基于电化学-应力耦合模型的锂离子电池硅/碳核壳结构的模拟与优化

柳小伟; 宋辉; 郭美卿; 王根伟; 迟青卓

doi:10.7498/aps.70.20210455

摘要

硅基电极材料在应用中的一个主要问题是巨大的体积膨胀, 以及由此带来的电极材料破裂、粉化. 本文在有限变形假设前提下, 基于电化学-力学耦合理论, 研究球形Si/C核壳结构在嵌锂过程中的浓度、应力场的演化, 并在此基础上讨论了核壳结构的优化设计. 计算结果显示: 壳层可以很好地保护硅颗粒的膨胀; 然而核内产生的较大的径向压缩应力可能导致核壳界面的脱黏, 而核壳界面处的切向拉伸应力可能会导致壳层的断裂. 进一步为有效提高核壳结构的电化学与力学性能, 从而实现锂离子电池更长的循环寿命, 考虑了两种结构的优化: 1)单层核壳结构; 2)双层核壳结构. 结果表明对于单层核壳结构应使用更软的包覆层材料; 而双层核壳结构中优化的材料布置方案为内软外硬, 对双层核壳结构的硬度分析表明, 内层材料的杨氏模量应低于10 GPa, 而外层材料的应不高于70 GPa. 本文的结论对球形材料颗粒电极的设计及优化具有一定的指导意义.

关键词:

Abstract

Silicon is considered as a first candidate for ideal anode material of the next-generation lithium-ion battery due to its high theoretical capacity to meet the demand for higher energy density. On the other hand, high theoretical capacity is accompanied by massive volume expansion, which gives arise to high stress and crack and pulverization of anode particles. Finally, the capacity of the battery fades gradually. While some kinds of factors contribute to the failure of silicon-based electrodes, the most important one is the diffusion-induced stress generated in silicon-based electrode particles. The cyclic processes of lithiation and delithiation are accomplished by the intercalation into and deintercalation from the silicon particles of lithium ions. During the cycle, physical processes and chemical processes, such as diffusion of lithium ions, phase transition, and volume expansion, take place simultaneously, making the cyclic process a strong-coupling problem to be addressed. For example, the intercalation of lithium ions into the electrode results in volume expansion and phase transition of anodes, thereby inducing stress; in turn, stress affects the diffusion process of lithium ions. Aiming to probe this problem, with the finite deformation hypothesis, an electrochemical-mechanical coupling model is used to study the variation and distribution of concentration and stress of core-shell structure during lithiation. And more importantly, great emphasis is put on the optimal design of core-shell structure. The numerical results show that the shell is useful in prohibiting the volume expansion of silicon core, but large compressive radial stress in silicon core may cause the core and shell to be detached, while the tangential tensile stress at the core-shell interface leads the shell to fracture. To improve the electrochemical and mechanical performance and hence lengthen the cycle life of lithium-ion batteries, two kinds of optimal designs are considered: 1) single-layered core-shell structure and 2) double-layered core-shell structure. The numerical results suggest that the softer shell material is suitable for a single-layered core-shell structure and the inner-soft & outer-hard design is optimal for the double-layered core-shell structure. Furthermore, the effects of Young's modulus of the inner and outer carbon layer materials on the chemical and mechanical performance of anode are explored. The simulation shows that the optimal Young's modulus of the inner shell is less than 10 GPa, and that of the outer shell is not higher than 70 GPa. This research is helpful in designing and optimizing the silicon-based anode electrodes of lithium-ion batteries.

Keywords:

作者及机构信息

1.
太原理工大学机械与运载工程学院, 太原　030024

2.
太原理工大学, 材料强度与结构冲击山西省重点实验室, 太原　030024

3.
太原理工大学机械与运载工程学院, 应用力学研究所, 太原　030024

4.
大连理工大学能源与动力学院, 大连　116024

通信作者: 宋辉, songhui@tyut.edu.cn ; 郭美卿, guomeiqing@tyut.edu.cn ;

基金项目: 国家自然科学基金 (批准号: 11872265)和山西省自然科学基金 (批准号: 201901D111087, 201801D121281)资助的课题

Authors and contacts

1.
College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China

2.
Shanxi Key Laboratory of Material Strength and Structural Impact, Taiyuan University of Technology, Taiyuan 030024, China

3.
Institute of Applied Mechanics, College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China

4.
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education Affiliation, Dalian University of Technology, Dalian 116024, China

Corresponding author: Song Hui, songhui@tyut.edu.cn ; Guo Mei-Qing, guomeiqing@tyut.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11872265) and the Natural Science Foundation of Shanxi Province of China (Grant Nos. 201901D111087, 201801D121281)

