Electrocatalysts for Low Temperature Fuel Cells E-Book
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- Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Meeting the need for a text on solutions to conditions which have so far been a drawback for this important and trend-setting technology, this monograph places special emphasis on novel, alternative catalysts of low temperature fuel cells. Comprehensive in its coverage, the text discusses not only the electrochemical, mechanistic, and material scientific background, but also provides extensive chapters on the design and fabrication of electrocatalysts.
A valuable resource aimed at multidisciplinary audiences in the fields of academia and industry.
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Veröffentlichungsjahr: 2017
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CONTENTS
Cover
Title Page
Copyright
List of Contributors
Preface
Chapter 1: Principle of Low-temperature Fuel Cells Using an Ionic Membrane
1.1 Introduction
1.2 Thermodynamic Data and Theoretical Energy Efficiency under Equilibrium (j = 0)
1.3 Electrocatalysis and the Rate of Electrochemical Reactions
1.4 Influence of the Properties of the PEMFC Components (Electrode Catalyst Structure, Membrane Resistance, and Mass Transfer Limitations) on the Polarization Curves
1.5 Representative Examples of Low-temperature Fuel Cells
1.6 Conclusions and Outlook
Acknowledgments
References
Chapter 2: Research Advancements in Low-temperature Fuel Cells
2.1 Introduction
2.2 Proton Exchange Membrane Fuel Cells
2.3 Alkaline Fuel Cells
2.4 Direct Borohydride Fuel Cells
2.5 Regenerative Fuel Cells
2.6 Conclusions and Outlook
Acknowledgments
References
Chapter 3: Electrocatalytic Reactions Involved in Low-temperature Fuel Cells
3.1 Introduction
3.2 Preparation and Characterization of Pt-based Plurimetallic Electrocatalysts
3.3 Mechanisms of the Electrocatalytic Reactions Involved in Low-temperature Fuel Cells
3.4 Conclusions and Outlook
Acknowledgment
References
Chapter 4: Direct Hydrocarbon Low-temperature Fuel Cell
4.1 Introduction
4.2 Direct Methanol Fuel Cell
4.3 Direct Ethanol Fuel Cell
4.4 Direct Ethylene Glycol Fuel Cell
4.5 Direct Formic Acid Fuel Cell
4.6 Direct Glucose Fuel Cell
4.7 Commercialization Status of DHFC
4.8 Conclusions and Outlook
References
Chapter 5: The Oscillatory Electrooxidation of Small Organic Molecules
5.1 Introduction
5.2 In Situ and Online Approaches
5.3 The Effect of Temperature
5.4 Modified Surfaces
5.5 Conclusions and Outlook
Acknowledgments
References
Chapter 6: Degradation Mechanism of Membrane Fuel Cells with Monoplatinum and Multicomponent Cathode Catalysts
6.1 Introduction
6.2 Synthesis and Experimental Methods of Studying Catalytic Systems under Model Conditions
6.3 Characteristics of Commercial and Synthesized Catalysts
6.4 Methods of Testing Catalysts within FC MEAs
6.5 Mechanism of Degradation Phenomenon in MEAs with Commercial Pt/C Catalysts
6.6 Characteristics of MEAs with 40Pt/CNT-T-based Cathode
6.7 Characteristics of MEAs with 50PtCoCr/C-based Cathodes
6.8 Conclusions and Outlook
Acknowledgments
References
Chapter 7: Recent Developments in Electrocatalysts and Hybrid Electrocatalyst Support Systems for Polymer Electrolyte Fuel Cells
7.1 Introduction
7.2 Current State of Pt and Non-Pt Electrocatalysts Support Systems for PEFC
7.3 Novel Pt Electrocatalysts
7.4 Pt-based Electrocatalysts on Novel Carbon Supports
7.5 Pt-based Electrocatalysts on Novel Carbon-free Supports
7.6 Pt-free Metal Electrocatalysts
7.7 Influence of Support: Electrocatalyst–Support Interactions and Effect of Surface Functional Groups
7.8 Hybrid Catalyst Support Systems
7.9 Conclusions and Outlook
References
Chapter 8: Role of Catalyst Supports: Graphene Based Novel Electrocatalysts
8.1 Introduction
8.2 Graphene-based Cathode Catalysts for Oxygen Reduction Reaction
8.3 Graphene-based Anode Catalysts
8.4 Conclusions and Outlook
Acknowledgment
References
Chapter 9: Recent Progress in Nonnoble Metal Electrocatalysts for Oxygen Reduction for Alkaline Fuel Cells
9.1 Introduction
9.2 Nonnoble Metal Electrocatalysts
9.3 Conclusions and Outlook
References
Chapter 10: Anode Electrocatalysts for Direct Borohydride and Direct Ammonia Borane Fuel Cells
10.1 Introduction
10.2 Direct Borohydride (and Ammonia Borane) Fuel Cells
10.3 Mechanistic Investigations of the BOR and BH3OR at Noble Electrocatalysts
10.4 Toward Ideal Anode of DBFC and DABFC
10.5 Durability of DBFC and DABFC Electrocatalysts
10.6 Conclusions and Outlook
References
Chapter 11: Recent Advances in Nanostructured Electrocatalysts for Low-temperature Direct Alcohol Fuel Cells
11.1 Introduction
11.2 Fundamentals of Electrooxidation of Organic Molecules for Fuel Cells
11.3 Investigation of Electrocatalytic Properties of Nanomaterials
11.4 Anode Electrocatalysts for Direct Methanol or Ethanol Fuel Cells
11.5 Anode Catalysts for Direct Polyol Fuel Cells (Ethylene Glycol and Glycerol)
11.6 Conclusions and Outlook
References
Chapter 12: Electrocatalysis of Facet-controlled Noble Metal Nanomaterials for Low-temperature Fuel Cells
12.1 Introduction
12.2 Synthesis of Shape-controlled Noble Metal Nanomaterials
12.3 Applications of Shape-controlled Noble Metal Nanomaterials as Catalysts for Low-temperature Fuel Cells
