The increasing significance on the development of high-performance lithium-ion (Li-ion) batteries is calling for new battery materials, theoretical models, and simulation tools. Lithiation-induced deformation in electrodes calls attention to study the multiphysics coupling between mechanics and electrochemistry. In this paper, a simultaneous multiscale and multiphysics model to study the coupled electrochemistry and mechanics in the continuum battery cell level and the microscale particle level was developed and implemented in comsolmultiphysics. In the continuum scale, the porous electrode theory and the classical mechanics model were applied. In the microscale, the specific particle structure has been incorporated into the model. This model was demonstrated to study the effects of mechanical constraints, charging rate, and silicon/C ratio, on the electrochemical performance. This model provides a powerful tool to perform simultaneous multiscale and multiphysics design on Li-ion batteries, from the particle level to full-cell level.
Issue Section:
Research Papers
References
1.
Boukamp
, B. A.
, Lesh
, G. C.
, and Huggins
, R. A.
, 1981
, “All-Solid Lithium Electrodes With Mixed-Conductor Matrix
,” J. Electrochem. Soc.
, 128
(4
), pp. 725
–729
.2.
Di Leo
, C. V.
, Rejovitzky
, E.
, and Anand
, L.
, 2015
, “Diffusion-Deformation Theory for Amorphous Silicon Anodes: The Role of Plastic Deformation on Electrochemical Performance
,” Int. J. Solids Struct.
, 67–68
, pp. 283
–296
.3.
Wang
, X. J.
, Fan
, F. F.
, Wang
, J. W.
, Wang
, H. R.
, Tao
, S. Y.
, Yang
, A.
, Liu
, Y.
, Chew
, H. B.
, Mao
, S. X.
, Zhu
, T.
, and Xia
, S. M.
, 2015
, “High Damage Tolerance of Electrochemically Lithiated Silicon
,” Nat. Commun.
, 6
, p. 8417
.4.
Ding
, B.
, Li
, X.
, Zhang
, X.
, Wu
, H.
, Xu
, Z.
, and Gao
, H.
, 2015
, “Brittle Versus Ductile Fracture Mechanism Transition in Amorphous Lithiated Silicon: From Intrinsic Nanoscale Cavitation to Shear Banding
,” Nano Energy
, 18
, pp. 89
–96
.5.
Kuruba
, R.
, Datta
, M. K.
, Damodaran
, K.
, Jampani
, P. H.
, Gattu
, B.
, Patel
, P. P.
, Shanthi
, P. M.
, Damle
, S.
, and Kumta
, P. N.
, 2015
, “Guar Gum: Structural and Electrochemical Characterization of Natural Polymer Based Binder for Silicon–carbon Composite Rechargeable Li-Ion Battery Anodes
,” J. Power Sources
, 298
, pp. 331
–340
.6.
Yoon
, D.-E.
, Hwang
, C.
, Kang
, N.-R.
, Lee
, U.
, Ahn
, D.
, Kim
, J.-Y.
, and Song
, H.-K.
, 2016
, “Dependency of Electrochemical Performances of Silicon Lithium-Ion Batteries on Glycosidic Linkages of Polysaccharide Binders
,” ACS Appl. Mater. Interfaces
, 8
(6
), pp. 4042
–4047
.7.
Xie
, Y.
, Li
, J.
, and Yuan
, C.
, 2014
, “Multiphysics Modeling of Lithium Ion Battery Capacity Fading Process With Solid-Electrolyte Interphase Growth by Elementary Reaction Kinetics
,” J. Power Sources
, 248
, pp. 172
–179
.8.
Shi
, D. H.
, Xiao
, X. R.
, Huang
, X. S.
, and Kia
, H.
, 2011
, “Modeling Stresses in the Separator of a Pouch Lithium-Ion Cell
,” J. Power Sources
, 196
(19
), pp. 8129
–8139
.9.
Chan
, C. K.
, Peng
, H. L.
, Liu
, G.
