eis nace template - ohio university › nace › presentations › 02_eis_ j ketter_teg097… · 1...

3/2/2011

1

Electrochemical ImpedanceElectrochemical Impedance Spectroscopy: Theory and Application

Dr. Jacob KetterGamry Instruments

www gamry com

Leaders in Corrosion Control Technology

www.gamry.com

Electrochemical Impedance Spectroscopy: EIS

• Basics of EIS– What Impedance is– How to run EIS– Circuit Elements/Equivalent Circuits– EIS instrumentation

• EIS for Corrosion


• EIS for Corrosion– General Corrosion– Coatings and Passive Films

Impedance

• The term impedance refers to the frequency dependant resistance to current flow of a circuitdependant resistance to current flow of a circuit element (resistor, capacitor, inductor,etc.)

• Impedance assumes an AC current of a specific frequency in Hertz (cycles/s).

• Impedance: Z = E/I• E = Frequency-dependent potential• I = Frequency-dependent current


q y p

• Ohm’s Law: R = E/I– R = impedance at the limit of zero frequency

Some Trigonometry

A voltage excitation has the form:

)sin()sin(

)sin()sin(

00

ttZ

tItE

IEZ t

The resulting current has the form:

t)sin( E=E 0t

)+t (sin I=I 0t

Ohm’s Law becomes:


)sin()sin(0 ttIIt

The impedance is expressed in terms of a magnitude, Zo, and a phase shift, .

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Making EIS Measurements• Apply a small sinusoidal perturbation

(potential or current) of fixed frequency(potential or current) of fixed frequency • Measure the response and compute the

impedance at each frequency.• Z = E/I

• Repeat for a wide range of frequencies• Plot and analyze


• Plot and analyze

Excitation and Response in EISApplied Voltage

Measured CurrentPhaseShift

Mag

nitu

de

Current Magnitude


Time

Voltage Magnitude

EIS Data Presentation

• EIS data may be displayed as either a vector y p yor a complex quantity.

• A vector is defined by the impedance magnitude and the phase angle.

• As a complex quantity, Ztotal = Zreal + Zimag

• The vector and the complex quantity are


The vector and the complex quantity are different representations of the impedance and are mathematically equivalent.

Vector and Complex Plane Representations of EIS

Vector Complex Plane

ary

Impe

danc

e, Z

”


Real Impedance, Z’

Imag

ina

= Phase Angle

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EIS data may be presented as a Bode Plot or a Complex Plane (Nyquist) Plot

3.60 10.00

2.60

2.80

3.00

3.20

3.40

Log

Mod

ulus

(O

hm)

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

Pha

se (D

egre

e)

3 00E+02

8.00E+02

1.30E+03

1.80E+03

2.30E+03

-Imag

(Ohm

)

Bode Plot

Nyquist Plot


2.20

2.40

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

Log Freq (Hz)

-70.00

-60.00

-2.00E+02

3.00E+02

0.00E+00 5.00E+02 1.00E+03 1.50E+03 2.00E+03 2.50E+03 3.00E+03 3.50E+03

Real (Ohm)

Bode Plot• Individual charge

Nyquist Plot• Individual charge transfer

Bode vs. Nyquist Plot

Individual charge transfer processes are resolvable.

• Frequency is explicit.• Small impedances in

presence of large impedances can be

Individual charge transfer processes may be more easily resolved.

• Frequency is not obvious.• Small impedances can be

swamped by large impedances


impedances can be identified easily.

impedances.

Analyzing EIS: Modeling

• Electrochemical cells can be modeled as a t k f i l t i l i it l tnetwork of passive electrical circuit elements.

• A network is called an “equivalent circuit”.• The EIS response of an equivalent circuit can

be calculated and compared to the actual EIS response of the electrochemical cell.


Frequency Response of Electrical Circuit Elements

R i t C it I d tResistor Capacitor InductorZ = R (Ohms) Z = -j/C (Farads) Z = jL (Henrys)0° Phase Shift -90° Phase Shift 90° Phase Shift

• j = -1


• = 2f radians/s, f = frequency (Hz or cycles/s)• A real response is in-phase (0°) with the excitation. An

imaginary response is ±90° out-of-phase.

