Porous-Electrode Theory of Lithium Ion Battery: Old Paradigm and New Challenge

Authors

Xiao-xiao WANG, 1. Hubei Key Laboratory of Electrochemical Power Sources, Key Laboratory of Analytical Chemistry for Biology and Medicine (Ministry of Education), Department of Chemistry, Wuhan University, Wuhan 430072, China;
Zi-rui ZHOU, 1. Hubei Key Laboratory of Electrochemical Power Sources, Key Laboratory of Analytical Chemistry for Biology and Medicine (Ministry of Education), Department of Chemistry, Wuhan University, Wuhan 430072, China;
Qiang SHAN, 1. Hubei Key Laboratory of Electrochemical Power Sources, Key Laboratory of Analytical Chemistry for Biology and Medicine (Ministry of Education), Department of Chemistry, Wuhan University, Wuhan 430072, China;
Zeng-ming ZHANG, 2. Hunan Provincial Key Laboratory of Chemical Power Sources, College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China;
Jun HUANG, 2. Hunan Provincial Key Laboratory of Chemical Power Sources, College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China;Follow
Yu-wen LIU, 1. Hubei Key Laboratory of Electrochemical Power Sources, Key Laboratory of Analytical Chemistry for Biology and Medicine (Ministry of Education), Department of Chemistry, Wuhan University, Wuhan 430072, China;
Sheng-li CHEN, 1. Hubei Key Laboratory of Electrochemical Power Sources, Key Laboratory of Analytical Chemistry for Biology and Medicine (Ministry of Education), Department of Chemistry, Wuhan University, Wuhan 430072, China;Follow

Corresponding Author

Jun HUANG(jhuangelectrochem@qq.com);
Sheng-li CHEN(slchen@whu.edu.cn)

Abstract

A critical review on the porous electrode theory developed by Newman and his colleagues is presented. We propose several ideas for further development of this theory by analyzing its limitations. The classical Newman theory does not consider ion steric effect in describing ion transport in electrolyte solutions, which can be amended by a newly developed ion-vacancy coupled charge transfer model for ion transport in concentrated solutions. Ion transport in solid particles of active materials is essentially an ion-electron coupled transport process, and its rationality is verified by comparing the calculated and experimental diffusion coefficients of Li + ion in intercalation materials. The methods for describing multiscale structures of porous electrodes and the theories of porous structure reconstruction are summarized, and their applications in determining the effective transport parameters are presented and discussed.
We would like to point out that further development remains necessary for porous electrode theory, especially with the emerging of new materials and systems to meet high energy and power density. A number of issues associated with/raised by high working current densities should be considered, for instances, nonlinear non-equilibrium mass transportation, overlapping of electrical double layer (EDL) and mass transport layer, the interfacial charge transfer kinetics, the fusion of phase and interface, the phase transformation of electrode materials in the process of charging and discharging, and the coupling among electrochemical, thermal and mechanical properties and processes.
It is our consensus to build a universal theoretical framework that can contain electrochemistry, thermodynamics and mechanics in the electrochemical systems, with careful consideration of microscopic mechanisms for charge and mass transfer in different spatial and temporal domains.

Graphical Abstract

Keywords

porous electrode theory, ion transport, interfacial charge transfer reaction, multi-scale description method, structure reconstruction

DOI Link

https://doi.org/10.13208/j.electrochem.200651

Publication Date

2020-10-28

Online Available Date

2020-09-23

Revised Date

2020-09-10

Received Date

2020-07-14

Recommended Citation

Xiao-xiao WANG, Zi-rui ZHOU, Qiang SHAN, Zeng-ming ZHANG, Jun HUANG, Yu-wen LIU, Sheng-li CHEN. Porous-Electrode Theory of Lithium Ion Battery: Old Paradigm and New Challenge[J]. Journal of Electrochemistry, 2020 , 26(5): 596-606.
DOI: 10.13208/j.electrochem.200651
Available at: https://jelectrochem.xmu.edu.cn/journal/vol26/iss5/6

References

[1] Ingham D B, Pop I. Transport phenomena in porous media[M]. Verlag Berlin Heidelberg: Elsevier, 1998.

[2] Hang H X(杨汉西), Zha Q X(查全性). Numerical solutions of polarizations of porous electrodes and theia distributions[J]. Journal of Wuhan University (Natural science) (武汉大学学报(自然科学版)), 1982,2:101-108.

[3] Yang H X(杨汉西), Lu J T(陆君涛), Zha Q X(查全性). Numerical solutions of polarizations of porous electrodes and its distributions. I. Effects of ohmic resistances[J]. Journal of Wuhan University(Natural Science) (武汉大学学报(自然科学版)), 1981,1:57-65.