, McIlwrath
, K.
, Zhang
, X. F.
, Huggins
, R. A.
, and Cui
, Y.
, 2008
, “High-Performance Lithium Battery Anodes Using Silicon Nanowires
,” Nat. Nanotechnol.
, 3
(1
), pp. 31
–35
.10.
Ma
, H.
, Cheng
, F. Y.
, Chen
, J.
, Zhao
, J. Z.
, Li
, C. S.
, Tao
, Z. L.
, and Liang
, J.
, 2007
, “Nest-Like Silicon Nanospheres for High-Capacity Lithium Storage
,” Adv. Mater.
, 19
(22
), pp. 4067
–4070
.11.
Wang
, X. Y.
, Wen
, Z. Y.
, Liu
, Y.
, and Wu
, X. W.
, 2009
, “A Novel Composite Containing Nanosized Silicon and Tin as Anode Material for Lithium Ion Batteries
,” Electrochim. Acta
, 54
(20
), pp. 4662
–4667
.12.
Si
, Q.
, Hanai
, K.
, Imanishi
, N.
, Kubo
, M.
, Hirano
, A.
, Takeda
, Y.
, and Yamamoto
, O.
, 2009
, “Highly Reversible Carbon-Nano-Silicon Composite Anodes for Lithium Rechargeable Batteries
,” J. Power Sources
, 189
(1
), pp. 761
–765
.13.
Park
, M. H.
, Kim
, M. G.
, Joo
, J.
, Kim
, K.
, Kim
, J.
, Ahn
, S.
, Cui
, Y.
, and Cho
, J.
, 2009
, “Silicon Nanotube Battery Anodes
,” Nano Lett.
, 9
(11
), pp. 3844
–3847
.14.
Bourderau
, S.
, Brousse
, T.
, and Schleich
, D. M.
, 1999
, “Amorphous Silicon as a Possible Anode Material for Li-Ion Batteries
,” J. Power Sources
, 81
, pp. 233
–236
.15.
Yu
, C.
, Li
, X.
, Ma
, T.
, Rong
, J.
, Zhang
, R.
, Shaffer
, J.
, An
, Y.
, Liu
, Q.
, Wei
, B. Q.
, and Jiang
, H.
, 2012
, “Silicon Thin Films as Anodes for High Performance Lithium Ion Batteries With Effective Stress Relaxation
,” Adv. Energy Mater.
, 2
(1
), pp. 68
–73
.16.
Christensen
, J.
, and Newman
, J.
, 2006
, “Stress Generation and Fracture in Lithium Insertion Materials
,” J. Solid State Electrochem.
, 10
(5
), pp. 293
–319
.17.
Gao
, Y. F.
, and Zhou
, M.
, 2011
, “Strong Stress-Enhanced Diffusion in Amorphous Lithium Alloy Nanowire Electrodes
,” J. Appl. Phys.
, 109
(1
), p. 014310
.18.
Cui
, Z. W.
, Gao
, F.
, and Qu
, J. M.
, 2012
, “A Finite Deformation Stress-Dependent Chemical Potential and Its Applications to Lithium Ion Batteries
,” J. Mech. Phys. Solids
, 60
(7
), pp. 1280
–1295
.19.
Yang
, X. G.
, Bauer
, C.
, and Wang
, C. Y.
, 2016
, “Sinusoidal Current and Stress Evolutions in Lithium-Ion Batteries
,” J. Power Sources
, 327
, pp. 414
–422
.20.
Bower
, A. F.
, Guduru
, P. R.
, and Sethuraman
, V. A.
, 2011
, “A Finite Strain Model of Stress, Diffusion, Plastic Flow, and Electrochemical Reactions in a Lithium-Ion Half-Cell
,” J. Mech. Phys. Solids
, 59
(4
), pp. 804
–828
.21.
Yang
, H.
, Fan
, F.
, Liang
, W.
, Guo
, X.
, Zhu
, T.
, and Zhang
, S.
