers
• Macdonald, Digby D. Reflections on the history of electrochemical impedance spectroscopy. Electrochimica Acta (2006) vol. 51 (8/9) pp. 1376-1388
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Copyright © M. L. Taylor `
Reading: Solartron Analytical
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TB/ANALYTICAL/001 High frequency, high current impedance spectroscopy: Experimental protocols enabling measurement up to 1MHz at high current densitiesBy John Harper, Mike Rust, Brian Sayers and Andrew SavageGet it here...
TB/ANALYTICAL/2Use of auxiliary channels for impedance analysis: Detecting failure mechanisms within a fuel cell / battery stackBy J Harper and B SayersGet it here...
TB/ANALYTICAL/3Parallel Channel CombinationsBy J Harper and B SayersGet it here...
TB/ANALYTICAL/004Solartron CellTest® SystemImpedance measurement techniquesBrian SayersGet it here...
Technote 04Identification of Electrochemical Processes by Frequency Response AnalysisBy C GabrielliGet it here...
Technote 06An Introduction to Electrochemical Impedance MeasurementBy N D Cogger and N J EvansGet it here...
Technote 10Frequency Response AnalysisBy N D Cogger and R V WebbGet it here...
Technote 17Understanding Electrochemical CellsBy A M KaufmannGet it here...
Technote 24Use and Applications of Electrochemical Impedance TechniquesBy C GabrielliGet it here...
Technote 26Analysis and Interpretation of EIS Data for Metals and Alloys
By F MansfeldGet it here...
Technote 29The Application of Impedance Spectroscopy to Cementitious SystemsBy W. J. McCarterGet it here...
Technote 31Electrochemical Impedance Spectroscopy (EIS) for Battery Research and DevelopmentBy Hong Shih and Tai-Chin LoGet it here...
Technote 33The Potentiodynamic Polarization ScanBy D G Evans and L L ScribnerGet it here...
1470 TechInstrumentation for the Characterization of Energy Storage Devices and Multi-Cell SystemsBy B Sayers and A HintonGet it here...
Coatings TechDetermination of Coating Adhesion Using Electrochemical Impedance SpectroscopyBy A HintonGet it here...
Advanced Instrumentation for Solid State ApplicationsBy A Hinton and B SayersGet it here...
Beyond the Limits: 1296 Dielectric InterfaceBy A Hinton and B SayersGet it here...
Advanced Instrumentation for Civil Engineering ApplicationsBy A Hinton and B SayersGet it here...
Advanced Instrumentation for Bioimpedance MeasurementsBy A Hinton and B SayersGet it here...
ImpedTech 1Impedance Measurement Techniques: Sine CorrelationBy B Sayers and A HintonGet it here...
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Copyright © M. L. Taylor `
Reading: Gamry Instruments
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Electrochemical Applications
Basics of EIS
Equivalent Circuit Modeling in EIS
EIS on Painted Samples
Multiplexed EIS on Painted Samples
DC Corrosion Techniques
Determination of Double-LayerCapacitance from a CPE
Rapid Electrochemical Assessment of Paints (REAP)
Electrochemical Instrumentation
Potentiostat Fundamentals
Compliance Voltage - How Much is Enough?
Reference Electrodes
Care of Vycor® Porous Glass Frits
Trouble-Shooting Your Gamry Potentiostat with the Universal Dummy Cell 3
Measurement of Small Electrochemical Signals
Accuracy Contour Plots
EIS Measurement of a Very Low Impedance Lithium Ion Battery
Verification of Low Impedance EIS Using a 1 mOhm Resistor NEW!
Open Source Scripting
Understanding iR Compensation
You can also find a list of Frequently Asked Questions here.
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