PPT.pptx

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

Utsav KumarAtanu K. Metya Jayant K. Singh

Department of Chemical Engineering IIT Kanpur

2Stress Analysis of Lithium-Based Rechargeable Batteries using micro and macro

scale analysis

INTRODUCTIONChristensen and Newman, Journal of Electrochemical Society, 2006

• Estimated stress generation in LiyMn2O4 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.


scale analysis

STRUCTURE

Source: spectrum.ieee.org

Source: srinivasan et al., 2003

( )( )0(exp exp )caFF

loc RTRTi i a ha h -= -

0 ,max ,( ) ( ) ( ) ( ) ( / )a c a c ac a s s s l l refi F k k c c c c ca a a a a= -

,s s film l eqEh ff f= - D - -

,s seff si s f=- Ñ

Butler-Volmer Reaction

Source: NREL ,National Renewable

Energy Laboratory

Reference: Doyle et al., 1996; Rosas et al., 2011 and Fuel cells and Battery module, COMSOL

Battery Electrode Battery Electrolyte

Thermal Analysis

Stress Analysis

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

4

.( ( ))s ss s h

c cD c

t RTs

¶ W= Ñ Ñ - Ñ

¶

Effect of hydrostatic stress on Li ion flux


Thermal Analysis Stress

.ll l l

cN R

te

¶+Ñ =

¶

,l

l l effl

i tN D c

F+=- Ñ +

Diffusion and MigrationSource: spectrum.ieee.org

Reference: Doyle et al., 1996; Rosas et al., 2011 and Fuel cells and Battery module, COMSOLStress Analysis of Lithium-Based Rechargeable Batteries using micro and macro

scale analysis5

Reaction

Flux

,,

2(1 ln / ln )(1 ) lnl eff

l l effl l l

RTi f c t c

F

ss f +=- Ñ + +¶ ¶ - Ñ

Concentration gradient

,,

Li m locl v m

m

iR a

F

u +=- å

irr act ohmQ Q Q= +

, , , ,( )act v i loc i s i l i iQ a i Uff= - -

, ,i

rea v i loc i

UQ a i T

T

¶=

¶

2( 1)(1 ln / ln )eff eff

DRT

t d f d cF

k k += - +

. . .eff eff eff lohm s s s l l D l

l

cQ

cs ff k ff k f

Ñ= Ñ Ñ + Ñ Ñ + Ñ



Source: Comsol Multiphysics

Reference: Srinivasan and Wang, 2003; Kumaresan et al., 2008 and Fuel cells and Battery module, COMSOL

rev reaQ Q=


6

thermal Te a=Thermal Strain

.( ( ))s ss s h

c cD c

t RTs

¶ W= Ñ Ñ - Ñ

¶( 2 ) / 3h r ts s s= +

0

2 23 3

0 0 0

2 1 1( )

3(1 )

r r

r

Ecr dr cr dr

r rs

JW

= -- ò ò% %

0

2 23 3

0 0 0

2 1( )

3(1 )

r r

t

Ecr dr cr dr c

r rs

JW

= - -- ò ò% % %

1( 2 )

3r r t cE

e s J sW

= - + %

1[( ( )]

3t t r t cE

e s J s sW

= - + + %



Effect of hydrostatic stress on Li ion flux

Source: intechopen.com

Reference: Zhang et al., 2007; Zhang et al., 2008 and Xiao et al., 2010

sJ Mc m=- Ñ 0 ln hRT Xm m s= + - W


7

MODELING

8

ElectrodeSolids State

Diffusion

ThermalHeat

Generation/ Transport

StressIntercalatio

n and Thermal

Electrode & ElectrolyteSpecies/Charge

Transport

Butler Volmer

Cs

T

TT

J

J Cs

ɸ, i

Cl, ɸ



scale analysis


Diffusion

ThermalHeat


StressIntercalatio

n and Thermal


Transport

Butler Volmer

Cs

T

TT

J

J Cs

ɸ, i

Cl, ɸ

MODELING


scale analysis


Diffusion

ThermalHeat


StressIntercalatio

n and Thermal


Transport

Butler Volmer

Cs

T

TT

J

J Cs

ɸ, i

Ds (T) Ds (Cs ,T)

Cl, ɸ

Ds as a function of Cs?