[4] Newman J S, Tobias C W. Theoretical analysis of current distribution in porous electrodes[J]. Journal of The Electrochemical Society, 1962,109(12):1183-1191.

[5] Newman J S, Thomas-Alyea K E. Electrochemical systems[M]. Hoboken, New Jersey: Wiley-Interscience, 2004.

[6] Newman J S, Tiedemann W. Porous-electrode theory with battery applications[J]. AIChE Journal, 1975,21(1):25-41.

[7] Huang J, Li Z, Zhang J B, et al. An analytical three-scale impedance model for porous electrode with agglomerates in lithium-ion batteries[J]. Journal of The Electrochemical Society, 2015,162(4):A585-A595.

[8] Huang J, Ge H, Li Z, et al. An agglomerate model for the impedance of secondary particle in lithium-ion battery electrode[J]. Journal of The Electrochemical Society, 2014,161(8):E3202-E3215.

[9] Huang J, Peng Z Q. Understanding the reaction interface in lithium-oxygen batteries[J]. Batteries & Supercaps, 2019,2(1):37-48.

[10] Huang J, Tong B. Probing the reaction interface in Li-O₂ batteries using electrochemical impedance spectroscopy: dual roles of Li₂O₂[J]. Chemical Communications, 2017,53(83):11418-11421.
URL pmid: 28975180

[11] Ohma A, Mashio T, Sato K, et al. Analysis of proton exchange membrane fuel cell catalyst layers for reduction of platinum loading at Nissan[J]. Electrochimica Acta, 2011,56(28):10832-10841.

[12] Bai P, Bazant M Z. Charge transfer kinetics at the solid-solid interface in porous electrodes[J]. Nature Communications, 2014,5(1):3585.

[13] Huang J, Li Z, Ge H, et al. Analytical solution to the impedance of electrode/electrolyte interface in lithium-ion batteries[J]. Journal of The Electrochemical Society, 2015,162(13):A7037-A7048.

[14] Schmuck M, Bazant M Z. Homogenization of the poisson-nernst-planck equations for ion transport in charged porous media[J]. SIAM Journal on Applied Mathematics, 2015,75(3):1369-1401.

[15] Ciucci F, Lai W. Derivation of micro/macro lithium battery models from homogenization[J]. Transport in Porous Media, 2011,88(2):249-270.

[16] Sethuraman V A, Albertus P. Academic family tree of professor John Newman[J]. ECS Transcations, 2008,16(13):1-12.

[17] Ksenzhek O S, Stender V V. Opredelenie udel' noǐ poverkhnosti poristykh elektrodov metodami izmereniya emkosti[C] //Dokl. Akad. Nauk SSSR. 1956,106:487.

[18] 化学系电化学研究室. 防水型气体扩散电极的极化理论[J]. Journal of Wuhan University(Natural science) (武汉大学学报(自然科学版)), 1975,3:83-106.

[19] Lu J T(陆君涛), Zha Q X(查全性), Yan H Q(严河清), et al. On the mechanism of weeping and salt recipitation of air electrodes.[J]. ACta Chimica Sinica (化学学报), 1978,36(4):249-260

[20] Tian Z W(田昭武), Lin Z G(林祖赓), You J K(尤金跨). 多孔电极极化理论-气体扩散多孔电极的不平整液膜模型[J]. 中国科学, 1981,5:581-587.

[21] Tian Z W(田昭武). Theory of polarization of porous electrodes[J]. Journal of Xiamen University (厦门大学学报), 1978,3:58-71.

[22] Tian Z W(田昭武). Theory of polarization of porous electrodes[J]. Journal of Xiamen University (厦门大学学报), 1978,3:47-57.

[23] You J K(尤金跨), Lin Z G(林祖赓), Tian Z W(田昭武). The effect of liquid film on the performance of the gas diffusion porous electrode[J]. Journal of Xiamen University(Natural science) (厦门大学学报(自然科学版)), 1993,32(5):589-593.

[24] Zhang Z M, Gao Y, Chen S L, et al. Understanding dynamics of electrochemical double layers via a modified concentrated solution theory[J]. Journal of The Electrochemical Society, 2020, 167(1): UNSP 013519.

[25] Gao Y, Huang J, Liu Y W, et al. Ion-vacancy coupled charge transfer model for ion transport in concentrated solutions[J]. Science China Chemistry, 2019,62(4):515-520.

[26] Huang J, Zhang J B. Theory of impedance response of porous electrodes: simplifications, inhomogeneities, non-stationarities and applications[J]. Journal of The Ele-ctrochemical Society, 2016,163(9):A1983-A2000.

[27] Suwanwarangkul R, Croiset E, Fowler M W, et al. Performance comparison of Fick’s, dusty-gas and Stefan-Maxwell models to predict the concentration overpotential of a SOFC anode[J]. Journal of Power Sources, 2003,122(1):9-18.

