Electrodeposition and stripping are fundamental electrochemical processes for metals and have gained importance in rechargeable Li-ion batteries due to lithium metal electrodes. The electrode kinetics associated with lithium metal electrodeposition and stripping is crucial in determining the performance at fast discharge and charge, which is important for electric vertical takeoff and landing (eVTOL) aircraft and electric vehicles (EV). In this work, we show the use of Marcus–Hush–Chidsey (MHC) kinetics to accurately predict the Tafel curve data from the work of Boyle et al. [ACS Energy Lett. 5(3), 701 (2020)]. We discuss the differences in predictions of reorganization energies from the Marcus–Hush and the MHC models for lithium metal electrodes in four solvents. The MHC kinetic model is implemented and open-sourced within Cantera. Using the reaction kinetic model in a pseudo-2D battery model with a lithium anode paired with a LiFePO4 cathode, we show the importance of accounting for the MHC kinetics and compare it to the use of Butler–Volmer and Marcus–Hush kinetic models. We find significant deviation in the limiting currents associated with reaction kinetics for the three different rate laws for conditions of fast charge and discharge relevant for eVTOL and EV, respectively.

1.
S.
Sripad
and
V.
Viswanathan
, “
Performance metrics required of next-generation batteries to make a practical electric semi truck
,”
ACS Energy Lett.
2
,
1669
1673
(
2017
).
2.
A.
Bills
,
S.
Sripad
,
W. L.
Fredericks
,
M.
Singh
, and
V.
Viswanathan
, “
Performance metrics required of next-generation batteries to electrify commercial aircraft
,”
ACS Energy Lett.
5
,
663
668
(
2020
).
3.
P.
Albertus
,
S.
Babinec
,
S.
Litzelman
, and
A.
Newman
, “
Status and challenges in enabling the lithium metal electrode for high-energy and low-cost rechargeable batteries
,”
Energy
3
,
16
21
(
2017
).
4.
A.
Mistry
and
V.
Srinivasan
, “
On our limited understanding of electrodeposition
,”
MRS Adv.
4
,
2843
2861
(
2019
).
5.
T.
Krauskopf
,
F. H.
Richter
,
W. G.
Zeier
, and
J.
Janek
, “
Physicochemical concepts of the lithium metal anode in solid-state batteries
,”
Chem. Rev.
120
,
7745
(
2020
).
6.
W. L.
Fredericks
,
S.
Sripad
,
G. C.
Bower
, and
V.
Viswanathan
, “
Performance metrics required of next-generation batteries to electrify vertical takeoff and landing (VTOL) aircraft
,”
ACS Energy Lett.
3
,
2989
2994
(
2018
).
7.
K. N.
Wood
,
E.
Kazyak
,
A. F.
Chadwick
,
K.-H.
Chen
,
J.-G.
Zhang
,
K.
Thornton
, and
N. P.
Dasgupta
, “
Dendrites and pits: Untangling the complex behavior of lithium metal anodes through operando video microscopy
,”
ACS Cent. Sci.
2
,
790
801
(
2016
).
8.
J.
Kasemchainan
,
S.
Zekoll
,
D.
Spencer Jolly
,
Z.
Ning
,
G. O.
Hartley
,
J.
Marrow
, and
P. G.
Bruce
, “
Critical stripping current leads to dendrite formation on plating in lithium anode solid electrolyte cells
,”
Nat. Mater.
18
,
1105
1111
(
2019
).
9.
M.
Doyle
,
T. F.
Fuller
, and
J.
Newman
, “
Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell
,”
J. Electrochem. Soc.
140
,
1526
(
1993
).
10.
D. T.
Boyle
,
X.
Kong
,
A.
Pei
,
P. E.
Rudnicki
,
F.
Shi
,
W.
Huang
,
Z.
Bao
,
J.
Qin
, and
Y.
Cui
, “
Transient voltammetry with ultramicroelectrodes reveals the electron transfer kinetics of lithium metal anodes
,”
ACS Energy Lett.
5
,
701
709
(
2020
).
11.
Y.
Zeng
,
R. B.
Smith
,
P.
Bai
, and
M. Z.
Bazant
, “
Simple formula for Marcus–Hush–Chidsey kinetics
,”
J. Electroanal. Chem.
735
,
77
83
(
2014
).
12.
D. G.
Goodwin
,
R. L.
Speth
,
H. K.
Moffat
, and
B. W.
Weber
(
2018
). “
Cantera: An object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes
,” Zenodo, version 2.4.0, https://www.cantera.org.
13.
A. J.
Bard
,
L. R.
Faulkner
 et al.,
Electrochemical Methods: Fundamentals and Applications
(
Wiley
,
New York
,
2001
).
