力学约束对锂离子电池双层电极中锂扩散和应力的影响

张凯; 徐鹏; 关学锋; 杜玉群; 王轲杰; 陆勇俊

doi:10.7498/aps.74.20241275

摘要

锂离子电池中的电极总是处于特定的约束当中, 这些约束既包括电池内部不可避免的被动结构约束, 又包括一些新兴技术应用场景可能赋予的外部主动约束. 本文主要利用化学-力学双向耦合的基本假设建立描述双层电极结构的理论模型, 考虑4种不同强弱的理想化变形约束作为其边界条件, 并通过数值求解研究在充电过程中这些外部约束对双层电极中Li扩散和应力的影响. 从力学的角度, 所研究的双层电极结构存在侧向伸缩和弯曲变形两个自由度, 弱化的约束条件能够部分或完全激活这些应力释放机制, 从而降低电极结构整体的应力水平, 并提升结构的力学稳定性. 然而, 从电化学的角度, 电极结构的正向弯曲变形所产生的应力梯度会阻碍嵌Li过程, 强化的约束能够部分或完全抑制电极的正向弯曲, 使活性层内Li浓度更加均匀, 从而提高活性层的容量利用率. 这些结果不仅为进一步理解双层电极在更加真实或极端服役条件下的化学-力学响应提供理论参考, 还从设计的角度表明折中的外部约束有利于平衡电极的结构耐久性和电化学性能.

关键词:

Abstract

Lithium-ion batteries (LIBs) are widely used in portable electronic devices, electric vehicles, and other fields. With the rapid development of its application fields, there is an urgent need to further improve its energy density and safety. In the charging/discharging process of the LIBs, the diffusion of Li will cause local volumetric change in the electrode material. The degradation and damage of the electrode material structure caused by diffusion-induced deformation is a major obstacle to the development of LIBs. Generally speaking, the electrode materials in LIBs are always subject to specific external constraints, including both inevitable passive structural constraints within the battery and external active constraints that may be imposed by emerging technology application scenarios, which can also affect the mechanical properties of the electrode materials. Therefore, a more in-depth understanding of the diffusion-induced stress and Li concentration changes in the electrode material is an engineering requirement for developing new material design paradigms to improve the overall performance of LIBs. In this work, a two-way diffusion-stress coupling model is used to discuss the effects of the four different levels of idealized deformation constraints on the Li concentration and stress in the bilayer plate electrode in the charging process through the numerical solution. From a mechanical perspective, the bilayer plate electrode structure has two degrees of freedom: lateral expansion and bending deformation. Weakened constraint conditions can partially or completely activate these stress release mechanisms, thereby reducing the overall stress level of the electrode structure and improving its mechanical stability. However, from an electrochemical perspective, the stress gradient generated by the forward bending deformation of the electrode structure can hinder the Li intercalation process. Enhanced constraints can partially or completely suppress the forward bending of the electrode, making the Li concentration in the active layer more uniform and thus improving the capacity utilization efficiency of the active layer. These results not only provide theoretical references for further understanding the chemical-mechanical response of the bilayer electrodes under more realistic or extreme service conditions, but also indicate from a design perspective that compromised external constraints are beneficial for balancing the structural durability and electrochemical performance of electrodes.

Keywords:

作者及机构信息

1.
中北大学工程力学系, 太原　030051

2.
中北大学应用化学系, 太原　030051

3.
西北工业大学工程力学系, 西安　710129

通信作者: 张凯, kzhang222@163.com ; 陆勇俊, luyongjun@mail.nwpu.edu.cn

基金项目: 山西省基础研究计划(批准号: 202103021223190, 20210302124218)资助的课题.

Authors and contacts

1.
Department of Engineering Mechanics, North University of China, Taiyuan 030051, China

2.
Department of Applied Chemistry, North University of China, Taiyuan 030051, China

3.
Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710129, China

Corresponding author: ZHANG Kai, kzhang222@163.com ; LU Yongjun, luyongjun@mail.nwpu.edu.cn

Funds: Project supported by the Fundamental Research Program of Shanxi Province, China (Grant Nos. 202103021223190, 20210302124218).

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 (a)活性层与集流体构成的双层电极横截面示意图(1, 2分别代表活性层和集流体); (b)四种电极的约束情况

Fig. 1. (a) Schematic diagram of the cross-section of a bilayer electrode composed of active layer and current collector (1 and 2 represents the active layer and the current collector); (b) four electrode constraint situations.

下载: 全尺寸图片幻灯片

图 2 恒流(${\bar J_0} = 0.5$)充电过程活性层中不同时刻浓度场的解析解与数值解

Fig. 2. Analytical and numerical solutions of concentration field in the active layer at different time under constant current (${\bar J_0} = 0.5$) charging.

下载: 全尺寸图片幻灯片

图 3 (a) 充电过程中双层电极内无量纲曲率随时间的变化情况; (b) 活性层中不同时刻无量纲锂浓度沿活性层厚度的分布情况

Fig. 3. (a) Variations of dimensionless curvature with time in the bilayer electrodes under charging; (b) distribution of dimensionless Li concentration at different time in the active layer.