, 2014
, “A Chemo-Mechanical Model of Lithiation in Silicon
,” J. Mech. Phys. Solids
, 70
, pp. 349
–361
.22.
Di Leo
, C. V.
, Rejovitzky
, E.
, and Anand
, L.
, 2014
, “A Cahn–Hilliard-Type Phase-Field Theory for Species Diffusion Coupled With Large Elastic Deformations: Application to Phase-Separating Li-Ion Electrode Materials
,” J. Mech. Phys. Solids
, 70
, pp. 1
–29
.23.
Huang
, S.
, Fan
, F.
, Li
, J.
, Zhang
, S.
, and Zhu
, T.
, 2013
, “Stress Generation During Lithiation of High-Capacity Electrode Particles in Lithium Ion Batteries
,” Acta Mater.
, 61
(12
), pp. 4354
–4364
.24.
Qi
, Y.
, Xu
, Q. C.
, and Van der Ven
, A.
, 2012
, “Chemically Induced Crack Instability When Electrodes Fracture
,” J. Electrochem. Soc.
, 159
(11
), pp. A1838
–A1843
.25.
Klinsmann
, M.
, Rosato
, D.
, Kamlah
, M.
, and McMeeking
, R. M.
, 2016
, “Modeling Crack Growth During Li Insertion in Storage Particles Using a Fracture Phase Field Approach
,” J. Mech. Phys. Solids
, 92
, pp. 313
–344
.26.
Hu
, Y. H.
, Zhao
, X. H.
, and Suo
, Z. G.
, 2010
, “Averting Cracks Caused by Insertion Reaction in Lithium-Ion Batteries
,” J. Mater. Res.
, 25
(6
), pp. 1007
–1010
.27.
DeLuca
, C. M.
, Maute
, K.
, and Dunn
, M. L.
, 2011
, “Effects of Electrode Particle Morphology on Stress Generation in Silicon During Lithium Insertion
,” J. Power Sources
, 196
(22
), pp. 9672
–9681
.28.
Purkayastha
, R. T.
, and McMeeking
, R. M.
, 2012
, “An Integrated 2-D Model of a Lithium Ion Battery: The Effect of Material Parameters and Morphology on Storage Particle Stress
,” Comput. Mech.
, 50
(2
), pp. 209
–227
.29.
Cheng
, Y. T.
, and Verbrugge
, M. W.
, 2009
, “Evolution of Stress Within a Spherical Insertion Electrode Particle Under Potentiostatic and Galvanostatic Operation
,” J. Power Sources
, 190
(2
), pp. 453
–460
.30.
Zhao
, K. J.
, Pharr
, M.
, Vlassak
, J. J.
, and Suo
, Z. G.
, 2010
, “Fracture of Electrodes in Lithium-Ion Batteries Caused by Fast Charging
,” J. Appl. Phys.
, 108
(7
), p. 045004.31.
Zhou
, W.
, 2015
, “Effects of External Mechanical Loading on Stress Generation During Lithiation in Li-Ion Battery Electrodes
,” Electrochim. Acta
, 185
, pp. 28
–33
.32.
Mendoza
, H.
, Roberts
, S. A.
, Brunini
, V. E.
, and Grillet
, A. M.
, 2016
, “Mechanical and Electrochemical Response of a LiCoO2 Cathode Using Reconstructed Microstructures
,” Electrochim. Acta
, 190
, pp. 1
–15
.33.
Kim
, S.
, Wee
, J.
, Peters
, K.
, and Huang
, H. Y. S.
, 2018
, “Multiphysics Coupling in Lithium-Ion Batteries With Reconstructed Porous Microstructures
,” J. Phys. Chem. C
, 122
(10
), pp. 5280
–5290
.34.
Wu
, W.
, Xiao
, X.
, Huang
, X.
, and Yan
, S.
, 2014
, “A Multiphysics Model for the in Situ Stress Analysis of the Separator in a Lithium-Ion Battery Cell
,” Comput. Mater. Sci.