12.4 Conclusions and Outlook
Acknowledgment
References
Chapter 13: Heteroatom-doped Nanostructured Carbon Materials as ORR Electrocatalysts for Low-temperature Fuel Cells
13.1 Introduction
13.2 Oxygen Reduction Reaction and Methanol-tolerant ORR Catalysts
13.3 Heteroatom-doped Nanostructured Carbon Materials
13.4 Heteroatom-doped Carbon-based Nanocomposites
13.5 Conclusions and Outlook
References
Chapter 14: Transition Metal Oxide, Oxynitride, and Nitride Electrocatalysts with and without Supports for Polymer Electrolyte Fuel Cell Cathodes
14.1 Introduction
14.2 Transition Metal Oxide and Oxynitride Electrocatalysts
14.3 Transition Metal Nitride Electrocatalysts
14.4 Carbon Support-Free Electrocatalysts
14.5 Conclusions and Outlook
Acknowledgment
References
Chapter 15: Spectroscopy and Microscopy for Characterization of Fuel Cell Catalysts
15.1 Introduction
15.2 Electron Microscopy
15.3 Electron Spectroscopy: Energy-dispersive Spectroscopy and Electron Energy Loss Spectroscopy
15.4 X-ray Spectroscopy
15.5 Gamma Spectroscopy: Mossbauer
15.6 Vibrational Spectroscopy: Fourier Transform Infrared Spectroscopy and Raman Spectroscopy
15.7 Complementary Techniques
15.8 Conclusions and Outlook
References
Chapter 16: Rational Catalyst Design Methodologies: Principles and Factors Affecting the Catalyst Design
16.1 Introduction
16.2 Oxygen Reduction Reaction
16.3 Recent Progress in Search for Efficient ORR Catalysts
16.4 Physics and Chemistry behind ORR
16.5 Rational Design of ORR Catalysts
16.6 Rationally Designed ORR Catalysts Addressing Cost-effectiveness
16.7 Conclusions and Outlook
References
Chapter 17: Effect of Gas Diffusion Layer Structure on the Performance of Polymer Electrolyte Membrane Fuel Cell
17.1 Introduction
17.2 Structure of Gas Diffusion Layer
17.3 Carbon Materials
17.4 Hydrophobic and Hydrophilic Treatments
17.5 Microporous Layer Thickness
17.6 Microstructure Modification
17.7 Conclusions and Outlook
Acknowledgment
References
Chapter 18: Efficient Design and Fabrication of Porous Metallic Electrocatalysts
18.1 Introduction
18.2 Advances in the Design and Fabrication of Mesoporous Metallic Materials
18.3 Nanoporous Metallic Materials at Work in Electrocatalysis
18.4 Conclusions and Outlook
References
Chapter 19: Design and Fabrication of Dealloying-driven Nanoporous Metallic Electrocatalyst
19.1 Introduction
19.2 Design of Precursors for Dealloying-driven Nanoporous Metallic Electrocatalysts
19.3 Microstructural Modulation of Dealloying-driven Nanoporous Metallic Electrocatalysts
19.4 Catalytic Properties of Dealloying-driven Nanoporous Metallic Electrocatalysts
19.5 Conclusions and Outlook
Acknowledgments
References
Chapter 20: Recent Advances in Platinum Monolayer Electrocatalysts for the Oxygen Reduction Reaction
20.1 Introduction
20.2 Pt ML on Pd Core Electrocatalysts (PtML/Pd/C)
20.3 Pt ML on PdAu Core Electrocatalyst (PtML/PdAu/C)
20.4 Further Improving Activity and Stability of Pt ML Electrocatalysts
20.5 Conclusions and Outlook
Acknowledgments
References
Index
End User License Agreement
List of Tables
Table 1.1
Table 1.2
Table 2.1
Table 2.2
Table 2.3
Table 2.4
Table 3.1
Table 3.2
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table 5.1
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 6.5
Table 6.6
Table 6.7
Table 6.8
Table 6.9
Table 6.10
Table 6.11
Table 6.12
Table 6.13
Table 6.14
Table 9.1
Table 9.2
Table 10.1
Table 12.1
Table 16.1
Table 16.2
Table 17.1
Table 17.2
List of Illustrations
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 1.6
Figure 1.7
Figure 1.8
Figure 1.9
Figure 1.10
Figure 1.11
Figure 1.12
Figure 1.13
Figure 1.14
Figure 1.15
Figure 1.16
Figure 1.17
Figure 1.18
Figure 1.19
Figure 1.20
Figure 1.21
Figure 1.22
Figure 1.23
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Scheme 2.1
Figure 2.7
Figure 2.8
Figure 2.9
Figure 2.10
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Scheme 3.1
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 3.9
Figure 3.10
Figure 3.11
Figure 3.12
Scheme 3.2
Figure 3.13
Figure 3.14
Figure 3.15
Figure 3.16
Scheme 3.3
Figure 3.17
Scheme 3.4
Figure 3.18
Scheme 3.5
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.9
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 6.10
Figure 6.11
Figure 6.12
Figure 6.13
Figure 6.14
Figure 6.15
Figure 7.1
Figure 7.2
Figure 7.3
Figure 7.4
Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8
Figure 7.9
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 8.9
Figure 8.10
Figure 9.1
Figure 9.2
Figure 9.3
Figure 9.4
Figure 9.5
Figure 9.6
Figure 9.7
Figure 9.8
Figure 9.9
Figure 9.10
Figure 9.11
Figure 9.12
Figure 9.13
Figure 9.14
Figure 9.15
Figure 9.16
Figure 9.17
Figure 9.18
Figure 10.1
Figure 10.2
Figure 10.3
Figure 10.4
Figure 10.5
Figure 10.6
Figure 10.7
Figure 10.8
Figure 10.9
Figure 10.10
Figure 10.11
Figure 10.12
Figure 10.13
Figure 11.1
Scheme 11.1
Scheme 11.2
Scheme 11.3
Scheme 11.4
Figure 11.2
Figure 11.3
Figure 11.4
Figure 11.5
Figure 12.1
Figure 12.2
Figure 12.3
Figure 12.4
Figure 12.5
Scheme 12.1
Scheme 12.2
Figure 12.6
Scheme 12.3
Scheme 13.1
Figure 13.1
Scheme 13.2
Figure 13.2
Figure 13.3
Figure 13.4
Figure 13.5
Figure 13.6
Figure 13.7
Figure 14.1
Figure 14.2
Figure 14.3
Figure 14.4
Figure 14.5
Figure 14.6
Figure 14.7
Figure 14.8
Figure 14.9
Figure 15.1
Figure 15.2
Figure 15.3
