Electrochemical Impedance Spectroscopy, John Wiley and Sons, New York, 2008
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ElectrochemicalElectrochemical ImpedanceImpedance SpectroscopySpectroscopy Mark E. Orazem Department of Chemical Engineering University of Florida Gainesville, Florida 32611 [email protected] 352-392-6207 © Mark E. Orazem, 2000-2008. All rights reserved. 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. Notation Chapter 1. Introduction page 1: 1 ElectrochemicalElectrochemical ImpedanceImpedance SpectroscopySpectroscopy Mark E. Orazem Department of Chemical Engineering University of Florida Gainesville, Florida 32611 [email protected] 352-392-6207 © Mark E. Orazem, 2000-2008. All rights reserved. Chapter 1. Introduction page 1: 2 ElectrochemicalElectrochemical ImpedanceImpedance SpectroscopySpectroscopy Chapter 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 reserved. Chapter 1. Introduction page 1: 3 1992 – no logo Chapter 1. Introduction page 1: 4 TheThe BlindBlind MenMen andand thethe ElephantElephant John Godfrey Saxe It was six men of Indostan To learning much inclined, Who went to see the Elephant (Though all of them were blind), That each by observation Might satisfy his mind. The First approached the Elephant, And happening to fall Against his broad and sturdy side, At once began to bawl: “God bless me! but the Elephant Is very like a wall!” ... Chapter 1. Introduction page 1: 5 ElectrochemicalElectrochemical ImpedanceImpedance 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 measurement Chapter 1. Introduction page 1: 6 ImpedanceImpedance SpectroscopySpectroscopy Current 10 Density, μA/cm2 ~ ΔI 5 ΔV ZZ()ω ==+jZ ΔI rj -0.2 -0.1 0.1 0.2 0.3 0.4 Potential, V ~ -5 ΔV -10 Chapter 1. Introduction page 1: 7 ImpedanceImpedance SpectroscopySpectroscopy Applications Fundamentals • Electrochemical systems • Dielectric spectroscopy – Corrosion • Acoustophoretic – Electrodeposition spectroscopy – Human Skin • Viscometry – Batteries • Electrohydrodynamic – Fuel Cells impedance spectroscopy • Materials Chapter 1. Introduction page 1: 8 PhysicalPhysical DescriptionDescription • Electrode-Electrolyte Interface – Electrical Double Layer – Diffusion Layer • Electrochemical Reactions • Electrical Circuit Analogues Chapter 1. Introduction page 1: 9 ElectrochemicalElectrochemical ReactionsReactions -- O22 + 2H O+ 4e→ 4OH Faradaic current density ⎧α F ⎫ ii== nFkcVexp O2 −V F OOO2222O2 ⎨ ()O⎬ ⎩⎭RT Total current density = Faradaic + charging dV ii=+ C Fddt Cell potential = electrode potential + Ohmic potential drop UViR= + e Chapter 1. Introduction page 1: 10 ElectricalElectrical AnaloguesAnalogues Chapter 1. Introduction page 1: 11 ElectricalElectrical AnalogueAnalogue Simple electrochemical reaction Simple electrochemical reaction with mass transfer Chapter 1. Introduction page 1: 12 CourseCourse ObjectivesObjectives • Benefits and advantages of impedance spectroscopy • Methods to improve experimental design • Interpretation of data – graphical representations – regression – error analysis – equivalent circuits – process models Chapter 1. Introduction page 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. Notation Chapter 1. Introduction page 1: 14 Chapter 2. Motivation page 2: 1 ElectrochemicalElectrochemical ImpedanceImpedance SpectroscopySpectroscopy Chapter 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 reserved. Chapter 2. Motivation page 2: 2 SteadySteady--StateState PolarizationPolarization CurveCurve 0.4 0.3 0.2 Current, mA 0.1 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Potential, V Chapter 2. Motivation page 2: 3 SteadySteady--StateState TechniquesTechniques • 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 reactions Chapter 2. Motivation page 2: 4 TransientTransient ResponseResponse toto aa StepStep inin PotentialPotential 1.5 0 potential input 10 ΔV=10 mV V } I = 1.0 C1 C2 RRVR0+() 1 + 2 10-1 R0 Current / mA Current Current / mA / Current 0.5 R1(V) R2 -2 current response 10 0246810 10-5 10-4 10-3 10-2 