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. Seife Thermodynamics and Kinetics of Processes of the Intercalation/De- Intercalation in Submicron Particles of Cathode Li-ions Batteries С.Н. Поляков
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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.
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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
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