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Lithium ion battery is nowadays one of the most popular energy storage devices due to its high energy, power density and cycle life characteristics. It has been known that the overall performance of battery depends on not only electrolyte and electrode materials, but also operation condition and choice of physical parameters. Designers need to understand the thermodynamic and kinetic characteristics of battery, which is costly and time-consuming by experimental methods. However, lithium ion battery is a complicated electrochemical system with multi physicochemical processes including the mass, charge, and energy conservations as well as the electrochemical kinetics. It not only has a typical multiple level arrangement: across the electrode level, cell level, and extending to the battery module level, which is different from the basic active material particle level arrangement, but also confronts the challenges to meeting the requirements for sorting and consistency method for battery. These facts increase the difficulties in designing the battery and evaluating the overall performance. Owing to the rapid development of multi-scale numerical simulation technology, the multi-scale mathematical models for lithium ion battery are developed to help battery designer comprehensively and systematically gain the interaction mechanisms between different physicochemical fields in the battery working process and analyze the regulations of these interaction mechanisms, which is significant in providing theoretical supports for designing and optimizing the battery systems. At present, multi-type lithium ion battery models coupled with many physicochemical processes have been developed on different scales to study different issues, such as thermal behavior, inner polarization, micro structure, inner stress and capacitance fading, etc. In this paper, we review the research statuses and development trends of multi-scale mathematical models for lithium ion battery. The primary theoretical models for lithium ion battery are systemized and their features, application ranges and limitations are also summarized. Furthermore, the future research area and the difficulty in industry application are discussed. All of these are helpful for the theoretic research and engineering application of the multi-scale numerical models for lithium ion battery.
[1] Lu L G, Han X B, Li J Q, Hua J F, Ouyang M G2013 J. Power Sources 226 272
[2] Rao Z H, Wang S F 2011 Renew Sust. Energ. Rev. 15 4554
[3] Newman J, Thomas-Alyea E K 2004 Electrochemical Systems (3rd Ed.) (Hoboken: John Wiley & Sons) pp1-21
[4] Tang Y W, Jia M, Li J, Lai Y Q, Cheng Y, Liu Y X 2014 J. Electrochem. Soc. 161 E3021
[5] Franco A A 2013 RSC Advances 3 13027
[6] Feng Y 2008 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese) [冯毅 2008 博士学位论文 (北京: 中国科学院研究生院)]