, 83
, pp. 127
–136
.35.
Liu
, B. H.
, Zhao
, H.
, Yu
, H. L.
, Li
, J.
, and Xu
, J.
, 2017
, “Multiphysics Computational Framework for Cylindrical Lithium-Ion Batteries Under Mechanical Abusive Loading
,” Electrochim. Acta
, 256
, pp. 172
–184
.36.
Zhao
, K.
, Pharr
, M.
, Cai
, S.
, Vlassak
, J. J.
, and Suo
, Z.
, 2011
, “Large Plastic Deformation in High‐Capacity Lithium‐Ion Batteries Caused by Charge and Discharge
,” J. Am. Ceram. Soc.
, 94
, pp. s226
–s235
.37.
Bower
, A. F.
, and Guduru
, P.
, 2012
, “A Simple Finite Element Model of Diffusion, Finite Deformation, Plasticity and Fracture in Lithium Ion Insertion Electrode Materials
,” Modell. Simul. Mater. Sci. Eng.
, 20
(4
), p. 045004
.38.
Wu
, W.
, Xiao
, X. R.
, Wang
, M.
, and Huang
, X. S.
, 2014
, “A Microstructural Resolved Model for the Stress Analysis of Lithium-Ion Batteries
,” J. Electrochem. Soc.
, 161
(5
), pp. A803
–A813
.39.
Wang
, M.
, Xiao
, X.
, and Huang
, X.
, 2017
, “A Multiphysics Microstructure-Resolved Model for Silicon Anode Lithium-Ion Batteries
,” J. Power Sources
, 348
, pp. 66
–79
.40.
Wu
, L.
, Wen
, Y.
, and Zhang
, J.
, 2016
, “Three-Dimensional Finite Element Study on Li Diffusion Induced Stress in FIB-SEM Reconstructed LiCoO2 Half Cell
,” Electrochim. Acta
, 222
, pp. 814
–820
.41.
Doyle
, C. M.
, Fuller
, T. F.
, and Newman
, J. S.
, 1993
, “Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell
,” J. Electrochem. Soc.
, 140
(6
), pp. 1526
–1533
.42.
Doyle
, C. M.
, 1995
, “Design and Simulation of Lithium Rechargeable Batteries
,” Ph.D. thesis
, Lawrence Berkeley National Laboratory, Berkeley, CA.https://cloudfront.escholarship.org/dist/prd/content/qt6j87z0sp/qt6j87z0sp.pdf43.
COMSOL Multiphysics
, 2015
, “COMSOL AB,” v. 5.2, Stockholm, Sweden.44.
Wang
, X.
, Singh
, S. S.
, Ma
, T.
, Lv
, C.
, Chawla
, N.
, and Jiang
, H. Q.
, 2017
, “Quantifying Electrochemical Reactions and Properties of Amorphous Silicon in a Conventional Lithium-Ion Battery Configuration
,” Chem. Mater.
, 29
(14
), pp. 5831
–5840
.45.
McDowell
, M. T.
, Lee
, S. W.
, Harris
, J. T.
, Korgel
, B. A.
, Wang
, C.
, Nix
, W. D.
, and Cui
, Y.
, 2013
, “In Situ TEM of Two-Phase Lithiation of Amorphous Silicon Nanospheres
,” Nano Lett.
, 13
(2
), pp. 758
–764
.46.
Zheng
, W. D.
, Shui
, M.
, Shu
, J.
, Gao
, S.
, Xu
, D.
, Chen
, L. L.
, Feng
, L.
, and Ren
, Y. L.
, 2013
, “GITT Studies on Oxide Cathode LiNi1/3Co1/3Mn1/3O2 Synthesized by Citric Acid Assisted High-Energy Ball Milling
,” Bull. Mater. Sci.
, 36
(3
), pp. 495
–498
.47.
Sethuraman
, V. A.
, Srinivasan
, V.
, and Newman
, J.
