Rechargeable Ion Batteries E-Book

• Herausgeber: Wiley-VCH GmbH
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 698

Veröffentlichungsjahr: 2022

Beschreibung

Rechargeable Ion Batteries

Highly informative and comprehensive resource providing knowledge on underlying concepts, materials, ongoing developments and the many applications of ion-based batteries

Rechargeable Ion Batteries explores the concepts and the design of rechargeable ion batteries, including their materials chemistries, applications, stability, and novel developments. Focus is given on state-of-the-art Li-based batteries used for portable electronics and electric vehicles, while other emerging ion-battery technologies are also introduced. The text addresses innovative approaches by reviewing nanostructured anodes and cathodes that pave new ways for enhancing the electrochemical performance.

The first three chapters are dedicated to the general concepts of electrochemical cells, enabling readers to understand all necessary concepts for batteries from a single book. The following chapter covers the exciting applications of lithium-ion and sodium-ion batteries, while the subsequent chapters on Li-battery components include new types of anodes, cathodes, and electrolytes that have been developed recently, complemented by an overview of designing mechanically stable ion-battery systems. The last three chapters summarize recent progress in lithium-sulfur, sodium-ion, magnesium-ion and zinc and emerging ion-battery technologies.

In Rechargeable Ion Batteries, readers can expect to find specific information on:

• Electrochemical cells, primary batteries, secondary batteries, recycling of batteries, applications of lithium and sodium batteries
• Next-generation cathodes, anodes and electrolytes for secondary lithium-ion batteries, which allow for improved performance and safety
• Multiphysics modeling for predicting design criteria for next generation ion-insertion electrodes
• Developments in lithium-sulfur batteries, sodium-ion batteries, and future ion-battery technologies

Rechargeable Ion Batteries provides informative and comprehensive coverage of the subject to interested researchers, academics, and professionals in various fields, including materials science, electrochemistry, physical chemistry, mechanics, engineering, recycling and industry including the battery manufacturers and supply chain ancillaries, automotive, aerospace, and marine sectors, energy storage installers and environmental stakeholders. Readers can easily acquire a base of knowledge on the subject while understanding future developments in the field.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

Preface

1 Introduction to Electrochemical Cells

1.1 What are Batteries?

1.2 Quantities Characterizing Batteries

1.3 Primary and Secondary Batteries

1.4 Conclusions

References

2 Primary Batteries

2.1 Introduction

2.2 The Early Batteries

2.3 The Zinc/Carbon Cell

2.4 Alkaline Batteries

2.5 Button Batteries

2.6 Li Primary Batteries

2.7 Oxyride Batteries

2.8 Damage in Primary Batteries

2.9 Conclusions

References

3 A Review of Materials and Chemistry for Secondary Batteries

3.1 The Lead–Acid Battery (LAB)

3.2 The Nickel–Cadmium Battery

3.3 Nickel–Metal Hydride (Ni–MH) Batteries

3.4 Secondary Alkaline Batteries

3.5 Secondary Lithium Batteries

3.6 Battery Market

3.7 Recycling and Safety Issues

3.8 Conclusions

References

4 Applications of Lithium Batteries

4.1 Portable Electronic Devices

4.2 Hybrid and Electric Vehicles

4.3 Aerospace Applications

4.4 Medical Applications

4.5 Grid Energy Storage

4.6 Conclusions

Acknowledgments

References

5 Cathode Materials for Lithium‐Ion Batteries

5.1 Layered Materials

5.2 Spinel Materials

5.3 Polyanion (Phosphate, Silicates) Framework Cathode Materials

5.4 Conclusions

References

6 Next‐Generation Anodes for Secondary Li‐Ion Batteries

6.1 Introduction

6.2 Mechanical Instabilities During Electrochemical Cycling

6.3 Nanostructured Anodes

6.4 Sn‐Based Materials

6.5 Si‐Based Materials

6.6 Other Anode Materials

6.7 Solid‐State Batteries

6.8 Conclusions

Acknowledgments

References

7 Electrolytes for Lithium Batteries: The Quest for Improving Lithium Battery Performance and Safety

7.1 Introduction

7.2 Nonaqueous Electrolytes

7.3 Gel Polymer Electrolytes

7.4 Solid‐State Batteries

7.5 Solid‐Polymer Electrolytes

7.6 Solid Electrolytes

7.7 Solid‐State Battery Companies

7.8 Conclusions

Acknowledgment

References

8 Developments in Lithium–Sulfur Batteries

8.1 Introduction to Lithium–Sulfur Batteries

8.2 Electrochemical Principles

8.3 Sulfur Utilization and Cycle Life

8.4 Potential Solutions to Hurdles

8.5 Carbon Materials

8.6 Metal Oxides

8.7 Polymers

8.8 Further Developments and Innovative Approaches

8.9 Key Parameters for Application Prospects

8.10 Conclusions

References

9 Sodium‐Ion Batteries

9.1 Introduction

9.2 Cathode Materials for Na‐Ion Batteries

9.3 Anode Materials for Na‐Ion Batteries

9.4 Electrolytes for Na‐Ion Batteries

9.5 Industrialization of SIBs

9.6 Conclusions

9.6 Acknowledgments

References

10 Modeling Ion Insertion for Predicting Next‐Generation Electrodes

10.1 Introduction

10.2 The Role of Mechanics in Batteries

10.3 Accounting for Li‐Ion Diffusion

10.4 Full Electrode Modeling

10.5 MD Simulations for Li‐Ion Batteries

10.6 Conclusions

Acknowledgment

References

11 Future Ion‐Battery Technologies

11.1 Magnesium‐Based Batteries

11.2 Zinc‐Based Batteries

11.3 Dual‐Ion Hybrid Batteries

11.4 Conclusions

References

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Dimensions of commercially available battery sizes [1].

Table 1.2 Standard electrode potentials in aqueous electrolyte at 298 K (wr...

Table 1.3 Battery characteristics.

Table 1.4 History of electrochemical cell development tabulated with years ...

Chapter 2

Table 2.1 Primary battery chemistries used today [1].

Table 2.2 Metal–air cells.

Chapter 3

Table 3.1 Some typical properties of secondary batteries.

Table 3.2 Global battery market for 2019.

Table 3.3 Comparison of properties of different cathode chemistries.

Table 3.4 Global battery market data for 2010 – 2020.

Table 3.5 Apparent recycling input ratios (RIR) for lead.

Table 3.6 Typical composition of lead–acid battery.

Table 3.7 Typical composition of lead–acid battery paste.

Chapter 4

Table 4.1 History sales and forecast of some electronics market.

