Stress analysis of lithium-based rechargeable batteries using micro and macro scale analysis

Transcription

1 Stress analysis of lithium-based rechargeable batteries using micro and macro scale analysis Utsav Kumar Atanu K. Metya Jayant K. Singh Department of Chemical Engineering IIT Kanpur

2 INTRODUCTION Christensen and Newman, Journal of Electrochemical Society, 2006 Estimated stress generation in Li y Mn 2 O 4 and carbon electrodes separately. Zhang et al., Journal of Electrochemical Society, 2007 Stress distribution inside one single electrode particle using numerical simulation. Zhang et al., Journal of Electrochemical Society, 2008 Intercalation induced stress and heat generation within single Lithium-Ion battery cathode particles. Golmon et al., Computers and Structures, 2009 Electrochemical mechanical interaction phenomena at macro, meso and micro scale. OBJECTIVE Study of intercalation and thermal stress generation in Li ion rechargeable battery incorporating the effect of Li ion electrode concentration on electrode diffusivity coefficient and stress generation. Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 2

3 STRUCTURE Source: spectrum.ieee.org Source: srinivasan et al., 2003 Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 3

4 Battery Electrode Battery Electrolyte Thermal Analysis Stress Analysis c t s i s s, eff s cs.( Ds ( cs h)) RT Effect of hydrostatic stress on Li ion flux Source: NREL,National Renewable Energy Laboratory i loc Butler-Volmer Reaction i ( ) ( ) 0 (exp af cf exp ) RT RT E s s, film l eq i F ( k ) ( k ) ( c c ) ( c ) ( c / c ) a c a c a 0 c a s,max s s l l, ref Reference: Doyle et al., 1996; Rosas et al., 2011 and Fuel cells and Battery module, COMSOL Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 4

5 Battery Electrode Battery Electrolyte Thermal Analysis Stress 2 RT i f c t c F l, eff l l, eff l (1 ln / ln l )(1 ) ln l c l l. Nl Rl t Concentration gradient Flux N D c l l, eff l it l F Reaction R l m a v, m Li, m loc F i Source: spectrum.ieee.org Diffusion and Migration Reference: Doyle et al., 1996; Rosas et al., 2011 and Fuel cells and Battery module, COMSOL Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 5

6 Battery Electrode Battery Electrolyte Thermal Analysis Stress Q rev Q rea Qirr Qact Qohm Q a i T rea v, i loc, i U T i Q a i ( U ) act v, i loc, i s, i l, i i Source: Comsol Multiphysics Q eff D 2RT eff ( t 1)(1 dln f / dln c) F c... c eff eff eff l ohm s s s l l D l l Thermal Strain thermal T Reference: Srinivasan and Wang, 2003; Kumaresan et al., 2008 and Fuel cells and Battery module, COMSOL Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 6

7 Battery Electrode Battery Electrolyte Thermal Analysis Stress c t s cs.( Ds ( cs h)) RT Effect of hydrostatic stress on Li ion flux ( 2 ) / 3 h r t J Mc 0 RT ln X h s 1 r ( r 2 t ) c E 3 r 1 t [( t ( r t )] c E 3 r r r0 r 2 2 E ( cr dr cr dr) 3 3 t 3 3 r r 3(1 ) r r Reference: Zhang et al., 2007; Zhang et al., 2008 and Xiao et al., E 1 1 3(1 ) Source: intechopen.com ( cr dr cr dr c) Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 7

8 MODELING Butler Volmer C l, ɸ J C s J Electrode Solids State Diffusion C s Electrode & Electrolyte Species/Charge Transport T ɸ, i T Thermal Heat Generation/ Transport T Stress Intercalation and Thermal Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 8

9 MODELING Butler Volmer C l, ɸ J C s J Electrode Solids State Diffusion C s Electrode & Electrolyte Species/Charge Transport T ɸ, i T Thermal Heat Generation/ Transport T Stress Intercalation and Thermal Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 9

10 D s as a function of C s? Butler Volmer C l, ɸ J C s J Electrode Solids State Diffusion D s (T) C s D s (C s,t) Electrode & Electrolyte Species/Charge Transport T ɸ, i T Thermal Heat Generation/ Transport T Stress Intercalation and Thermal Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 10

11 Li x C 6 Electrode phase diffusion value INTERACTION PARAMETERS (MD Simulation) Graphene Layers Li-Li interaction Graphene-Li interaction AIREBO (Adaptive Intermolecular Reactive Empirical Bond-Order) Stuart et. al, Journal of Chemical Physics, 2000 Field Parameter for Intermolecular and Columbic interactions. Wander and Shuford, Journal of Chemical Physics, 2011 Lorentz-Berthelot combining rules DIFFUSIVITY CALCULATION Einstein relation - diffusion coefficient is related to the slope of the mean square displacement (MSD) of the particles over time. 1 d D lim ri t t r t 6 t dt 0 i 0 2 Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 11

