Revisiting the t0.5 Dependence of SEI Growth

Attia, Peter M.; Chueh, William C.; Harris, Stephen J.

doi:10.1149/1945-7111/ab8ce4

Revisiting the t^0.5 Dependence of SEI Growth

Journal Article · Fri May 08 00:00:00 EDT 2020 · Journal of the Electrochemical Society (Online)

DOI:https://doi.org/10.1149/1945-7111/ab8ce4· OSTI ID:1635182

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Stanford Univ., CA (United States). Dept. of Materials Science and Engineering
Stanford Univ., CA (United States). Dept. of Materials Science and Engineering; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division

SEI growth in lithium-ion batteries is commonly assumed to scale with t^0.5, in line with simple models of diffusion-limited surface layer growth. As a result, this model is widely used for empirical predictions of capacity fade in lithium-ion batteries. However, the t^0.5 model is generally not theoretically sufficient to describe all of the various SEI growth modes. Furthermore, previous literature has not convincingly demonstrated that this model provides the best fit to measurements of SEI growth. In this work, we discuss the theoretical assumptions of the t^0.5 model, evaluate claims of t^0.5 dependence in six previously published datasets and one new dataset, and compare the performance of this model to that of other models. We find that few of the purported t^0.5 fits in literature are statistically justified, although t^0.5 generally describes SEI growth during storage better than SEI growth during cycling. Finally, we evaluate how the fitted exponents in the power-law models vary as a function of time, and we illustrate the limitations of using t^0.5 for prediction without validating its applicability to a particular dataset. This work illustrates the theoretical and empirical limitations of the t^0.5 model and highlights alternatives for more accurate estimates and predictions of SEI growth.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Energy Efficiency and Renewable Energy (EERE), Transportation Office. Vehicle Technologies Office

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1635182

Journal Information:: Journal of the Electrochemical Society (Online), Journal Name: Journal of the Electrochemical Society (Online) Journal Issue: 9 Vol. 167; ISSN 1945-7111

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (50)

