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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

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

2

INTRODUCTION Christensen 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.


3

STRUCTURE

Source: spectrum.ieee.org

Source: srinivasan et al., 2003

( )( )0(exp exp )ca

FFloc RTRTi i

0 ,max ,( ) ( ) ( ) ( ) ( / )a c a c a

c a s s s l l refi F k k c c c c c

,s s film l eqE

,s s eff si

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


4

.( ( ))s ss s h

c cD c

t RT

Effect of hydrostatic stress on Li ion flux


Electrolyte

Thermal

Analysis Stress

.ll l l

cN R

t

,l

l l eff l

i tN D c

F

Diffusion and Migration

Source: spectrum.ieee.org

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


5

Reaction Flux

,

,

2(1 ln / ln )(1 ) ln

l eff

l l eff l l l

RTi f c t c

F

Concentration gradient

,

,

Li m loc

l v m

m

iR a

F

irr act ohmQ Q Q

, , , ,( )

act v i loc i s i l i iQ a i U

, ,i

rea v i loc i

UQ a i T

T

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

D

RTt d f d c

F

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

l

cQ

c


Electrolyte

Thermal

Analysis Stress

Source: Comsol Multiphysics

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

rev reaQ Q


6

thermalTThermal Strain

.( ( ))s ss s h

c cD c

t RT( 2 ) / 3

h r t

0

2 2

3 3

0 0 0

2 1 1( )

3(1 )

r r

r

Ecr dr cr dr

r r

0

2 2

3 3

0 0 0

2 1( )

3(1 )

r r

t

Ecr dr cr dr c

r r

1( 2 )

3r r tc

E

1[( ( )]

3t t r tc

E


Electrolyte

Thermal

Analysis Stress

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 0

lnh

RT X


7

MODELING

8

Electrode

Solids State

Diffusion

Thermal

Heat

Generation/

Transport

Stress

Intercalation

and Thermal

Electrode &

Electrolyte

Species/Charge

Transport

Butler

Volmer

Cs

T

T

T

J

J Cs

ɸ, i

Cl, ɸ



9

Electrode

Solids State

Diffusion

Thermal

Heat

Generation/

Transport

Stress

Intercalation

and Thermal

Electrode &

Electrolyte

Species/Charge

Transport

Butler

Volmer

Cs

T

T

T

J

J Cs

ɸ, i

Cl, ɸ

MODELING


10

Electrode

Solids State

Diffusion

Thermal

Heat

Generation/

Transport

Stress

Intercalation

and Thermal

Electrode &

Electrolyte

Species/Charge

Transport

Butler

Volmer

Cs

T

T

T

J

J Cs

ɸ, i

Ds (T) Ds (Cs ,T)

Cl, ɸ

Ds as a function of Cs?

LixC6 Electrode phase diffusion value

(MD Simulation)

INTERACTION PARAMETERS

DIFFUSIVITY CALCULATION

Einstein relation - diffusion coefficient is related to the slope of the mean square

displacement (MSD) of the particles over time.


11

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

2

0 0

1lim

6 i it

dD r t t r t

dt


12

298, exp (1/ 1/ )

s K ref

ED C T D x T T

R

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


13

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 potential


14

APPLIED CURRENT

ANODE CATHODE SEPARATOR

Source: srinivasan et al., 2003


15

Electrode

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

Electrolyte

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


Cs variation


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)

Anode – Tangential Stress Cathode – Tangential Stress


INTERCALATION STRESS

0

2 2

3 3

0 0 0

2 1( )

3(1 )

r r

t

Ecr dr cr dr c

r r


20

Electrode Potential


21

Normalized Stress and Potential

• 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.


22

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

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


24

, , ,

1.

2

REBO LJ torsij ij kijl

i j i k i j l i j k

E E E EREBO R Aij ij ij ijE V r b V r

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


25

2

0 0

1lim

6 i it

dD r t t r t

dt

0 0 00

1

3 iD V t t V t dt

DIFFUSIVITY CALCULATION

Lithium intercalated graphite Li0.396C6 (MD Simulation snapshot)


26

INITIAL CONFIGURATION FINAL CONFIGURATION (1ns)

SIDE

VIEW

TOP

VIEW

NVT

Ensemble


27

0 10 20 30 4

0

50

100

200

300

400

500

600

Li0.604C6

Li0.500C6

Li0.396C6

Li0.208C6

Time (ps)

MSD

(Å

2)

2

0 0

1lim

6 i it

dD r t t r t

dt(MSD)

DIFFUSIVITY at 298K

50 100 150 200 0

400

800

1200

MSD

(Å

2) 233K

265K 298K 353K

Time (ps)


THERMAL ANALYSIS

Qirrev = Qohm + Qact , ,i

rev v i loc i

UQ a i T

T

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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