[7] Buller S, Thele M, De Doncker R W A A, Karden E 2005 IEEE T. Ind. Appl. 41 742
[8] Karden E, Mauracher P, Schöpe F 1997 J. Power Sources 64 175
[9] Gomez J, Nelson R, Kalu E E, Weatherspoon M H, Zheng J P 2011 J. Power Sources 196 4826
[10] Cho S, Jeong H, Han C, Jin S, Lim J H, Oh J 2012 Computers & Amp; Chemical Engineering 4 1
[11] Hu X, Li S, Peng H 2012 J. Power Sources 198 359
[12] Wang Z P, Liu P, Wang L 2013 Chin. Phys. B 22 088801
[13] Xu L, Wang J P, Chen Q S 2012 Energy Conversion and Management 53 33
[14] Fang K, Mu D, Chen S, Wu B, Wu F 2012 J. Power Sources 208 378
[15] Capizzi G, Bonanno F, Tina G M 2011 IEEE T. Energy Conver 26 435
[16] Bi J, Shao S, Guan W, Wang L 2012 Chin. Phys. B 21 118801
[17] Brand J, Zhang Z, Agarwal R K 2014 J. Power Sources 247 729
[18] Forman J C, Moura S J, Stein J L, Fathy H K 2012 J. Power Sources 210 263
[19] Shi J X, Xue X J 2011 J. Electrochem. Soc. 158 B143
[20] Yann Liaw B, Nagasubramanian G, Jungst R G, Doughty D H 2004 Solid State Ionics 175 835
[21] Chiang Y H, Sean W Y, Ke J C 2011 J. Power Sources 196 3921
[22] Kim T, Qiao W 2011 IEEE T. Energy Conver 26 1172
[23] Cho S, Jeong H, Han C, Jin S, Lim J H, Oh J 2012 Comput Chem. Eng. 41 1
[24] Daniel C, Besenhard J O 2011 Handbook of Battery Materials Second Edition (Weinheim: Wiley-VCH) pp844
[25] Bernardi D, Pawlikowski E, Newman J 1985 J. Electrochem. Soc. 132 5
[26] Kim U S, Shin C B, Kim C S 2009 J. Power Sources. 189 841
[27] Lee J, Choi K W, Yao N P, Christianson C C 1986 J. Electrochem. Soc. 133 1286
[28] Gu W B, Wang C Y 2000 J. Electrochem. Soc. 147 2910
[29] Guo G F, Long B, Cheng B, Zhou S Q, Xu P, Cao B G 2010 J. Power Sources 195 2393
[30] Lee K-J, Smith K, Pesaran A, Kim G-H 2013 J. Power Sources 241 20
[31] Guo M, Kim G-H, White R E 2013 J. Power Sources 240 80
[32] Jeon D H, Baek S M 2011 Energy Convers. Manage. 52 2973
[33] Zhang X W 2011 Electrochim. Acta 56 1246
[34] Newman J, Tiedemann W 1975 AIChE Journal 21 25
[35] Doyle M, Newman J 1995 Electrochim. Acta 40 2191
[36] Doyle M, Newman J, Gozdz A S, Schmutz C N, Tarascon J M 1996 J. Electrochem. Soc. 143 1890
[37] Rao L, Newman J 1997 J. Electrochem. Soc. 144 2697
[38] Zhang Q, Guo Q Z, White R E 2007 J. Power Sources 165 427
[39] Zhang Q, White R E 2007 J. Electrochem. Soc. 154 A587
[40] Srinivasan V, Newman J 2004 J. Electrochem. Soc. 151 A1517
[41] Srinivasan V, Newman J 2004 J. Electrochem. Soc. 151 A1530
[42] Ye Y H, Shi Y X, Tay A A O 2012 J. Power Sources 217 509
[43] Saw L H, Ye Y, Tay A A O 2013 Energy Convers. Manage 75 162
[44] Safari M, Delacourt C 2011 J. Electrochem. Soc. 158 A562
[45] Li J, Cheng Y, Jia M, Tang Y, Lin Y, Zhang Z, Liu Y 2014 J. Power Sources 255 130
[46] Wang S R, Lu L L, Liu X J 2013 J. Power Sources 244 101
[47] Chen Y F, Evans J W 1994 J. Electrochem. Soc. 141 2947
