Electrochemical Phenomena in the Cathode Impedance Spectrum of PEM Fuel Cells
Fundamentals and Applications
- 1st Edition - June 18, 2022
- Imprint: Elsevier
- Authors: Samuel Cruz-Manzo, Paul Greenwood
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 9 0 6 0 7 - 4
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 1 4 3 2 - 1
Electrochemical Phenomena in the Cathode Impedance Spectrum of PEM Fuel Cells: Fundamentals, Modelling, and Applications establishes how the electrochemical and diffusion m… Read more
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Electrochemical Phenomena in the Cathode Impedance Spectrum of PEM Fuel Cells: Fundamentals, Modelling, and Applications establishes how the electrochemical and diffusion mechanisms of a polymer electrolyte membrane fuel cell (PEMFC) are related to electrochemical impedance spectroscopy (EIS) measurements using physics-based impedance models derived from fundamental electrode and diffusion theories. The contribution of the different phenomena occurring at the different layers comprising the cathode on the impedance response of the PEMFC is revealed through EIS-modelling analysis. The relation between EIS measurements and polarisation curves representing the performance of PEMFCs is established. Insight is gained into how the EIS response of the PEMFC changes at different operating conditions e.g. relative humidity, load demand, gas reactant stoichiometry and temperature using physics-based impedance models. The application of impedance models with EIS measurements carried out in the individual cells comprising a PEMFC stack is demonstrated, while recent modelling approaches and other impedance models reported in the literature to represent the EIS response of the PEMFC are also considered and discussed.
- Provides further understanding of ambiguities during the interpretation of the electrochemical impedance spectrum of the PEMFC
- Includes impedance models written in MATLAB® for replication or application to other PEMFC-EIS measurements
- Includes impedance spectra of the PEMFC at different operating conditions, electro/diffusion pathways for derivation of the impedance models and flowcharts for application of the impedance models with real-world measured EIS data
Students new to the field of EIS-PEMFC technology as well as engineers from the fuel cell industry who aim to understand how electrochemistry, thermodynamics, kinetics, and mass transport phenomena of PEMFCs are related to EIS measurements will gain benefit from this book.
