A multiscale-compatible approach in modeling ionic transport in the electrolyte of (Lithium ion) batteries

Abstract A novel approach in modeling the ionic transport in the electrolyte of Li-ion batteries is here presented. Diffusion and migration processes govern the transport of ions in solution in the absence of convection. In the porous electrode theory [1] it is common to model these processes via mass balance equations and electroneutrality. A parabolic set of equations arises, in terms of a non constant electric field which is afflicted by the paradox of being generated without electrical charges. To remedy this contradiction, Maxwell's equations have been used here, coupled to Faraday's law of electrochemical charge transfer. The set of continuity equations for mass and Maxwell's equations lead to a consistent model, with distinctive energy characteristics. Numerical examples show the robustness of the approach, which is well suited for multi-scale analyses [2,3].

[1]  Jun Wang,et al.  In operando tracking phase transformation evolution of lithium iron phosphate with hard X-ray microscopy , 2014, Nature Communications.

[2]  Dl Dmitry Danilov,et al.  Finite element simulations of 3D ionic transportation properties in Li-ion electrolytes , 2012 .

[3]  Attay Kovetz,et al.  The principles of electromagnetic theory , 1990 .

[4]  John N. Harb,et al.  Modeling of Particle-Particle Interactions in Porous Cathodes for Lithium-Ion Batteries , 2007 .

[5]  Shengbo Zhang.  A review on the separators of liquid electrolyte Li-ion batteries , 2007 .

[6]  Wolfgang Dreyer,et al.  A mixture theory of electrolytes containing solvation effects , 2013 .

[7]  R. Toupin.  The Elastic Dielectric , 1956 .

[8]  R. McMeeking,et al.  Electrostatic Forces and Stored Energy for Deformable Dielectric Materials , 2005 .

[9]  Xiaosong Huang,et al.  A multiphysics model for the in situ stress analysis of the separator in a lithium-ion battery cell , 2014 .

[10]  Yi Cui,et al.  Size-dependent fracture of Si nanowire battery anodes , 2011 .

[11]  Jonas Larsson,et al.  Electromagnetics from a quasistatic perspective , 2007 .

[12]  K. Maute,et al.  Multiscale design optimization of lithium ion batteries using adjoint sensitivity analysis , 2012 .

[13]  M. Gurtin,et al.  The Mechanics and Thermodynamics of Continua , 2010 .

[14]  W. Craig Carter,et al.  Microstructural Modeling and Design of Rechargeable Lithium-Ion Batteries , 2005 .

[15]  A. Quarteroni,et al.  Numerical Approximation of Partial Differential Equations , 2008 .

[16]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .

[17]  Jake Christensen,et al.  Modeling Diffusion-Induced Stress in Li-Ion Cells with Porous Electrodes , 2010 .

[18]  K. Abraham.  Directions in secondary lithium battery research and development , 1993 .

[19]  Lars Ole Valøen,et al.  Transport Properties of LiPF6-Based Li-Ion Battery Electrolytes , 2005 .

[20]  Phl Peter Notten,et al.  Mathematical modelling of ionic transport in the electrolyte of Li-ion batteries , 2008 .

[21]  S. Kjelstrup,et al.  Mesoscopic Nonequilibrium Thermodynamics Gives the Same Thermodynamic Basis to Butler-Volmer and Nernst Equations , 2003 .

[22]  P. M. Squet.  Local and Global Aspects in the Mathematical Theory of Plasticity , 1985 .

[23]  Phl Peter Notten,et al.  On the Deviation of Electro-Neutrality in Li-Ion Battery Electrolytes , 2014 .

[24]  Kurt Maute,et al.  Numerical modeling of electrochemical-mechanical interactions in lithium polymer batteries , 2009 .

[25]  K. Zaghib,et al.  Quantifying tortuosity in porous Li-ion battery materials , 2009 .

[26]  Xiaosong Huang,et al.  A multi-scale approach for the stress analysis of polymeric separators in a lithium-ion battery , 2010 .

[27]  Allan F. Bower,et al.  Measurement and modeling of the mechanical and electrochemical response of amorphous Si thin film electrodes during cyclic lithiation , 2013, 1311.5844.

[28]  Xiaosong Huang,et al.  Separator technologies for lithium-ion batteries , 2011 .

[29]  V. G. Kouznetsova,et al.  Multi-scale computational homogenization: Trends and challenges , 2010, J. Comput. Appl. Math..

[30]  Ralph E. White,et al.  Theoretical Analysis of Stresses in a Lithium Ion Cell , 2010 .

[31]  Jiang Ziqiang,et al.  SiをドープしたMg 3 Y 2 Ge 3 O 12 :Ce 3+ ガーネット蛍光体の暖かい白色発光ダイオード用黄橙色発光の増進 , 2010 .

[32]  Rajlakshmi Purkayastha,et al.  An integrated 2-D model of a lithium ion battery: the effect of material parameters and morphology on storage particle stress , 2012 .

[33]  Ann Marie Sastry,et al.  Mesoscale Modeling of a Li-Ion Polymer Cell , 2007 .

[34]  Mgd Marc Geers,et al.  Governing equations for a two-scale analysis of Li-ion battery cells , 2015 .

[35]  J. Paulsen,et al.  Numerical simulation of porous networks in relation to battery electrodes and separators , 2003 .

[36]  Jochen Zausch,et al.  Thermodynamic consistent transport theory of Li-ion batteries , 2011 .

[37]  M. Doyle,et al.  Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell , 1993 .

[38]  R. Compton,et al.  The electroneutrality approximation in electrochemistry , 2011 .

[39]  Sébastien Martinet,et al.  Lithium-ion batteries with high charge rate capacity: Influence of the porous separator , 2007 .

[40]  Alberto Salvadori,et al.  A computational homogenization approach for Li-ion battery cells : Part 1 – formulation , 2014 .

[41]  Ronald E. Miller,et al.  Continuum mechanics and thermodynamics , 2011 .

[42]  Matthew B. Pinson,et al.  Theory of SEI Formation in Rechargeable Batteries: Capacity Fade, Accelerated Aging and Lifetime Prediction , 2012, 1210.3672.

[43]  D. A. G. Bruggeman.  Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen , 1935 .

[44]  G. A. Muccini,et al.  Characteristics of porous beds and structures , 1956 .

[45]  Dl Dmitry Danilov,et al.  Modeling All-Solid-State Li-Ion Batteries , 2011 .