[48] Li J, Cheng Y, Ai L H, Jia M, Du S L, Yin B H, Woo S, Zhang H L 2015 J. Power Sources 293 993
[49] Du S L, Jia M, Cheng Y, Tang Y W, Zhang H L, Ai L H, Zhang K, Lai Y Q 2015 Int. J. Therm. Sci. 89 327
[50] Tang Y W, Jia M, Cheng Y, Zhang K, Zhang H L, Li J 2013 Acta Phys. Sin. 62 158201 (in Chinese) [汤依伟, 贾明, 程昀, 张凯, 张红亮, 李劼 2013 62 158201]
[51] Bandhauer T M, Garimella S, Fuller T F 2011 J. Electrochem. Soc. 158 R1
[52] Xun J Z, Liu R, Jiao K 2013 J. Power Sources 233 47
[53] Xu X M, He R 2013 J. Power Sources 240 33
[54] Khateeb S A, Farid M M, Selman J R, Al-Hallaj S 2004 J. Power Sources 128 292
[55] Zavalis T G, Klett M, Kjell M H, Behm M, Lindström R W, Lindbergh G 2013 Electrochim. Acta 110 335
[56] Bohn E, Eckl T, Kamlah M, McMeeking R 2013 J. Electrochem. Soc. 160 A1638
[57] Dai Y, Cai L, White R E 2014 J. Power Sources 247 365
[58] Hao F, Fang D N 2013 J. Electrochem. Soc. 160 A595
[59] Song Y C, Lu B, Ji X, Zhang J Q 2012 J. Electrochem. Soc. 159 A2060
[60] Schalkwijk W V, Scrosati B 2002 Advances in Lithium-Ion Batteries (New York: Kluwer Academic Publishers) pp378
[61] Zhang D, Popov B N, White R E 2000 J. Electrochem. Soc. 147 831
[62] Guo M, Kumaresan K, Sikha G, White R 2008 ECS Meeting Abstracts 801 39
[63] Ning G, Popov B N 2004 J. Electrochem. Soc. 151 A1584
[64] Ning G, White R E, Popov B N 2006 Electrochim. Acta 51 2012
[65] Evans T I, White R E 1987 J. Electrochem. Soc. 134 2725
[66] Santhanagopalan S, Guo Q Z, Ramadass P, White R E 2006 J. Power Sources 156 620
[67] Huang L, Li Jian Y 2015 Acta Phys. Sin. 64 108202 (in Chinese) [黄亮, 李建远 2015 64 108202]
[68] Guo M, Sikha G, White R E 2011 J. Electrochem. Soc. 158 S11
[69] Renganathan S, White R E 2011 J. Power Sources 196 442
[70] Chung M D, Seo J H, Zhang X C, Sastry A M 2011 J. Electrochem. Soc. 158 A371
[71] Yi Y B, Wang C W; Sastry A M 2006 ASME J. Eng. Mater. Techonol. 128 73
[72] Wang C W, Sastry A M 2007 J. Electrochem. Soc. 154 A1035
[73] Goldin G M, Colclasure A M, Wiedemann A H, Kee R 2012 J Electrochim. Acta 64 118
[74] Gupta A, Seo J H, Zhang X, Du W, Sastry A M, Shyy W 2011 J. Electrochem. Soc. 158 A487
[75] Garcia R E, Chiang Y M, Carter W C, Limthongkul P, Bishop C M 2005 J. Electrochem. Soc. 152 A255
[76] Zeng J B, Jiang F M 2013 Acta Phys. Chim. Sin. 29 2371 (in Chinese) [曾建邦, 蒋方明 2013 物理化学学报 29 2371]
[77] Smith M, García R E, Horn Q C 2009 J. Electrochem. Soc. 156 A896
[78] Wargo E A, Kotaka T, Tabuchi Y, Kumbur E C 2013 J. Power Sources 241 608
[79] Wilson J R, Cronin J S, Barnett S A, Harris S J 2011 J. Power Sources 196 3443
[80] Stephenson D E, Walker B C, Skelton C B, Gorzkowski E P, Rowenhorst D J, Wheeler D R 2011 J. Electrochem. Soc. 158 A781
[81] Ender M, Joos J, Carraro T, Ivers-Tiffée E 2012 J. Electrochem. Soc. 159 A972
[82] Wu W, Jiang F M, Chen Z, Wang Y, Zhao F G, ZENG Y Q 2013 J Inorg Mater 28 1243 (in Chinese) [吴伟, 蒋方明, 陈治, 汪颖, 赵丰刚, 曾毓群 2013 无机材料学报 28 1243]