Figure 15.4
Figure 15.5
Figure 15.6
Figure 15.7
Figure 15.8
Figure 15.9
Figure 15.10
Figure 16.1
Figure 16.2
Scheme 16.1
Figure 17.1
Figure 17.2
Figure 17.3
Figure 17.4
Figure 17.5
Figure 17.6
Figure 17.7
Figure 17.8
Figure 17.9
Figure 18.1
Figure 18.2
Figure 18.3
Figure 18.4
Figure 18.5
Figure 18.6
Figure 18.7
Figure 18.8
Figure 18.9
Figure 18.10
Figure 18.11
Figure 19.1
Figure 19.2
Figure 19.3
Figure 19.4
Figure 19.5
Figure 19.6
Figure 19.7
Figure 19.8
Figure 19.9
Figure 19.10
Figure 19.11
Figure 19.12
Figure 19.13
Figure 19.14
Figure 19.15
Figure 19.16
Figure 19.17
Figure 19.18
Figure 20.1
Figure 20.2
Figure 20.3
Figure 20.4
Figure 20.5
Figure 20.6
Figure 20.7
Figure 20.8
Figure 20.9
Figure 20.10
Figure 20.11
Figure 20.12
Figure 20.13
Figure 20.14
Figure 20.15
Figure 20.16
Guide
Cover
Table of Contents
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Electrocatalysts for Low Temperature Fuel Cells
Fundamentals and Recent Trends
Edited by Thandavarayan Maiyalagan and Viswanathan S. Saji
All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
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© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
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List of Contributors
Claude Lamy*
Université de Montpellier
Institut Européen des Membranes
UMR CNRS no 5635
2 Place Eugène Bataillon
CC 047
34095 Montpellier Cedex
France
and
Université de Nantes
Groupe de Recherches HySPàC
CNRS GDR 3652
2 rue de la Houssinière
44322 Nantes Cedex 3
France
[email protected] (Chapters 1 and 3)
N. Rajalakshmi*
International Advanced Research Centre for Powder Metallurgy and New Materials (ARCI)
Centre for Fuel Cell Technology
IIT Madras Research Park, 6 Kanagam Road
Taramani
600113 Chennai
India
[email protected] (Chapter 2)
R. Imran Jafri
International Advanced Research Centre for Powder Metallurgy and New Materials (ARCI)
Centre for Fuel Cell Technology
IIT Madras Research Park, 6 Kanagam Road
Taramani
600113 Chennai
India
K.S. Dhathathreyan
International Advanced Research Centre for Powder Metallurgy and New Materials (ARCI)
Centre for Fuel Cell Technology
IIT Madras Research Park, 6 Kanagam Road
Taramani
600113 Chennai
India
Ayan Mukherjee
Indian Institute of Technology Delhi
Department of Chemical Engineering
Hauz Khas
110016 New Delhi
India
Suddhasatwa Basu*
Indian Institute of Technology Delhi
Department of Chemical Engineering
Hauz Khas
110016 New Delhi
India
[email protected] (Chapter 4)
Hamilton Varela*
University of São Paulo
Institute of Chemistry of São Carlos
P.O. Box 780, 13560-970
São Carlos
SP
Brazil
[email protected] (Chapter 5)
Marcelo V.F. Delmonde
University of São Paulo
Institute of Chemistry of São Carlos
P.O. Box 780, 13560-970
São Carlos
SP
Brazil
Alana A. Zülke
University of São Paulo
Institute of Chemistry of São Carlos
P.O. Box 780, 13560-970
São Carlos
SP
Brazil
Mikhail R. Tarasevich
Russian Academy of Sciences
Frumkin Institute of Physical Chemistry and Electrochemistry
Leninskii pr. 31
119071 Moscow
Russian Federation
Vera A. Bogdanovskaya*
Russian Academy of Sciences
Frumkin Institute of Physical Chemistry and Electrochemistry
Leninskii pr. 31
119071 Moscow
Russian Federation
[email protected] (Chapter 6)
Surbhi Sharma*
University of Birmingham
School of Biosciences
Edgbaston
B15 2TT Birmingham
UK
[email protected] (Chapter 7)
Chunmei Zhang
Chinese Academy of Sciences
Changchun Institute of Applied Chemistry
State Key Laboratory of Electroanalytical Chemistry
5625 Renmin Street
Changchun
130022 Jilin
China
and
University of Chinese Academy of Sciences
19 A Yuquan Rd.
Shijingshan District
100039 Beijing
China
Wei Chen*
Chinese Academy of Sciences
Changchun Institute of Applied Chemistry
State Key Laboratory of Electroanalytical Chemistry
5625 Renmin Street
Changchun
130022 Jilin
China
[email protected] (Chapter 8)
Xin Deng
Zhejiang University
College of Chemical and Biological Engineering
38 Zheda Road
Hangzhou
310027 Zhejiang
China
Qinggang He*
Zhejiang University
College of Chemical and Biological Engineering
38 Zheda Road
Hangzhou
310027 Zhejiang
China
[email protected] (Chapter 9)
Pierre-Yves Olu
University Grenoble Alpes
LEPMI
1130 rue de la piscine
BP75
38000 Grenoble
France
and
CNRS
LEPMI
1130 rue de la piscine
BP75
38000 Grenoble
France
and
University of Liège
Department of Chemical Engineering – Nanomaterials Catalysis Electrochemistry
Building B6a
Sart-Tilman
4000 Liège
Belgium
Anicet Zadick
University Grenoble Alpes
LEPMI
1130 rue de la piscine
BP75
38000 Grenoble
France
and
CNRS
LEPMI
1130 rue de la piscine
BP75
38000 Grenoble
France
Nathalie Job
University of Liège
Department of Chemical Engineering – Nanomaterials Catalysis Electrochemistry
Building B6a
Sart-Tilman
4000 Liège
Belgium
Marian Chatenet*
University Grenoble Alpes
LEPMI
1130 rue de la piscine
BP75
38000 Grenoble
France
and
CNRS
LEPMI
1130 rue de la piscine
BP75
38000 Grenoble
France
and
French University Institute (IUF)
103 Blvd Saint Michel
75005 Paris
France
[email protected] (Chapter 10)
Srabanti Ghosh*
Central Glass and Ceramic Research Institute
196 Raja S.C. Mullick Road
700032 Kolkata
India
[email protected] (Chapter 11)
Rajendra N. Basu*
Central Glass and Ceramic Research Institute
196 Raja S.C. Mullick Road
700032 Kolkata
India
[email protected] (Chapter 11)
