LiFePO4锂离子电池的数值模拟：正极材料颗粒粒径的影响

doi:10.11949/0438-1157.20191199

摘要/Abstract

摘要：

LiFePO₄（LFP）作为正极材料时，锂离子电池安全性高且循环寿命长，是目前应用最广泛的正极材料，但其电池倍率性能较差。提升倍率性能的有效手段之一是将LFP材料颗粒纳米化，但材料纳米化过程中颗粒粒径减小对于锂离子电池充放电过程中锂在固液相的扩散及表面电化学反应的影响机制仍缺乏清晰的认识。采用锂离子电池的准二维模型，模拟锂离子电池的放电过程，定量研究了正极材料颗粒粒径对锂离子电池倍率性能的影响，分析了固液相扩散速率与电化学反应速率受LFP材料颗粒粒径的影响程度。研究结果表明：电极材料中固相扩散阻力是锂离子电池电化学性能的主要限制因素。小粒径的LFP作为正极材料时，电极材料内的金属锂的迁移路径较短，同时颗粒与电解液的接触面积增加，界面的电化学反应速率较快，放电倍率对于锂离子电池性能影响较小；大粒径的LFP作为正极材料时，电极材料内的金属锂扩散路径的增加和较高的固相扩散阻力限制了界面的电化学反应速率，导致锂离子电池的倍率性能显著降低。LFP材料的纳米化可以有效减小固相扩散阻力，提升锂离子电池的倍率性能。

关键词: 锂离子电池, 数学模拟, 磷酸铁锂, 颗粒粒径, 倍率性能

Abstract:

When LiFePO₄ (LFP) is used as a cathode material, the lithium-ion battery has high safety and long cycle life. It is currently the most widely used cathode material, but its battery rate performance is poor. One of the effective means to improve the rate performance of lithium-ion battery is to use LFP material of nanometer size. However, the mechanism of the LFP particle of nano size affecting the eletrochemical process during the charge and discharge of lithium-ion battery still remain unclear. In this work, a quasi-two-dimensional model of lithium-ion battery was established to simulate the discharge process. The influence of LFP particle size on the rate performance of lithium-ion battery was quantitatively studied. The diffusion rate and electrochemical reaction rate at solid-liquid interface were quantitatively analyzed. The results indicate that the resistance in solid phase is the key factor limiting the performance of lithium-ion battery. In the case of small particle LFP as electrode material, the diffusion path of lithium metal within the particles was shortened and the interface between electrode material and electrolyte increased, thus the electrochemical reaction rate was faster, presenting better rate performance. While in the case of large particle LFP as electrode material, the low solid phase diffusion rate of LFP material resulted in low electrochemical reaction rate and thus deteriorate rate performance of the lithium-ion battery. Size reduction of LFP could effectively shorten the migration path of the metal lithium in the electrode material and reduce solid phase diffusion resistance, therefore enhance the rate performance of the lithium-ion battery.

Key words: lithium-ion battery, mathematical modeling, lithium iron phosphate, particle size, rate performance

中图分类号:

TQ 028.8

许于, 陈怡沁, 周静红, 隋志军, 周兴贵. LiFePO₄锂离子电池的数值模拟：正极材料颗粒粒径的影响[J]. 化工学报, 2020, 71(2): 821-830.

Yu XU, Yiqin CHEN, Jinghong ZHOU, Zhijun SUI, Xinggui ZHOU. Numerical simulation of lithium-ion battery with LiFePO₄ as cathode material: effect of particle size[J]. CIESC Journal, 2020, 71(2): 821-830.