文章全文 : translate this paragraph

参考文献

[1]	程昀, 李劼, 贾明, 汤依伟, 杜双龙, 艾立华, 殷宝华, 艾亮 2015 64 210202 Google Scholar Cheng Y, Li J, Jia M, Tang Y W, Du S L, Ai L H, Yin B H, Ai L 2015 Acta Phys. Sin. 64 210202 Google Scholar
[2]	Li M, Lu J, Chen Z, Khalil A 2018 Adv. Mater. 30 1800561 Google Scholar
[3]	Xie Z, Ma Z, Wang Y, Zhou Y, Lu C 2016 RSC Adv. 6 22383 Google Scholar
[4]	Vetter J, Novák P, Wagner M R, Veit C, Möller K C, Besenhard J O, Winter M, Wohlfahrt-Mehrens M, Vogler C, Hammouche A 2005 J. Power Sources 147 269 Google Scholar
[5]	孙凤楠, 冯露, 卜家贺, 张静, 李林安, 王世斌 2019 68 120201 Google Scholar Sun F N, Feng L, Bu J H, Zhang J, Li L A, Wang S B 2019 Acta Phys. Sin. 68 120201 Google Scholar
[6]	Baggetto L, Niessen R A H, Roozeboom F, Notten P H L 2008 Adv. Funct. Mater. 18 1057 Google Scholar
[7]	Panat R 2015 Thin Solid Films 596 174 Google Scholar
[8]	Zhao Y, Stein P, Bai Y, Al-Siraj M, Yang Y, Xu B X 2019 J. Power Sources 413 259 Google Scholar
[9]	Prussin S 1961 J. Appl. Phys. 32 1876 Google Scholar
[10]	Zhang X, Shyy W, Sastry A M 2007 J. Electrochem. Soc. 154 A910 Google Scholar
[11]	Song Y, Lu B, Ji X, Zhang J 2012 J. Electrochem. Soc. 159 A2060 Google Scholar
[12]	Bagheri A, Arghavani J, Naghdabadi R 2019 Mech. Mater. 137 103134 Google Scholar
[13]	Lu Y, Zhang P, Wang F, Zhang K, Zhao X 2018 Electrochim. Acta 274 359 Google Scholar
[14]	Christensen J 2010 J. Electrochem. Soc. 157 A366 Google Scholar
[15]	Zhang X Y, Hao F, Chen H S, Fang D N 2014 J. Electrochem. Soc. 161 A2243 Google Scholar
[16]	Cheng Y T, Verbrugge M W 2008 J. Appl. Phys. 104 1876
[17]	Deluca C M, Maute K, Dunn M L 2011 J. Power Sources 196 9672 Google Scholar
[18]	Li Y, Zhang K, Zheng B, Zhang X Q, Wang Q 2015 J. Appl. Phys. 117 245103
[19]	Hu B, Ma Z S, Lei W X, Zou Y L, Lu C S 2017 Theor. Appl. Mech. Lett. 7 199 Google Scholar
[20]	Zhao Y F, Lu B, Zhang J 2018 Acta. Mech. Solida. Sin. 31 290 Google Scholar
[21]	Gao X, Lu W, Xu J 2020 J. Power Sources 449 227501 Google Scholar
[22]	Hao F, Fang D 2013 J. Electrochem. Soc. 160 A595 Google Scholar
[23]	Zhao K J, Pharr M, Hartle L, Vlassak J J, Suo Z G 2012 J. Power Sources 218 6 Google Scholar
[24]	Wu B, Lu W 2017 J. Phys. Chem. C 121 19022 Google Scholar
[25]	Zhang Y, Zhu Z 2020 Int. J. Adv. Manuf. Technol. 108 499 Google Scholar
[26]	Bohn E, Eckl T, Kamlah M, McMeekingc R 2013 J. Electrochem. Soc. 160 A1638 Google Scholar
[27]	Zhang X, Chen H S, Fang D 2019 Int. J. Mech. Sci. 169 105323
[28]	Xu C, Weng L, Chen B, Zhou J Q, Cai R 2019 Int. J. Mech. Sci. 157 87
[29]	Zhao K, Pharr M, Cai S, Vlassak J J, Suo Z G 2011 J. Am. Ceram. Soc. 94 s226 Google Scholar
[30]	Zhang K, Zheng B, Yang F, Li Y 2020 Int. J. Mech. Sci. 177 105602 Google Scholar
[31]	Liu B H, Wang X, Chen H S, Chen S, Yang H X, Xu J, Jiang H Q, Fang D N 2019 J. Appl. Mech. 86 041005 Google Scholar
[32]	Ding N, Xu J, Yao Y X, Wegner G, Fang X, . Chen C.H, Lieberwirth I 2009 Solid State Ionics 180 222 Google Scholar
[33]	Sethuraman V A, Chon M J, Shimshak M, Winkle N V, Guduru P R 2010 Electrochem. Commun. 12 1614 Google Scholar
[34]	Wu B, Lu W 2017 J. Power Sources 360 360 Google Scholar
[35]	Deng Q, Hu R, Xu C, Chen B, Zhou J 2019 J. Solid State Electrochem. 23 2999 Google Scholar

施引文献

图 1 锂离子电池的用途

Fig. 1. Usage of lithium-ion batteries.

