Journal of The Electrochemical Society, 161 (9) A1453-A1460 (2014) A1453 0013-4651/2014/161(9)/A1453/8/$31.00 © The Electrochemical Society A Study of Transport Properties and Stress Analysis Using Atomistic and Macro Simulations for Lithium-Ion Batteries Utsav Kumar, a Atanu K. Metya, a N. Ramakrishnan, b and Jayant K. Singh a, z a Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India b Centre for Study of Science Technology and Policy, Gokula, Bangalore 560054, India Performance of a lithium-ion based rechargeable battery is investigated using coupled battery model including heat and stress models via finite element method simulations. An effort is made to elucidate the importance of using diffusivity equation, in the model, as a function of lithium-ion concentration and temperature. Diffusivity expressions for both anode and cathode material are developed using atomistic simulations. Simulation results show ∼10% drop in the battery potential after 100 charge-discharge cycles. This decline in performance is attributed to the concentration gradient, heat generation and stress accumulation, substantiating the need to address these effects simultaneously. Finally, intercalation stress values due to the modified diffusivity expression are found to differ considerably with that due to the constant diffusion values used in earlier works. The findings validate the assertion that intercalation stress values depend greatly on the lithium-ion concentration based diffusivity expression. © 2014 The Electrochemical Society. [DOI: 10.1149/2.1171409jes] All rights reserved. Manuscript submitted March 3, 2014; revised manuscript received June 9, 2014. Published June 25, 2014. Lithium-ion batteries are an excellent source of energy storage, 1 and can provide a high energy density. Further, they are flexible, lightweight, and have longer lifespan. 2 On the other hand, some of the major shortcomings are high cost, low temperature tolerance, 3 cell degradation 4 and thermal runaway. 5 Overall, the battery perfor- mance is dependent on the nature of the electrodes, electrolytes, and the electrode-electrolyte interfaces. On the other hand, safety is re- lated to the stability of the electrode materials and its interface with electrolyte. Hence, there have been extensive investigations 6,7 into the battery electrodes and electrolyte materials for improving safety and performance of lithium-ion batteries. Some of the notable advances in recent years are the use of LiFePO 4 (olivine structure) as a cathode material in doped nano-sized form, 8 improving both capacity reten- tion during charge-discharge cycle and high discharge performance. In particular, use of free standing silicon-single wall carbon nanotube as a anode has increased the anode capacity up to 20 times compared to the conventional anode. 9 In case of battery electrolytes, replace- ment of liquid electrolytes with polymer or solid electrolytes resulted in increased safety and flexibility. 6 Further, adding certain additives improved its conductivity, which was one of the key issues with such electrolytes. 7 Improving battery setup in terms of its performance requires anal- ysis of overall battery behavior for different combinations of elec- trodes and electrolytes. Spectroscopy or diffraction techniques like nuclear magnetic resonance (NMR), 10 electrochemical impedance spectroscopy (EIS) 11 and in situ X-ray diffraction (XRD) 12 are typ- ically used in experiments to investigate lithium-ion battery per- formance. Moreover, for investigation at nano-scale, requiring high spatial resolution optical microscopy, scanning electron microscopy (SEM) 13 and transmission electron microscopy (TEM) 13 are used for in-depth analysis. However, requirement of high level of vacuum, constant danger of contamination and possibility of high-energy elec- trons interfering with battery operations limits its usability. On the other hand, modeling and simulation can emulate the battery process allowing investigation on parameters that are usually not accessible in experiments. Battery modeling has been done at different length and time scales. For example, ab-initio simulations are used to study elec- trode structure and lithium migration barriers; 14,15 molecular dynam- ics simulations 16–18 are used to understand the electrode-electrolyte interface physics, electrode stability and transport of lithium ions. Macroscopic model can be used to monitor overall performance, life, cost and safety of battery. 19 Most of the earlier works related to modeling of battery perfor- mance and safety are based on battery model developed by Doyle et al. 20 Recently, few workers have appended a heat model to the bat- tery model of Doyle et al. 20 to analyze the discharge performance, and z E-mail: jayantks@iitk.ac.in obtained heat effects and temperature dependent expression 21–23 for various transport, kinetics and mass-transfer parameters. These modi- fied models are developed to inspect the change in temperature during charging and discharging processes, and its further effect on battery performance through temperature dependent parameters. More im- portantly, from safety point of view, it can be used to analyze thermal runaway condition. 5 In addition to the inclusion of a heat model in the model of Doyle and co-workers, it was also felt important to include an intercalation stress model. 24,25 The decline in the battery perfor- mance is predominantly attributed to the capacity fade problem as a consequence of intercalation stress. It has also been reported that prolong accumulation of stress may even lead to electrode cracking. 26 Apart from insertion/extraction of lithium-ion, structural failures also arise due to heat generation and concentration gradient developed dur- ing charge-discharge cycles at different operating conditions. These findings demand the need to simultaneously monitor the effect of predominant parameters on the performance of lithium-ion batteries. Stress generated in battery is classified typically into two types: me- chanical and non-mechanical. This paper focuses on non-mechanical part of stress, which is further classified into two kinds viz., in- tercalation and thermal. Among these stress components, diffu- sion induced stress or intercalation stress have been studied more extensively. 24,25,27,28 Zhang et al. 24,25 developed a mathematical model for calculating intercalation-induced stress, and subsequently ap- pended a heat model to it. Among several factors affecting outcome of stress in lithium-ion battery, diffusion of lithium-ions in electrode particles plays a vital role. Lithium-ion diffusivity expression used in earlier intercalation stress model was mainly a function of tem- perature; whereas, electrode diffusivity also depends on lithium-ion concentration. There is not much work done that has incorporated lithium-ion diffusivity variation with lithium-ion concentration for the study of battery performance. Chen and Verbrugge 29–32 have studied the variation of diffusion induced stress with respect to lithium-ion concentration, electrode material and electrode geometry; however, there is no specific interlink of electrode diffusivity expression with lithium-ion concentration, and its effect on intercalation stress. The understanding of ionic mechanisms in solid phases and determination of diffusivity variation with lithium-ion concentration and tempera- ture is extremely important for an efficient battery design. There have been only few studies on the diffusion characteristics of lithium-ion in battery anode and cathode materials. For example, first-principles calculation has been used to study lithium-ion diffusion in carbon anodes. 15,33,34 The diffusivity values for carbon anodes have also been evaluated in experiments. 35–37 Similarly, ab-initio calculations have been used for finding diffusivity of lithium-ion in LiMn 2 O 4 (cathode material). 38 In addition, classical molecular dynamics (MD) have also been used to study the lithium-ion diffusivity in LiMn 2 O 4 . 16–18 This paper aims to couple micro and macro scale model to ad- dress the questions raised in the above section. First, a relation ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 115.248.114.51 Downloaded on 2014-07-27 to IP