14.
J. A. V.
Butler
, “
The mechanism of overvoltage and its relation to the combination of hydrogen atoms at metal electrodes
,”
Trans. Faraday Soc.
28
,
379
382
(
1932
).
15.
T.
Erdey-Gruz
and
M.
Volmer
, “
Zur theorie der wasserstoff Überspannung” (“The theory of hydrogen overvoltage
”),
Z. Phys. Chem.
150
,
203
213
(
1930
).
16.
R. A.
Marcus
, “
On the theory of oxidation-reduction reactions involving electron transfer. I
,”
J. Chem. Phys.
24
,
966
978
(
1956
).
17.
N. S.
Hush
, “
Adiabatic rate processes at electrodes. I. Energy-charge relationships
,”
J. Chem. Phys.
28
,
962
972
(
1958
).
18.
N. S.
Hush
, “
Electron transfer in retrospect and prospect: 1: Adiabatic electrode processes
,”
J. Electroanal. Chem.
460
,
5
29
(
1999
).
19.
C. E. D.
Chidsey
, “
Free energy and temperature dependence of electron transfer at the metal-electrolyte interface
,”
Science
251
,
919
922
(
1991
).
20.
J.
Newman
and
K. E.
Thomas-Alyea
,
Electrochemical Systems
(
John Wiley & Sons
,
2012
).
21.
V.
Ramadesigan
,
P. W. C.
Northrop
,
S.
De
,
S.
Santhanagopalan
,
R. D.
Braatz
, and
V. R.
Subramanian
, “
Modeling and simulation of lithium-ion batteries from a systems engineering perspective
,”
J. Electrochem. Soc.
159
,
R31
(
2012
).
22.
C.
Monroe
and
J.
Newman
, “
The impact of elastic deformation on deposition kinetics at lithium/polymer interfaces
,”
J. Electrochem. Soc.
152
,
A396
(
2005
).
23.
V.
Srinivasan
,
K.
Higa
,
P.
Barai
, and
Y.
Xie
, “
Computational modeling of morphology evolution in metal-based battery electrodes
,” in
Handbook of Materials Modeling: Methods: Theory and Modeling
, edited by
W.
Andreoni
and
S.
Yip
(
Springer International Publishing
,
Cham
,
2020
), pp.
1193
1219
.
24.
F.
Hao
,
A.
Verma
, and
P. P.
Mukherjee
, “
Mesoscale complexations in lithium electrodeposition
,”
ACS Appl. Mater. Interfaces
10
,
26320
26327
(
2018
).
25.
E.
Laborda
,
M. C.
Henstridge
,
C.
Batchelor-McAuley
, and
R. G.
Compton
, “
Asymmetric Marcus–Hush theory for voltammetry
,”
Chem. Soc. Rev.
42
,
4894
4905
(
2013
).
26.
J.
Savéant
and
D.
Tessier
, “
Convolution potential sweep voltammetry V. Determination of charge transfer kinetics deviating from the Butler-Volmer behaviour
,”
J. Electroanal. Chem.
65
,
57
66
(
1975
).
27.
R. A.
Marcus
and
N.
Sutin
, “
Electron transfers in chemistry and biology
,”
Biochim. Biophys. Acta
811
,
265
322
(
1985
).
28.
R. A.
Marcus
, “
On the theory of electron-transfer reactions. VI. Unified treatment for homogeneous and electrode reactions
,”
J. Chem. Phys.
43
,
679
701
(
1965
).
29.
M. C.
Henstridge
,
E.
Laborda
,
N. V.
Rees
, and
R. G.
Compton
, “
Marcus–Hush–Chidsey theory of electron transfer applied to voltammetry: A review
,”
Electrochim. Acta
84
,
12
20
(
2012
).
30.
R.
Nissim
,
C.
Batchelor-McAuley
,
M. C.
Henstridge
, and
R. G.
Compton
, “
Electrode kinetics at carbon electrodes and the density of electronic states
,”
Chem. Commun.
48
,
3294
3296
(
2012
).
31.
R.
Kurchin
and
V.
Viswanathan
, “
Marcus–Hush–Chidsey kinetics at electrode–electrolyte interfaces
,”
J. Chem. Phys.
153
,
134706
(
2020
).
32.
W. F.
Howard
and
R. M.
Spotnitz
, “
Theoretical evaluation of high-energy lithium metal phosphate cathode materials in Li-ion batteries
,”
J. Power Sources
165
,
887
891
(
2007
).
33.
D.
Wang
,
H.
Li
,
S.
Shi
,
X.