图/表 7

图1 锂离子电池与准二维模型示意图

Fig.1 Schematic diagram of lithium-ion battery and pseudo two-dimensional model

表1 锂离子电池的模型参数

Table 1 Model parameters for lithium-ion battery

参数	负极	隔膜	正极
A_cell/m²	0.1694
l_i/μm	34	30	70
R_i/μm	0.0365		3.5
ε₁_,i	0.550		0.430
ε₂_,i	0.330	0.540	0.332
c₀/(mol/m³)	1200
c_max_,i/(mol/m³)	31370		22806
SOC₀_,i	0.8		0.03
α_i	0.5		0.5
brug	1.5	1.5	1.5
D₁/(m²/s)	3.9×10^-14		1.18×10^-18
σ₁/(S/m)	100		0.5
t₊	0.363
T/K	298.15
F /(C/mol)	96487
k_i/(m^2.5/(mol^0.5·s))	3×10^-11		1.4×10^-12

图2 商用电池的Newman模型模拟放电曲线与实测放电曲线比较

Fig.2 Comparison between simulated and experimental discharge curve for commercial lithium ion battery

图3 不同LFP颗粒粒径的锂离子电池在不同倍率下的放电曲线

Fig.3 Discharge curves of lithium-ion batteries with LFP of different particle sizes at different discharge rates

图4 不同LFP粒径锂离子电池在不同放电倍率下稳定输出电压（a）和最大容量（b）

Fig.4 Stable output voltage (a) and maximum capacity (b) of lithium-ion batteries with different LFP particle sizes at different discharge rates

图5 不同LFP粒径锂离子电池在1 C放电时的液相扩散系数

Fig.5 Liquid phase diffusion rate of lithium-ion batteries with different LFP particle sizes at 1 C discharge rate

图6 不同LFP粒径锂离子电池正极与隔膜界面处颗粒表面锂离子浓度(a)与局部电流密度(b)

Fig.6 Lithium ion concentration (a) and local current density (b) at interface of cathode and separator in battery with different LFP particle sizes at different discharge rates

