Electrochemical Impedance Spectroscopy

1 Electrochemical Impedance Electrochemical Impedance SpectroscopySpectroscopyMark E. OrazemDepartment of Chemical EngineeringUniversity of FloridaGainesville, Florida Mark E. Orazem, 2000-2008. All rights Chapter 1. Introduction Chapter 2. Motivation Chapter 3. Impedance Measurement Chapter 4. Representations of Impedance Data Chapter 5. Development of Process Models Chapter 6. Regression Analysis Chapter 7. Error Structure Chapter 8. Kramers-Kronig Relations Chapter 9. Use of Measurement Models Chapter 10. Conclusions Chapter 11. Suggested Reading Chapter 12. NotationChapter 1. Introductionpage 1:1 Electrochemical Impedance Electrochemical Impedance SpectroscopySpectroscopyMark E. OrazemDepartment of Chemical EngineeringUniversity of FloridaGainesville, Florida Mark E. Orazem, 2000-2008. All rights 1. Introductionpage 1:2 Electrochemical Impedance Electrochemical Impedance SpectroscopySpectroscopyChapter 1.

2 IntroductionChapter 1. Introduction How to think about Impedance Spectroscopy EIS as a generalized transfer function Overview of applications of EIS Objective and outline of course Mark E. Orazem, 2000-2007. All rights 1. Introductionpage 1:31992 no logoChapter 1. Introductionpage 1:4 The Blind Men and the ElephantThe Blind Men and the ElephantJohn Godfrey SaxeJohn Godfrey SaxeIt was six men of IndostanTo learning much inclined,Who went to see the Elephant(Though all of them were blind),That each by observationMight satisfy his First approached the Elephant,And happening to fallAgainst his broad and sturdy side,At once began to bawl: God bless me! but the ElephantIs very like a wall! ..Chapter 1. Introductionpage 1:5 Electrochemical Impedance Electrochemical Impedance SpectroscopySpectroscopy Electrochemical technique steady-state transient Impedance Spectroscopy Measurement in terms of macroscopic quantities total current averaged potential Not a chemical Spectroscopy Type of generalized transfer-function measurementChapter 1.

3 Introductionpage 1 , VCurrentDensity, A/cm2~ I V~() Impedance SpectroscopyImpedance SpectroscopyrjVZZjZI ==+ Chapter 1. Introductionpage 1:7 Impedance SpectroscopyImpedance Spectroscopy Electrochemical systems Corrosion Electrodeposition Human Skin Batteries Fuel Cells Materials Dielectric Spectroscopy Acoustophoreticspectroscopy Viscometry Electrohydrodynamicimpedance spectroscopyApplicationsFundamentalsChap ter 1. Introductionpage 1:8 Physical DescriptionPhysical Description Electrode-Electrolyte Interface Electrical Double Layer Diffusion Layer Electrochemical Reactions Electrical Circuit AnaloguesChapter 1. Introductionpage 1:9 Electrochemical ReactionsElectrochemical ReactionseUViR=+FddVii Cdt=+()222222 OOOOOOexpFFii nFkVRTcV == Faradaic current density --22O + 2H O + 4e4 OHTotal current density = Faradaic + chargingCell potential = electrode potential + Ohmic potential dropChapter 1.

4 Introductionpage 1:10 Electrical AnaloguesElectrical AnaloguesChapter 1. Introductionpage 1:11 Electrical AnalogueElectrical AnalogueSimple Electrochemical reactionSimple Electrochemical reaction with mass transferChapter 1. Introductionpage 1:12 Course ObjectivesCourse Objectives Benefits and advantages of Impedance Spectroscopy Methods to improve experimental design Interpretation of data graphical representations regression error analysis equivalent circuits process modelsChapter 1. Introductionpage 1:13 ContentsContents Chapter 1. Introduction Chapter 2. Motivation Chapter 3. Impedance Measurement Chapter 4. Representations of Impedance Data Chapter 5. Development of Process Models Chapter 6. Regression Analysis Chapter 7. Error Structure Chapter 8. Kramers-Kronig Relations Chapter 9. Use of Measurement Models Chapter 10. Conclusions Chapter 11. Suggested Reading Chapter 12.

5 NotationChapter 1. Introductionpage 1:14 Chapter 2. Motivationpage 2:1 Electrochemical Impedance Electrochemical Impedance SpectroscopySpectroscopyChapter 2. MotivationChapter 2. Motivation Comparison of measurements steady state step transients single-sine Impedance In principle, step and single-sine perturbations yield same results Impedance measurements have better error structure Mark E. Orazem, 2000-2007. All rights 2. Motivationpage 2:2 SteadySteady--State State Polarization Polarization , VCurrent, mAChapter 2. Motivationpage 2:3 SteadySteady--State TechniquesState Techniques Yield information on state after transient is completed Do not provide information on system time constants capacitance Influenced by Ohmic potential drop non-stationarity film growth coupled reactionsChapter 2. Motivationpage 2:4 Transient Response to a Step in PotentialTransient Response to a Step in (V)C1R2C2 Current / mA(t-t0) / mscurrent responsepotential input V=10 mV}10-510-410-310-210-110010-210-1100 Current / mA(t-t0) / s210)(RVRRVI++=Chapter 2.