Table 4.2 Different generations of Panasonic 18650 cells, which have been o...

Table 4.3 Market sales of different EVs from 2015 and forecast of this mark...

Table 4.4 Various forms of Li‐ion cells and their features.

Table 4.5 Several investment projects for large‐scale chemical energy‐stora...

Chapter 7

Table 7.1 General classification of the electrolytes types for secondary li...

Table 7.2 Solvent most commonly used in today's lithium‐ion batteries.

Table 7.3 Salts most commonly used in lithium‐ion batteries with the produc...

Table 7.4a Most common type of additives for Li‐ion cells using graphite‐ba...

Table 7.4b Most common additives used in nonaqueous electrolytes with diffe...

Chapter 8

Table 8.1 Cost breakdown of commercial Li batteries.

Table 8.2 Comparison of different cathode materials.

Chapter 9

Table 9.1 The world's major sodium‐ion battery manufacturers.

Chapter 10

Table 10.1 Parameters for simulating the stress evolution during lithiation...

Table 10.2 Young's modulus of some cathode and anode materials in both lith...

Table 10.3 Material properties of LiFePO

4

.

Table 10.4 Simulation parameters for Si anodes.

Table 10.5 Simulation parameters for PBA cathodes.

List of Illustrations

Chapter 1

Figure 1.1 (a) The schematic diagram of a simple galvanic cell. (b) Terminal...

Figure 1.2 (a) An illustration of batteries connected in parallel to obtain ...

Figure 1.3 (a) Single‐flat‐cell configuration; (b) composite‐flat‐cell confi...

Figure 1.4 Illustration of double layer.

Figure 1.5 A typical Tafel plot.

Figure 1.6 Tafel plot for a copper electrode.

Figure 1.7 Diffusion limited current for the cathodic reaction.

Figure 1.8 Theoretical and actual voltages of various battery systems.

Figure 1.9 Change of voltage with time behavior in different cells..

Figure 1.10 Ideal Ragone plot.

Figure 1.11 Effects of temperature on battery capacity.

Chapter 2

Figure 2.1 Galvani's experiment on frog legs.

Figure 2.2 An illustration of Volta's cell, called a “Voltaic Pile”.

Figure 2.3 Illustration of a crowfoot cell.

Figure 2.4 (a) Original Leclanché cell.(b) The commercial design structu...

Figure 2.5 Discharge curve for a Zn/C cell at 500 mA.

Figure 2.6 (a) The commercial design structure of an alkaline cell (b) Micro...

Figure 2.7 Discharge curve at 500 mA for an alkaline cell.

Figure 2.8 Configuration of a button battery.

Figure 2.9 Discharge curve at 6.5 kΩ for a HgO cell.

Figure 2.10 Discharge curve at 1 kΩ for a Zn/Ag cell.

Figure 2.11 Discharge curve at 620 Ω for a Zn/air cell.

Figure 2.12 Schematic depiction of a standard aluminum–air battery.

Figure 2.13 Discharge curve at 36 kΩ for a lithium/thionyl cell.

Figure 2.14 The schematic presentation of cathode and anode characteristics ...

Figure 2.15 Dendrite formation on Zn anode.

Figure 2.16 SEM and TEM images of InSb dendrite; the InSb anode material was...

Chapter 3

Figure 3.1 Growth of e‐bikes (note the number of e‐bikes produced was less t...

Figure 3.2 A cut‐away version of a lead–acid battery; over 80% lead is consu...

Figure 3.3 A corroded conventional lead grid on the positive plate.

Figure 3.4 SEM image of Microcell™ foam electrode by Firefly energy.

Figure 3.5 The comparison of Microcell™ foam electrode (right) and conventio...

Figure 3.6 Microcell™ foams do not experience mechanical damage during elect...

Figure 3.7 Oasis battery from Firefly energy.

Figure 3.8 Micrograph of a sintered metallic plate.

Figure 3.9 Schematic representation of discharge in a Li‐ion battery.

Figure 3.10 Working principle of Li movement between the two electrodes.

Figure 3.11 Energy density evolution of Li‐ion batteries.

Figure 3.12 Evolution of volume and cost for Li‐ion batteries.

Figure 3.13 Curve obtained from electrochemical cycling.

Figure 3.14 Comparison of energy density for various battery chemistries.

Figure 3.15 Overview of the current lead–acid battery recycling process flow...

Figure 3.16 SEM image of the lead citrate product from PbO.

Figure 3.17 SEM image of nano‐PbO from combustion–calcination.

Figure 3.18 TEM image of nanocrystalline PbO.

Figure 3.19 Schematic flowsheet for recycling lead battery waste.

Chapter 4

Figure 4.1 (a) 400 mAh Li‐ion battery by BYD Company Ltd. In 2015. (b) 2500 ...

Figure 4.2 Global PEV sales prediction.

Figure 4.3 Hybrid‐wing VTOL UAV;

Figure 4.4 Schematic diagram of electric propulsion configurations;

Chapter 5

Figure 5.1 (a) Cell voltage as a function of 1−

x

in Li

1−

x

CoO

2

at the i...

Figure 5.2 Structure of R‐NaFeO

2

(R3m).

Figure 5.3 A map of relationship between discharge capacity, and thermal sta...

Figure 5.4 The SEM images of pristine NCM811 (a, b) and NCM811@SiO2 (c, d); ...

Figure 5.5 Electrochemical performance of pristine NCM811 and NCM811@SiO

2

Cy...

Figure 5.6 Rate performance (a); The charge–discharge curve of pristine NCM8...

Figure 5.7 SEM images after 100 cycles of (a, b) pristine NCM811 and (c, d) ...

Figure 5.8 Layered structures of (a) Li

2

MnO

3

, (b) LiMO

2

.

Figure 5.9 Compositional phase diagram showing the electrochemical reaction ...

Figure 5.10 Schemes of the proposed surface reaction mechanisms in the Li

1.2

Figure 5.11 The crystal structure of spinel LiMn

2

O

4

.

Figure 5.12 Crystal structure of LiMn

1.5

Ni

0.5

O

4

. The cation ordering in the ...

Figure 5.13 Typical electrochemical charge and discharge profiles of ordered...

Figure 5.14 (a) The crystal structure of LiFePO

4

viewed along with C‐axis....

Figure 5.15 (a) crystal structure of Li

2

MnSiO

4

.(b) The typical charge–di...

Figure 5.16

In situ

carbon coating process of preparing LiFePO

4

.

Chapter 6

Figure 6.1 Si thin films cycled in a VC‐free and VC‐containing electrolyte....

Figure 6.2 Experimental evidence taken from [11] on electrochemical cycling ...