Identifying the Mechanism of Continued Growth of the Solid–Electrolyte Interphase Single, Fabian; Latz, Arnulf; Horstmann, Birger ChemSusChem, Vol. 11, Issue 12 https://doi.org/10.1002/cssc.201800077	journal	March 2018
Estimating data from figures with a Web-based program: Considerations for a systematic review Burda, Brittany U.; O'Connor, Elizabeth A.; Webber, Elizabeth M. Research Synthesis Methods, Vol. 8, Issue 3 https://doi.org/10.1002/jrsm.1232	journal	March 2017
Evaluation and propagation of confidence intervals in nonlinear, asymmetrical variance spaces. Analysis of ligand-binding data Johnson, M. L. Biophysical Journal, Vol. 44, Issue 1 https://doi.org/10.1016/S0006-3495(83)84281-7	journal	October 1983
A state space framework for automatic forecasting using exponential smoothing methods Hyndman, Rob J.; Koehler, Anne B.; Snyder, Ralph D. International Journal of Forecasting, Vol. 18, Issue 3 https://doi.org/10.1016/S0169-2070(01)00110-8	journal	July 2002
The random walk's guide to anomalous diffusion: a fractional dynamics approach Metzler, Ralf; Klafter, Joseph Physics Reports, Vol. 339, Issue 1 https://doi.org/10.1016/S0370-1573(00)00070-3	journal	December 2000
Aging mechanism in Li ion cells and calendar life predictions Broussely, M.; Herreyre, S.; Biensan, P. Journal of Power Sources, Vol. 97-98 https://doi.org/10.1016/S0378-7753(01)00722-4	journal	July 2001
An accelerated calendar and cycle life study of Li-ion cells Bloom, I.; Cole, B. W.; Sohn, J. J. Journal of Power Sources, Vol. 101, Issue 2 https://doi.org/10.1016/S0378-7753(01)00783-2	journal	October 2001
Calendar- and cycle-life studies of advanced technology development program generation 1 lithium-ion batteries Wright, R. B.; Motloch, C. G.; Belt, J. R. Journal of Power Sources, Vol. 110, Issue 2 https://doi.org/10.1016/S0378-7753(02)00210-0	journal	August 2002
The role of Li-ion battery electrolyte reactivity in performance decline and self-discharge Sloop, Steven E.; Kerr, John B.; Kinoshita, Kim Journal of Power Sources, Vol. 119-121, p. 330-337 https://doi.org/10.1016/S0378-7753(03)00149-6	journal	June 2003
Thermal stability of lithium-ion battery electrolytes Ravdel, Boris; Abraham, K. M.; Gitzendanner, Robert Journal of Power Sources, Vol. 119-121 https://doi.org/10.1016/S0378-7753(03)00257-X	journal	June 2003
The influence of the local current density on the electrochemical exfoliation of graphite in lithium-ion battery negative electrodes Goers, Dietrich; Spahr, Michael E.; Leone, Antonio Electrochimica Acta, Vol. 56, Issue 11 https://doi.org/10.1016/j.electacta.2011.02.046	journal	April 2011
Understanding Full-Cell Evolution and Non-chemical Electrode Crosstalk of Li-Ion Batteries Knehr, Kevin W.; Hodson, Thomas; Bommier, Clement Joule, Vol. 2, Issue 6 https://doi.org/10.1016/j.joule.2018.03.016	journal	June 2018
Systematic aging of commercial LiFePO 4 \|Graphite cylindrical cells including a theory explaining rise of capacity during aging Lewerenz, Meinert; Münnix, Jens; Schmalstieg, Johannes Journal of Power Sources, Vol. 345 https://doi.org/10.1016/j.jpowsour.2017.01.133	journal	March 2017
Electrochemical Cross-Talk Leading to Gas Evolution and Capacity Fade in LiNi _0.5 Mn _1.5 O ₄ /Graphite Full-Cells Michalak, Barbara; Berkes, Balázs B.; Sommer, Heino The Journal of Physical Chemistry C, Vol. 121, Issue 1 https://doi.org/10.1021/acs.jpcc.6b11184	journal	December 2016
Evolution of the Solid–Electrolyte Interphase on Carbonaceous Anodes Visualized by Atomic-Resolution Cryogenic Electron Microscopy Huang, William; Attia, Peter M.; Wang, Hansen Nano Letters, Vol. 19, Issue 8 https://doi.org/10.1021/acs.nanolett.9b01515	journal	July 2019
Nonaqueous Liquid Electrolytes for Lithium-Based Rechargeable Batteries Xu, Kang Chemical Reviews, Vol. 104, Issue 10, p. 4303-4418 https://doi.org/10.1021/cr030203g	journal	October 2004
