多孔电极电池的循环伏安法模拟

doi:10.13208/j.electrochem.210210

摘要/Abstract

摘要：

锂离子电池的全电池建模模拟对现代新能源领域的发展至关重要。伪二维（P2D）电化学模型是最常使用的全电池模拟模型,但一直被用于输入为电流,输出为电压的模拟中。本文基于P2D模型,通过对内电位、电极电位以及电池端电压的详细讨论,首次采用电压边界条件,利用COMSOL仿真软件完成了实验中常用的两电极体系和三电极体系的循环伏安法建模和模拟。并对比分析了两/三电极体系中扫描速率、颗粒半径、电极锂扩散速率以及最大嵌锂浓度这四个参数对循环伏安曲线形状的影响。结果表明,循环伏安测试时扫描速率越大,循环伏安曲线的峰值电流越大;固相锂扩散速率越大、电活性颗粒半径越小、最大嵌锂浓度越大,峰值电流越大。在相同的测试条件下,三电极体系比两电极体系的循环伏安图对称性更好,电流响应更大,并且颗粒半径、锂扩散速率及最大嵌锂浓度这三个参数对峰值电流的影响也更为明显。

关键词: 锂离子电池, 循环伏安法, P2D模型, 两/三电极体系, COMSOL仿真模拟

Abstract:

Lithium-ion batteries (LIBs) are among the most widely used energy storage devices. Whole-cell modeling and simulations of LIBs can optimize the design of batteries with lower costs and higher speeds. The Pseudo-Two-Dimensional (P2D) electrochemical model is among the most famous whole-cell models and widely applied in LIB simulations. P2D model consists of a series of kinetic equations to model Li⁺/Li diffusion in working/counter electrodes and electrolytes, which are filled in the porous electrodes and separator, and reactions at the interface of electrolyte and active particles. The traditional applications of P2D model, however, are limited to the cases where the current is the control variable and the voltage is the dependent variable. The present work tries to apply boundary conditions with the electrode potential as the control variable to simulate cyclic voltammetric (CV) experiments on the whole battery, based on a detailed analysis on different potentials, including Galvani potential, Volta potential, electrode potential and battery terminal voltage, as well as their relationships. In many CV experiments, only two electrodes, the working and the counter electrodes, are used. The experimental results are usually explained by using theoretical results directly taken from textbooks. The theories of CV are, however, based on three-electrode systems with a reference electrode to provide a reference voltage. The differences of CV curves between the two- and the three-electrode systems have never been studied by using P2D models. The present work performs numerical simulations of CV on both two- and three-electrode systems by using finite element methods, brought with the software of COMSOL Multiphysics, to study the influences of scanning rate, effective radius of active particles, lithium ion diffusivity and stoichiometric maximum concentration in electrode on CV curves. The three-electrode system is simulated by applying a potential detector at the separator region of a battery. The applied potentials are changed in time based on the magnitude of the detected potential. Results show that, for CV curves on both two- and three-electrodes systems, the peak current determined by the complex electrode dynamics process increases with the increases of scanning rate, lithium ion diffusivity in electrode and stoichiometric maximum lithium ion concentration, but with the decrease of the radius of electrode active particles. The peak currents obtained from CV curves are larger in three-electrode systems than in two-electrode systems under the same applied parameters. CV curves of three-electrode systems are more symmetric for the anodic and cathodic currents than those in two-electrode systems.

Key words: lithium ion battery, cyclic voltammetry, P2D model, two/three electrode system, finite element simulation

蔡雪凡, 孙升. 多孔电极电池的循环伏安法模拟[J]. 电化学（中英文）, 2021, 27(6): 646-657.

Xue-Fan Cai, Sheng Sun. Cyclic Voltammetric Simulations on Batteries with Porous Electrodes[J]. Journal of Electrochemistry, 2021, 27(6): 646-657.