下载: 全尺寸图片幻灯片

图 2 电化学-力学耦合机理

Fig. 2. Electrochemistry-mechanics coupling mechanism.

下载: 全尺寸图片幻灯片

图 3 (a) 锂离子电池核壳结构示意图; (b) 径向和切向示意图

Fig. 3. (a) Schematic diagram of core-shell structure of lithium-ion battery; (b) radial and tangential schematic diagram.

下载: 全尺寸图片幻灯片

图 4 不同假设条件下充电过程中沿着半径方向的径向应力和切向应力　(a)小变形下的径向应力; (b)有限变形下的径向应力; (c)小变形下的切向应力; (d)有限变形下的切向应力

Fig. 4. Radial stress and tangential stress along the radial direction during charging under different hypothesis: (a) Radial stress under small deformation; (b) radial stress under finite deformation; (c) tangential stress under small deformation; (d) tangential stress under finite deformation.

下载: 全尺寸图片幻灯片

图 5 嵌锂过程中沿着半径方向的(a)浓度和(b) von Mises 应力分布示意图

Fig. 5. Schematic diagram of (a) concentration; (b) von Mises stress along the radius during lithium insertion.

下载: 全尺寸图片幻灯片

图 6 嵌锂过程中(a)浓度, (b) von Mises应力, (c)径向应力, (d)切向应力随着时间的分布示意

Fig. 6. Schematic diagram of the distribution of (a) concentration, (b) von Mises stress, (c) radial stress, and (d) tangential stress over time during lithium insertion.

下载: 全尺寸图片幻灯片

图 7 双层核壳结构在嵌锂过程(a)浓度, (b) von Mises应力, (c)径向应力, (d)切向应力的分布示意图

Fig. 7. Schematic diagram of the distribution of the double-layer core-shell structure during lithium insertion process: (a) concentration; (b) von Mises stress; (c) radial stress; and (d) tangential stress.

下载: 全尺寸图片幻灯片

图 8 Si/C¹/C³双层核壳结构和Si/C³/C¹双层核壳结构的(a)浓度, (b) von Mises应力, (c)径向应力, (d)切向应力分布示意图

Fig. 8. (a) Concentration, (b) von Mises stress, (c) radial stress, and (d) tangential stress distribution schematic diagram of Si/C¹/C³ double-layer core-shell structure and Si/C³/C¹ double-layer core-shell structure.

下载: 全尺寸图片幻灯片

图 9 不同的内外层壳杨氏模量情况下 (a)浓度, (b)浓度, (c) von Mises应力, (d)径向应力分布示意图

Fig. 9. (a) Concentration, (b) concentration, (c) von Mises stress, (d) schematic diagram of radial stress distribution under different Young's modulus of inner and outer shells.

下载: 全尺寸图片幻灯片

表 1 核壳结构材料参数^[16,32,33]

Table 1. Material parameters of core-shell structure^[16,32,33]

参数	核	壳
饱和浓度 C_max/(mol·m^–3)	2.95 × 10⁵	2.4 × 10⁴
初始浓度C₀/(mol·m^–3)	0	0
扩散系数 D/(m²·s^–1)	1.0 × 10^–16	1.45 × 10^–13
内径/外径 R/m	4 × 10^–8	5 × 10^–8
泊松比 ν	0.23	0.30
杨氏模量E/Pa	8 × 10¹⁰	6 × 10¹⁰
偏摩尔体积 Ω/(m³·mol^–1)	3/C_max	3.497 × 10^–6
室温 T/K	298

下载: 导出CSV

表 2 包覆层碳的材料参数

Table 2. Material parameters of the outer shell.

参数	杨氏模量E/Pa	饱和浓度C_max/(mol·m^–3)	偏摩尔体积Ω/(m³·mol^–1)	泊松比ν	扩散系数D/(m²·s^–1)
碳层^[34]	1 × 10¹⁰	24161	3.497 × 10^–6	0.3	1.0 × 10^–14
外包覆层^[35]	3 × 10¹⁰	2.5 × 10⁴	3.497 × 10^–6	0.3	1.0 × 10^–14