Xiaojun Liu
American University
Department of Chemistry
4400 Massachusetts Avenue N.W.
Washington, DC 20016
USA
Wenyue Li
American University
Department of Chemistry
4400 Massachusetts Avenue N.W.
Washington, DC 20016
USA
Shouzhong Zou*
American University
Department of Chemistry
4400 Massachusetts Avenue N.W.
Washington, DC 20016
USA
[email protected] (Chapter 12)
Thandavarayan Maiyalagan*
SRM University
SRM Research Institute
Department of Chemistry
Kattankulathur
603203 Chennai
India
[email protected] (Chapter 13)
Subbiah Maheswari
SRM University
SRM Research Institute
Department of Chemistry
Kattankulathur
603203 Chennai
India
Viswanathan S. Saji
CIOSHI Attingal
Thiruvananthapuram
695101 Kerala
India
Mitsuharu Chisaka*
Hirosaki University
Department of Sustainable Energy
3 Bunkyo-cho
Hirosaki
036–8561 Aomori
Japan
[email protected] (Chapter 14)
Chilan Ngo
Colorado School of Mines
Department of Chemistry
1012 14th St.
Golden, CO 80401
USA
Michael J. Dzara
Colorado School of Mines
Department of Chemistry
1012 14th St.
Golden, CO 80401
USA
Sarah Shulda
Colorado School of Mines
Department of Chemistry
1012 14th St.
Golden, CO 80401
USA
Svitlana Pylypenko*
Colorado School of Mines
Department of Chemistry
1012 14th St.
Golden, CO 80401
USA
[email protected] (Chapter 15)
Sergey Stolbov*
University of Central Florida
4111 Libra Drive, Physical Sciences
Bldg. 430
Orlando, FL 32816-2385
USA
[email protected] (Chapter 16)
Marisol Alcántara Ortigoza
Tuskegee University
Luther Foster Hall
1200 W. Montgomery Rd
Tuskegee, AL 36088
USA
Branko N. Popov*
University of South Carolina
Center for Electrochemical Engineering
Department of Chemical Engineering
301 Main Street, Columbia, SC 29208
USA
[email protected] (Chapter 17)
Sehkyu Park
Kwangwoon University
Department of Chemical Engineering
20 Kwangwoon-ro, Nowon-gu, 01897 Seoul
South Korea
Jong-Won Lee
Korea Institute of Energy Research
New and Renewable Energy Research Division
152 Gajeong-ro, Yuseong-gu, 34129 Daejeon
South Korea
Yaovi Holade
Université de Poitiers
IC2MP
UMR CNRS 7285
Équipe SAMCat
4 rue Michel Brunet
B27 TSA 51106
86073 Poitiers Cedex 09
France
Anaïs Lehoux
Université Paris-Sud
Université Paris-Saclay
Laboratoire de Chimie Physique
Bât 349 Campus d'Orsay
91405 Orsay
France
and
CNRS
Laboratoire de Chimie Physique
UMR 8000
91405 Orsay
France
Hynd Remita
Université Paris-Sud
Université Paris-Saclay
Laboratoire de Chimie Physique
Bât 349 Campus d'Orsay
91405 Orsay
France
and
CNRS
Laboratoire de Chimie Physique
UMR 8000
91405 Orsay
France
Kouakou B. Kokoh
Université de Poitiers
IC2MP
UMR CNRS 7285
Équipe SAMCat
4 rue Michel Brunet
B27 TSA 51106
86073 Poitiers Cedex 09
France
Têko W. Napporn*
Université de Poitiers
IC2MP
UMR CNRS 7285
Équipe SAMCat
4 rue Michel Brunet
B27 TSA 51106
86073 Poitiers Cedex 09
France
[email protected] (Chapter 18)
Zhonghua Zhang*
Shandong University
School of Materials Science and Engineering
Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education)
250061 Jinan
P.R. China
[email protected] (Chapter 19)
Wang Ying
Shandong University
School of Materials Science and Engineering
Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education)
250061 Jinan
P.R. China
Kotaro Sasaki*
Brookhaven National Laboratory
Chemistry Department
Upton, NY 11973
USA
[email protected] (Chapter 20)
Kurian A. Kuttiyiel
Brookhaven National Laboratory
Chemistry Department
Upton, NY 11973
USA
Jia X. Wang
Brookhaven National Laboratory
Chemistry Department
Upton, NY 11973
USA
Miomir B. Vukmirovic
Brookhaven National Laboratory
Chemistry Department
Upton, NY 11973
USA
Radoslav R. Adzic
Brookhaven National Laboratory
Chemistry Department
Upton, NY 11973
USA
Preface
Fuel cells are relatively a new technology, opening new frontiers in revolutionary clean power generation. Electrocatalysts for oxygen/fuel reduction or hydrogen oxidation play an essential role in fuel cell operation. This book highlights the high cost and existing technical barriers that make it difficult for the commercialization of the fuel cell technology. The book covers the most recent advances in fuel cell technology highlighting the recent developments of novel low cost, high efficient nanostructured electrocatalysts to alleviate the current situation of heavily relying on the noble metal platinum. The book could serve as a valuable resource for a better understanding of the most current state of electrocatalysis research on low-temperature fuel cells.