[83] Wu W, Jiang F M, Zeng J B 2013 Acta Phys. Chim. Sin. 29 2361 (in Chinese) [吴伟, 蒋方明, 曾建邦 2013 物理化学学报 29 2361]
[84] Wu W, Jiang F M, Zeng J B 2014 Acta Phys. Sin. 63 048202 (in Chinese) [吴伟, 蒋方明, 曾建邦 2014 63 048202]
[85] Hutzenlaub T, Asthana A, Becker J, Wheeler D R, Zengerle R, Thiele S 2013 Electrochem Commun. 27 77
[86] Hutzenlaub T, Thiele S, Paust N, Spotnitz R, Zengerle R, Walchshofer C 2014 Electrochim. Acta 115 131
[87] Shearing P R, Howard L E, Jørgensen P S, Brandon N P, Harris S J 2010 Electrochem Commun. 12 374
[88] Yan B, Lim C, Yin L L, Zhu L K 2012 J. Electrochem. Soc. 159 A1604
[89] Yan B, Lim C, Yin L L, Zhu L K 2013 Electrochim. Acta 100 171
[90] Tariq F, Yufit V, Kishimoto M, Shearing P R, Menkin S, Golodnitsky D, Gelb J, Peled E, Brandon N P 2014 J. Power Sources 248 1014
[91] Lim C, Yan B, Yin L, Zhu L K 2012 Electrochim. Acta 75 279
[92] Liu Z, Cronin J S, Chen-Wiegart Y-C K, Wilson J R, Yakal-Kremski K J, Wang J, Faber K T, Barnett S A 2013 J. Power Sources 227 267
[93] Chen-Wiegart, Karen Y-c, Liu Z, Faber K T, Barnett S A, Wang J 2013 Electrochem Commun. 28 127
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[1] Lu L G, Han X B, Li J Q, Hua J F, Ouyang M G2013 J. Power Sources 226 272
[2] Rao Z H, Wang S F 2011 Renew Sust. Energ. Rev. 15 4554
[3] Newman J, Thomas-Alyea E K 2004 Electrochemical Systems (3rd Ed.) (Hoboken: John Wiley & Sons) pp1-21
[4] Tang Y W, Jia M, Li J, Lai Y Q, Cheng Y, Liu Y X 2014 J. Electrochem. Soc. 161 E3021
[5] Franco A A 2013 RSC Advances 3 13027
[6] Feng Y 2008 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese) [冯毅 2008 博士学位论文 (北京: 中国科学院研究生院)]
[7] Buller S, Thele M, De Doncker R W A A, Karden E 2005 IEEE T. Ind. Appl. 41 742
[8] Karden E, Mauracher P, Schöpe F 1997 J. Power Sources 64 175
[9] Gomez J, Nelson R, Kalu E E, Weatherspoon M H, Zheng J P 2011 J. Power Sources 196 4826
[10] Cho S, Jeong H, Han C, Jin S, Lim J H, Oh J 2012 Computers & Amp; Chemical Engineering 4 1
[11] Hu X, Li S, Peng H 2012 J. Power Sources 198 359
[12] Wang Z P, Liu P, Wang L 2013 Chin. Phys. B 22 088801
[13] Xu L, Wang J P, Chen Q S 2012 Energy Conversion and Management 53 33
[14] Fang K, Mu D, Chen S, Wu B, Wu F 2012 J. Power Sources 208 378
[15] Capizzi G, Bonanno F, Tina G M 2011 IEEE T. Energy Conver 26 435
[16] Bi J, Shao S, Guan W, Wang L 2012 Chin. Phys. B 21 118801
[17] Brand J, Zhang Z, Agarwal R K 2014 J. Power Sources 247 729
[18] Forman J C, Moura S J, Stein J L, Fathy H K 2012 J. Power Sources 210 263
[19] Shi J X, Xue X J 2011 J. Electrochem. Soc. 158 B143
[20] Yann Liaw B, Nagasubramanian G, Jungst R G, Doughty D H 2004 Solid State Ionics 175 835
[21] Chiang Y H, Sean W Y, Ke J C 2011 J. Power Sources 196 3921
[22] Kim T, Qiao W 2011 IEEE T. Energy Conver 26 1172
[23] Cho S, Jeong H, Han C, Jin S, Lim J H, Oh J 2012 Comput Chem. Eng. 41 1