Part I. Fundamentals of PEM Fuel Cells and EIS
Chapter 1 Introduction to Electrochemical Impedance Spectroscopy
1.1 Fundamental Concepts of Electrochemical Impedance Spectroscopy
1.1.1 Impedance response in the frequency domain
1.2 Methods for Analysis of Impedance Measurements
1.2.1 Lissajous analysis
1.2.2 Frequency Fourier analysis
1.3 Validity of EIS Measurements
1.3.1 Kramers-Kronig relations
1.3.2 Hilbert transformation
1.4 Equivalent Electrical Circuits for EIS analysis
1.4.1 Impedance response of a capacitor
1.4.2 Impedance response of an inductor
1.4.3 Impedance response of a Warburg element considering finite-diffusion
1.4.4 Impedance response of a resistor-capacitor (parallel-series configuration)
1.4.5 Impedance response of a constant-phase element
1.4.6 Impedance response of the Randles circuit
1.4.7 Impedance response of the Randles circuit featuring an inductive loop
1.5 Application of Kramers-Kronig Relations and Hilbert Transformation
1.5.1 Kramers-Kronig analysis using the Voigt circuit in MATLAB software
1.5.2 Hilbert transformation through fast Fourier transform
1.5.3 Kramers-Kronig analysis through ZView software
1.5.4 Application with real-world EIS measurements
1.6 References
Chapter 2 Fundamentals of PEM Fuel Cells
2.1 The Structure of the PEM Fuel Cell
2.2 The Voltage Output in the PEM Fuel Cell
2.2.1 Reversible potential
2.2.2 Activation overpotential
2.2.3 Ohmic overpotential
2.2.4 Mass transport overpotential
2.2.5 Operating voltage in a PEM fuel Cell
2.3 Electrochemical Phenomena in the Catalyst Layer
2.3.1 Faradaic process
2.3.2 The charge double-layer in the catalyst layer
2.3.3 Faradaic and non-faradaic processes
2.3.4 Multi-step mechanisms during the oxygen reduction reaction
2.4 Electrochemical Dynamic Response
2.4.1 Simulation of dynamic voltage of the PEMFC in MATLAB/Simulink environment
2.5 References
Chapter 3 Electrochemical Impedance Spectroscopy in PEM Fuel Cells
3.1 Representation of the Impedance Response of a PEM Fuel Cell
3.2 Equipment for EIS Measurements
3.3 Reference Electrodes
3.4 Inductive Effect on the Impedance Spectrum
3.4.1 Inductive effect of the measurement system
3.4.2 Inductive loops at low frequencies
3.5 Effect of Sinusoidal Signal Amplitude on EIS Measurements
3.6 Relation between Polarisation Resistance from EIS and the Polarisation Curve
3.7 Local EIS Measurements
3.8 EIS Measurements in PEMFCs under Different Operating Conditions
3.8.1 Anodic impedance response
3.8.2 Current density
3.8.3 PEMFC temperature
3.8.4 Oxygen stoichiometry
3.8.5 Relative humidity
3.8.6 Nitrox or Heliox as a gas reactant
3.9 Errors during the Interpretation of EIS Measurements
3.10 Electrochemical Pressure Impedance Spectroscopy
3.11 Electrical Circuits for EIS Analysis
3.11.1 Randles circuit
3.11.2 Transmission line model
3.11.3 Voigt circuit
3.12 Evaluation of Validity of EIS Measurements
3.12.1 Kramers-Kronig analysis
3.12.1.1 Stability analysis
3.12.1.2 Linearity analysis
3.12.2 Hilbert transformation
3.13 References
Part II. Modelling
Chapter 4 Impedance Model of the Cathode Catalyst Layer
4.1 Oscillating Current and Voltage in the Charge Double-Layer
4.2 Transmission-Line Model for Porous Electrodes
4.2.1 Transmission-line model with negligible electron resistance
4.2.2 Transmission-line model with no Faradaic resistance
4.3 Impedance Model of the Cathode Catalyst Layer with Low Electron Conductivity
4.4 Electrochemical Phenomena in the Cathode Catalyst Layer
4.4.1 Faradaic current and current in double-layer capacitance
4.4.2 Proton and electron resistances in the cathode catalyst layer
4.5 Electrochemical Impedance of the Cathode Catalyst Layer at Low Current
4.5.1 Effect of proton resistance on steady-state overpotential
4.5.2 Impedance model of the cathode catalyst layer
4.5.3 External capacitance for high frequency analysis
4.5.4 Impedance response of the cathode catalyst layer considering proton and electron resistivities
4.6 Electrochemical Impedance of the Cathode Catalyst Layer at High Current
4.6.1. Solution of Fick’s second law in Laplace domain
4.6.2 Finite length-Warburg impedance and charge transfer resistance
4.6.3 Impedance response of the cathode catalyst layer
4.7 Electrochemical Phenomena of the Cathode Catalyst Layer at Low Frequencies
4.7.1 Effect of oxygen diffusion parameters on the impedance spectrum
4.8 Further Application of the Impedance Model of the Cathode Catalyst Layer
4.9 References
Chapter 5 Impedance Model of the Gas Diffusion Layer and Air Channel
5.1 Oxygen Transport through the Gas Diffusion Layer and Air Channel
5.2 Finite-Length Warburg Impedance