Electrolytes and Interphases in Li-Ion Batteries and Beyond Xu, Kang Chemical Reviews, Vol. 114, Issue 23 https://doi.org/10.1021/cr500003w	journal	October 2014
Effects of Inhomogeneities—Nanoscale to Mesoscale—on the Durability of Li-Ion Batteries Harris, Stephen J.; Lu, Peng The Journal of Physical Chemistry C, Vol. 117, Issue 13 https://doi.org/10.1021/jp311431z	journal	February 2013
Nonlinear least-squares data fitting in Excel spreadsheets Kemmer, Gerdi; Keller, Sandro Nature Protocols, Vol. 5, Issue 2 https://doi.org/10.1038/nprot.2009.182	journal	January 2010
General Relationship for the Thermal Oxidation of Silicon Deal, B. E.; Grove, A. S. Journal of Applied Physics, Vol. 36, Issue 12 https://doi.org/10.1063/1.1713945	journal	December 1965
Probing microscopic origins of confined subdiffusion by first-passage observables Condamin, S.; Tejedor, V.; Voituriez, R. Proceedings of the National Academy of Sciences, Vol. 105, Issue 15 https://doi.org/10.1073/pnas.0712158105	journal	April 2008
Graphs in Statistical Analysis Anscombe, F. J. The American Statistician, Vol. 27, Issue 1 https://doi.org/10.1080/00031305.1973.10478966	journal	February 1973
Science and Statistics Box, George E. P. Journal of the American Statistical Association, Vol. 71, Issue 356 https://doi.org/10.1080/01621459.1976.10480949	journal	December 1976
Theory of the oxidation of metals Cabrera, N.; Mott, N. F. Reports on Progress in Physics, Vol. 12, Issue 1 https://doi.org/10.1088/0034-4885/12/1/308	journal	January 1949
The oxidation of metals Lawless, K. R. Reports on Progress in Physics, Vol. 37, Issue 2 https://doi.org/10.1088/0034-4885/37/2/002	journal	February 1974
Fitting curves to data using nonlinear regression: a practical and nonmathematical review Motulsky, Harvey J.; Ransnas, Lennart A. The FASEB Journal, Vol. 1, Issue 5 https://doi.org/10.1096/fasebj.1.5.3315805	journal	November 1987
Atomic structure of sensitive battery materials and interfaces revealed by cryo–electron microscopy Li, Yuzhang; Li, Yanbin; Pei, Allen Science, Vol. 358, Issue 6362 https://doi.org/10.1126/science.aam6014	journal	October 2017
Power-Law Distributions in Empirical Data Clauset, Aaron; Shalizi, Cosma Rohilla; Newman, M. E. J. SIAM Review, Vol. 51, Issue 4 https://doi.org/10.1137/070710111	journal	November 2009
Electrochemical and Chemical Insertion for Energy Transformation and Switching Li, Yiyang; Chueh, William C. Annual Review of Materials Research, Vol. 48, Issue 1 https://doi.org/10.1146/annurev-matsci-070317-124525	journal	July 2018
Solvent Diffusion Model for Aging of Lithium-Ion Battery Cells Ploehn, Harry J.; Ramadass, Premanand; White, Ralph E. Journal of The Electrochemical Society, Vol. 151, Issue 3 https://doi.org/10.1149/1.1644601	journal	January 2004
Self-Discharge of Graphite Electrodes at Elevated Temperatures Studied by CV and Electrochemical Impedance Spectroscopy Levi, M. D.; Wang, C.; Aurbach, D. Journal of The Electrochemical Society, Vol. 151, Issue 5 https://doi.org/10.1149/1.1697411	journal	January 2004
A Mathematical Model for the Lithium-Ion Negative Electrode Solid Electrolyte Interphase Christensen, John; Newman, John Journal of The Electrochemical Society, Vol. 151, Issue 11 https://doi.org/10.1149/1.1804812	journal	January 2004
Thermal Decomposition of LiPF[sub 6]-Based Electrolytes for Lithium-Ion Batteries Campion, Christopher L.; Li, Wentao; Lucht, Brett L. Journal of The Electrochemical Society, Vol. 152, Issue 12 https://doi.org/10.1149/1.2083267	journal	January 2005
Thermal Oxidation of Silicon in Dry Oxygen Growth-Rate Enhancement in the Thin Regime Massoud, Hisham Z. Journal of The Electrochemical Society, Vol. 132, Issue 11 https://doi.org/10.1149/1.2113648	journal	January 1985