Figure 6.3 (a) an optical micrograph of a Li alloy film after expansion and ...

Figure 6.4 Capacity retention of SnS/C nanocomposite thin film.

Figure 6.5 SnS/C nanocomposite film. The left high resolution transmission e...

Figure 6.6 TEM images, obtained by rotating the TEM holder stage 90°, indica...

Figure 6.7 (a) TEM and (b) field emission scanning electron microscopy (FESE...

Figure 6.8 (a) Capacity retention of SnS

2

nanoplates.(b) Li‐insertion in...

Figure 6.9 (a) Cell voltage vs. specific capacity profile, (b) specific capa...

Figure 6.10 (a) Sn nanoparticles.

Figure 6.11 The cyclability of Sn

2

Sb alloy powder and CM/Sn

2

Sb composite ele...

Figure 6.12 TEM image of Sn or SnO

2

islands on Vulcan C. The Sn or SnO

2

isla...

Figure 6.13 Capacity retention at various current densities for 8 wt% Sn C n...

Figure 6.14 (a) SEM image of Sn attached in artificial graphite before cycli...

Figure 6.15 (A) Voltage‐time curve for the first two cycles of Sn attached o...

Figure 6.16 (a) Scanning electron micrograph of the nanostructured SnO

2

elec...

Figure 6.17 Capacity vs. cycle number for the nanostructured and thin‐film c...

Figure 6.18 SEM images of SnO

2

produced by heat treatment of Sn–Ag alloys: (...

Figure 6.19 Superior capacity retention of SnO

2

nanorods over SnO

2

nanoparti...

Figure 6.20 Electrode failure mechanisms for silicon active material: (a) ma...

Figure 6.21 Phase diagram describing the phases that form during charge‐disc...

Figure 6.22 SEM images of Si‐films deposited on Ti. (a) Side view of the fil...

Figure 6.23 Morphologies of the 5‐μm thick Si thin film deposited on Cu subs...

Figure 6.24 SEM images of a 6‐μm Si film anode after 250 cycles (produced ca...

Figure 6.25 (a) Cyclic performance and (b) rate performance of the four samp...

Figure 6.26 (a) HRTEM micrograph of an amorphous 2 μm Si thin film deposited...

Figure 6.27 (a) SEM micrograph of Si thin film (2 μm thick) deposited on Cu ...

Figure 6.28 Cycle‐life performance of amorphous, 200 nm‐thick (a) Si, (b) Si

Figure 6.29 Cr‐doped Si, coated with carbon nanotube.

Figure 6.30 SEM, TEM, and SAED images of the c‐a core−shell NWs after cyclin...

Figure 6.31 Micron‐scale Si electrode. (a) Initial galvanostatic charge/disc...

Figure 6.32 SEM image capturing the fracture in micron‐scale Si (a) SEM imag...

Figure 6.33 Cyclic performance of the CNTs/Si composites cycled between 0.0 ...

Figure 6.34 (a) SEM image of Si nanoparticles attached on cellulose fibers; ...

Figure 6.35 (a, b) TEM images of Si/DPA nanocomposite (c) TGA of Si/DPA nano...

Figure 6.36 Initial voltage profile of (a) nano Si electrode, (b) Si/DPA nan...

Figure 6.37 Discharge capacity of Si anode with different binders.

X

‐axis de...

Figure 6.38 Capacity retention of Si–SiO

2

–C nanocomposite.

Figure 6.39 Si nanoparticle covered by a SiO layer.

Figure 6.40 Carbon coated Si; (a) SEM and (b) TEM images.

Figure 6.41 TEM image of a silicon–carbon core‐shell composite after 30 cycl...

Figure 6.42 TEM images and simulated structures of multilayer MXene. (a) TEM...

Figure 6.43 (a) Schematic illustration of replacement of the Ti‐OH bond on t...

Figure 6.44 (a) Sb nanoparticles adhered on the surface of cellulose fibers,...

Figure 6.45 Comparison between capacity retention in pure Sb nanoparticles a...

Figure 6.46 (a) Pure Al particles before cycling; (b) pure Al particles afte...

Figure 6.47 (a) Al particles covered with 10 wt% SnO nanoparticles before cy...

Figure 6.48 Capacity vs. cycle for various Al‐wt% SnO particles.

Figure 6.49 Micrographs showing Bi nanoparticles of 300 nm diameter (a) befo...

Figure 6.50 Cycling performance of coated Li

4

Ti

5

O

12

. Inset: The cycling perf...

Figure 6.51 Dendrites formed on Li metal in solid‐state batteries.

Chapter 7

Figure 7.1 Schematic representation of lithium dendrite formation.

Figure 7.2 SEM micrograph of a sample with 50 wt% of EC:DEC 2:3 LiN(CF

3

SO

2

)2...

Figure 7.3 Arrhenius plots of the conductivity for the gel electrolytes prep...

Figure 7.4 Schematic representation of PEO‐based polymer electrolyte morphol...

Figure 7.5 The Arrhenius plots of the conductivity for (PEO)

8

–LiClO

4

with 5 ...

Figure 7.6 Lithium diffusion on other nonaqueous electrolytes and single‐lit...

Figure 7.7 Representation of the effect of Li concentration on Sulfide elect...

Chapter 8

Figure 8.1 Even at a low% of theoretical energy usage, Li–S cells have a hig...

Figure 8.2 Current demonstrations of Li–S batteries have achieved over 400 W...

Figure 8.3 Electrochemical reduction of sulfur to various polysulfides in a ...

Figure 8.4 Representation of “Shuttle Mechanism.”

Figure 8.5 Electrochemical reduction mechanism of sulfur electrode as a func...

Figure 8.6 Typical discharge–charge profile for a Li–S cell, indicating the ...

Figure 8.7 Structural representation of a sulfur crown molecule.

Figure 8.8 Illustration of the charge (red)/discharge (black) process in a l...

Figure 8.9

Transmission electron microscopes

(

TEM

) images of (a) mesoporous ...

Figure 8.10 (a) Schematic illustration of confined S

2–4

molecules in t...

Figure 8.11 (a) Schematic illustration of the constrained electrochemical re...

Figure 8.12 (a, b) SEM images of S–FLG foam; (c) scheme of the fast 3D elect...

Figure 8.13 (a) Schematic illustration of the Li–S battery with a MWCNT sepa...

Figure 8.14 (a) Schematic illustration of the construction of the sulfur–TiO

Figure 8.15 (a) Schematic illustration of the sulfur (yellow) confined in CM...

Figure 8.16 Schematic illustration of the concept of the “polysulfide reserv...

