S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Cooperation: Prof....

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow

Cooperation: Prof. Dr. J. Kortus Cooperation: Prof. Dr. H.J. Seifert

Thermodynamics and Kinetics of Processes of the Intercalation/De-

Intercalation in Submicron Particles of Cathode Li-ions Batteries

С.Н. Поляков

World production

S.N. Polyakov, J. Kortus, H.J. Seifert МГТУ им.Баумана, 26-28 января, 2011, Москва


Lithium-ion batteryCathodes

Electrode materialAverage potential

differenceSpecific capacity Specific energy

LiCoO2 3.7 V 140 mA·h/g 0.518 kW·h/kg

LiMn2O4 4.0 V 100 mA·h/g 0.400 kW·h/kg

LiNiO2 3.5 V 180 mA·h/g 0.630 kW·h/kg

LiFePO4 3.3 V 150 mA·h/g 0.495 kW·h/kg

Li2FePO4F 3.6 V 115 mA·h/g 0.414 kW·h/kg

LiCo1/3Ni1/3Mn1/3O2 3.6 V 160 mA·h/g 0.576 kW·h/kg

Li(LiaNixMnyCoz)O2 4.2 V 220 mA·h/g 0.920 kW·h/kg


Comparison of the gravimetric and volumetric energy densities of various rechargeable battery systems*

*) A. Manthiram, Lithium batteries, Edited by Gholam-Abbas Nazri, USA, Springer, 2009.


Schematic illustration of the charge/discharge in lithium-ion cell

42

dischargeion,intercalat

chargeation,deintercal42

+ OLiMnOMn+e+Li

6x42x1642 CLiOMnLiCOLiMn

Discharge (intercalation)Charge (de-intercalation)

c

Li

Li O

Mn


Problem of the cyclability (Material degradation)

Crack after cycling [*]

Cycling crumbling (chemical corrosion) [**]

Cyclability data for LiMn2O4 cathode[***]

[*] J. of Power Sources 140 (2005) 125-128

[**] J. of Power Sources 143 (2005) 203-211

[***] Solid State Ionics 167 (2004) 237-242

Optimal distribution of size of the cathode particles


ThermodynamicLarch-Cahn-Theory

LiLiijij dcVdVsdTdG '' 0V

V

ij

Li

Li

ij

c

Li

ijij c

iiijLiij

3 ),( TcLi

hLiLiLiijLi xx ),0(),(

)()( 0VdVd

Maxwell’s relations

(1)

3/)( 332211 h

The chemical strain tenzor for cubic symmetry

Partial molar volume of Li in the host latticeFor small deformations

- hydrostatic stress

(2) (3)

(4)

Cubic cell LiMn2O4


Kinetics of the Li-ion in Electrode

hLiLiLiLiLi σΩcμMc=J 0,

hLiLiLiLiLi σΩMccD=t

c

Li

LiLiLiLi c

μMc=D

ijLikkijij δccα+νσσν+E

=ε 011

Electrolyte

Particle

Porous electrode

BinderLiLiLiLi μMc=J

(5)

(6)

Kinetic model for one particle

LiM

Li-ion flux density, Onsager Theory

- Li-ion mobility

Li-ion mobility, Larch-Cahn-Theory

(7)


DiffusionSpherical particle

RT

βFu

RT

Fuβj=j exp

1exp0

hLiLiLiLiLi σΩMccDr

r=

t

c

2

2

1

F

jtr

r

cDJ Li

Li

),( 0

βs

βθ

βl cc=Fkcj 11

0

The Butler-Volmer equation

- exchange flux density

0UU=u a

(8)

(9)

(10)


Open-circuit potential

F

TTcTcU LiLiOLiMn

Li

)(),(),( 42

0

[*] Solid State Ionics, 69 (1994) 59.[**] J. Electrochem. Soc., 143, 1890 (1996)

(11)

355540exp8102390

047380exp1571230

90111199843200754790

609428554614tanh0566610198294424650

0

.x+,+

x,,

,x,,

,x+,,+,=U,

0U

0c

cx Li

Experiment [*] Calphad-Method [**]


Intercalation/De-Intercalation stressin a spherical particle

02

=σσr

+dr

dσtr

r

)=(rσ=)=(rσ rt 00 00 =)r=(rσ r

021

ccα+νσσE

=ε Litrr

0

1ccα+σ+σνσ

E=ε Lirttt

E - elastic modulus

ν - Poisson’s ratio

Charge (contraction/expansion)

Discharge (expansion/contraction)

