锂离子电池异构建模及内部传质机理探究：粒径分布的影响

doi:10.11949/0438-1157.20201095

摘要/Abstract

摘要：

锂离子电池是目前应用较广的储能设备，具有能量密度高、使用寿命长等特点。随着锂离子电池正极材料实际能量密度接近理论值，电池组装工艺参数的优化成了提升其性能的重要途径，其中电极颗粒粒径及分布是十分重要的参数。因此，本文针对石墨-LiFePO₄体系锂离子电池，利用异构模型构建单粒径和双粒径电极的几何结构，再结合Newman模型模拟其放电过程，定量研究了正极材料粒径分布对锂离子电池性能的影响，探究了存在粒径分布的电极中不同粒径的颗粒在充放电过程的作用机制。模拟结果表明，粒径的减小可以减小固相扩散系数对电池性能的影响，但会增加液相扩散阻力；而粒径的分布可以促进锂离子在电解液中的扩散，提高小粒径颗粒的锂嵌入量，但会引起极化增大，导致大颗粒的锂嵌入量降低。粒径分布宽度越大，总体粒度越大，锂离子电池的能量密度越小。选择合适的粒径分布宽度，适当减小总体粒度的大小，能有效提升电极的能量密度。研究结果对于锂离子电池电极活性材料颗粒粒径分布的选择提供了有益的基础知识和指导。

关键词: 锂离子电池, 数学模拟, 异构模型, 粒径分布

Abstract:

Lithium-ion batteries, as a kind of energy storage device with high energy density and long service life, have been widely applied in many fields. As the actual energy densities of cathode materials approach their theoretical values, the optimization of assembling parameters has become a crucial way to improve the performance of lithium-ion batteries. And the particle size distribution of the electrode particles is a very important parameter. In this work, heterogeneous models were used to construct geometry of electrode with single-sized particles and bimodal-sized LiFePO₄(LFP) particles. Then the corresponding discharge processes of C-LFP system were quantitatively simulated by Newman model to investigate the impact of particle size distribution on the performance of lithium-ion batteries. The simulation results show that the reduction of the particle size reduced the influence of solid phase diffusion coefficient on battery performance, but increased the liquid phase diffusion resistance. Proper particle size distribution of active material could promote the diffusion of lithium ion in electrolyte and increase the lithium insertion amount inside the small particles, but cause heavier polarization, thus decreasing the lithium insertion amount inside the large particles. The wider distribution of the particles and the larger overall particle size, the smaller the energy density of the lithium ion battery. Choosing an appropriate active particle size with proper distribution can effectively enhance the energy density of lithium-ion batteries. The research results provide useful basic knowledge and guidance for the selection of particle size distribution of electrode active materials for lithium-ion batteries.

Key words: lithium-ion battery, mathematical modeling, heterogeneous model, particle size distribution

中图分类号:

TQ 028.8

陈怡沁, 许于, 周静红, 隋志军, 周兴贵. 锂离子电池异构建模及内部传质机理探究：粒径分布的影响[J]. 化工学报, 2021, 72(2): 1078-1088.

CHEN Yiqin, XU Yu, ZHOU Jinghong, SUI Zhijun, ZHOU Xinggui. Heterogeneous modeling and internal mass transfer mechanism of lithium-ion batteries: effect of particle size distribution[J]. CIESC Journal, 2021, 72(2): 1078-1088.

图/表 11

图1 单粒径锂离子电池几何结构示意图(a)；双粒径锂离子电池几何结构示意图(b)

Fig.1 Geometry schematic of lithium ion battery with positive electrode of single-sized particles (a); Geometry schematic of lithium ion battery with positive electrode of bimodel-sized particles (b)

图2 单粒径（a）和双粒径（b）锂离子电池网格划分示意图

Fig.2 Schematic of model meshing for lithium-ion battery with single-sized particle (a) and bimodel-sized particles (b)

图3 商用电池的异构模型模拟放电曲线与实测放电曲线比较

Fig.3 Comparison between the simulated and the experimental discharge curves for commercial lithium ion battery