12 DIFFUSIVITY E = 81.5 mev E D C, T D x exp (1/ T 1/ T ) s 298K ref R Similarly for LiMn 2 O 4 Wakhira et al., Ionic State Solids, 1996 and Srinivasan et al., Journal of The Electrochemical Society, 2003 gives us the same kind of expression Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 12

13 COMSOL MODEL Anode Separator Cathode 1D electrochemical finite element model (FEM) Charge Conservation Chemical Kinetics Mass Transport (except for electrode particles) Heat Transport Fuel cell and battery module Heat Transfer module r=12.5µm r=8.5µm 2D electrode particle FEM model Li ion concentration in electrode particle Intercalation and Thermal Stress Cathode PDE module Anode Parameter Reference: Doyle et al, 1996; Srinivasan et al, 2003 and Zhang et al, 2007 Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 13

14 APPLIED CURRENT ANODE SEPARATOR CATHODE Source: srinivasan et al., 2003 Current density of 17.5 A/m 2 applied Charge cycle of 1600s with 800s of discharging and charging Total number of cycles - 10 Anode kept at constant potential Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 14

15 Electrode Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 15

16 Electrolyte Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 16

17 Cs variation Discharging (200s-600s) Charging (1100s-1500s) Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 17

18 T (K) AVERAGE TEMPERATURE Qtotal is taken as heat generated inside Li ion battery and on the basis of that an average Temperature is calculated and used for further studies including thermal stress t (s) Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 18

19 INTERCALATION STRESS Anode Tangential Stress Cathode Tangential Stress t r r r E 2 1 ( cr dr cr dr c) 3(1 ) r Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 19

20 Electrode Potential Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 20

21 Normalized Stress and Potential Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 21

22 CONCLUSION Diffusion coefficient as a function of Temperature and Li ion concentration is developed for electrodes and incorporated into model. Effect of Diffusion coefficient as a function of Li ion electrode concentration on stress value can be seen. T avg reaches an asymptotic value as counterbalance between heat generation and heat rejection comes to an equilibrium as time progresses. There is an accumulation of stress with continuous use of battery, this may lead to break down of battery if it reaches the break through point limit. With continuous use of battery there is a decrease in maximum battery potential, i.e. more charge required for achieving the previous potential value as we keep on using battery. Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 22

23 Thank You ACKNOWLEDGEMENT Chemical Engineering Department and DRPG, IIT Kanpur for travel support Dr. Ramakrishnan Narayanrao, General Motors, India Computational Nano Science Group, IIT Kanpur for their help and support

24 Li x C 6 Electrode phase diffusion value (MD Simulation) INTERACTION PARAMETERS Graphite : AIREBO (Adaptive Intermolecular Reactive Empirical Bond-Order). Stuart et. al, Journal of Chemical Physics, E E E E 2 REBO LJ tors ij ij kijl i j i k i, j l i, j, k. REBO R A Eij V rij bijv rij Li-Li interaction - Field Parameter for Intermolecular and Columbic interactions. Wander and Shuford, Journal of Chemical Physics, 2011 Graphite-Li interaction - Lorentz-Berthelot combining rules are employed for the cross interactions Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 24

25 DIFFUSIVITY CALCULATION The diffusion coefficient can be obtained using two equivalent equilibrium methods. Einstein relation - diffusion coefficient is related to the slope of the mean square displacement (MSD) of the particles over time. 1 d D lim ri t t r t 6 t dt 0 i 0 2 Green-Kubo (GK) - integration over the velocity autocorrelation function 1 D Vi t t0 V0 t0 dt 3 0 Green-Kubo gives too much fluctuation as compared to Einstein relation because of low concentration of Li Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 25

26 Lithium intercalated graphite Li0.396C6 (MD Simulation snapshot) SIDE VIEW INITIAL CONFIGURATION NVT FINAL CONFIGURATION (1ns) Ensemble TOP VIEW Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 26

27 MSD (Å 2 ) MSD (Å 2 ) DIFFUSIVITY at 298K Li C 6 Li C 6 Li C 6 Li C K 298K 265K 233K Time (ps) 0 1 d D lim ri t t r t 6 t dt 0 i Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis Time (ps) (MSD)

28 THERMAL ANALYSIS Q irrev = Q ohm + Q act Qrev av, iiloc, it U i T Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 28

29 Anode-Tangential Stress Difference Tangential Stress for Diffusivity as function of electrode Li ion and Temperature subtracted from Tangential Stress for Diffusivity as function of Temperature only vs. time Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro scale analysis 29