(12)

(13)

(14)


Analysis of the diffusion by stresses in a spherical particle

)()(1

2)( 0 rprp

Err

00 )()(21

)( ccrprpE

rt

00 )(313

23/2)( ccrp

Er trh

r

Li drrccr

rp0

203

1)(

r

c

ν

E=(r)

r

σ LiLih

13

2α

LiLi Mν

EΩ=θ

19

2 2

(15) (16)

(17)

r

cθc+D=μMc=J Li

LiLiLiLiLi

(18)

(5)


Numerical procedure

11,2... 1

11

12

2/12/1

1112

2/12/1

2

1

m=iΔr

Δr

ccrD

Δr

ccrD

r=

Δt

cc

+ni

+ni

ii

+ni

+n+i

+i+i

i

ni

+ni

11

10

+n+n c=c

RT

βu

RT

β)(uccc

D

kc=

Δx

cc +ni

+niβ+n

m

β+nm

e+n

m+n

m11

110

111

1

exp1

exp

0

1

01

c

cUvt+U=u

+ni

n+n

i

)(xf

)f(xx=x

i'

ii+i 1

(19)

(20)

RT

βη

RT

β)(ηxcx

D

kc=Φ(x)

Φ(x)dx

d

α

Δr=(x)f

α

β+

RT

βη

RT

β)(ηxcx

D

kc

α

Δrx=f(x)

+ni

+niββe

m

'

m

m+n

i+n

iββe

m

111

0

1

1

111

10

1

exp1

exp

where

11

1exp

1exp

1


Material properties of LiMn2O4 and parameters for the lithium intercalation reaction

)(VU a

)(VU a

OCP

0c

cLi

0.5

1.0

0.1-10.0

0.00019

10

0.3

)( 12 scmD

) ( 3dmmolcl

) /( 30 mmolc

)(0 mr

)( 2/112/5 molscmk

)(GPaE

v

)/( 3 molm 610497.3

41029.2

913 1010 Deintercalation

Intercalation


Stress and Li-concentration

Deintercalation Intercalation


Hydrostatic stress (deintercalation/intercalation)


Stress in a submicron particle

tB+rtA=cc=tr,τ 20 DFri/=rt,rc/=A 0 02

DFcir=j 0 0/

20 113

0.2xj

ν

EΩc=(x)σ r

20 2x113

0.2

j

ν

EΩc=xσ t

20 5x319

0.2

j

ν

EΩc=xσ h

0r

rx

mr

smVv

1

/1

0

0r

r

(21)

(22)

(23)


Stress in a 10μm particle

mr

smVv

10

/1

0

0r

rx


Hydrostatic stress in a particle

Deintercalation Intercalation

Dangerous zone r = 10μm (deintercalation, v = 1 μV/s)


Extreme values of hydrostatic stresses on the particle surface[*]

Deintercalation

Intercalation

Hydrostatic stress for various scan rates in a particle of 2 μm radius

[* ] С. Н. Поляков, ПЖТФ, 2010, Vol. 36, No. 24, pp. 25–32.


Numerical simulation (diffusion)Deintercalation

Intercalation

.1 ,100 smVvmr .1 ,5.00 smVvmr


Numerical simulation (current density )

Deintercalation

Intercalation

smVvmr /1 ,100 smVvmr /1 ,5.00


Analysis of the current density in submicron particles

01111 1 χ=τ,yτ,y+ωτ,xy/ ββ

10 /1/ lkc/Drω=

20τ=tD/r 0x=r/r 0y=c/c

0ω

00 =τ,xy/

βFη/RTRTFηβχ= exp/1exp

010 τ,y,τy

(24)


Current density in submicron particles

00 SV

sdcgradD=dvcgradDdiv

0

01S

sdcgradDS=J

000 =J+dc/dt/SV

dc/dt=Vdvdtdc=dvdc/dt=dvtc/VVV

0

000

(25)


Current density in submicron particles


Conclusions• The effect of stresses and deformations in a cathode material (LiMn2O4) is

taken into account using the Larche–Cahn thermo-chemical theory.

• Equations for calculating kinetics of mechanical stresses in submicron particles were derived.

• The Li-ion current density dependence of the particle size and of the ID rate was obtained for a cathode material.

• A kinetic equation for the current density in the absence of diffusion polarization was derived; it was shown that diffusion polarization decreased for submicron particles.

• The influence of a particle size on the maximum Li-ion current density was evaluated.


I thank you for your attention

Большое спасибо за внимание!

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Cooperation: Prof....

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