[24] Daniel C, Besenhard J O 2011 Handbook of Battery Materials Second Edition (Weinheim: Wiley-VCH) pp844
[25] Bernardi D, Pawlikowski E, Newman J 1985 J. Electrochem. Soc. 132 5
[26] Kim U S, Shin C B, Kim C S 2009 J. Power Sources. 189 841
[27] Lee J, Choi K W, Yao N P, Christianson C C 1986 J. Electrochem. Soc. 133 1286
[28] Gu W B, Wang C Y 2000 J. Electrochem. Soc. 147 2910
[29] Guo G F, Long B, Cheng B, Zhou S Q, Xu P, Cao B G 2010 J. Power Sources 195 2393
[30] Lee K-J, Smith K, Pesaran A, Kim G-H 2013 J. Power Sources 241 20
[31] Guo M, Kim G-H, White R E 2013 J. Power Sources 240 80
[32] Jeon D H, Baek S M 2011 Energy Convers. Manage. 52 2973
[33] Zhang X W 2011 Electrochim. Acta 56 1246
[34] Newman J, Tiedemann W 1975 AIChE Journal 21 25
[35] Doyle M, Newman J 1995 Electrochim. Acta 40 2191
[36] Doyle M, Newman J, Gozdz A S, Schmutz C N, Tarascon J M 1996 J. Electrochem. Soc. 143 1890
[37] Rao L, Newman J 1997 J. Electrochem. Soc. 144 2697
[38] Zhang Q, Guo Q Z, White R E 2007 J. Power Sources 165 427
[39] Zhang Q, White R E 2007 J. Electrochem. Soc. 154 A587
[40] Srinivasan V, Newman J 2004 J. Electrochem. Soc. 151 A1517
[41] Srinivasan V, Newman J 2004 J. Electrochem. Soc. 151 A1530
[42] Ye Y H, Shi Y X, Tay A A O 2012 J. Power Sources 217 509
[43] Saw L H, Ye Y, Tay A A O 2013 Energy Convers. Manage 75 162
[44] Safari M, Delacourt C 2011 J. Electrochem. Soc. 158 A562
[45] Li J, Cheng Y, Jia M, Tang Y, Lin Y, Zhang Z, Liu Y 2014 J. Power Sources 255 130
[46] Wang S R, Lu L L, Liu X J 2013 J. Power Sources 244 101
[47] Chen Y F, Evans J W 1994 J. Electrochem. Soc. 141 2947
[48] Li J, Cheng Y, Ai L H, Jia M, Du S L, Yin B H, Woo S, Zhang H L 2015 J. Power Sources 293 993
[49] Du S L, Jia M, Cheng Y, Tang Y W, Zhang H L, Ai L H, Zhang K, Lai Y Q 2015 Int. J. Therm. Sci. 89 327
[50] Tang Y W, Jia M, Cheng Y, Zhang K, Zhang H L, Li J 2013 Acta Phys. Sin. 62 158201 (in Chinese) [汤依伟, 贾明, 程昀, 张凯, 张红亮, 李劼 2013 62 158201]
[51] Bandhauer T M, Garimella S, Fuller T F 2011 J. Electrochem. Soc. 158 R1
[52] Xun J Z, Liu R, Jiao K 2013 J. Power Sources 233 47
[53] Xu X M, He R 2013 J. Power Sources 240 33
[54] Khateeb S A, Farid M M, Selman J R, Al-Hallaj S 2004 J. Power Sources 128 292
[55] Zavalis T G, Klett M, Kjell M H, Behm M, Lindström R W, Lindbergh G 2013 Electrochim. Acta 110 335
[56] Bohn E, Eckl T, Kamlah M, McMeeking R 2013 J. Electrochem. Soc. 160 A1638
[57] Dai Y, Cai L, White R E 2014 J. Power Sources 247 365
[58] Hao F, Fang D N 2013 J. Electrochem. Soc. 160 A595
[59] Song Y C, Lu B, Ji X, Zhang J Q 2012 J. Electrochem. Soc. 159 A2060
[60] Schalkwijk W V, Scrosati B 2002 Advances in Lithium-Ion Batteries (New York: Kluwer Academic Publishers) pp378
[61] Zhang D, Popov B N, White R E 2000 J. Electrochem. Soc. 147 831
[62] Guo M, Kumaresan K, Sikha G, White R 2008 ECS Meeting Abstracts 801 39