, 2013
, “Analysis of Electrochemical Lithiation and Delithiation Kinetics in Silicon
,” J. Electrochem. Soc.
, 160
(2
), pp. A394
–A403
.48.
Srinivasan
, V.
, and Newman
, J.
, 2004
, “Design and Optimization of a Natural Graphite/Iron Phosphate Lithium-Ion Cell
,” J. Electrochem. Soc.
, 151
(10
), pp. A1530
–A1538
.49.
Doyle
, M.
, Newman
, J.
, Gozdz
, A. S.
, Schmutz
, C. N.
, and Tarascon
, J. M.
, 1996
, “Comparison of Modeling Predictions With Experimental Data From Plastic Lithium Ion Cells
,” J. Electrochem. Soc.
, 143
(6
), pp. 1890
–1903
.50.
Xu
, J.
, Liu
, B.
, and Hu
, D.
, 2016
, “State of Charge Dependent Mechanical Integrity Behavior of 18650 Lithium-Ion Batteries
,” Sci. Rep.
, 6
, p. 21829
.51.
Xu
, J.
, Wang
, L. B.
, Guan
, J.
, and Yin
, S.
, 2016
, “Coupled Effect of Strain Rate and Solvent on Dynamic Mechanical Behaviors of Separators in Lithium Ion Batteries
,” Mater. Des.
, 95
, pp. 319
–328
.52.
Wang
, M.
, Xiao
, X.
, and Huang
, X.
, 2016
, “Study of Lithium Diffusivity in Amorphous Silicon Via Finite Element Analysis
,” J. Power Sources
, 307
, pp. 77
–85
.53.
Johari
, P.
, Qi
, Y.
, and Shenoy
, V. B.
, 2011
, “The Mixing Mechanism During Lithiation of Si Negative Electrode in Li-Ion Batteries: An Ab Initio Molecular Dynamics Study
,” Nano Lett.
, 11
(12
), pp. 5494
–5500
.54.
Park
, M.
, Zhang
, X. C.
, Chung
, M. D.
, Less
, G. B.
, and Sastry
, A. M.
, 2010
, “A Review of Conduction Phenomena in Li-Ion Batteries
,” J. Power Sources
, 195
(24
), pp. 7904
–7929
.55.
Qi
, Y.
, Guo
, H. B.
, Hector
, L. G.
, and Timmons
, A.
, 2010
, “Threefold Increase in the Young's Modulus of Graphite Negative Electrode During Lithium Intercalation
,” J. Electrochem. Soc.
, 157
(5
), pp. A558
–A566
.56.
Liu
, X. H.
, Zhong
, L.
, Huang
, S.
, Mao
, S. X.
, Zhu
, T.
, and Huang
, J. Y.
, 2012
, “Size-Dependent Fracture of Silicon Nanoparticles During Lithiation
,” ACS Nano
, 6
(2
), pp. 1522
–1531
.57.
Wen
, J.
, Wei
, Y.
, and Cheng
, Y.-T.
, 2018
, “Stress Evolution in Elastic-Plastic Electrodes During Electrochemical Processes: A Numerical Method and Its Applications
,” J. Mech. Phys. Solids
, 116
, pp. 403
–415
.58.
Wang
, L.
, Yin
, S.
, Zhang
, C.
, Huan
, Y.
, and Xu
, J.
, 2018
, “Mechanical Characterization and Modeling for Anodes and Cathodes in Lithium-Ion Batteries
,” J. Power Sources
, 392
, pp. 265
–273
.59.
Zhao
, K.
, Wang
, W. L.
, Gregoire
, J.
, Pharr
, M.
, Suo
, Z.
, Vlassak
, J. J.
, and Kaxiras
, E.
, 2011
, “Lithium-Assisted Plastic Deformation of Silicon Electrodes in Lithium-Ion Batteries: A First-Principles Theoretical Study
,” Nano Lett.
, 11
(7
), pp. 2962
–2967
.Copyright © 2019 by ASME
You do not currently have access to this content.
