s.n. polyakov, j. kortus, h.j. seifert bauman mhtu, january 26-28, 2011, moscow cooperation: prof....
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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
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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.
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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 [**]
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
Stress and Li-concentration
Deintercalation Intercalation
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
Hydrostatic stress (deintercalation/intercalation)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
Hydrostatic stress (deintercalation/intercalation)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
Stress in a 10μm particle
mr
smVv
10
/1
0
0r
rx
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
Hydrostatic stress in a particle
Deintercalation Intercalation
Dangerous zone r = 10μm (deintercalation, v = 1 μV/s)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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.
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
Numerical simulation (diffusion)Deintercalation
Intercalation
.1 ,100 smVvmr .1 ,5.00 smVvmr
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
Numerical simulation (current density )
Deintercalation
Intercalation
smVvmr /1 ,100 smVvmr /1 ,5.00
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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)
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
Current density in submicron particles
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
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.
S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow
I thank you for your attention
Большое спасибо за внимание!
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