[28] Monchick L, Munn R J, Mason E A. Thermal diffusion in polyatomic gases: A generalized stefan-maxwell diffusion equation[J]. The Journal of Chemical Physics, 1966,45(8):3051-3058.

[29] Whitaker S. The method of volume averaging[M]. Berlin: Springer Science, 1998.

[30] Goncharenko A V. Generalizations of the Bruggeman equation and a concept of shape-distributed particle composites[J]. Physical Review E, 2003,68(4):041108.
doi: 10.1103/PhysRevE.68.041108 URL

[31] Chung D-W, Ebner M, Ely D R, et al. Validity of the Bruggeman relation for porous electrodes[J]. Modelling and Simulation in Materials Science and Engineering, 2013,21(7):074009.

[32] Gao Y(高雨). Theoretical and computational studies of electrochemical behavior in ultra-concentrated system[D]. Wuhan University(武汉大学), 2019.

[33] Chen S L, Liu Y W, Chen J X. Heterogeneous electron transfer at nanoscopic electrodes: importance of electronic structures and electric double layers[J]. Chemical Society Reviews, 2014,43(15):5372-5386.
URL pmid: 24871071

[34] Wang X H, Mehandzhiyski A Y, Arstad B, et al. Selective charging behavior in an ionic mixture electrolyte-supercapacitor system for higher energy and power[J]. Journal of the American Chemical Society, 2017,139(51):18681-18687.
URL pmid: 29185334

[35] Suo L, Borodin O, Wang Y, et al. “Water-in-salt” electrolyte makes aqueous sodium-ion battery safe, green, and long-lasting[J]. Advanced Energy Materials, 2017,7(21):1701189.
doi: 10.1002/aenm.201701189 URL

[36] Giordani V, Tozier D, Tan H, et al. A molten salt lithium-oxygen battery[J]. Journal of the American Chemical Society, 2016,138(8):2656-2663.
doi: 10.1021/jacs.5b11744 URL pmid: 26871485

[37] Cogswell D A, Bazant M Z. Theory of coherent nucleation in phase-separating nanoparticles[J]. Nano Letters, 2013,13(7):36-41.

[38] Zhao Y, Daemen L L. Superionic conductivity in lithium-rich anti-perovskites[J]. Journal of the American Chemical Society, 2012,134(36):15042-15047.
URL pmid: 22849550

[39] Bazant M Z, Thornton K, Ajdari A. Diffuse-charge dynamics in electrochemical systems[J]. Physical Review E, 2004,70(2):021506.

[40] Bazant M Z, Kilic M S, Storey B D, et al. Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions[J]. Advances in Colloid and Interface Science, 2009,152(1):48-88.

[41] Bazant M Z, Storey B D, Kornyshev A A. Double layer in ionic liquids: overscreening versus crowding[J]. Physical Review Letters, 2011,106(4):046102.
URL pmid: 21405339

[42] Lee A A, Kondrat S, Vella D, et al. Dynamics of ion transport in ionic liquids[J]. Physical Review Letters, 2015,115(10):106101.
doi: 10.1103/PhysRevLett.115.106101 URL pmid: 26382685

[43] Winter M. The solid electrolyte interphase—the most important and the least understood solid electrolyte in rechargeable Li batteries[J]. Zeitschrift für physikalische Chemie, 2009,223(10/11):1395-1406.

[44] Peled E, Menkin S. SEI: past, present and future[J]. Journal of The Electrochemical Society, 2017,164(7):A1703-A1709.

[45] Kaiser N, Bradler S, König C, et al. In situ investigation of mixed ionic and electronic transport across dense lithium peroxide films[J]. Journal of The Electrochemical Society, 2017,164(4):A744-A749.

[46] Fraggedakis D, McEldrew M, Smith R B, et al. Theory of coupled ion-electron transfer kinetics[J]. ArXiv, 2020: 12980.

[47] Newton M D, Sutin N. Electron transfer reactions in condensed phases[J]. Annual Review of Physical Chemistry, 1984,35(1):437-480.
doi: 10.1146/annurev.pc.35.100184.002253 URL

[48] Brunschwig B S, Logan J, Newton M D, et al. A semiclassical treatment of electron-exchange reactions. Application to the hexaaquoiron(II)-hexaaquoiron(III) system[J]. Journal of the American Chemical Society, 1980,102(118):5798-5809.

[49] Sutin N. Nuclear, electronic, and frequency factors in electron-transfer reactions[J]. Accounts of Chemical Research, 1982,15(9):275-282.
doi: 10.1021/ar00081a002 URL

[50] Prosini P P, Lisi M, Zane D, et al. Determination of the chemical diffusion coefficient of lithium in LiFePO₄[J]. Solid State Ionics, 2012,148(1/2):45-51.