10-1 100 (t-t ) / ms (t-t ) / s 0 0 Chapter 2. Motivation page 2: 5 TransientTransient ResponseResponse toto aa StepStep inin PotentialPotential 1.5 Short times/high frequency potential input } ΔV=10 mV 1.0 C1 C2 R0 Current / mA / Current 0.5 R1(V) R2 current response long times/low frequency 0246810 (t-t ) / ms 0 Chapter 2. Motivation page 2: 6 TransientTransient Techniques:Techniques: potentialpotential oror currentcurrent stepssteps • Decouples phenomena – characteristic time constants • mass transfer • kinetics – capacitance • Limited by accuracy of measurements – current – potential – time • Limited by sample rate – <~1 kHz Chapter 2. Motivation page 2: 7 SinusoidalSinusoidal PerturbationPerturbation Vt()=+Δ V0 V cos(ω t) it( )=−− i0 {} exp( bVac ) exp( bV ) dV iC= C 0 dt i f = f (V ) Vt() Chapter 2. Motivation page 2: 8 SinusoidalSinusoidal PerturbationPerturbation 1.0 10 kHz 100 Hz 1 mHz ) 0.5 0 0.0 ) / max(i-i 0 (i-i -0.5 -1.0 -1.0 -0.5 0.0 0.5 1.0 (V-V ) / V 0 0 Chapter 2. Motivation page 2: 9 LissajousLissajous RepresentationRepresentation B 1.0 Vt()= Δ V cos(ω t ) ΔV 0.5 It()= cos(ω t+ φ ) 0 Z OD A 0 Y(t)/Y ΔV OA -0.5 ||Z == ΔI OB OD -1.0 sin(φ ) =− OA -1.0 -0.5 0 0.5 1.0 X(t)/X 0 Chapter 2. Motivation page 2: 10 ImpedanceImpedance ResponseResponse -25 100 Hz -2 -20 -15 cm Ω -10 / j Z -5 0 0 1020304050 -2 Z / Ω cm r Chapter 2. Motivation page 2: 11 ImpedanceImpedance SpectroscopySpectroscopy • 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 consistency. Chapter 2. Motivation page 2: 12 SystemSystem withwith LargeLarge OhmicOhmic ResistanceResistance •R0 =10,000 Ω •R1 =1,000 Ω •C1 = 10.5 μF – τ = 0.0105 s (15 Hz) M. E. Orazem, T. El Moustafid, C. Deslouis, and B. Tribollet, J. Electrochem. Soc., 143 (1996), 3880-3890. Chapter 2. Motivation page 2: 13 ImpedanceImpedance SpectrumSpectrum -600 -400 Ω , j Z -200 0 9800 10000 10200 10400 10600 10800 11000 11200 Zr, Ω 100000 Zr, Ω 10000 -Zj, Ω Ω 1000 100 10 Impedance, 1 0.1 0.1 1 10 100 1000 10000 100000 Frequency, Hz Chapter 2. Motivation page 2: 14 ExperimentalExperimental DataData 100000 10000 1000 Ω 100 10 Impedance, 1 0.1 0.01 0.1 1 10 100 1000 10000 100000 Frequency, Hz Chapter 2. Motivation page 2: 15 ImpedanceImpedance SpectroscopySpectroscopy vs.vs. StepStep--ChangeChange TransientsTransients • Information sought is the same • Increased sensitivity – stochastic errors – frequency range – consistency check • Better decoupling of physical phenomena Chapter 2. Motivation page 2: 16 Chapter 3. Impedance Measurement page 3: 1 ElectrochemicalElectrochemical ImpedanceImpedance SpectroscopySpectroscopy Chapter 3. Impedance Measurement • Overview of techniques – A.C. bridge – Lissajous analysis – phase-sensitive detection (lock-in amplifier) – Fourier analysis • Experimental design © Mark E. Orazem, 2000-2008. All rights reserved. Chapter 3. Impedance Measurement page 3: 2 MeasurementMeasurement TechniquesTechniques • A.C. Bridge • Lissajous analysis • Phase-sensitive detection (lock-in amplifier) • Fourier analysis – digital transfer function analyzer – fast Fourier transform D. Macdonald, Transient Techniques in Electrochemistry, Plenum Press, NY, 1977. J. Ross Macdonald, editor, Impedance Spectroscopy Emphasizing Solid Materials and Analysis, John Wiley and Sons, New York, 1987. C. Gabrielli, Use and Applications of Electrochemical Impedance Techniques, Technical Report, Schlumberger, Farnborough, England, 1990. Chapter 3. Impedance Measurement page 3: 3 ACAC BridgeBridge Z1 Z2 • Bridge is balanced when current at D is equal to zero ZZ= ZZ D 14 23 • Time consuming • Accurate f ≥10 Hz Z3 Z4 Generator Chapter 3. Impedance Measurement page 3: 4 LissajousLissajous AnalysisAnalysis Vt()= Δ V sin(ω t ) Current B ΔV It()= sin(ω t+φ ) Z A' D' O AD Potential ΔV OA A'A ||Z === B' ΔI OB B'B OD D'D sin(φ ) =− =− OA A'A Chapter 3. Impedance Measurement page 3: 5 PhasePhase SensitiveSensitive DetectionDetection General Signal AA= 0 sin(ω t+φA ) 41∞ Reference Signal Sn=+∑ sin⎣⎡() 2 1 ωt+φS ⎦⎤ π n=0 21n + ∞ 41A0 AS =