Figure 8.17 (a) Scheme illustration of sulfur/hierarchical porous carbon com...

Figure 8.18 (a) Schematic illustration of the construction and charge/discha...

Figure 8.19 (a) Schematic illustration of a CMK‐3 mesoporous carbon‐embedded...

Figure 8.20 (a) Schematic illustration of a Li–S cell with a bifunctional mi...

Figure 8.21 (a) Schematic illustration of the hybrid anode designed to manip...

Figure 8.22 Schematic of the lithiation process in sulfur/CNT array composit...

Figure 8.23 SEM images of Al foam (a) which can directly support Fe catalyst...

Figure 8.24 Mass distribution of Li–S pouch and coin cell.

Figure 8.25 (a) Schematic showing the main issues leading to a low‐energy‐de...

Figure 8.26 (a) Projected volumetric energy density of various S‐cathodes as...

Figure 8.27 (a–c) Illustration of the reaction process of lithium polysulfid...

Figure 8.28 (a) Scheme of dilemma for Li metal anode in Li‐ion batteries....

Figure 8.29 (a, b) Schematic illustrations of the working principle of the c...

Chapter 9

Figure 9.1 The working principle and components of Na‐ion battery are simila...

Figure 9.2 The charge–discharge curves of LiCoO

2

/Li and NaCoO

2

/Na half‐cell....

Figure 9.3 The stacking types of (a) O3 and (b) P2 phases in Na

x

MO

2

.

Figure 9.4 (a) Initial charge/discharge curves of

a

‐NaFeO

2

cells with differ...

Figure 9.5 Initial charge and discharge curves of the Na/NaNi

0.5

Mn

0.5

O

2

cell...

Figure 9.6 Initial charge/discharge curves of P2‐NaCoO

2

cells.

Figure 9.7 Charge/discharge curves of P2‐Na

2/3

Ni

1/3

Mn

2/3

O

2

cell.

Figure 9.8 Crystal structure of NASICON‐typed Na

3

V

2

(PO

4

)

3

.

Figure 9.9 Voltage‐capacity profile for Na

3

V

2

(PO

4

)

3

.

Figure 9.10 Voltage‐capacity profile for Na

4

MnV(PO

4

)

3

[21], Na

3

MnTi(PO

4

)

3

[22]...

Figure 9.11 Structure of Prussian blue and its analogs: a new framework of e...

Figure 9.12 The charge/discharge profiles of MnHCF [26] and Na

2

MnMn(CN)

6

[27]...

Figure 9.13 (a–c) Low‐magnification SEM images of MnHCF materials after (a) ...

Figure 9.14 STEM images and element mapping for g‐(Ni

0.3

Mn

0.7

)HCF before cyc...

Figure 9.15 Comparison of performance between concentration gradient and hom...

Figure 9.16 SEM images and elemental mapping for g‐(Ni

0.1

Mn

0.9

)HCF after 100...

Figure 9.17 Charge–discharge curves of graphite in carbonate‐based (a) and d...

Figure 9.18 Charge–discharge curves of hard carbon.

Figure 9.19 Theoretical gravimetric capacity and volume change of alloying a...

Figure 9.20 Discharge curve for Sn anode and the phase composition of Na

x

Sn ...

Figure 9.21 (a) Size‐dependent morphological complexity for the pristine and...

Figure 9.22 SEM images of Sn thin film (a) before cycling and (b) after full...

Figure 9.23 SEM images of surface morphology of the thick Sn foil electrode....

Figure 9.24 Comparison of electrochemical window, thermal stability, and con...

Figure 9.25 Capacity retention for hard‐carbon electrodes with 1 mol dm

−3

...

Figure 9.26 Comparison of the discharge–charge curves of TiS

2

electrodes in ...

Figure 9.27 STEM images and the corresponding elements map for TiS

2

electrod...

Chapter 10

Figure 10.1 Failure mechanisms of silicon anodes in LIBs [1]. These mechanis...

Figure 10.2 Schematic illustrations of (a) constraining effects of neighbori...

Figure 10.3 Damage distribution along the radial distance from the active pa...

Figure 10.4 Schematic diagram of the stress components in a spherical partic...

Figure 10.5 Radial distribution of (a) concentration profiles, (b) normalize...

Figure 10.6 Radial distribution of (a) concentration profiles, (b) normalize...

Figure 10.7 Radial distribution of (a) concentration profiles, (b) normalize...

Figure 10.8 Radial distribution of (a) concentration profiles, (b) normalize...

Figure 10.9 Stress generation in a Si nanoparticle. (a) and (b) Radial distr...

Figure 10.10 Comparison of scanning electron microscopy (SEM) experimental o...

Figure 10.11 Damage profile of Si particles of diameter 0.95 μm after (a) fu...

Figure 10.12 Microscale Si electrode after 1 cycle (a) SEM image, (b) EDS ma...

Figure 10.13 (a) Schematic diagram of a PBA particle with cubic structure, w...

Figure 10.14 (a) Concentration distribution, (d) modulated von Mises stress ...

Figure 10.15 (a–c) Low‐magnification SEM images of MnHCF materials after (a)...

Figure 10.16 Fracture of porous electrode after electrochemical cycling. SEM...

Figure 10.17 Experimental observations of c‐SiNPs after lithiation, with dif...

Figure 10.18 (a) Solid and (b) hollow SiNPs before and after lithiation. Sou...

Figure 10.19 Lithiation protocol for different SiNPs. (a) a‐SiNPs and (b–d) ...

Figure 10.20 Energy minimization strategy used during lithiation of SiNPs. (...

Figure 10.21 Morphologies of (a) a‐SiNP and (b–d) c‐SiNPs with and without t...

Figure 10.22 Distribution of hoop stress for a‐SiNP with initial radius of 3...

Figure 10.23 Simulation results of solid a‐SiNPs with different diameters. (...

Figure 10.24 Simulation results of hollow a‐SiNPs with different

R

in

. (a, b)...

Figure 10.25 (a–c) Deformed shapes and hoop stress distribution in the whole...

Figure 10.26 Plastic flow in c‐SiNP. (a–d) Trajectories of selected atoms in...

Figure 10.27 Simulation results of lithiation in a solid a‐SiNP with

R

in

 = 3...

Figure 10.28 Von Mises stress near three dislocations in the c‐Si core durin...

Chapter 11

Figure 11.1 Reduction potential, specific capacity, and volumetric capacity ...

Figure 11.2 Steady‐state cyclic voltammograms of 0.25 M BEC and 0.4 M APC so...

Figure 11.3 Typical electrochemical behavior and the basic structure of the ...