下载: 导出CSV

map

[1]	程昀, 李劼, 贾明, 汤依伟, 杜双龙, 艾立华, 殷宝华, 艾亮 2015 64 210202 Google Scholar Cheng Y, Li J, Jia M, Tang Y W, Du S L, Ai L H, Yin B H, Ai L 2015 Acta Phys. Sin. 64 210202 Google Scholar
[2]	Li M, Lu J, Chen Z, Khalil A 2018 Adv. Mater. 30 1800561 Google Scholar
[3]	Xie Z, Ma Z, Wang Y, Zhou Y, Lu C 2016 RSC Adv. 6 22383 Google Scholar
[4]	Vetter J, Novák P, Wagner M R, Veit C, Möller K C, Besenhard J O, Winter M, Wohlfahrt-Mehrens M, Vogler C, Hammouche A 2005 J. Power Sources 147 269 Google Scholar
[5]	孙凤楠, 冯露, 卜家贺, 张静, 李林安, 王世斌 2019 68 120201 Google Scholar Sun F N, Feng L, Bu J H, Zhang J, Li L A, Wang S B 2019 Acta Phys. Sin. 68 120201 Google Scholar
[6]	Baggetto L, Niessen R A H, Roozeboom F, Notten P H L 2008 Adv. Funct. Mater. 18 1057 Google Scholar
[7]	Panat R 2015 Thin Solid Films 596 174 Google Scholar
[8]	Zhao Y, Stein P, Bai Y, Al-Siraj M, Yang Y, Xu B X 2019 J. Power Sources 413 259 Google Scholar
[9]	Prussin S 1961 J. Appl. Phys. 32 1876 Google Scholar
[10]	Zhang X, Shyy W, Sastry A M 2007 J. Electrochem. Soc. 154 A910 Google Scholar
[11]	Song Y, Lu B, Ji X, Zhang J 2012 J. Electrochem. Soc. 159 A2060 Google Scholar
[12]	Bagheri A, Arghavani J, Naghdabadi R 2019 Mech. Mater. 137 103134 Google Scholar
[13]	Lu Y, Zhang P, Wang F, Zhang K, Zhao X 2018 Electrochim. Acta 274 359 Google Scholar
[14]	Christensen J 2010 J. Electrochem. Soc. 157 A366 Google Scholar
[15]	Zhang X Y, Hao F, Chen H S, Fang D N 2014 J. Electrochem. Soc. 161 A2243 Google Scholar
[16]	Cheng Y T, Verbrugge M W 2008 J. Appl. Phys. 104 1876
[17]	Deluca C M, Maute K, Dunn M L 2011 J. Power Sources 196 9672 Google Scholar
[18]	Li Y, Zhang K, Zheng B, Zhang X Q, Wang Q 2015 J. Appl. Phys. 117 245103
[19]	Hu B, Ma Z S, Lei W X, Zou Y L, Lu C S 2017 Theor. Appl. Mech. Lett. 7 199 Google Scholar
[20]	Zhao Y F, Lu B, Zhang J 2018 Acta. Mech. Solida. Sin. 31 290 Google Scholar
[21]	Gao X, Lu W, Xu J 2020 J. Power Sources 449 227501 Google Scholar
[22]	Hao F, Fang D 2013 J. Electrochem. Soc. 160 A595 Google Scholar
[23]	Zhao K J, Pharr M, Hartle L, Vlassak J J, Suo Z G 2012 J. Power Sources 218 6 Google Scholar
[24]	Wu B, Lu W 2017 J. Phys. Chem. C 121 19022 Google Scholar
[25]	Zhang Y, Zhu Z 2020 Int. J. Adv. Manuf. Technol. 108 499 Google Scholar
[26]	Bohn E, Eckl T, Kamlah M, McMeekingc R 2013 J. Electrochem. Soc. 160 A1638 Google Scholar
[27]	Zhang X, Chen H S, Fang D 2019 Int. J. Mech. Sci. 169 105323
[28]	Xu C, Weng L, Chen B, Zhou J Q, Cai R 2019 Int. J. Mech. Sci. 157 87
[29]	Zhao K, Pharr M, Cai S, Vlassak J J, Suo Z G 2011 J. Am. Ceram. Soc. 94 s226 Google Scholar
[30]	Zhang K, Zheng B, Yang F, Li Y 2020 Int. J. Mech. Sci. 177 105602 Google Scholar
[31]	Liu B H, Wang X, Chen H S, Chen S, Yang H X, Xu J, Jiang H Q, Fang D N 2019 J. Appl. Mech. 86 041005 Google Scholar
[32]	Ding N, Xu J, Yao Y X, Wegner G, Fang X, . Chen C.H, Lieberwirth I 2009 Solid State Ionics 180 222 Google Scholar
[33]	Sethuraman V A, Chon M J, Shimshak M, Winkle N V, Guduru P R 2010 Electrochem. Commun. 12 1614 Google Scholar
[34]	Wu B, Lu W 2017 J. Power Sources 360 360 Google Scholar
[35]	Deng Q, Hu R, Xu C, Chen B, Zhou J 2019 J. Solid State Electrochem. 23 2999 Google Scholar

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