5.2.1 Effect of capacitance of the cathode catalyst layer on impedance response of the gas diffusion layer
5.2.2 Local Warburg Impedance
5.3 Impedance Model of the Segmented Cathode
5.4 Mathematical Model for Oxygen Transport in the Gas Diffusion Layer and Air Channel
5.4.1 Oxygen diffusion in the gas diffusion layer
5.4.2 Oxygen transport in the air channel
5.4.3 Steady-state oxygen transport in the channel
5.5 Impedance Model of the GDL-Channel
5.5.1 Impedance model considering non-stationary oxygen depletion along the air channel during AC conditions.
5.5.2 Impedance model considering steady-state oxygen depletion along the air channel
5.5.3 Current distribution along the channel
5.5.4 Total impedance model of the GDL-channel
5.6 Simulation of Total Impedance Response of the GDL-Channel
5.6.1 Estimation of diffusion parameters in the gas diffusion layer
5.6.2 Simulation of the total GDL-channel impedance at different oxygen stoichiometry
5.7 Simulation of Local Impedance Response of the GDL-Channel
5.8 Effect of Relative Humidity on GDL-Channel Impedance Spectrum
5.9 Oscillating Oxygen Concentration in the Channel
5.10 Randles Circuit with Analytical Warburg Impedance Model
5.11 Effect of Double-Layer Capacitance of Catalyst Layer on the GDL-Channel Impedance
5.12 References
Part III. Modelling Application
Chapter 6 Electrochemical Phenomena in the Cathodic Impedance Spectrum
6.1 Cathodic Impedance Model
6.1.1 Impedance model of the gas diffusion layer and air channel
6.1.2 Impedance model of the cathode catalyst layer
6.1.3 Impedance model of the cathodic side of the PEMFC
6.2 Modelling Architecture of the Cathodic Impedance Model
6.2.1 Model execution
6.2.2 Lumped impedance model of the cathode
6.2.3 Estimation of lumped parameters
6.2.4 Estimation of diffusion parameters
6.2.5 Simulation results from cathodic modelling architecture
6.3 Application of Cathodic Impedance Model with EIS Measurements
6.3.1 Validity of EIS measurements
6.3.2 Parameter estimation from EIS measurements
6.3.3 Simulation of impedance responses of the CCL, GDL-channel and cathode
6.4 Analysis of the Cathodic Impedance Spectrum at Low Current Density
6.5 Simulation of Cathodic Impedance spectrum at Different PEMFC Temperatures
6.6 Simulation of the Cathodic Impedance Spectrum at Different Oxygen Stoichiometry
6.7 Simulation of the Cathodic Impedance Spectrum at High Current Density
6.8 References
Chapter 7 Impedance Analysis on the Individual Cells of a PEMFC Stack
7.1 EIS in PEMFC Stacks
7.2 Analysis of EIS Measurements Featuring an Inductive Loop at Low Frequencies
7.2.1 EIS Measurements in an open-cathode PEMFC stack
7.2.2 Electrical circuits
7.2.3 Fitting process
7.2.4 Impedance analysis
7.2.5 Limitations with electrical circuits
7.3 Analysis of Inductive Loops at Low Frequencies in PEMFC-EIS Measurements
7.3.1 Hydrogen peroxide formation
7.3.2 Platinum oxide formation
7.3.3 Water transport in the electrode
7.3.4 Water vapour diffusion in the cathode catalyst layer
7.4 References
Appendix
Appendix A Impedance Models in MATLAB Software
Appendix B Alternative Tests
- Edition: 1
- Published: June 18, 2022
- Imprint: Elsevier
- Language: English
SC
Samuel Cruz-Manzo
Dr. Samuel Cruz-Manzo is a research fellow from the University of Lincoln, UK with a solid understanding of electrochemical impedance spectroscopy (EIS) in polymer electrolyte membrane fuel cells (PEMFCs) and has also worked with EIS and modelling in Nickel-metal hydride and Lithium-ion batteries. Dr. Cruz-Manzo has experience in real-time dynamic modelling and diagnostic of failures in industrial gas turbines on projects funded by Siemens Energy, Lincoln, UK and previously worked as a simulation engineer at a UK fuel cell company (Intelligent Energy Ltd.). He obtained his PhD degree at Loughborough University UK with a research project related to EIS modelling in PEMFCs. During his PhD study Dr. Cruz-Manzo obtained a prestigious international student research award in Fuel Cells, the Fuel Cell Baker Award 2013, USA
Affiliations and expertise
Research Fellow, University of Lincoln; External Research Engineer, Siemens Energy Ltd., Lincoln, UKPG
Paul Greenwood
Dr. Paul Greenwood is a research engineer from the Abastecedora Electrica Tehuacan, Mexico and his interests include the performance analysis of electrochemical systems through EIS and modelling. Dr. Greenwood has obtained a PhD degree in Loughborough University UK with a research project related to enhancement of flow field plates in PEMFCs.
Affiliations and expertise
Research Engineer, Abastecedora Electrica Tehuacan, MexicoRead Electrochemical Phenomena in the Cathode Impedance Spectrum of PEM Fuel Cells on ScienceDirect