The Electrochemical Behavior of Alkali and Alkaline Earth Metals in Nonaqueous Battery Systems—The Solid Electrolyte Interphase Model Peled, E. Journal of The Electrochemical Society, Vol. 126, Issue 12 https://doi.org/10.1149/1.2128859	journal	January 1979
A High Precision Coulometry Study of the SEI Growth in Li/Graphite Cells Smith, A. J.; Burns, J. C.; Zhao, Xuemei Journal of The Electrochemical Society, Vol. 158, Issue 5 https://doi.org/10.1149/1.3557892	journal	January 2011
Interpreting High Precision Coulometry Results on Li-ion Cells Smith, A. J.; Burns, J. C.; Xiong, D. Journal of The Electrochemical Society, Vol. 158, Issue 10 https://doi.org/10.1149/1.3625232	journal	January 2011
Revealing SEI Morphology: In-Depth Analysis of a Modeling Approach Single, Fabian; Horstmann, Birger; Latz, Arnulf Journal of The Electrochemical Society, Vol. 164, Issue 11 https://doi.org/10.1149/2.0121711jes	journal	January 2017
Understanding Anomalous Behavior in Coulombic Efficiency Measurements on Li-Ion Batteries Gyenes, Balazs; Stevens, D. A.; Chevrier, V. L. Journal of The Electrochemical Society, Vol. 162, Issue 3 https://doi.org/10.1149/2.0191503jes	journal	December 2014
Electrochemical Kinetics of SEI Growth on Carbon Black: Part I. Experiments Attia, Peter M.; Das, Supratim; Harris, Stephen J. Journal of The Electrochemical Society, Vol. 166, Issue 4 https://doi.org/10.1149/2.0231904jes	journal	January 2019
Electrochemical Kinetics of SEI Growth on Carbon Black: Part II. Modeling Das, Supratim; Attia, Peter M.; Chueh, William C. Journal of The Electrochemical Society, Vol. 166, Issue 4 https://doi.org/10.1149/2.0241904jes	journal	January 2019
Experimental and Theoretical Investigation of Solid-Electrolyte-Interphase Formation Mechanisms on Glassy Carbon Tang, Maureen; Lu, Sida; Newman, John Journal of The Electrochemical Society, Vol. 159, Issue 11 https://doi.org/10.1149/2.025211jes	journal	January 2012
Ultra High-Precision Studies of Degradation Mechanisms in Aged LiCoO ₂ /Graphite Li-Ion Cells Fathi, R.; Burns, J. C.; Stevens, D. A. Journal of The Electrochemical Society, Vol. 161, Issue 10 https://doi.org/10.1149/2.0321410jes	journal	January 2014
Effect of Manganese Contamination on the Solid-Electrolyte-Interphase Properties in Li-Ion Batteries Delacourt, C.; Kwong, A.; Liu, X. Journal of The Electrochemical Society, Vol. 160, Issue 8 https://doi.org/10.1149/2.035308jes	journal	January 2013
Calendar Aging of Lithium-Ion Batteries: I. Impact of the Graphite Anode on Capacity Fade Keil, Peter; Schuster, Simon F.; Wilhelm, Jörn Journal of The Electrochemical Society, Vol. 163, Issue 9 https://doi.org/10.1149/2.0411609jes	journal	January 2016
Theory of SEI Formation in Rechargeable Batteries: Capacity Fade, Accelerated Aging and Lifetime Prediction Pinson, Matthew B.; Bazant, Martin Z. Journal of The Electrochemical Society, Vol. 160, Issue 2 https://doi.org/10.1149/2.044302jes	journal	December 2012
Rapid Impedance Growth and Gas Production at the Li-Ion Cell Positive Electrode in the Absence of a Negative Electrode Xiong, D. J.; Ellis, L. D.; Nelson, K. J. Journal of The Electrochemical Society, Vol. 163, Issue 14 https://doi.org/10.1149/2.1031614jes	journal	January 2016
Review—SEI: Past, Present and Future Peled, E.; Menkin, S. Journal of The Electrochemical Society, Vol. 164, Issue 7 https://doi.org/10.1149/2.1441707jes	journal	January 2017
Intercoder Reliability and Validity of WebPlotDigitizer in Extracting Graphed Data Drevon, Daniel; Fursa, Sophie R.; Malcolm, Allura L. Behavior Modification, Vol. 41, Issue 2 https://doi.org/10.1177/0145445516673998	journal	September 2016
The Solid Electrolyte Interphase – The Most Important and the Least Understood Solid Electrolyte in Rechargeable Li Batteries Winter, Martin Zeitschrift für Physikalische Chemie, Vol. 223, Issue 10-11 https://doi.org/10.1524/zpch.2009.6086	journal	December 2009