[51] Manjunatha H, Venkatesha T V, Suresh G S. Kinetics of electrochemical insertion of lithium ion into LiFePO₄ from aqueous 2M Li₂SO₄ solution studied by potentiostatic intermittent titration technique[J]. Electrochimica Acta, 2011,58:247-257.

[52] Zhu Y J, Wang C S. Galvanostatic intermittent titration technique for phase-transformation electrodes[J]. The Journal of Physical Chemistry C, 2010,114(6):2830-2841.

[53] Zhu Y R, Xie Y, Zhu R S, et al. Kinetic study on LiFePO₄-positive electrode material of lithium-ion battery[J]. Ionics, 2011,17(5):437-441.

[54] Zhang Y, Pan Y, Liu J, et al. Synjournal and electrochemical studies of carbon-modified LiNiPO₄ as the cathode material of Li-ion batteries[J]. Chemical Research in Chinese Universities, 2015,31(1):117-122.
doi: 10.1007/s40242-015-4261-9 URL

[55] Sugiyama J, Nozaki H, Harada M, et al. Diffusive behavior in LiMPO₄ with M=Fe, Co, Ni probed by muon-spin relaxation[J]. Physical Review B, 2012,85(5):054111.
doi: 10.1103/PhysRevB.85.054111 URL

[56] Timofte C. Homogenization results for ionic transport in periodic porous media[J]. Computers and Mathematics with Applications, 2014,68(9):1024-1032.

[57] Arunachalam H. A new multiscale modeling framework for lithium-ion battery dynamics: theory, experiments, and comparative study with the doyle-fuller-newman model[D]. Clemson University, 2017.

[58] Arunachalam H, Onori S, Battiatob I. On veracity of ma-croscopic lithium-ion battery models[J]. Journal of The Electrochemical Society, 2015,162(10):A1940-A1951.

[59] Auriault J L. Heterogeneous medium. Is an equivalent macroscopic description possible?[J]. International Journal of Engineering Science, 1991,29(7):785-795.

[60] Zhang X, Tartakovsky D M. Effective ion diffusion in charged nanoporous materials[J]. Journal of The Electrochemical Society, 2017,164(4):E53-E61.

[61] Arunachalam H, Onori S. What if the Doyle-Fuller-Newman model fails? A new macroscale modeling framework[C] //2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018: 5702-5707.

[62] Korneev S, Arunachalam H, Onori S, et al. A data-driven multiscale framework to estimate effective properties of lithium-ion batteries from microstructure images[J]. Transport in Porous Media, 2020,134(1):173-194.

[63] Arunachalam H, Onori S. Full homogenized macroscale model and pseudo-2-dimensional model for lithium-ion battery dynamics: comparative analysis, experimental verification and sensitivity analysis[J]. Journal of The Electrochemical Society, 2019,166(8):A1380-A1392.

[64] Shan Q(单强). Numerical reconstruction and characteristic parameter analysis of 3D microstructure model of porous electrode of lithium-ion battery[D]. Wuhan University(武汉大学), 2020.

[65] Promentilla M A, Sugiyama T, Hitomi T, et al. Quantification of tortuosity in hardened cement pastes using synchrotron-based X-ray computed microtomography[J]. Cement Concrete Research, 2009,39(6):548-557.

[66] Krüger T, Shardt O, Kuzmin A, et al. The lattice Boltzmann method[M]. Switzerland: Springer Nature, 2017.

[67] Chen C F, Verma A, Mukherjee P P. Probing the role of electrode microstructure in the lithium-ion battery thermal behavior[J]. Journal of The Electrochemical Society, 2017,164(11):E3146-E3158.

[68] Tariq F, Yufit V, Kishimoto M, et al. Three-dimensional high resolution X-ray imaging and quantification of lithium ion battery mesocarbon microbead anodes[J]. Journal of Power Sources, 2014,248:1014-1020.

[69] Kishimoto M, Iwai H, Saito M, et al. Three-dimensional simulation of SOFC anode polarization characteristics based on sub-grid scale modeling of microstructure[J]. Journal of The Electrochemical Society, 2012,159(3):B315-B323.

[70] Wu W(吴伟), Jiang F M(蒋方明), Zeng J B(曾建邦). Simulated annealing reconstruction of LiCoO₂ cathode microstructure and prediction of its effective transport properties[J]. Acta Physica Sinica(物理学报), 2014,63(4):48202-048202.

[71] Thorat I V, Stephenson D E, Zacharias N A, et al. Quantifying tortuosity in porous Li-ion battery materials[J]. Journal of Power Sources, 2009,188(2):592-600.