The book starts with Chapter 1 on the principles of low-temperature fuel cells using an ionic membrane. A detailed description of thermodynamics, theoretical energy efficiency, and electrical characteristics of hydrogen/oxygen and direct alcohol fuel cells is provided. The chapter also provides two typical examples of low-temperature fuel cells under development and commercialization; that is, direct methanol fuel cell for portable electronics and hydrogen/air polymer electrolyte membrane fuel cell for electrical vehicle application. Chapter 2 gives an account of recent research and developments in the different low-temperature fuel cells that include acidic polymer electrolyte membrane fuel cell, membrane-based alkaline electrolyte fuel cell, direct borohydride fuel cell, and regenerative fuel cell. Chapter 3 provides an interesting account of the electrocatalytic reactions involved in low-temperature fuel cells. The chapter discusses detailed mechanisms of the most important electrochemical reactions involved in low-temperature fuel cells, namely, oxidation of hydrogen, reduction of oxygen, oxidation of carbon monoxide, oxidation of methanol, and ethanol. The next, Chapter 4, presents a comprehensive account of various direct hydrocarbon low-temperature fuel cells. Five different direct hydrocarbon fuel cells, namely, direct methanol, direct ethanol, direct ethylene glycol, direct formic acid, and direct glucose fuel cells, are described. An account of commercialization status of the direct hydrocarbon fuel cells is also provided. Chapter 5 concentrates on oscillatory electrooxidation of small organic molecules with emphasis on the general phenomenology, the use of in situ and online approaches, and the effect of temperature and oscillations on modified surfaces. The electrooxidation of small organic molecules such as formaldehyde, formic acid, methanol, ethanol, and so on is of relevance for the interconversion between chemical and electrical energies. Chapter 6 provides an interpretation of degradation mechanisms of membrane fuel cells. The chapter explains the relationship between the kinetics and the mechanism of degradation processes and parameters of the cathode active layer under different conditions of hydrogen/oxygen fuel cell tests. The support degradation is addressed in detail.
Chapters 7 to 15 focus on the latest developments in platinum and non-platinum catalysts for low-temperature fuel cells. Chapter 7 concentrates on electrocatalysts and hybrid electrocatalyst-support systems for polymer electrolyte fuel cells. The chapter examines the recent developments in platinum- and nonplatinum-based nanostructured electrocatalysts as well as different carbon and noncarbon materials used as supports. Hybrid electrocatalyst-support systems combining carbon and noncarbon supports along with the use of polymers and polyoxometalates have also been discussed. Chapter 8 summarizes the graphene-based nanostructured electrocatalysts for fuel cells, including graphene-based oxygen reduction catalysts and graphene-based methanol, ethanol, and formic acid oxidation catalysts. Among the different carbon materials, graphene exhibits several advantages as catalyst support, such as large surface area, high electrical conductivity, and high stability. Chapter 9 explains the current progress in nonnoble metal electrocatalysts for oxygen reduction for alkaline fuel cells. The chapter provides a detailed account of nonnoble metal electrocatalysts that includes carbon-supported metal–Nx matrix, transition metal oxides, transition metal chalcogenides, transition metal carbides/nitrides/oxynitrides, and perovskites, and that is followed by an account of carbon-based metal-free electrocatalysts. Chapter 10 emphasizes the importance of anode electrocatalysts for direct borohydride and ammonia borane fuel cells. The chapter presents the basic concepts and mechanisms of these fuel cells, strategies to isolate ideal anode catalysts, practical benchmarks to evaluate such anode electrocatalyst materials, and insight into the durability of anode materials. Chapter 11 presents recent advances in nanostructured electrocatalysts for low-temperature direct alcohol fuel cells. The next, Chapter 12, presents electrocatalysis of facet-controlled noble metal nanomaterials for low-temperature fuel cells. The chapter starts with an account of the synthesis approaches for various nanostructures followed by the applications of these nanomaterials in oxygen reduction and fuel oxidation, and illustrates structure–activity relationships. Chapter 13 explains heteroatom-doped nanostructured carbon materials as oxygen reduction electrocatalysts for low-temperature fuel cells. Single, dual, and multiheteroatom-doped carbon-based materials are described. Transition metal-oxide, oxynitride, and nitride oxygen reduction electrocatalysts for acidic polymer electrolyte fuel cells are reviewed in Chapter 14. Chapter 15 describes novel spectroscopy and microscopy characterization of fuel cell catalysts.
Chapters 16 to 20 focus on catalyst design strategies. Chapter 16 explains in detail the rational design of efficient and cost-effective electrocatalysts for the oxygen reduction reaction. The rational design approach combines and applies the existing pieces of knowledge on composition, morphology, electronic structure, energetics, and so on in order to propose compositions and structures of novel electrocatalysts that directly tackle specific goals. The chapter encompasses a description of fundamentals of oxygen reduction reaction followed by an account of design factors affecting electrochemical and thermodynamic stability, and catalytic activity with special reference to core–shell structures and doped graphene. The next, Chapter 17, reviews novel strategies used in the development of advanced highly efficient single and dual-layer gas diffusion layers for polymer electrolyte membrane fuel cells. The chapter provides a detailed account of the structure of single and dual layer gas diffusion layers and recently developed macroporous substrate materials. Water managements using hydrophilic and hydrophobic additives are addressed. Chapter 18 gives a thorough description of design and fabrication of porous metallic electrocatalysts. Because of their high surface area and tunable porosity, nanoporous metallic materials are expected to provide large number of active sites and aid diffusion during the entire catalytic process. The chapter also explains advanced radiolysis process for synthesis of various core–shell mesoporous nanostructures. Chapter 19 focuses on design and fabrication of dealloying-driven nanoporous metallic electrocatalysts. Besides pure metals, nanoporous binary, ternary, and multicomponent alloys and nanocomposites are also addressed. Chapter 20 provides an interesting account of the synthesis, structure, and performance of the highly active and stable platinum monolayer electrocatalysts for oxygen reduction reaction. Platinum monolayer electrocatalysts offer a drastically reduced platinum content while providing potentials for enhancing their catalytic activity and stability.
We hope that the book will be a handy reference tool for researchers working with low-temperature fuel cells.
T. Maiyalagan Viswanathan S. Saji
1Principle of Low-temperature Fuel Cells Using an Ionic Membrane
Claude Lamy1,2
1Université de Montpellier, Institut Européen des Membranes, UMR CNRS no 5635, 2 Place Eugène Bataillon, CC 047, 34095 Montpellier Cedex, France
2Université de Nantes, Groupe de Recherches HySPàC, CNRS GDR 3652, 2 rue de la Houssinière, 44322 Nantes Cedex 3, France
1.1 Introduction
A technology-oriented civilization needs more and more energy, particularly the emerging and developing countries. Fossil resources, such as coal, natural gas, and hydrocarbons, are the main primary sources of energy, but they are limited in size and volume and may be exhausted in coming few decades. Moreover, they are the main contributors to carbon dioxide (CO2) emission that is the principal component of the greenhouse effect. An alternative approach is to use hydrogen (H2) either to feed fuel cells in power plants, electric vehicles, and electrical devices or to store the intermittent energy (solar, photovoltaic, wind energy, etc.). This approach will strongly limit the production of greenhouse gases (GHGs), depending on the primary sources used for H2 production since it is not a primary source. Among the renewable energy sources, such as hydroelectric power, wind, solar, and tidal power, the production of H2 by water (H2O) electrolysis is the most efficient process, leading to high-purity H2, which is suitable to feed a low-temperature fuel cell (LTFC), such as a proton exchange membrane fuel cell (PEMFC) or an alkaline fuel cell (AFC) [1–5].