Figure 11.4 Structure of the Chevrel phase Mg

2

Mo

6

S

8

after Mg insertion: (a) ...

Figure 11.5 The desolvation and intercalation mechanism of APC electrolyte a...

Figure 11.6 Schematics of the chemistry of the zinc‐ion battery. (b) Cyclic ...

Figure 11.7 (a)

Cyclic voltammetry

(

CV

) of the Zn and NVP in 1 M NaAC and Zn...

Figure 11.8 The charge–discharge curve of battery in electrolyte with differ...

Figure 11.9 (a) Cycling stability of battery with Na

+

/Zn

2+

hybrid el...

Guide

Cover Page

Table of Contents

Title Page

Copyright

Dedication

Preface

Begin Reading

Index

Wiley End User License Agreement

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Rechargeable Ion Batteries

Materials, Design, and Applications of Li‐Ion Cells and Beyond

Edited by Katerina E. Aifantis, R. Vasant Kumar, and Pu Hu

Editors

Prof. Katerina E. Aifantis

Department of Mechanical & Aerospace Engineering

University of Florida, Gainesville

1064 Center Drive

Florida

United States

Prof. R. Vasant Kumar

Materials Science + Metallurgy

University of Cambridge

27 Charles Babbage Road

CB3 0FS Cambridge

United Kingdom

Prof. Pu Hu

Wuhan Institute of Technology

School of Material Sciences & Engineering

No.206, Guanggu 1st road

430205 Wuhan

China

Cover: © Black_Kira/Shutterstock

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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The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.

© 2023 WILEY‐VCH GmbH, Boschstraße 12, 69469 Weinheim, Germany

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

Print ISBN: 978‐3‐527‐35018‐6

ePDF ISBN: 978‐3‐527‐83669‐7

ePub ISBN: 978‐3‐527‐83671‐0

oBook ISBN: 978‐3‐527‐83670‐3

Typesetting Straive, Chennai, India

Katerina Aifantis would like to dedicate this book to her parents, Maria & Elias for their neverending support, and Fr. Symeon Krayiopoulos, who was asking her when she would begin the second book ever since the first one got published.

R. Vasant Kumar would like to dedicate this book to Gill, Vijay, Kailo, and Anastasia.

Pu Hu would like to dedicate this book to his wife Ping and his daughter Tong.

Preface

The development of electrochemical energy storage systems is a fascinating field that bridges many disciplines, such as electrochemistry, nanotechnology, synthesis, engineering, materials science, mechanics and recycling. Our motivation in writing this book was to inspire students and young researchers from all these fields to lend their expertise to the battery community in reaching one of the main goals that seem to unite our society: build a future that will limit carbon emissions and allow us to retain the sustainability of our world. Battery developers will also find our book as a useful guide since we summarize the current state of the art for the electrodes and electrolytes of different electrochemical systems.

We began working on this book in 2013, as a second edition to High Energy Density Lithium Batteries, Materials, Engineering, Applications (Editors: Aifantis, Hackney, Kumar), which was published in 2010. However, as additional rechargeable battery systems have emerged, we decided to write a new book that covers not only lithium‐ion, but also other next‐generation systems such as lithium–sulfur, sodium‐ion, magnesium‐ion, and zinc‐ion. Apart from lithium–sulfur batteries, which are targeted for future vehicle applications, the other ion batteries (aside from Li-ion) are considered for grid storage applications.

To make our book accessible to a wide audience, we start with introductory chapters on the working principles and development of batteries, and as we progress, we go into greater depths on the open issues that must be addressed for the most promising rechargeable ion systems. To ensure continuity throughout the book we did not only act as editors, but each chapter except for Chapter 7 is co‐written by one of us, and we decided together on the layout of each chapter. The lead editor in particular supervised closely all chapters, ensuring the uniformity and consistency of an authored, rather than edited scientific book.

We are very close collaborators with friendly scientific and technological engagements among ourselves and with the authors, and hope that the enthusiasm and joy that we had in preparing our book is transmitted to the readers. In ending, we would like to specially thank our publisher Martin Preuss for his continuous advice and encouragement.

4 July 2022

Katerina E. Aifantis, R. Vasant Kumar, Pu Hu

1Introduction to Electrochemical Cells

R. Vasant Kumar1 and Thapanee Sarakonsri2

1University of Cambridge, Department of Materials Science and Metallurgy, 27 Charles Babbage Road, Cambridge, CB3 0FS, UK

2Chiang Mai University, Department of Chemistry, Faculty of Science, Chiang Mai, 50200, Thailand

1.1 What are Batteries?

The purpose of this chapter is to provide basic knowledge on batteries, which will allow for their general understanding. Therefore, after defining their components and structure, an overview of the quantities that characterize these storage devices will be given. Scientifically, batteries are referred to as electrochemical or galvanic cells, due to the fact that they store electrical energy in the form of chemical energy and because the electrochemical reactions that take place are also termed galvanic. Galvanic reactions are thermodynamically favorable (the free‐energy difference, ΔG, is negative) and occur spontaneously when two materials of different positive standard reduction potentials are connected by an electronic load (meaning that a voltage is derived). The material with the lower positive standard reduction potential undergoes oxidation providing electrons by the external circuit to the material with the higher positive standard reduction potential, which in turn undergoes a reduction reaction. These half‐reactions occur concurrently and allow for the conversion of chemical energy to electrical energy by means of electron transfer through an external circuit. It follows that the material with the lower positive standard reduction potential is called the negative electrode or anode on discharge (since it provides electrons), while the material with the higher positive standard reduction is called the positive electrode or cathode on discharge (since it accepts electrons). It follows that the discharge process occurs in the electrochemical cells upon operation of the devices they power.

In addition to the electrodes, the two other constituents that are required for such reactions to take place are the electrolyte phase/solution and the separator. The electrolyte is an ion‐conducting material, which can be in the form of an aqueous, molten salt, or solid solution, while the separator is a membrane that physically prevents direct contact between the two electrodes and allows ions but not electrons to pass through; it, therefore, ensures electronic insulation for charge neutralization in both the anode and cathode once the reaction is completed and prevents internal short‐circuiting of electrons. Internal short‐circuiting implies the movement of electrons from the anode to cathode through the electrolyte, which dissipates the chemical energy without providing electrical potential in the external circuit. When the electrolyte is solid, it simultaneously functions as a membrane (separator) and an ionic conductor. Two final parts required to complete a commercial galvanic cell are the terminals. They are necessary when applying the batteries to electrical appliances with specific holder designs to prevent a short circuit from the reverse installation of the battery, and they are shaped to match the receptacle facilities provided in the appliances. For example, in cylindrical batteries, the negative terminal is either designed to be flat, or to protrude out of the battery end, while the positive terminal extends as a pip at the opposite end. A simple galvanic cell is illustrated in Figure 1.1a, while Figure 1.1b shows terminal designs for cylindrical batteries.