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参考文献 34

[1]	Li M, Lu J, Chen Z W, Amine K. 30 years of lithium-ion batteries[J]. Adv. Mater., 2018, 30(33): 1800561. doi: 10.1002/adma.v30.33 URL
[2]	Song Y H(宋永华), Yang Y X(阳岳希), Hu Z C(胡泽春). Present status and development trend of batteries for electric vehicles[J]. Power Sys. Techno.(电网技术), 2011, 35(4): 1-7.
[3]	Yan J D(闫金定). Current status and development analysis of lithium-ion batteries[J]. Acta Aeronaut. Astronaut. Sin.(航空学报), 2014, 35(10): 2767-2775.
[4]	Huang X J(黄学杰), Zhao W W(赵文武), Shao Z G(邵志刚), Chen L Q(陈立泉). Development strategies for new energy materials in China[J/OL]. Strategic Study of CAE(中国工程科学), 2020, 22(5): 60-67.
[5]	Yang Y S(杨裕生). A review of electrochemical energy storage researches in the past 22 years[J]. J. Electrochem.(电化学), 2020, 26(4): 443-463.
[6]	Doyle M, Fuller T F, Newman J. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell[J]. J. Electrochem. Soc., 1993, 140(6): 1526-1533. doi: 10.1149/1.2221597 URL
[7]	Fuller T F, Doyle M, Newman J. Simulation and optimization of the dual lithium ion insertion cell[J]. J. Electrochem. Soc., 1994, 141(1): 1-10. doi: 10.1149/1.2054684 URL
[8]	Doyle M, Newman J. The use of mathematical modeling in the design of lithium/polymer battery systems[J]. Electrochim. Acta, 1995, 40(13/14): 2191-2196. doi: 10.1016/0013-4686(95)00162-8 URL
[9]	Santhanagopalan S, Guo Q Z, Ramadass P, White R E. Review of models for predicting the cycling performance of lithium ion batteries[J]. J. Power Sources, 2006, 156(2): 620-628. doi: 10.1016/j.jpowsour.2005.05.070 URL
[10]	Xiao M, Choe S Y. Dynamic modeling and analysis of a pouch type LiMn₂O₄/Carbon high power Li-polymer battery based on electrochemical-thermal principles[J]. J. Power Sources, 2012, 218: 357-367. doi: 10.1016/j.jpowsour.2012.05.103 URL
[11]	Kemper P, Li S E, Kum D. Simplification of pseudo two dimensional battery model using dynamic profile of lithium concentration[J]. J. Power Sources, 2015, 286: 510-525. doi: 10.1016/j.jpowsour.2015.03.134 URL
[12]	Farag M, Fleckenstein M, Habibi S. Continuous piecewise-linear, reduced-order electrochemical model for lithium-ion batteries in real-time applications[J]. J. Power Sources, 2017, 342: 351-362. doi: 10.1016/j.jpowsour.2016.12.044 URL
[13]	Lamorgese A, Mauri R. Tellini B. Electrochemical-thermal P2D aging model of a LiCoO₂/graphite cell: Capacity fade simulations[J]. J. Energy Storage, 2018, 20: 289-297. doi: 10.1016/j.est.2018.08.011 URL
[14]	Ge Y M(葛亚明), Li J(李军). Parameters identification of lithium-ion batterie model and simulation of the discharge voltage curves[J]. J. Ordnance Equip. Eng.(兵器装备工程学报), 2018, 39(6): 188-191.
[15]	Wang X X(王晓晓), Zhou Z R(周子睿), Shan Q(单强), Zhang Z M(张增明), Huang J(黄俊), Liu Y W(刘欲文), Chen S L(陈胜利). Porous-electrode theory of lithium ion battery: old paradigm and new challenge[J]. J.electrochem.(电化学), 2020, 26(5): 596-606.
[16]	Levi M D, Aurbach D. The mechanism of lithium intercalation in graphite film electrodes in aprotic media. Part 1. High resolution slow scan rate cyclic voltammetric studies and modeling[J]. J. Electroanal. Chem., 1997, 421(1/2): 79-88. doi: 10.1016/S0022-0728(96)04832-2 URL
[17]	Davies T J, Compton R G. The cyclic and linear sweep voltammetry of regular and random arrays of microdisc electrodes: Theory[J]. J. Electroanal. Chem., 2005, 585(1): 63-82. doi: 10.1016/j.jelechem.2005.07.022 URL
[18]	Streeter L, Wildgoose G G, Shao L D, Compton R G. Cy-clic voltammetry on electrode surfaces covered with porous layers: An analysis of electron transfer kinetics at single-walled carbon nanotube modified electrodes[J]. Sensor Actuat. B - Chem., 2008, 133(2): 462-466. doi: 10.1016/j.snb.2008.03.015 URL
[19]	Pérez-Brokate C F, Caprio D D, Mahéé, Férona D, Lamare J D. Cyclic voltammetry simulations with cellular automata[J]. J. Comput. Sci., 2015, 11: 269-278. doi: 10.1016/j.jocs.2015.08.005 URL
[20]	Gavilán-Arriazu E M, Mercer M P, Pinto O A, Oviedo O A, Barraco D E, Hoster H E, Leiva E P M. Numerical simulations of cyclic voltammetry for lithium-ion intercalation in nanosized systems: finiteness of diffusion versus electrode kinetics[J]. J. Solid State Electrochem., 2020, 24(11/12): 3279-3287. doi: 10.1007/s10008-020-04717-9 URL
[21]	Zhang S L(张胜利), Yu Z B(余仲宝), Han Z X(韩周祥). Research and development of lithium-ion batteries[J]. Battery Ind.(电池工业), 1999, 4(1): 26-28.
[22]	Liu L(刘璐), Wang H L(王红蕾), Zhang Z G(张志刚). Working principle of lithium ion battery and its main materials[J]. Sci. & Technol. Inf.(科技信息), 2009, 23: 454, 484.
[23]	Trasatti S. The absolute electrode potential: an explanatory note[J]. Pure & Appl Chem., 1986, 58(7): 955-966.
[24]	Zha Q X(查全性). Introduction to kinetics of electrode process[M]. Science Press Co., Ltd.(科学出版社), 2002.
[25]	Gu H B(顾宏邦). A wrong concept of electrode potential[J]. J. Shanxi Univ.(山西大学学报), 1979, 2: 163-174.
[26]	Doyle M, Newman J, Gozdz A S, Schmutz C N, Tarascon J M. Comparison of modeling predictions with experimental data from plastic lithium ion cells[J]. J. Electrochem. Soc., 1996, 143(6): 1890-1903. doi: 10.1149/1.1836921 URL
[27]	Smith K, Wang C Y. Power and thermal characterization of a lithium-ion battery pack for hybrid-electric vehicles[J]. J. Power Sources, 2006, 160(1): 662-673. doi: 10.1016/j.jpowsour.2006.01.038 URL
[28]	Pang H, Mou L J, Guo L, Zhang F Q. Parameter identification and systematic validation of an enhanced single-particle model with aging degradation physics for Li-ion batteries[J]. Electrochim. Acta, 2019, 307: 474-487. doi: 10.1016/j.electacta.2019.03.199
[29]	Chaturvedi N A, Klein R, Christensen J, Ahmed J, Kojic A. Algorithms for advanced battery-management systems[J]. IEEE Control Syst. Mag., 2010, 30(3): 49-68.
[30]	Prada E, Domenico D D, Creff Y, Bernard J, Sauvant-Moynot V, Huet F. Simplified electrochemical and thermal model of LiFePO₄-Graphite Li-ion batteries for fast charge applications[J]. J. Electrochem. Soc., 2012, 159(9): A1508-A1519. doi: 10.1149/2.064209jes URL
[31]	Klein R, Chaturvedi N A, Christensen J, Ahmed J, Findeisen R, Kojic A. Electrochemical model based observer design for a lithium-ion battery[J]. IEEE Trans. Control Syst. Technol., 2013, 21(2): 289-301. doi: 10.1109/TCST.2011.2178604 URL
[32]	Pang H(庞辉). Multi-scale modeling and its simplification method of Li-ion battery based on electrochemical model[J]. Acta Phys. Sin.(物理学报), 2017, 66(23): 238801.
[33]	Chen H N, Liu Y, Zhang X F, Lan Q, Chu Y, Li Y L, Wu Q X. Single-component slurry based lithium-ion flow battery with 3D current collectors[J]. J. Power Sour-ces, 2021, 485: 229319.
[34]	Chen D, Tan H T, Rui X H, Zhang Q, Feng Y Z, Geng H B, Li C C, Huang S M, Yu Y. Oxyvanite V₃O₅: A new intercalation-type anode for lithium-ion battery[J]. Infomat, 2019, 1(2): 251-259.