图4 单粒径锂离子电池放电曲线（a）和能量密度（b）

Fig.4 Discharge curves (a) and energy densities (b) of lithium ion battery with single-sized particle

图5 单粒径锂离子电池的电解液内锂离子浓度与颗粒内固态锂浓度分布随时间的变化(a) Rp = 1.5 μm，放电时间300 s；(b) Rp = 1.5 μm，放电时间3000 s；(c) Rp = 4.0 μm，放电时间300 s；(d) Rp = 4.0 μm，放电时间3000 s；(e) Rp = 6.0 μm，放电时间300 s；(f) Rp = 6.0 μm，放电时间3000 s

Fig.5 The concentration distribution of lithium ion in the electrolyte and metal lithium in active particles for lithium-ion battery with single-sized particles(a) Rp = 1.5 μm, discharge time is 300 s; (b) Rp = 1.5 μm, discharge time is 3000 s; (c) Rp = 4.0 μm, discharge time is 300 s; (d) Rp = 4.0 μm, discharge time is 3000 s; (e) Rp = 6.0 μm, discharge time is 300 s; (f) Rp = 6.0 μm, discharge time is 3000 s

图6 1 C放电条件下放电500 s时，单粒径锂离子电池正极内部锂离子通量

Fig.6 The lithium ion flux inside the positive electrode with single-sized particles when discharging for 500 s under 1 C discharge rate

图7 单粒径与双粒径的锂离子电池的能量密度

Fig. 7 Comparison of the energy densities of lithium ion batteries with single-sized particles and bimodel-sized particles

图8 双粒径锂离子电池电解质溶液中锂离子与颗粒内固态锂的浓度分布随时间的变化(a) （1.5&4.0）μm，放电时间300 s；(b) （1.5&4.0）μm，放电时间3000 s; (c) （1.5&6.0）μm，放电时间300 s；(d) （1.5&6.0）μm，放电时间3000 s; (e) （4.0&6.0）μm，放电时间300 s；(f) （4.0&6.0）μm，放电时间3000 s

Fig. 8 The concentration distribution of lithium ion in the electrolyte and metal lithium in active material particles for the lithium-ion battery with bimodel-sized particles(a) (1.5&4.0) μm, discharge time is 300 s; (b) (1.5&4.0) μm, discharge time is 3000 s; (c) (1.5&6.0) μm, discharge time is 300 s; (d) (1.5&6.0) μm, discharge time is 3000 s; (e) (4.0&6.0) μm, discharge time is 300 s; (f) (4.0&6.0) μm, discharge time is 3000 s

表1 1 C条件下放电3000 s时，单粒径和双粒径锂离子电池正极内部最大/最小固态锂浓度

Table 1 The maximum and minimum concentration of the metal lithium in the positive electrode with single-sized particles and bimodel-sized particles when discharging for 500 s under 1 C discharge rate

R_p/μm		c₁/(mol/m³)
R_p/μm		Max	Min	Δ
单粒径	1.5	20445.0	3411.8	17033.2
	4.0	17066.0	5275.8	11790.2
	6.0	15565.0	5454.4	10110.6
双粒径	1.5&4.0	15064.0	6273.8	8790.2
	1.5&6.0	19848.0	5153.1	14694.9
	4.0&6.0	14854.0	5519.5	9334.5

图9 1 C 放电时，双粒径及单粒径锂离子电池正极中（x=100 μm），靠近集流体处的锂离子通量随时间的变化曲线

Fig.9 The lithium ion flux during discharge time inside the positive electrode with single-sized particles and bimodel-sized particles（x=100 μm） under 1 C discharge rate

图10 1 C 放电时，单粒径与双粒径锂离子电池正极大颗粒与小颗粒平均固态锂浓度[（a）、（c）、（e）]和表面电流密度[（b）、（d）、（f）]随放电时间变化的比较

Fig.10 The average solid lithium concentration [(a),(c),(e)] and surface current density [(b),(d),(f)] of the large and small particles in the positive electrode of the lithium ion battery with single-sized and bimodal-sized particles during the discharge time under 1 C discharge rate

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