In this context, many investigations were carried out on the development of fuel cells fed either with pure H2 [3–5] or with other fuels, for example, liquid fuels such as methanol (CH3OH) [6,7] or ethanol (C2H5OH) [5,8]. In particular H2/O2 (air) fuel cells, such as PEMFCs, working at relatively low temperatures (ranging from ambient to 70–80 °C), are becoming a mature technology for powering electrical vehicles with an autonomy range approaching 600 km without H2 refueling or for stationary power plants with relatively good electrical efficiencies (40–55%) depending on the applications and working conditions.
On the other hand, the direct alcohol fuel cell (DAFC), fed with CH3OH [7] or C2H5OH [8], directly converts the chemical energy of alcohol combustion with O2 into electrical energy. Such devices are particularly suitable for portable electronics, either to recharge their lithium battery or to power them directly. These fuel cells can work either with an acidic electrolyte, such as a proton exchange membrane (PEM), or with a solid alkaline electrolyte, for example, an anion exchange membrane (AEM) in a solid alkaline membrane fuel cell (SAMFC) of similar structure to that of a PEMFC.
In this chapter, we will present the working principle of LTFCs based on the PEM technology, either fed with H2 (pure H2 or reformate gases) or with a low-weight alcohol (CH3OH or C2H5OH). Then, we will discuss the electrical energy efficiency either under equilibrium conditions (j = 0) or under working conditions at a current density (j), the variation of which with the electrode potential (E), that is, the fuel cell characteristics E(j), will be established from a theoretical analysis of the reaction kinetics. Finally, two typical examples of LTFCs under development and commercialization will be given, the first one concerning the direct methanol fuel cell (DMFC) for portable electronics and the second one the H2/air PEMFC for the electrical vehicle.
1.2 Thermodynamic Data and Theoretical Energy Efficiency under Equilibrium (j = 0)
An elementary fuel cell directly converts the chemical energy of combustion with O2 of a given fuel (H2, natural gas, hydrocarbons, kerosene, alcohols, etc.) into electricity (i.e., the Gibbs energy change, −ΔGr) [6,9–11]. Electrons liberated at the anode (negative pole of the cell) by the electrooxidation of the fuel pass through the external circuit and produce an electrical energy, We = nFEcell, equal to −ΔGr, where Ecell is the cell voltage, n the number of electrons involved in the overall electrochemical reaction, and F = 96 485 C the Faraday constant (i.e., the electric charge of one electron mole), and reach the cathode (positive pole), where they reduce O2 (either pure or from air). Inside the fuel cell, the electrical current is transported by migration and diffusion of the electrolyte ions (H+, OH−, O2−, and ).
1.2.1 Hydrogen/oxygen Fuel Cell
The electrochemical reactions involved in the elementary processes of a H2/O2 fuel cell under acidic environment, for example, in a PEMFC (Figure 1.1) are the electrooxidation of H2 at the anode:
and the electroreduction of O2 at the cathode:
where is the electrode potential versus the standard hydrogen electrode (SHE) as reference, and is the Gibbs energy change involved in the electrochemical reaction. since the reactions involved are spontaneous for producing energy.
Figure 1.1 Schematic representation of a PEMFC elementary cell showing a PEM on which are pressed the catalytic layers both for the H2 anode and for the O2 cathode.
Similarly, in a fuel cell working in alkaline medium (e.g., an AFC or a SAMFC), the following electrochemical reactions do occur:
In the fuel cell, the electrical balance corresponds to the complete combustion of the fuel in the presence of O2 as follows:
where the thermodynamic data associated with this reaction, under standard conditions (T = 25 °C, p = 1 bar, and liquid H2O), have the opposite sign to those of H2O decomposition:
However, the thermodynamic data to consider (ΔH, ΔG) are those at the working temperature of the device, for example, between 280 and 350 K for the PEMFC and 280–400 K for the AFC (see Table 1.1, where the negative values of the thermodynamic data concern the formation of H2O, which is a spontaneous process).
Table 1.1 Thermodynamic data for the formation of H2O under a pressure of 1 bar as a function of absolute temperature (T = 298–400 K).
H
2
O state
T
(K)
Δ
S
(J mol
−1
K
−1
)
Δ
H
(kJ mol
−1
)
Δ
G
(kJ mol
−1
)
E
eq
(V)
Liquid
298.15
−163.3
−285.83
−237.17
1.229
0.829
Gaseous
298.15
−44.42
−241.81
−228.57
1.184
0.945
Gaseous
300.00
−44.48
−241.83
−228.49
1.184
0.945
Gaseous
310.00
−44.81
−241.93
−228.04
1.182
0.943
Gaseous
320.00
−45.13
−242.03
−227.59
1.179
0.940
Gaseous
330.00
−45.44
−242.13
−227.14
1.177
0.938
Gaseous
340.00
−45.74
−242.23
−226.68
1.175
0.936
Gaseous
350.00
−46.03
−242.33
−226.23
1.172
0.934
Gaseous
360.00
−46.31
−242.44
−225.76
1.170
0.931
Gaseous
370.00
−46.59
−242.54
−225.30
1.168
0.929
Gaseous
380.00
−46.85
−242.64
−224.83
1.165
0.927
Gaseous
390.00
−47.11
−242.74
−224.36
1.163
0.924
Gaseous
400.00
−47.37
−242.84
−223.89
1.160
0.922
The equilibrium cell voltage (Eeq) can thus be evaluated from the Nernst potential at each electrode:
with E0 = −ΔG0/2F the standard cell voltage, that is, at 25 °C, and pH2, pO2, and pH2O the partial pressures of H2, O2, and H2O, respectively. Therefore, by increasing the pressure of reactants (H2 and O2) and decreasing the pressure of the product (H2O), one can increase the cell voltage.