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EIS of a ResistorApplied Voltage

Measured CurrentPhase

Shift of 0º

Mag

nitu

de


Time

EIS of a CapacitorApplied Voltage

Measured CurrentPhase

Shift of 90º

Mag

nitu

de


Time

Electrochemistry as a Circuit

• Double Layer CapacitanceCapacitance

• Electron Transfer Resistance

• Uncompensated (electrolyte)


(electrolyte) Resistance

Randles Cell(Simplified)

Bode Plot

3.20

3.40

3.60

-10.00

0.00

10.00

Ru + Rp

2.60

2.80

3.00

Log

Mod

ulus

(O

hm)

-50.00

-40.00

-30.00

-20.00

Pha

se (D

egre

e)

Phase Angle

Impedance

Ru


2.20

2.40

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

Log Freq (Hz)

-70.00

-60.00

Ru

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Complex Plane (Nyquist) Plot

1.80E+03

2.30E+03

High Freq Low Freq

3 00E+02

8.00E+02

1.30E+03

-Imag

(Ohm

)g q q


-2.00E+02

3.00E+02

0.00E+00 5.00E+02 1.00E+03 1.50E+03 2.00E+03 2.50E+03 3.00E+03 3.50E+03

Real (Ohm)

Ru Ru + Rp

Nyquist Plot with Fit

1.80E+03

2.30E+03

3.00E+02

8.00E+02

1.30E+03

-Imag

(Ohm

)

ResultsRp = 3.019E+03 ±

1.2E+01

Ru = 1.995E+02 ±1.1E+00


-2.00E+020.00E+00 5.00E+02 1.00E+03 1.50E+03 2.00E+03 2.50E+03 3.00E+03 3.50E+03

Real (Ohm)

Cdl = 9.61E-07 ± 7E-09

Other Modeling Elements

• Warburg Impedance: General impedance whichWarburg Impedance: General impedance which represents a resistance to mass transfer, i.e., diffusion control. A Warburg typically exhibits a 45° phase shift.– Open, Bound, Porous Bound

• Constant Phase Element: A very general


• Constant Phase Element: A very general element used to model “imperfect” capacitors. CPE’s normally exhibit a 80-90° phase shift.

Mass Transfer and Kinetics - Spectra

5001 104

100

200

300

400

500

( )imag i 10

100

1000

0.001 0.01 0.1 1 10 100 1000 1 1041 105

magi

freqi

0


00 100 200 300 400 500

reali

100

50

0.001 0.01 0.1 1 10 100 1000 1 1041 105

phase i

freqi

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EIS Modeling

• Complex systems may require complex d lmodels.

• Each element in the equivalent circuit should correspond to some specific activity in the electrochemical cell.

• It is not acceptable to simply add elements til d fit i bt i d


until a good fit is obtained.• Use the simplest model that fits the data.

Criteria For Valid EIS• Linear: The system obeys Ohm’s Law, E = iZ. The

value of Z is independent of the magnitude of the perturbation If linear no harmonics are generatedperturbation. If linear, no harmonics are generated during the experiment.

• Stable: The system does not change with time and returns to its original state after the perturbation is removed.


• Causal: The response of the system is due only to the applied perturbation.

Electrochemistry: A Linear System?Circuit theory is simplified when the system is “linear”. Z in a linear system is independent of excitation amplitude. The response of a linear system is always at the excitation frequency (no harmonics

t d)are generated).

Look at a small enough region of a current versus voltage curve and it becomes linear.

If the excitation is too big, harmonics are generated and EIS modeling does not work.

•Current

•Voltage


not work.

The non-linear region can be utilized.

Electrochemistry: A Stable System?Impedance analysis only works if the system being measured is stable (for the duration of the experiment).

An EIS experiment may take up to several hours to run.

Electrochemical (Corroding) systems may exhibit drift.

Open circuit potential should be checked at the beginning and end of th i t

•Current

•Voltage


the experiment.

Kramers-Kronig may help.

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Kramers-Kronig Transform• The K-K Transform states that the phase and magnitude in a

real (linear, stable, and causal) system are related.

• Apply the Transform to the EIS data. Calculate the magnitude from the experimental phase. If the calculated magnitudes match the experimental magnitudes, then you can have some confidence in the data. The converse is also true.

• If the values do not match, then the probability is high that your t i t li t t bl t l


system is not linear, not stable, or not causal.

• The K-K Transform as a validator of the data is not accepted by all of the electrochemical community.

Steps to Doing Analysis

• Look at data(R K K)– (Run K-K)

– Determine number of RC loops– Figure whether W exists

• If so determine boundary conditions• Pick/design a model

– Randles as starting point• Fit it

Check to see if CPEs needed


– Check to see if CPEs needed• Repeat as necessary• Extract data

EIS Instrumentation

• Sine wave generator• Time synchronization (phase locking)• Potentiostat/Galvanostat• All-in-ones, Portable & Floating SystemsThings to be aware of…• Software/Control


Software/Control• Accuracy• Performance limitations

Accuracy and System Limits

• Check Your Potentiostat…To Understand a System and Its Limits– To Understand a System and Its Limits

– Comparison 2+ Different Systems– Manufacturer Specifications:

• Are Not Standardized• Do Not Tell the Whole Story

– For EIS: Setup Matters


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EIS: Accuracy Contour Plot

• A complete ACP shows total, normal system performance (see right)system performance (see right)

• Preferably collected using normal operating parameters (e.g. 10 mV potentiostatic EIS)

• May also be optimized for each point/region

• Takes a long time to measure and


Takes a long time to measure and determine

• Open and Shorted Lead EIS spectra are Not the ACP

Reasons To Run EIS

• EIS is theoretically complex (and can be expensive) –h b th ?why bother?