下载: 全尺寸图片幻灯片

图 4 充电过程中无量纲通量沿活性层厚度方向的分布情况. 扩散和弯曲应力诱导通量　(a) $ \bar t = 0.1 $, (b) $ \bar t = 1.2 $; 总通量 (c) $ \bar t = 0.1 $, (d) $ \bar t = 1.2 $

Fig. 4. Distribution of dimensionless flux along the thickness of the active layer under charging. Diffusion and bending stress-induced flux: (a) $ \bar t = 0.1 $; (b) $ \bar t = 1.2 $. Total flux: (c) $ \bar t = 0.1 $; (d) $ \bar t = 1.2 $.

下载: 全尺寸图片幻灯片

图 5 充电过程中双层电极中无量纲应力沿电极厚度方向的分布情况　(a) $ \bar t = 0.1 $; (b) $ \bar t = 1.2 $. (c)活性层与集流体界面以及(d)活性层表面处无量纲应力随时间的变化情况

Fig. 5. Distribution of dimensionless stress along the thickness direction of the bilayer electrode during charging process: (a) $ \bar t = 0.1 $; (b) $ \bar t = 1.2 $. (c) The variation of dimensionless stress over time at the interface between the active layer and the current collector, as well as at (d) the surface of the active layer.

下载: 全尺寸图片幻灯片

[1]	Zhang H, Li C M, Eshetu G G, et al. 2020 Angew. Chem. Int. Ed. 59 534 Google Scholar
[2]	Mukhopadhyay A, Sheldon B W 2014 Prog. Mater. Sci. 63 58 Google Scholar
[3]	张俊乾, 吕浡, 宋亦诚 2017 力学季刊 38 14 Zhang J Q, Lü B, Song Y C 2017 Chin. Q. Mech. 38 14
[4]	Zhao Y, Stein P, Bai Y, Al-Siraj M, Yang Y, Xu B X 2019 J. Power Sources 413 259 Google Scholar
[5]	de Vasconcelos L S, Xu R, Xu Z, et al. 2022 Chem. Rev. 122 13043 Google Scholar
[6]	Yang F 2024 J. Energy Storage 75 109634 Google Scholar
[7]	Haftbaradaran H, Gao H, Curtin W A 2010 Appl. Phys. Lett. 96 091909 Google Scholar
[8]	Vanimisetti S K, Ramakrishnan N 2012 Proc. IMechE Part C: J. Mech. Eng. Sci. 226 2192 Google Scholar
[9]	Lu B, Ning C Q, Shi D X, Zhao Y F, Zhang J Q 2020 Chin. Phys. B 29 026201 Google Scholar
[10]	Li J, Dozier A K, Li Y, Yang F, Cheng Y T 2011 J. Electrochem. Soc. 158 A689 Google Scholar
[11]	Chew H B, Hou B, Wang X, Xia S 2014 Int. J. Solids Struct. 51 4176 Google Scholar
[12]	Xie H, Zhang Q, Song H, Shi B, Kang Y 2017 J. Power Sources 342 896 Google Scholar
[13]	Li D, Wang Y, Hu J, Lu B, Cheng Y T, Zhang J 2017 J. Power Sources 366 80 Google Scholar
[14]	Sethuraman V A, Chon M J, Shimshak M, Srinivasan V, Guduru P R 2010 J. Power Sources 195 5062 Google Scholar
[15]	Pharr M, Suo Z, Vlassak J J 2013 Nano Lett. 13 5570 Google Scholar
[16]	Guo Z S, Zhang T, Zhu J, Wang Y 2014 Comput. Mater. Sci. 94 218 Google Scholar
[17]	宋旭, 陆勇俊, 石明亮, 赵翔, 王峰会 2018 物理学报 67 140201 Google Scholar Song X, Lu Y J, Shi M L, Zhao X, Wang F H 2018 Acta Phys. Sin. 67 140201 Google Scholar
[18]	Lu Y, Che Q, Song X, Wang F, Zhao X 2018 Scr. Mater. 150 164 Google Scholar
[19]	Zhang J, Lu B, Song Y, Ji X 2012 J. Power Sources 209 220 Google Scholar
[20]	Yang B, He Y P, Irsa J, Lundgren C A, Ratchford J B, Zhao Y P 2012 J. Power Sources 204 168 Google Scholar
[21]	Hao F, Fang D 2013 J. Power Sources 242 415 Google Scholar
[22]	Song Y, Shao X, Guo Z, Zhang J 2013 J. Phys. D: Appl. Phys. 46 105307 Google Scholar
[23]	He Y L, Hu H J, Song Y C, Guo Z S, Liu C, Zhang J Q 2014 J. Power Sources 248 517 Google Scholar
[24]	Song Y, Li Z, Zhang J 2014 J. Power Sources 263 22 Google Scholar
[25]	Zhang X Y, Hao F, Chen H S, Fang D N 2015 Mech. Mater. 91 351 Google Scholar
[26]	Ji L, Guo Z, Du S, Chen L 2017 Int. J. Mech. Sci. 134 599 Google Scholar