The variation of Eeq with T is contained mainly in the entropic term, that is, ΔS0 = nF (dE0/dT), which is the temperature coefficient of the fuel cell. Thus, assuming that ΔH and ΔS are nearly independent of temperature (see Table 1.1), one may calculate Eeq as follows:
for H2O in the liquid state at 25 °C (ΔH0 = −285.8 kJ mol−1 and ΔS0 = −163.3 J mol−1 K−1).
For H2O in the gaseous state at 25 °C (ΔH = −241.8 kJ mol−1 and ΔS = −44.42 J mol−1 K−1), one obtains the following:
In summary, Eeq may be expressed as a function of temperature and pressure (liquid state) by
or
In the gaseous state (e.g., at T = 400 K with ΔH = −242.8 kJ mol−1 and ΔS = −47.37 J mol−1 K−1), Eeq can be calculated by the following expressions:
or
A fuel cell working under reversible thermodynamic conditions (i.e., at equilibrium with j = 0) does not follow Carnot's theorem, which controls the energy efficiency of an internal combustion engine (ICE), so the theoretical energy efficiency of an elementary cell, , defined as the ratio of the electrical energy produced (We = nFEcell = −ΔGr) to the chemical energy of combustion (−ΔH), that is,
which can be very high (if TǀΔSǀ ≪ ǀΔHǀ).
In the case of a H2/O2 fuel cell working at 25 °C, the energy efficiency of an elementary cell will be , if ΔH is taken with H2O in the liquid state (standard conditions), that is, ΔH is the high heating value (ΔHHHV). But the heat of H2O condensation ΔQcond = ΔHHHV − ΔHLHV = 285.8 − 241.8 = 44 kJ mol−1 (where ΔHLHV = low heating value = 241.8 kJ mol−1 – see Table 1.1) is not useful for producing electrical energy, so a more realistic energy efficiency will be using the thermodynamic data of H2O formation under the gaseous state at 25 °C (Table 1.1). On the other hand, using the Gibbs energy change , given in Table 1.1, allows us to evaluate the specific energy Ws of H2 (expressed in kWh kg−1) as follows:
with M = 0.002 kg the molecular mass of H2. This gives
which is a very high value when not taking into account the weight of the H2 tank.
1.2.2 Direct Alcohol Fuel Cell
The DAFC directly converts the Gibbs energy of combustion of an alcohol into electricity, without a fuel processor. This greatly simplifies the system, reducing its volume and cost [12,13]. Important developments of DAFCs are due to the use of a PEM as electrolyte, instead of a liquid acid electrolyte, as previously done.
The electrical energy We = nFEcell = −ΔGr is related to the Gibbs energy change, ΔGr, of the oxidation reaction of an alcohol with O2. The overall combustion reaction of a monoalcohol CxHyO leading to H2O and CO2, that is,
involves the participation of H2O or of its adsorbed residue (OHads) provided by the cathodic reaction (electroreduction of dioxygen).
The electrochemical oxidation of a monoalcohol in acid medium to reject the CO2 produced can thus be written as follows:
with n = 4x + y − 2. Such an anodic reaction is very complicated from a kinetics point of view since it involves multielectron transfers and the presence of different adsorbed intermediates and several reaction products and by-products (see Section 3.3.4 in Chapter 3). However, from the thermodynamic data it is easy to calculate the standard equilibrium potential, , the theoretical efficiency and the energy density under standard conditions.
According to reaction 1.11, the standard Gibbs energy change, allowing to calculate the standard anode potential , can be evaluated from the standard energy of the formation of reactant (i):
In the cathodic compartment, the electroreduction of O2 does occur as follows:
with , leading to a standard cathodic potential :
The standard Gibbs energy change, , of the overall reaction 1.10 can be evaluated as follows:
leading to under standard conditions:
Then, it is possible to evaluate the specific energy Ws in kWh kg−1, using equation 1.9 where M is the molecular mass of the alcohol, and knowing the enthalpy of formation from the thermodynamic data, one may calculate
and the reversible energy efficiency under standard conditions .
For example, for CH3OH and C2H5OH, the electrochemical oxidation reactions and the standard anode potentials are, respectively, as follows:
This corresponds to the overall combustion reaction of these alcohols in O2:
with the thermodynamic data under standard conditions (see Table 1.2). The corresponding are the following:
Table 1.2 Thermodynamic data associated with the electrochemical oxidation of some alcohols under standard conditions (25 °C, 1 bar, and liquid phase).
Alcohol
(kJ mol
−1
)
(V) versus SHE
(kJ mol
−1
)
(V)
W
s
(kWh kg
−1
)
(kJ mol
−1
)
CH
3
OH
−9.3
0.016
−702
1.213
6.09
−726
0.967
C
2
H
5
OH
−97.3
0.084
−1326
1.145
8.00
−1367
0.969
C
3
H
7
OH
−171
0.098
−1963
1.131
9.09
−2027
0.968
1-C
4
H
9
OH
−409
0.177
−2436
1.052
9.14
−2676
0.910
CH
2
OH–CH
2
OH
−25.5
0.026
−1160
1.203
5.20
−1189
0.976
CH
2
OH–CHOH–CH
2
OH
1
−0.001
−1661
1.230
5.02
−1650
1.01
For higher alcohols, such as n-propanol, for example, the following calculations can be made:
and
with
under standard conditions is thus
and the specific energy is
The enthalpy change of reaction 1.23 is
so the reversible energy efficiency under standard condition is
For all the alcohols listed in Table 1.2, varies from 1.23 to 1.05 V, which is very similar to that of a H2/O2 fuel cell (). The energy density varies from 0.5 to 1 of that of gasoline (which is around 10–11 kWh kg−1); therefore, these compounds are good alternative fuels to hydrocarbons. Furthermore, the reversible energy efficiency is close to 1, while that of the H2/O2 fuel cell is 0.83 at 25 °C (standard conditions).