– EIS is a non-destructive technique– The information content of EIS is much higher than DC

techniques like polarization resistance.– If two or more electrochemical reactions are taking place,

EIS may be able to distinguish between them.– EIS can identify diffusion-limited reactions, e.g., diffusion


y , g ,through a passive film.

– EIS provides information on the capacitive behavior of the system. This is always useful, but particularly for coatings.

EIS of Corrosion and Coatings• Impedance from a tens of Ω to over several GΩ

EIS f l i l k t R (b it lf)• EIS of general corrosion looks to measure Rp (by itself)• Corrosion events like pitting/passivation can be identified with

EIS, but complicate analysis

• Insulating coatings model as (very) small capacitors

• EIS is often used in conjunction with stress to measure how coatings/ surfaces change/breakdown


change/breakdown

• Systems can exhibit drift• Diffusion related events may occur

430 SS in H2SO4, Randles Model

• Data from a 430 Stainless SteelStainless Steel sample


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430 Stainless Steel, CPE Model

• Same Data Fit to CPE d lCPE model


Randles versus CPE model


Bode Plot of Carbon Steel in Aerated Water with 1000 ppm Cl-

Impedance

Phase Angle

Leaders in Corrosion Control TechnologySilverman et al, Corrosion, 44, 280 (1988).

Complex Plane Plot of Carbon Steel in Aerated Water with 1000 ppm Cl-

Warburg Impedance, evidence of diffusion

control


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EIS of Passive Films and Coatings

• Because of the barrier properties, a coated metal substrate may initially exhibit a very high impedance

10(>1010 Ω).• A high impedance sample will exhibit low cell currents

which are more difficult to measure.– Use a system designed for low-current applications.– Use a Faraday Cage.

• It may be necessary to increase the AC amplitude to 30-


It may be necessary to increase the AC amplitude to 3050 mV to see a measurable current.

• Use of larger sample areas will improve results.

Capacitive Drift (Challenges of Very Good Barrier Coatings)

• An undamaged intact coating is a capacitorTh bi t f t l l h thi• The bias current of a system slowly charges this capacitor, causing what appears to be a drift in EOC.

• Unless checked, the EOC will continue to increase, and can reach values over 5 volts.

• To obtain the “first” EIS measurement, use an applied DC voltage that is equal to the EOC of the metal


substrate.• As exposure time increases, a stable EOC may be

observed.

Experimental Procedure

• EIS is a very sensitive detector of coating conditioncondition

• Only look at relative changes• Need a stress mechanism to induce failure• As EIS is non destructive, failure can be tracked

with time


Description of Coated Surface


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Evaluation of Coated samples

• Degradation can be described in 5 stages:– Capacitive– Water Uptake– Pore Resistance– Corrosion Initiation– Major Damage


Stage One: Capacitive


Stage One: Capacitive


Stage Two: Water Uptake


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Stage Two: Water Uptake


Stage Three: Pore Resistance


Stage Three: Pore Resistance


Stage Four: Corrosion Initiation


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Stage Four: Corrosion Initiation


Stage Five: Major Damage


Stage Five: Major Damage


Example: Aluminum


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Example: Aluminum


Experimental Methods Of Coating Evaluation

• Single Frequency Measurement (0.1 Hz)EIS d C bi t T t• EIS and Cabinet Tests

• Thermal Cycling• Rapid Electrochemical Assessment of Paint

(REAP)• AC-DC-AC


• Free standing films

EIS Take Home

• EIS is a versatile technique– Non-destructive– High information content

• Running EIS is easy• EIS modeling analysis is very powerful

Simplest working model is best


– Simplest working model is best– Complex system analysis is possible– User expertise can be helpful

References for EIS• Electrochemical Impedance and Noise, R. Cottis and S. Turgoose,

NACE International, 1999. ISBN 1-57590-093-9.An excellent tutorial that is highly recommended.g y

• Electrochemical Techniques in Corrosion Engineering, 1986, NACE InternationalProceedings from a Symposium held in 1986. 36 papers. Covers the basics of the various electrochemical techniques and a wide variety of papers on the application of these techniques. Includes impedance spectroscopy.

• Electrochemical Impedance: Analysis and Interpretation, STP 1188, Edited by Scully Silverman and Kendig ASTM ISBN 0-8031-1861-9


Edited by Scully, Silverman, and Kendig, ASTM, ISBN 0 8031 1861 9.26 papers covering modeling, corrosion, inhibitors, soil, concrete, and coatings.

• EIS Primer, Gamry Instruments website, www.gamry.com

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Electrochemical ImpedanceElectrochemical Impedance Spectroscopy: Theory and Application

Dr. Jacob KetterGamry Instruments

www gamry com


www.gamry.com

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