To meet the voltage or current used in specific appliances, cylindrical galvanic cells are connected in series or parallel. Figure 1.2a,brepresents parallel and series connections; parallel connections allow for the current to be doubled, while series connections allow for the voltage to be doubled.

In addition to cylindrical battery cells, as those shown in Figures 1.1 and 1.2, flat battery configurations are also quite common. The biggest impetus for these configurations came from the rapid growth of portable radios since the flat cells use the space of the battery box more efficiently than cylindrical ones. The electrodes are made in the form of flat plates, which are suspended in the electrolyte and are held immobilized in a microporous separator (Figure 1.3a). The separator also helps in isolating the electrodes, preventing any short‐circuiting whereby ions can directly move internally between the anode and cathode. Short‐circuiting will result in capacity loss, parasitic reactions, and heat generation. This can also lead to catastrophic situations causing fires, explosions, leakage of materials, and accidents. The configuration of Figure 1.3a can be scaled up to very large sizes, for high currents and large storage capacities, by placing each cell inside a plastic envelope and stacking them inside a steel jacket. Connector strips are used to collect and connect the positive and the negative electrodes to a common positive and negative terminal; a sketch of such cell compaction is shown in Figure 1.3b.

Figure 1.1 (a) The schematic diagram of a simple galvanic cell. (b) Terminal designs for cylindrical batteries.

Figure 1.2 (a) An illustration of batteries connected in parallel to obtain double current. (b) An illustration of batteries connected in series to obtain 3 V.

Figure 1.3 (a) Single‐flat‐cell configuration; (b) composite‐flat‐cell configuration.

Both cylindrical and flat cells come in various sizes so that they can fit a wide range of portable appliances and devices. Table 1.1 summarizes the various battery sizes that are available commercially.

Table 1.1 Dimensions of commercially available battery sizes [1].

Source: Republished with permission of Linden and Reddy [1], Copyright Clearance Center, Inc.

Battery size

Diameter (mm)

Height (mm)

N

12

30.2

AAA

10.5

44.5

AA

14.5

50.5

C

26.2

50

D

34.2

61.5

F

32.0

91.0

Length (mm)

Width (mm)

Thickness (mm)

Flat cells

24

13.5

 6.0

43

43

 6.4

Rectangular cells

48.5

26.5

17.5

1.2 Quantities Characterizing Batteries

Upon operation of galvanic cells, implying that the device is in power mode, it is said that the galvanic cell is discharged and electrons flow, through an external circuit, from the anode to the cathode. As a result, the cathode attains a negative charge, while the anode becomes positively charged. Consequently, cations are attracted from the anode to the cathode (and vice versa for the anions) and diffuse through the electrolyte. Typical electrochemical redox reactions that may take place upon operation of batteries are shown in Table 1.2, whereas the quantities that characterize batteries are defined in Table 1.3.

To better understand the differences between various battery chemistries, some of the quantities in Table 1.3 are further elaborated on below.

1.2.1 Voltage

The theoretical standard cell voltage, E0(cell), can be determined using the electrochemical series and is given by the difference between the standard electrode potential at the cathode, E0(cathode), and the standard electrode potential at the anode, E0(anode) [2] as

(1.1)

The standard electrode potential, E0, for an electrode reaction, written (by convention) as a reduction reaction (i.e. involving consumption of electrons), is the potential generated by that reaction under the condition that the reactants and the products are in their standard state in relation to a reference electrode. (A reactant or product is defined to be in its standard state when the component in a condensed phase is at unit activity and any component in the gas phase is at a partial pressure of 1 atm.) In aqueous systems, the standard hydrogen potential is taken as the universal reference electrode, whose potential is defined as zero. In practical terms, the standard hydrogen electrode can be constructed as follows: (i) a high surface area of platinum is deposited on a platinum foil or plate, which is then dipped into an acid solution of unit activity of H+ ions, corresponding to 1 M acid solution, then (ii) pure hydrogen at one atmosphere is passed over this electrode. A list containing selected standard electrode potentials at 298 K in an aqueous solution is given in Table 1.2 and these refer to equilibrium potentials at zero net current values at each of the electrodes. The batteries that make use of these materials as electrodes will be described in Chapter 2. It should be noted that the standard electrode potential for a reduction reaction in an aqueous solution is relative to the hydrogen electrode, which is taken as zero. Thus, potentials that are defined for half‐cells are represented as reduction reactions. In a battery, two half‐cells are present such that reduction takes place on one electrode and oxidation on the other.

Table 1.2 Standard electrode potentials in aqueous electrolyte at 298 K (written as reduction reactions by convention).

Reaction

E

0

(V)

Li

+

+ e

−

→ Li

−3.10

Na

+

+ e

−

→ Na

−2.71

Mg

2+

+ 2e

−

→ Mg

−2.36

½H

2

+ e

−

→ H

−

−2.25

Mn

2+

+ 2e

−

→ Mn

−1.18

MnO

2

+ 2H

2

O + 4e

−

→ Mn + 4OH

−

−0.98

2H

2

O + 2e

−

→ H

2

+ 2OH

−

−0.83

Cd(OH)

2

+ 2e

−

→ Cd + 2OH

−

−0.82

Zn

2+

+ 2e

−

→ Zn

−0.76

Ni(OH)

2

+ 2e

−

→ Ni + 2OH

−

−0.72

Fe

2+

+ 2e

−

→ Fe

−0.44

Cd

2+

+ 2e

−

→ Cd

−0.40

PbSO

4

+ 2e

−

→ Pb + SO

4

2−

−0.35

Ni

2+

+ 2e

−

→ Ni

−0.26

MnO

2

+ 2H

2

O + 4e

−

→ Mn(OH)

2

+ 2OH

−

−0.05

2H

+

+ 2e

−

→ H

2

  0.00

Cu

2+

+ e

−

→ Cu

+

+0.16

Ag

2

O + H

2

O + 2e

−

→ 2Ag + 2OH

−

+0.34

Cu

2+

+ 2e

−

→ Cu

+0.34

O

2

+ 2H

2

O + 4e

−

→ 4OH

−

+0.40

2NiOOH + 2H

2

O + 2e

−

→ 2Ni(OH)

2

+ 2OH

−

+0.48

NiO

2

+ 2H

2

O + 2e

−

→ Ni(OH)