11

LixC6 Electrode phase diffusion value

(MD Simulation)

INTERACTION PARAMETERS

DIFFUSIVITY CALCULATIONEinstein relation - diffusion coefficient is related to the slope of the mean

square displacement (MSD) of the particles over time.


Graphene Layers

AIREBO (Adaptive Intermolecular Reactive Empirical Bond-Order)

Stuart et. al, Journal of Chemical Physics, 2000

Li-Li interaction

Field Parameter for Intermolecular and Columbic interactions.

Wander and Shuford, Journal of Chemical Physics, 2011

Graphene-Li interaction Lorentz-Berthelot combining rules

( ) ( )®¥

é ù= + -ê úë û2

0 01

lim6 i it

dD r t t r t

dt


scale analysis

( ) ( )298, exp (1/ 1/ )s K ref

ED C T D x T T

R

æ öD ÷ç ÷= - -ç ÷ç ÷çè ø

DIFFUSIVITY

∆E = 81.5 meV

Similarly for LiMn2O4 Wakhira et al., Ionic State Solids, 1996 and Srinivasan et

al., Journal of The Electrochemical Society, 2003 gives us the same kind of expression


scale analysis

Anode Cathode Separator

Anode

1D electrochemical finite element model (FEM)• Charge Conservation• Chemical Kinetics• Mass Transport (except for electrode particles)• Heat Transport

2D electrode particle FEM model• Li ion concentration in electrode particle • Intercalation and Thermal Stress

Fuel cell and battery module

Heat Transfer module

PDE module

r=12.5µm r=8.5µm

Cathode

COMSOL MODEL

Parameter Reference: Doyle et al, 1996; Srinivasan et al, 2003 and Zhang et al, 2007

• Current density of 17.5 A/m2 applied

• Charge cycle of 1600s with 800s of discharging and charging

• Total number of cycles - 10

• Anode kept at constant potentialStress Analysis of Lithium-Based Rechargeable Batteries using micro and macro

scale analysis14

APPLIED CURRENT

ANODE CATHODESEPARATOR

Source: srinivasan et al., 2003


scale analysis

Electrode


16

Electrolyte


17

Discharging (200s-600s) Charging (1100s-1500s)

Cs variation


18

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 (

K)

t (s)


19

Anode – Tangential Stress

Cathode – Tangential Stress

INTERCALATION STRESS

0

2 23 3

0 0 0

2 1( )

3(1 )

r r

t

Ecr dr cr dr c

r rs

JW

= - -- ò ò% % %


scale analysis

Electrode Potential


scale analysis

Normalized Stress and Potential

22

• 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.

• Tavg 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

CONCLUSION

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

Thank You

24

LixC6 Electrode phase diffusion value(MD Simulation)

INTERACTION PARAMETERS

Graphite : AIREBO (Adaptive Intermolecular Reactive Empirical Bond-Order). Stuart et. al, Journal of Chemical Physics, 2000

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


¹ ¹ ¹

é ùê ú= + +ê úê úë û

å å å å, , ,

1.

2REBO LJ torsij ij kijl

i j i k i j l i j k

E E E E ( ) ( )= +REBO R Aij ij ij ijE V r b V r

25

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.

Green-Kubo (GK) - integration over the velocity autocorrelation function

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

( ) ( )®¥


0 01

lim6 i it

dD r t t r t

dt

( ) ( )¥

= + ×ò 0 0 00

13 iD V t t V t dt

DIFFUSIVITY CALCULATION

26

Lithium intercalated graphite Li0.396C6

(MD Simulation snapshot)


INITIAL CONFIGURATION FINAL CONFIGURATION (1ns)

SIDE VIEW

TOP VIEW

NVT Ensembl

e


scale analysis

0 10

20 30

40

50

100

200

300

400

500

600

Li0.604C6

Li0.500C

6

Li0.396C6

Li0.208C

6

Time (ps)

MSD

(Å

2)

( ) ( )®¥


0 01

lim6 i it

dD r t t r t

dt(MSD)

DIFFUSIVITY at 298K

50 100 150 2000

400

800

1200

MSD

(Å

2) 233K

265K298K353K

Time (ps)


28

THERMAL ANALYSIS

Qirrev = Qohm + Qact

, ,i

rev v i loc i

UQ a i T

T

¶=

¶


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

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