[63] Ning G, Popov B N 2004 J. Electrochem. Soc. 151 A1584
[64] Ning G, White R E, Popov B N 2006 Electrochim. Acta 51 2012
[65] Evans T I, White R E 1987 J. Electrochem. Soc. 134 2725
[66] Santhanagopalan S, Guo Q Z, Ramadass P, White R E 2006 J. Power Sources 156 620
[67] Huang L, Li Jian Y 2015 Acta Phys. Sin. 64 108202 (in Chinese) [黄亮, 李建远 2015 64 108202]
[68] Guo M, Sikha G, White R E 2011 J. Electrochem. Soc. 158 S11
[69] Renganathan S, White R E 2011 J. Power Sources 196 442
[70] Chung M D, Seo J H, Zhang X C, Sastry A M 2011 J. Electrochem. Soc. 158 A371
[71] Yi Y B, Wang C W; Sastry A M 2006 ASME J. Eng. Mater. Techonol. 128 73
[72] Wang C W, Sastry A M 2007 J. Electrochem. Soc. 154 A1035
[73] Goldin G M, Colclasure A M, Wiedemann A H, Kee R 2012 J Electrochim. Acta 64 118
[74] Gupta A, Seo J H, Zhang X, Du W, Sastry A M, Shyy W 2011 J. Electrochem. Soc. 158 A487
[75] Garcia R E, Chiang Y M, Carter W C, Limthongkul P, Bishop C M 2005 J. Electrochem. Soc. 152 A255
[76] Zeng J B, Jiang F M 2013 Acta Phys. Chim. Sin. 29 2371 (in Chinese) [曾建邦, 蒋方明 2013 物理化学学报 29 2371]
[77] Smith M, García R E, Horn Q C 2009 J. Electrochem. Soc. 156 A896
[78] Wargo E A, Kotaka T, Tabuchi Y, Kumbur E C 2013 J. Power Sources 241 608
[79] Wilson J R, Cronin J S, Barnett S A, Harris S J 2011 J. Power Sources 196 3443
[80] Stephenson D E, Walker B C, Skelton C B, Gorzkowski E P, Rowenhorst D J, Wheeler D R 2011 J. Electrochem. Soc. 158 A781
[81] Ender M, Joos J, Carraro T, Ivers-Tiffée E 2012 J. Electrochem. Soc. 159 A972
[82] Wu W, Jiang F M, Chen Z, Wang Y, Zhao F G, ZENG Y Q 2013 J Inorg Mater 28 1243 (in Chinese) [吴伟, 蒋方明, 陈治, 汪颖, 赵丰刚, 曾毓群 2013 无机材料学报 28 1243]
[83] Wu W, Jiang F M, Zeng J B 2013 Acta Phys. Chim. Sin. 29 2361 (in Chinese) [吴伟, 蒋方明, 曾建邦 2013 物理化学学报 29 2361]
[84] Wu W, Jiang F M, Zeng J B 2014 Acta Phys. Sin. 63 048202 (in Chinese) [吴伟, 蒋方明, 曾建邦 2014 63 048202]
[85] Hutzenlaub T, Asthana A, Becker J, Wheeler D R, Zengerle R, Thiele S 2013 Electrochem Commun. 27 77
[86] Hutzenlaub T, Thiele S, Paust N, Spotnitz R, Zengerle R, Walchshofer C 2014 Electrochim. Acta 115 131
[87] Shearing P R, Howard L E, Jørgensen P S, Brandon N P, Harris S J 2010 Electrochem Commun. 12 374
[88] Yan B, Lim C, Yin L L, Zhu L K 2012 J. Electrochem. Soc. 159 A1604
[89] Yan B, Lim C, Yin L L, Zhu L K 2013 Electrochim. Acta 100 171
[90] Tariq F, Yufit V, Kishimoto M, Shearing P R, Menkin S, Golodnitsky D, Gelb J, Peled E, Brandon N P 2014 J. Power Sources 248 1014
[91] Lim C, Yan B, Yin L, Zhu L K 2012 Electrochim. Acta 75 279
[92] Liu Z, Cronin J S, Chen-Wiegart Y-C K, Wilson J R, Yakal-Kremski K J, Wang J, Faber K T, Barnett S A 2013 J. Power Sources 227 267
[93] Chen-Wiegart, Karen Y-c, Liu Z, Faber K T, Barnett S A, Wang J 2013 Electrochem Commun. 28 127
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