2

+ 2OH

−

+0.49

MnO

4

2−

+ 2H

2

O + 2e

−

→ MnO

2

+ 4OH

−

+0.62

2AgO + H

2

O + 2e

−

→ Ag

2

O + 2OH

−

+0.64

Fe

3+

+ e

−

→ Fe

2+

+0.77

Hg

2+

+ e

−

→ Hg

+

+0.80

Ag

+

+ e

−

→ Ag

+0.80

2Hg

2+

+ 2e

−

→ Hg

+

+0.91

O

2

+ 4H

+

+ 4e

−

→ 2H

2

O

+1.23

ZnO + H

2

O + 2e

−

→ Zn + 2OH

−

+1.26

Cl

2

+ 2e

−

→ 2Cl

−

+1.36

PbO

2

+ 4H

+

+ 2e

−

→ Pb

2+

+ 2H

2

O

+1.47

PbO

2

+ SO

4

2−

+ 4H

+

+ 2e

−

→ PbSO

4

+ 2H

2

O

+1.70

F

2

+ 2e

−

→ 2F

−

+2.87

Table 1.3 Battery characteristics.

Source: Reproduced with permission from Weal et al. [2]/University of Cambridge.

Battery characteristics

Definition

Unit

Open‐circuit voltage

Maximum voltage in the charged state at zero current

Volt (V)

Current

Low currents are characterized by activation losses, while the maximum current is normally determined by mass‐transfer limitations

Ampere (A)

Energy density

The energy that can be derived per unit volume of the weight of the cell

Watt‐hours per liter (Wh m

−3

)

Specific energy density

The energy that can be derived per unit weight of the cell (or sometimes per unit weight of the active electrode material)

Watt‐hours per kilogram (Wh kg

−1

)

Power density

The power that can be derived per unit weight of the cell

Watt per kilogram (W kg

−1

)

Capacity

The theoretical capacity of a battery is the quantity of electricity involved in the electrochemical reaction

Ampere‐hours per gram (Ah g

−1

).

Shelf life

The time a battery can be stored inactive before its capacity falls to 80%

Years

Service life

The time a battery can be used at various loads and temperatures

Hours (usually normalized for ampere per kilogram (A kg

−1

) and ampere per liter (A l

−1

))

Cycle life

The number of discharge/charge cycles it can undergo before its capacity falls to 80%

Cycles

To obtain a true estimate of the actual open‐circuit cell voltage, Eeq in the fully charged state for operation of the battery; the theoretical cell voltage is modified by the Nernst equation, which takes into account the nonstandard state of the reacting component as

(1.2)

where T is the operating temperature in kelvin (k), Q = aproducts/areactants is the chemical quotient for the overall cell reaction, and R is the gas constant (8.314 J k−1 mol−1). Q is represented in the same way as the equilibrium constant K, except that the activities (a) and partial pressures (p) in Eq. (1.2) reflect the actual nonstandard values prevailing in the system. For example, for the electrode reaction

(1.3)

the actual Nernstian electrode potential (E), also referred to as open‐circuit voltage (OCV) under equilibrium (for net zero current) is

(1.4)

Notation Ee (rather than E) is also often used to denote that the actual equilibrium potential of the electrode is determined by the Nernst equation and the standard electrode potential E0 refers to a very specific situation of reaction species being held in their “standard states,” The Nernstian potential in Eq. (1.4) will change with time due to any self‐discharge by which the activity (or concentration) of the electroactive component in the cell is modified. Thus, the nominal voltage is determined by the cell chemistry at any given point of time. M and M2+ refer to the effective concentrations of the two components in the phase within which they are present. (For the hydrogen reaction, as an example where a gas phase is involved, the activity of metal is replaced by the partial pressure term, pH2.)

The operating voltage produced is further modified as a result of discharge reactions actually taking place and will always be lower than the thermodynamically calculated theoretical voltage (also referred to as equilibrium potential) by the Nernst equation (OCV) due to polarization losses (these arise from overpotentials for overcoming activation barrier and/or diffusional limitations) and the resistance losses (IR drop) of the battery as the voltage is dependent on the current, I, drawn by an external load and the cell resistance, R, in the path of the current. Specifically, polarization losses arise to overcome any activation energy for the electrode reaction and/or concentration gradients near the electrode(s). The factors determining the overpotentials are dependent upon electrode kinetics from rates of electrodic reactions and diffusional rates of one or more active components, and, thus, vary with temperature, state of charge, and with the age of the cell. It is important to note that the actual voltage appearing at the terminal needs to be sufficient for the intended application.

1.2.2 Electrode Kinetics (Polarization and Cell Impedance)

Before continuing to the other quantities indicated in Table 1.3, the electrode kinetics, which was previously shown to affect the voltage, must be described. Thermodynamics expressed in terms of the electrode potentials can tell us the theoretical and open‐circuit cell voltage, as well as how feasible it is for a cell reaction to occur. However, it is necessary to consider kinetics to obtain a better understanding of what the actual cell voltage maybe, since the charge transfer, the rates of the reactions at the electrodes and diffusional barriers are usually the limiting factors. In continuing, therefore, the main kinetic issues that affect battery performance are summarized.

1.2.2.1 Electrical Double Layer

When a metal electrode is in an electrolyte, the charge on the metal will attract ions of opposite charge in the electrolyte, and the dipoles in the solvent will align. This forms a layer of charge in both the metal and the electrolyte, called the electrical double layer, as shown in Figure 1.4. The electrochemical reactions take place in this layer, and all atoms or ions that are reduced or oxidized must pass through this layer. Thus, the ability of ions to pass through this layer controls the kinetics, and is, therefore, the limiting factor in controlling the electrode reaction. The energy barrier toward the electrode reaction, described as the activation energy of the electrochemical reaction, lies across this double layer.

Figure 1.4 Illustration of double layer.

Source: Reproduced with permission from Weal et al. [2]/University of Cambridge.

1.2.2.2 Rate of Reaction

The rates of the chemical reactions are governed by the Arrhenius relationship, such that the rate of reaction, k, is

(1.5)

where Q* is the activation energy for the reaction, T is the temperature in Kelvin, and R is the universal gas constant.

In this case, the rate of the reaction can be measured by the current produced, since current is the amount of charge produced per unit amount of time, and therefore proportional to the number of electrons produced per unit amount of time that is proportional to the rate of the reaction.

1.2.2.3 Electrodes Away from Equilibrium

When an electrode is not at the equilibrium potential, an overpotential exists, given by

(1.6)

where η is the overpotential, E is the actual potential, and Ee is the equilibrium potential, calculated using the Nernst equation. Overpotential is used synonymously with polarization potential and described as arising from “polarization process” at a given electrode.