参考文献 31

1	Manthiram A, Fu Y, Su Y S. Challenges and prospects of lithium-sulfur batteries[J]. Accounts of Chemical Research, 2012, 46(5): 1125-1134.
2	Goodenough J B. How we made the Li-ion rechargeable battery[J]. Nature Electronics, 2018, 1(3): 204.
3	Goodenough J B, Park K S. The Li-ion rechargeable battery: a perspective[J]. Journal of the American Chemcial Society, 2013, 135(4): 1167-1176.
4	Simon P, Gogotsi Y, Dunn B. Where do batteries end and supercapacitors begin?[J]. Science, 2014, 343(6176): 1210-1211.
5	Cao B, Zhang Q, Liu H, et al. Graphitic carbon nanocage as a stable and high power anode for potassium-ion batteries[J]. Advanced Energy Materials, 2018, 8(25): 1801149.
6	Shi J L, Xiao D D, Ge M Y, et al. High-capacity cathode material with high voltage for Li-ion batteries[J]. Advanced Materials, 2018, 30(9): 1705575.
7	Padhi A K, Goodenough J B, Nanjundaswamy K S. Phospho-olivines as positive-electrode materials for recharageable lithium batteries[J]. Journal of the Electrochemical Society, 1997, 144(4): 1188-1194.
8	Chung S Y, Bloking J T, Chiang Y M. Electronically conductive phospho-olivines as lithium storage electrodes[J]. Nature Materials, 2002, 1(2): 123-128.
9	胡江涛, 郑家新, 潘锋. 锂电池磷酸铁锂正极材料的结构与性能相关性的研究进展[J]. 物理化学学报, 2019, 35(4): 22-31.
	Hu J T, Zheng J X, Pan F. Research progress on the correlation between structure and properties of lithium iron phosphate cathode materials[J]. Acta Physico-Chimica Sinica, 2019, 35(4): 22-31.
10	Ferrari S, Lavall R L, Capsoni D, et al. Influence of particle size and crystal orientation on the electrochemical behavior of carbon-coated LiFePO₄[J]. The Journal of Physical Chemistry C, 2010, 114(29): 12598-12603.
11	Ouyang C Y, Shi S Q, Wang Z X, et al. The effect of Cr doping on Li ion diffusion in LiFePO₄ from first principles investigations and Monte Carlo simulations[J]. Journal of Physics: Condensed Matter, 2004, 16(13): 2265-2272.
12	Takahashi M, Tobishima S I, Takei K, et al. Reaction behavior of LiFePO₄ as a cathode material for rechargeable lithium batteries[J]. Solid State Ionics, Diffusion & Reactions, 2002, 148(3/4): 283-289.
13	Yamada A, Chung S C, Hinokuma K. Optimized LiFePO₄ for lithium battery cathodes[J]. Journal of the Electrochemical Society, 2001, 148(3): A224-A229.
14	Lee K T, Kan W H, Nazar L F. Proof of intercrystallite ionic transport in LiMPO₄ electrodes (M = Fe, Mn)[J]. Journal of the American Chemical Society, 2009, 131(17): 6044-6045.
15	Ferrari S, Lavall R L, Capsoni D, et al. Influence of particle size and crystal orientation on the electrochemical behavior of carbon-coated LiFePO₄[J]. The Journal of Physical Chemistry C, 2010, 114(29): 12598-12603.
16	Satyavani T V S L, Ramya K B, Rajesh K V, et al. Effect of particle size on DC conductivity, activation energy and diffusion coefficient of lithium iron phosphate in Li-ion cells[J]. Engineering Science and Technology, an International Journal, 2016, 19(1): 40-44.
17	王琦, 邓思旭, 刘晶冰, 等. 提高正极材料磷酸铁锂倍率性能的研究进展[J]. 化工进展, 2011, 30(12): 2652-2657.
	Wang Q, Deng S X, Liu J B, et al. Research progress in improving the performance of lithium iron phosphate in cathode materials[J]. Chemical Industry and Engineering Progress, 2011, 30(12): 2652-2657.
18	Doyle M, Newman J. Modeling the performance of rechargeable lithium based cells design correlations for limiting cases[J]. Journal of Power Sources, 1995, 54(1): 46-51.
19	Doyle M, Fuller T F, Newman J. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell[J]. Journal of the Electrochemical Society, 1993, 140(6): 1526-1533.
20	Newman J, Tiedemann W. Porous-electrode theory with battery applications[J]. AIChE Journal, 1975, 21(1): 25-41.
21	Shirazi A H N, Azadi K M R, Rabczuk T. Numerical study of composite electrode s particle size effect on the electrochemical and heat generation of a Li-ion battery[J]. Journal of Nanotechnology in Engineering and Medicine, 2016, 6(4): 041003.
22	Newman J, Thomas-Alyea K E. Electrochemical Systems[M]. John Wiley & Sons, 2012.
23	Ye Y, Shi Y, Tay A A O. Electro-thermal cycle life model for lithium iron phosphate battery[J]. Journal of Power Sources, 2012, 217: 509-518.
24	Safari M, Delacourt C. Modeling of a commercial graphite/LiFePO₄ cell[J]. Journal of the Electrochemical Society, 2011, 158(5): A562-A571.
25	郭孝东, 钟本和, 唐艳, 等. 一次粒径和二次粒径对LiFePO₄性能的影响[J]. 高校化学工程学报, 2013, (5): 884-888.
	Guo X D, Zhong B H, Tang Y, et al. Effect of primary particle size and secondary particle size on the properties of LiFePO₄[J]. Journal of Chemical Engineering of Chinese Universities, 2013, (5): 884-888.
26	Santhanagopalan S, Guo Q, Ramadass P, et al. Review of models for predicting the cycling performance of lithium ion batteries[J]. Journal of Power Sources, 2006, 156(2): 620-628.
27	Kumaresan K, Sikha G, White R E. Thermal model for a Li-ion cell[J]. Journal of the Electrochemical Society, 2008, 155(2): A164-A171.
28	Gerver R E, Meyers J P. Three-dimensional modeling of electrochemical performance and heat generation of lithium-ion batteries in tabbed planar configurations[J]. Journal of the Electrochemical Society, 2011, 158(7): A835-A843.
29	Valoen L O, Reimers J N. Transport properties of LiPF₆-based Li-ion battery electrolytes[J]. Journal of the Electrochemical Society, 2005, 152(5): A882-A891.
30	Taleghani S T, Marcos B, Lantagne G. Modeling and simulation of a commercial graphite-LiFePO₄ cell in a full range of C-rates[J]. Journal of Applied Electrochemistry, 2018, 48(12): 1389-1400.
31	Liu H, Strobridge F C, Borkiewicz O J, et al. Capturing metastable structures during high-rate cycling of LiFePO₄ nanoparticle electrodes[J]. Science, 2014, 344(6191): 1252817.