Huang
, and
L.
Chen
, “
Improving the rate performance of LiFePO4 by Fe-site doping
,”
Electrochim. Acta
50
,
2955
2958
(
2005
).
34.
Y.
Meng
,
Y.
Li
,
J.
Xia
,
Q.
Hu
,
X.
Ke
,
G.
Ren
, and
F.
Zhu
, “
F-doped LiFePO4@N/B/F-doped carbon as high performance cathode materials for Li-ion batteries
,”
Appl. Surf. Sci.
476
,
761
768
(
2019
).
35.
T. R.
Jow
,
M. B.
Marx
, and
J. L.
Allen
, “
Distinguishing Li+ charge transfer kinetics at NCA/electrolyte and graphite/electrolyte interfaces, and NCA/electrolyte and LFP/electrolyte interfaces in Li-ion cells
,”
J. Electrochem. Soc.
159
,
A604
A612
(
2012
).
36.
X.
Zhou
,
F.
Wang
,
Y.
Zhu
, and
Z.
Liu
, “
Graphene modified LiFePO4 cathode materials for high power lithium ion batteries
,”
J. Mater. Chem.
21
,
3353
3358
(
2011
).
37.
H.
Li
,
L.
Peng
,
D.
Wu
,
J.
Wu
,
Y.-J.
Zhu
, and
X.
Hu
, “
Ultrahigh-capacity and fire-resistant LiFePO4-based composite cathodes for advanced lithium-ion batteries
,”
Adv. Energy Mater.
9
,
1802930
(
2019
).
38.
A. M.
Colclasure
and
R. J.
Kee
, “
Thermodynamically consistent modeling of elementary electrochemistry in lithium-ion batteries
,”
Electrochim. Acta
55
,
8960
8973
(
2010
).
39.
J.
Chiew
,
C. S.
Chin
,
W. D.
Toh
,
Z.
Gao
,
J.
Jia
, and
C. Z.
Zhang
, “
A pseudo three-dimensional electrochemical thermal model of a cylindrical LiFePO4/graphite battery
,”
Appl. Therm. Eng.
147
,
450
463
(
2019
).
40.
M. D.
Murbach
and
D. T.
Schwartz
, “
Extending newman’s pseudo-two-dimensional lithium-ion battery impedance simulation approach to include the nonlinear harmonic response
,”
J. Electrochem. Soc.
164
,
E3311
E3320
(
2017
).
41.
C.
Kupper
and
W. G.
Bessler
, “
Multi-scale thermo-electrochemical modeling of performance and aging of a LiFePO4/graphite lithium-ion cell
,”
J. Electrochem. Soc.
164
,
A304
A320
(
2017
).
42.
P.
Lu
,
C.
Li
,
E. W.
Schneider
, and
S. J.
Harris
, “
Chemistry, impedance, and morphology evolution in solid electrolyte interphase films during formation in lithium ion batteries
,”
J. Phys. Chem. C
118
,
896
903
(
2014
).
43.
P.
Bai
and
M. Z.
Bazant
, “
Charge transfer kinetics at the solid–solid interface in porous electrodes
,”
Nat. Commun.
5
,
3585
(
2014
).
44.
Y.-C.
Chang
,
C.-T.
Peng
, and
I.-M.
Hung
, “
Effects of particle size and carbon coating on electrochemical properties of LiFePO4/C prepared by hydrothermal method
,”
J. Mater. Sci.
49
,
6907
6916
(
2014
).
45.
J.
Tang
,
X.
Zhong
,
H.
Li
,
Y.
Li
,
F.
Pan
, and
B.
Xu
, “
In-situ and selectively laser reduced graphene oxide sheets as excellent conductive additive for high rate capability LiFePO4 lithium ion batteries
,”
J. Power Sources
412
,
677
682
(
2019
).
46.
See https://github.com/coresresearch/BatCan/tree/MHC/li_ion for Batcan: Battery modeling with Cantera.
47.
48.
D. A.
Cogswell
, “
Quantitative phase-field modeling of dendritic electrodeposition
,”
Phys. Rev. E
92
,
011301
(
2015
).
49.
W. R.
Fawcett
, “
Potential dependence of the elementary steps in the kinetics of electrode reactions involving amalgam formation
,”
J. Phys. Chem.
93
,
2675
2682
(
1989
).
50.
Y.
Zeng
,
P.
Bai
,
R. B.
Smith
, and
M. Z.
Bazant
, “
Simple formula for asymmetric Marcus–Hush kinetics
,”
J. Electroanal. Chem.
748
,
52
57
(
2015
).

Supplementary Material

You do not currently have access to this content.