1.2.2.4 The Tafel Equation

The Tafel equation provides a relationship between the current and the overpotential during the oxidation or reduction reaction of an electrode. Consider a general reaction for the oxidation of a metal anode:

(1.7)

where z is the number of cations/electrons. The rate of this reaction, ka, is governed by the Arrhenius relationship:

(1.8)

where A is a frequency factor, which takes into account the rate of collision between the electroactive species and the electrode surface. From Faraday's law, one can express the rate in terms of the exchange current density at the anode, i0,a:

(1.9)

where F = 96 540 C mol−1 is Faraday's constant. If an overpotential ηa (ηa = Ea – Ee; where Ee is the Nernst potential for the oxidation half‐cell) is now applied in the anodic direction, the activation energy of the reaction becomes

(1.10)

where α is the “symmetry factor” of the electrical double layer, nominally taken as 0.5, assuming symmetrical behavior in both directions.

Therefore the anodic current density, ia, is

(1.11)

which by Eq. (1.9) reduces to

(1.12)

The subscript a here refers to process at the anode. Equation (1.12) is known as the Tafel equation. By taking natural logs and rearranging them, Eq. (1.12) can be written as

(1.13)

By setting RT/(αzF) = ba and lni0 = −aa/ba, Eq. (1.13) can be rewritten as

(1.14)

Or in terms of the anode potential, Ea,

(1.15)

Solving Eq. (1.15) for Ea, gives

(1.16)

where ba is the anodic Tafel slope. Similarly, we can consider the reduction of metal ions at a cathode:

(1.17)

The activation energy will be decreased by (1–α)zFηc (subscripts c indicate cathode), giving the cathodic current density as

(1.18)

and

(1.19)

Therefore, the cathode overpotential is ηc= Ec – Ee, where Ee is the Nernst potential, and Ec is expressed as

(1.20)

where bc is the cathodic Tafel slope. A typical representation of a Tafel plot – a plot of log i vs. E – is shown in Figure 1.5. Thus, for an applied potential, the current density, i, can be found from the Tafel plot in an electrolytic cell when the battery is being charged or discharged.

Figure 1.5 A typical Tafel plot.

Source: Reproduced with permission from Weal et al. [2]/University of Cambridge.

1.2.2.5 Example: Plotting a Tafel Curve for a Copper Electrode

Let us consider an electrode made of copper immersed in a half‐cell containing copper ions at a 1 M concentration, referring to an aqueous solution. The half‐cell reaction for copper is

(1.21)

The exchange current density at 1 M concentration of copper ions, for the above reaction, is i0 = 1 A m−2, reflecting the current density at zero overpotential (thus at Ee, in this example Ee = E0, as both Cu and Cu2+(aq) are in their standard states), that is, at zero net reaction (and thus at zero net current). Therefore, the magnitude of the exchange current density is a reflection of the reversibility of a given electrode reaction and signifies the rate at which equilibrium is established on being disturbed away from a given equilibrium condition.

For the Tafel equation

(1.22)

the general expression for the Tafel slope is

(1.23)

Taking T = 300 K, and allowing for copper α = 0.5 and z = 2, the Tafel slopes are calculated as ba = 0.059 V decade–1 of current and bc = −0.059 V decade–1 (of log current). Furthermore, for the anodic curve

(1.24)

and for the cathodic curve

(1.25)

The corresponding Tafel plot for copper is shown in the diagram in Figure 1.6. For example, during discharge, if the redox reaction is in the direction opposite of Eq. (1.21), where Cu is oxidized to copper ions in the solution, the electrode potential will be less than 0.34 V along the polarization line. The greater the operating current density, the lower the electrode potential. This in‐effect contributes to the reduction in the cell potential during discharge as a result of overpotential losses, signifying the energy barrier for the electron‐transfer reaction. On the other hand, during charging, the electrode potential increases with the applied current, thus increasing the potential required for charging the cell back to its original state (by electrochemical reduction in this example). For a faster charging rate, a higher current density is desirable, but this can arise only at the expense of a higher applied voltage (higher energy) to overcome the increasing overpotentials. (Note that E0 is modified by the Nernst equation to obtain a value for Ee, for species in nonstandard states.)

Figure 1.6 Tafel plot for a copper electrode.

Source: Reproduced with permission from Weal et al. [2]/University of Cambridge.

1.2.2.6 Other Limiting Factors

At very high currents, a limiting current may be reached as a result of the concentration overpotential, ηc, restricting mass‐transfer rates to the diffusion rate of the electroactive species. A limiting current arises, which can be derived from Fick's first law of diffusion, under the condition that the electrode surface is depleted of the ion, and the recovery of the ion concentration is limited by ion transport through the electrolyte diffusion boundary layer.

The limiting current is diffusion limited, and can be determined by Fick's law of diffusion as

(1.26)

where iL is the limiting current density over a boundary layer, D is the diffusion coefficient of metal cations in the electrolyte, C is the concentration of metal cations in the bulk electrolyte, and δ is the thickness of the boundary layer. Typical values for Cu2+, for example, would be D = 2 × 10−9 m2 s−1, C = 0.05 × 104 kg m−3, and δ = 6 × 10−4 m; these values give a limiting current density of iL = 3.2 × 102 A m−2.

The concentration overpotential, thus, represents the difference between the cell potential at the electrolyte concentration and the cell potential at the surface concentration because of depletion (or accumulation) at high‐current densities, given by

(1.27)

A Tafel curve showing this diffusion limiting of the current is depicted in Figure 1.7.

Figure 1.7 Diffusion limited current for the cathodic reaction.

Source: Reproduced with permission from Weal et al. [2]/University of Cambridge.

1.2.2.7 Tafel Curves for a Battery

In a battery, there are two sets of Tafel curves present, one for each electrode material. During discharge, one material will act as the anode (termed as the negative [−] electrode being at the lower potential) and the other as the cathode (termed as the positive [+] electrode being at the higher potential). During charging, the roles will be reversed such that at the negative [−] electrode, cathodic reactions take place and at the positive [+] electrode, anodic reactions occur by an externally applied potential difference to recover species back to the state before discharge. The actual potential difference between the two electrodes for a given current density can be found in the Tafel curve. The total cell potential is the difference between the anodic potential, Ea, and the cathodic potential, Ec.

In a galvanic cell, the actual potential, V′cell, discharge, is less than the Nernst potential

(1.28)

Ea, ηc,Ec, and ηa are defined in Section 1.2.2.3. Upon discharge, the cell potential may be further decreased by the ohmic drop due to the internal resistance of the cell, r