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, января, 2011, Москва

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Lithium-ion battery Cathodes Electrode material Average potential difference Specific capacitySpecific energy LiCoO V140 mA·h/g0.518 kW·h/kg LiMn 2 O V100 mA·h/g0.400 kW·h/kg LiNiO V180 mA·h/g0.630 kW·h/kg LiFePO V150 mA·h/g0.495 kW·h/kg Li 2 FePO 4 F3.6 V115 mA·h/g0.414 kW·h/kg LiCo 1/3 Ni 1/3 Mn 1/3 O V160 mA·h/g0.576 kW·h/kg Li(Li a Ni x Mn y Co z )O V220 mA·h/g0.920 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 Discharge (intercalation)Charge (de-intercalation) c 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 LiMn 2 O 4 cathode[***] [*] J. of Power Sources 140 (2005) [**] J. of Power Sources 143 (2005) [***] Solid State Ionics 167 (2004) Optimal distribution of size of the cathode particles

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Thermodynamic Larch-Cahn-Theory Maxwell’s relations (1) 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 LiMn 2 O 4

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Kinetics of the Li-ion in Electrode Electrolyte Particle Porous electrode Binder (5) (6) Kinetic model for one particle 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 Diffusion Spherical particle The Butler-Volmer equation - exchange flux density (8) (9) (10)

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Open-circuit potential [*] Solid State Ionics, 69 (1994) 59.[**] J. Electrochem. Soc., 143, 1890 (1996) (11) Experiment [*]Calphad-Method [**]

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Intercalation/De-Intercalation stress in a spherical particle E - elastic modulus - 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 (15)(16) (17) (18) (5)

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Numerical procedure (19) (20)

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Material properties of LiMn 2 O 4 and parameters for the lithium intercalation reaction OCP 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 (21) (22) (23)

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Stress in a 10μm particle

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

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Numerical simulation (current density ) Deintercalation Intercalation

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Analysis of the current density in submicron particles (24)

S.N. Polyakov, J. Kortus, H.J. Seifert Bauman MHTU, January 26-28, 2011, Moscow Current density in submicron particles (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 (LiMn 2 O 4 ) 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!