	Parameter	Negative electrode	Separator	Positive electrode	Unit
Geometry and volume fraction	Thickness	1.83×10^-4	5.2×10^-5	1.83×10^-4	m
	Particle radius	12.5		10; 40; 70	μm
	Active material volume fraction	0.471		0.297
	Electrolyte phase volume fraction	0.503	1	0.63
	Conductive filler volume fraction	0.026		0.073
Concentration	Initial solid phase concentration	20450		0	mol·m^-3
	Maximum solid phase concentration	31507		18860; 22860; 26860	mol·m^-3
	Initial electrolyte salt concentration	2000	2000	2000	mol·m^-3
Kinetic and transport properties	Solid phase Li⁺ diffusion coefficient	3.9×10^-10		1×10^-9; 1×10^-10; 1×10^-11	cm²·s^-1
	Electrolyte phase Li⁺ diffusion coefficient		7.5×10^-7		cm²·s^-1
	Solid phase conductivity	100		3.8	S·m^-1
	Electrolyte phase conductivity		f(C_l/C_l^ref)		S·m^-1
	Electrode open-circuit voltage	f(C_s/C_s^max)		0	V
	Charge-transfer coefficient	0.5,0.5		0.5,0.5
	Li⁺ transference number		0.363
	Film resistance of the SEI	10		0	Ω·cm²
	Faraday constant		96500		C·mol^-1
	Ideal gas constant		8.31		J·mol^-1·K^-1
	temperature		298		K