[1]	康飞, 吕伟光, 巨锋, 孙峙. 废锂离子电池放电路径与评价研究[J]. 化工学报, 2023, 74(9): 3903-3911.
[2]	王志龙, 杨烨, 赵真真, 田涛, 赵桐, 崔亚辉. 搅拌时间和混合顺序对锂离子电池正极浆料分散特性的影响[J]. 化工学报, 2023, 74(7): 3127-3138.
[3]	葛加丽, 管图祥, 邱新民, 吴健, 沈丽明, 暴宁钟. 垂直多孔碳包覆的FeF₃正极的构筑及储锂性能研究[J]. 化工学报, 2023, 74(7): 3058-3067.
[4]	陈朝光, 贾玉香, 汪锰. 以低浓度废酸驱动中和渗析脱盐的模拟与验证[J]. 化工学报, 2023, 74(6): 2486-2494.
[5]	李靖, 沈聪浩, 郭大亮, 李静, 沙力争, 童欣. 木质素基碳纤维复合材料在储能元件中的应用研究进展[J]. 化工学报, 2023, 74(6): 2322-2334.
[6]	肖忠良, 尹碧露, 宋刘斌, 匡尹杰, 赵亭亭, 刘成, 袁荣耀. 废旧锂离子电池回收工艺研究进展及其安全风险分析[J]. 化工学报, 2023, 74(4): 1446-1456.
[7]	罗来明, 张劲, 郭志斌, 王海宁, 卢善富, 相艳. 1~5 kW高温聚合物电解质膜燃料电池堆的理论模拟与组装测试[J]. 化工学报, 2023, 74(4): 1724-1734.
[8]	杜江龙, 杨雯棋, 黄凯, 练成, 刘洪来. 复合相变材料/空冷复合式锂离子电池模块散热性能[J]. 化工学报, 2023, 74(2): 674-689.
[9]	程伟江, 汪何琦, 高翔, 李娜, 马赛男. 锂离子电池硅基负极电解液成膜添加剂的研究进展[J]. 化工学报, 2023, 74(2): 571-584.
[10]	钟磊, 邱学青, 张文礼. 木质素衍生炭在碱金属离子电池负极中的研究进展[J]. 化工学报, 2022, 73(8): 3369-3380.
[11]	胡华坤, 薛文东, 霍思达, 李勇, 蒋朋. 锂离子电池电解液SEI成膜添加剂的研究进展[J]. 化工学报, 2022, 73(4): 1436-1454.
[12]	杨伟, 王昱杰, 方凯斌, 邹汉波, 陈胜洲, 刘自力. Co-Mn比例调控对LiNi_0.8Co_0.10-_y Mn_0.05+_y Al_0.05O₂材料性能影响探究[J]. 化工学报, 2022, 73(12): 5615-5624.
[13]	刘伯峥, 王静波, 曾涛, 殷雅侠, 郭玉国. 磷酸铁锂电池寿命初期与末期安全性差异[J]. 化工学报, 2022, 73(12): 5555-5563.
[14]	王朋朋, 贾洋刚, 邵霞, 程婕, 冒爱琴, 檀杰, 方道来. K⁺掺杂尖晶石型（Co_0.2Cr_0.2Fe_0.2Mn_0.2Ni_0.2）₃O₄高熵氧化物负极材料制备与储锂性能研究[J]. 化工学报, 2022, 73(12): 5625-5637.
[15]	贾理男, 杜一博, 郭邦军, 张希. 基于硫化物电解质的全固态锂离子电池负极研究进展[J]. 化工学报, 2022, 73(12): 5289-5304.

LiFePO₄锂离子电池的数值模拟：正极材料颗粒粒径的影响

Numerical simulation of lithium-ion battery with LiFePO₄ as cathode material: effect of particle size

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 7

参考文献 31

相关文章 15

编辑推荐

Metrics

本文评价