1.3 Electrocatalysis and the Rate of Electrochemical Reactions
However, under working conditions, the practical electric efficiency of a fuel cell depends on the current density j that is delivered by the cell and is lower than that of the equilibrium reversible efficiency (at j = 0). This is due to the irreversibility of the electrochemical reactions involved at the electrodes, leading to overpotentials ηa at the anode, ηc at the cathode, so the working Ecell becomes (taking into account the ohmic losses Rej coming from the cell resistance Re)
where the overpotentials ηi are defined as the deviation of the working electrode potential Ei(j) from the equilibrium potential [14–16]; that is, ηi = Ei(j) − .
For the H2 electrode, ηa is very small and can be approximated by a linear relationship with j, that is, ηa = Rtj, where Rt is the charge transfer resistance (see Section 1.3.1). But for the alcohol oxidation, ηa is at least 0.3–0.4 V for a reasonable j value (100 mA cm−2), so Ecell, including an overpotential ηc = −0.3 to −0.4 V for the cathodic reaction, will be on the order of 0.4–0.6 V, and the voltage efficiency will be = (0.4/1.2 = 0.33) to (0.6/1.2 = 0.50), under operating conditions. Such a drawback of the direct alcohol fuel cell can be removed only by improving the kinetics of the electrooxidation of the fuel. This needs to have a relative good knowledge of the reaction mechanisms, particularly of the rate determining step, and to search for electrode materials (Pt-X binary and Pt-X-Y ternary electrocatalysts) with improved catalytic properties (see Chapter 3, Section 3.3.4).
From Eq. 1.24, it follows that the increase in the practical fuel cell efficiency ɛcell can be achieved by increasing the voltage efficiency and the Faradaic efficiency ɛF = nexp/nth, the reversible efficiency, , being fixed by the thermodynamic data under the working conditions (temperature and pressure) (see Eq. 1.38.
For a given electrochemical system, the increase in voltage efficiency is directly related to the decrease in overpotentials of the oxygen reduction reaction (ORR), |ηc|, and alcohol oxidation reaction, ηa, which needs to enhance the activity of the catalysts at low potentials and low temperatures, whereas the increase in Faradaic efficiency is related to the ability of the catalyst to oxidize completely, or not, the fuel into CO2, that is, it is related to the selectivity of the catalyst. Indeed, in the case of C2H5OH, for example, acetaldehyde and acetic acid are formed at the anode [17], which corresponds to a number of electrons involved, 2 and 4, respectively, against 12 for the complete oxidation of C2H5OH to CO2. The enhancement of both these efficiencies is a challenge in electrocatalysis.
In the following section, we will evaluate the different overvoltages involved in an elementary fuel cell and establish the electrical characteristics Ecell(j) of the cell.
1.3.1 Establishment of the Butler–Volmer Law (Charge Transfer Overpotential)
For a given electrochemical reaction A + n e− ↔ B, which involves the transfer of n electrons at the electrode–electrolyte interface, the equilibrium potential (at j = 0), called the electrode potential, is given by the Nernst law as follows:
where is the standard electrode potential versus SHE (whose potential is zero at 25 °C by definition), and ai the activity of reactant (i). As soon as the electrode potential takes a value EA/B different from the equilibrium potential, , an electrical current of intensity I passes through the interface, whose magnitude depends on the deviation from the equilibrium potential. η, which is called the overpotential, is positive for an oxidation reaction (anodic reaction B → A + n e−) and negative for a reduction reaction (cathodic reaction A + n e− → B). The current intensity I is proportional to the rate of reaction (r), that is, I = nFr. For a heterogeneous reaction, r is proportional to the surface area S of the interface, so the kinetics of electrochemical reactions is better defined by the intrinsic rate ri = r/S and the current density j = I/S = nFri.
The electrical characteristics j(E) can then be obtained by introducing the exponential behavior of the rate constant (Arrhenius law) with the electrochemical activation energy, , which comprises two terms: the first one () is the chemical activation energy and the second one (αnFE) is the electrical component of the activation energy. The latter is a fraction α (0 ≤ α ≤ 1) of the total electric energy, nFE, coming from the applied electrode potential E, where α is called the charge transfer coefficient. The chemical activation energy can be decreased by a factor K coming from the presence of a catalytic material in the electrode structure, so electrocatalysis can be defined as the activation of electrochemical reactions both by the electrode potential and by the electrode material (Figure 1.2).
Figure 1.2 Activation barrier for an electrochemical reaction. K is the decrease in activation energy due to the electrode catalyst and αnFE is that due to the electrode potential E.
In the theory of absolute reaction rate, one obtains for a first-order electrochemical reaction, the rate of which is proportional to the concentration ci of reactant (i) [18],
where is the concentration of reactant (i) at the electrode surface and α is the charge transfer coefficient (0 < α < 1), that is, the fraction of the electrical energy that activates the reduction reaction (A → B), and (1 − α) nFE activating the oxidation reaction (B → A). Thus, I = nF(ra − rc) so that j = I/S, that is, the current intensity I divided by the electrode surface area S, is given by
where the indices “a” or “c” stands for the anodic or cathodic reaction, respectively, and ki are the corresponding rate constant.
*At equilibrium j = 0 and ra = rc, so that ja = −jc = j0, E = Eeq, and , where is the bulk concentration of reactant (i). This gives
leading to
j0 is called the exchange current density and the standard rate constant. Then,
where the activity ai of reactant (i) has been replaced by its concentration ci, Keq is the equilibrium constant of reaction A + n e− ↔ B and is the standard electrode potential, with the Gibbs energy of reaction.
This corresponds to the Nernst law.
*Out of equilibrium j = ja + jc ≠ 0 and dividing j by j0 one obtains
or
when assuming no mass transfer limitation, that is, .
This is the Butler–Volmer law with η = E − Eeq the overpotential and j0 the exchange current density.
The expression of the Butler–Volmer law can be simplified in some limiting cases:
For |
η
| ≪
RT
/
nF
(≈ 25.7/
n
mV at 25 °C) then
j
(
η
) =
j
0
(
nF
/
RT
)
η
=
η/R
t
or
This is the Ohm's law.
For
η
≫
RT
/
nF
then
j
(
η
) =
j
0
exp{(1 −
α
) (
nF
/
RT
)
η
} or
η
=
RT
/{(1 −
α
)
nF
)} Ln(
j
/
j
0
) (with
j
> 0),
and for η ≪ −RT/nF, then j(η) = −j0 exp{−α(