6 Motivationpage 2:5 Transient Response to a Step in PotentialTransient Response to a Step in Potentiallong times/low frequencyShort times/high (V)C1R2C2 Current / mA(t-t0) / mscurrent responsepotential input V=10 mV}Chapter 2. Motivationpage 2:6 Transient Techniques: Transient Techniques: potential or current stepspotential or current steps Decouples phenomena characteristic time constants mass transfer kinetics capacitance Limited by accuracy of measurements current potential time Limited by sample rate <~1 kHzChapter 2. Motivationpage 2:7 Sinusoidal PerturbationSinusoidal Perturbation0 CdViCdt=()fifV=()Vt(){}00()cos( )exp( ) exp()acVt VVtit ibVbV =+ = Chapter 2. Motivationpage 2:8 Sinusoidal PerturbationSinusoidal mHz100 Hz(i-i0) / max(i-i0)(V-V0) / V010 kHzChapter 2. Motivationpage 2:9 LissajousLissajousRepresentationRepresen tation||sin( )VZI == = OAOBODOA()cos( )()cos()VtVtVIttZ = =+ (t)/Y0X(t)/X0 ODABC hapter 2.

7 Motivationpage 2:10 Impedance ResponseImpedance Response0 10203040500-5-10-15-20-25 Zj / cm-2Zr / cm-2100 HzChapter 2. Motivationpage 2:11 Impedance SpectroscopyImpedance Spectroscopy Decouples phenomena characteristic time constants mass transfer kinetics capacitance Gives same type of information as DC transient. Improves information content and frequency range by repeated sampling. Takes advantage of relationship between real and imaginary Impedance to check 2. Motivationpage 2:12 System with Large Ohmic ResistanceSystem with Large Ohmic Resistance R0=10,000 R1=1,000 C1= F = s (15 Hz)M. E. Orazem, T. El Moustafid, C. Deslouis, and B. Tribollet, J. Electrochem. Soc.,143(1996), 2. Motivationpage 2:13 Impedance SpectrumImpedance Spectrum-600-400-2000980010000 10200 10400 10600 10800 11000 11200Zr, Zj, , HzImpedance, Zr, -Zj, Chapter 2. Motivationpage 2:14 Experimental DataExperimental 100000 Frequency, HzImpedance, Chapter 2.

8 Motivationpage 2:15 Impedance Spectroscopy Impedance Spectroscopy vs. Stepvs. Step--Change TransientsChange Transients Information sought is the same Increased sensitivity stochastic errors frequency range consistency check Better decoupling of physical phenomenaChapter 2. Motivationpage 2:16 Chapter 3. Impedance Measurementpage 3:1 Electrochemical Impedance Electrochemical Impedance SpectroscopySpectroscopyChapter 3. Impedance MeasurementChapter 3. Impedance Measurement Overview of techniques bridge Lissajous analysis phase-sensitive detection (lock-in amplifier) Fourier analysis Experimental design Mark E. Orazem, 2000-2008. All rights 3. Impedance Measurementpage 3:2 Measurement TechniquesMeasurement Techniques Bridge Lissajous analysis Phase-sensitive detection (lock-in amplifier) Fourier analysis digital transfer function analyzer fast Fourier transformD. Macdonald, Transient Techniques in Electrochemistry,Plenum Press, NY, Ross Macdonald, editor, Impedance Spectroscopy Emphasizing Solid Materials and Analysis,John Wiley and Sons, New York, Gabrielli, Use and applications of Electrochemical Impedance Techniques,Technical Report, Schlumberger, Farnborough, England, 3.

9 Impedance Measurementpage 3:3AC BridgeAC BridgeGeneratorZ2Z1Z3Z4D Bridge is balanced when current at D is equal to zero Time consuming Accurate14 23 ZZZ Z=10 Hzf Chapter 3. Impedance Measurementpage 3:4||sin( )VZI === = = OAA'AOBB'BODD'DOAA'A()sin( )()sin()VtVtVIttZ = =+PotentialCurrentADOBB'D'A'LissajousLis sajousAnalysisAnalysisChapter 3. Impedance Measurementpage 3:5 Phase Sensitive DetectionPhase Sensitive Detection0sin()AAAt =+()041sin 2 121 SnSntn ==++ + ()()0041sisin 2 121nSnAntnAAtS =++ ++= General SignalReference Signal()SAAdtAS = cos22020 Has maximum value when AS =Chapter 3. Impedance Measurementpage 3:6 Fourier Analysis:Fourier Analysis:singlesingle--frequency inputfrequency input0() cos()IIt It =+0() cos( )Vt Vt =()()()()00001()cos( )1()sin( )1()cos( )1()sin( )TrTjTrTjIIttdtTIIttdtTVVttdtTVVttdtT == == () Re() ImrjrrjrjjrjVjVZIjIVjVZIjI + = + + = + Chapter 3.

10 Impedance Measurementpage 3:7 Fourier Analysis:Fourier Analysis:multimulti--frequency inputfrequency inputTime Signal OutputTime Signal InputZZ( )Fast Fourier TransformChapter 3. Impedance Measurementpage 3:8 ComparisonComparisonsinglesingle--sine input multisine input multi--sine inputsine input Good accuracy for stationary systems Frequency intervals of f/f economical use of frequencies Used for entire frequency domain Kramers-Kronig inconsistent frequencies can be deleted Good accuracy for stationary systems Frequency intervals of f dense sampling at high frequency required to get good resolution at low frequency Often paired with Phase-Sensitive-Detection (f>10 Hz) Correlation coefficient used to determine whether spectrum is inconsistent with Kramers-Kronig relationsChapter 3. Impedance Measurementpage 3:9 Measurement TechniquesMeasurement Techniques bridge obsolete Lissajous analysis obsolete useful to visualize Impedance Phase-sensitive detection (lock-in amplifier) inexpensive accurate useful at high frequencies Fourier analysis techniques accurateChapter 3.