[27]	Liu D, Chen W, Shen X 2017 Compos. Struct. 165 91 Google Scholar
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[29]	Pouyanmehr R, Hassanzadeh-Aghdam M K, Ansari R 2020 Mech. Mater. 145 103390 Google Scholar
[30]	Zhang A, Wang B, Li G, Wang J, Du J 2020 Eng. Fract. Mech. 235 107189 Google Scholar
[31]	Gao C, Guan L, Shi Y, Zhou J, Cai R 2022 Acta Mech. 233 5265 Google Scholar
[32]	Zhang P, Wang Q, Qiu W, Feng L 2023 J. Electrochem. Soc. 170 050508 Google Scholar
[33]	Crank J 1979 The Mathematics of Diffusion (London: Oxford University Press) p61
[34]	Prussin S 1961 J. Appl. Phys. 32 1876 Google Scholar
[35]	Zhang X, Shyy W, Sastry A M 2007 J. Electrochem. Soc. 154 A910 Google Scholar
[36]	He Y, Hu H, Huang D 2016 Mater. Des. 92 438 Google Scholar
[37]	Xia X, Afshar A, Yang H, Portela C M, Kochmann D M, Di Leo C V, Greer J R 2019 Nature 573 205 Google Scholar
[38]	Qiu W, Zhang J, Su D, Zhang Y, Zhang P, Wang Q, Feng L 2023 Int. J. Mech. Sci. 248 108231 Google Scholar
[39]	Berg S, Akturk A, Kammoun M, Ardebili H 2017 Extreme Mech. Lett. 13 108 Google Scholar
[40]	Shi Y, Xu C, Weng L, Wei Y, Chen B, Wang Y, Zhou J, Cai R 2021 Mech. Mater. 161 104024 Google Scholar
[41]	Kim S, Choi S J, Zhao K, Yang H, Gobbi G, Zhang S, Li J 2016 Nat. Commun. 7 10146 Google Scholar
[42]	Johannisson W, Harnden R, Zenkert D, Lindbergh G 2020 Proc. Natl. Acad. Sci. U. S. A. 117 7658 Google Scholar
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[44]	Zhou W 2015 Electrochim. Acta 185 28 Google Scholar
[45]	Xuan F Z, Shao S S, Wang Z, Tu S T 2008 J. Phys. D: Appl. Phys. 42 015401
[46]	Zhu Z, Hu H, He Y, Tao B 2018 Compos. Struct. 204 822 Google Scholar
[47]	Zhu Z, Wan J, Wu T, Huang P 2022 Acta Mech. 233 2471 Google Scholar
[48]	Song X, Lu Y, Wang F, Zhao X, Chen H 2020 J. Power Sources 452 227803 Google Scholar
[49]	Peng Y, Hao F 2023 J. Energy Storage 57 106195 Google Scholar
[50]	Shi Y, Xu C, Chen B, Zhou J, Cai R 2023 Appl. Math. Mech. 44 189 Google Scholar
[51]	Guan L, Shi Y, Gao C, Wang T, Zhou J, Cai R 2023 Electrochim. Acta 440 141669 Google Scholar
[52]	Geng S, Zhang K, Zheng B, Zhang Y 2024 Acta Mech. 235 191 Google Scholar
[53]	Zhuang Y, Zou Z Y, Lu B, Li Y J, Wang D, Avdeev M, Shi S Q 2020 Chin. Phys. B 29 068202 Google Scholar
[54]	张静, 冯露, 仇巍张鹏飞 2021 应用力学学报 38 2306 Zhang J, Feng L, Qiu W, Zhang P F 2021 Chin. J. Appl. Mech. 38 2306
[55]	Yang S, Lu Y, Liu B, Che Q, Wang F 2023 Int. J. Hydrogen Energy 48 12461 Google Scholar
[56]	Freud L B 1993 J. Cryst. Growth 132 341 Google Scholar
[57]	陆勇俊, 杨溢, 王峰会, 楼康, 赵翔 2016 物理学报 65 098102 Google Scholar Lu Y J, Yang Y, Wang F H, Lou K, Zhao X 2016 Acta Phys. Sin. 65 098102 Google Scholar
[58]	Purkayastha R, McMeeking R 2013 Comput. Mater. Sci. 80 2 Google Scholar
[59]	Sethuraman V A, Srinivasan V, Bower A F, Guduru P R 2010 J. Electrochem. Soc. 157 A1253 Google Scholar
[60]	Yang F 2013 J. Power Sources 241 146 Google Scholar
[61]	Haftbaradaran H, Xiao X, Verbrugge M W, Gao H 2012 J. Power Sources 206 357 Google Scholar
[62]	Yang F 2011 J. Power Sources 196 465 Google Scholar

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力学约束对锂离子电池双层电极中锂扩散和应力的影响