Mathematical Modeling of Porous Battery Electrodes-Revisit of Newman's Model

Abstract The most established mathematical description of porous battery electrodes is Newman's model, which accounts for the behavior of both solid and liquid phases via concentrated solution theory and porous electrode theory. In the present work, formal volume averaging of reformulated generalized Poisson–Nernst–Planck (PNP) equations in the form of concentration and electrochemical potential, or in the form of equivalent circuit on a representative porous microstructure, lead to “upscaled” equations similar to those in Newman's model. The similarities and differences of the results from the two approaches are discussed throughout the paper.

[1]  Martin Z. Bazant,et al.  Intercalation dynamics in rechargeable battery materials : General theory and phase-transformation waves in LiFePO4 , 2008 .

[2]  A. Karma,et al.  Phase-Field Simulation of Solidification , 2002 .

[3]  Chaoyang Wang,et al.  Micro‐Macroscopic Coupled Modeling of Batteries and Fuel Cells I. Model Development , 1998 .

[4]  J. Ni,et al.  A volume-averaged two-phase model for transport phenomena during solidification , 1991 .

[5]  J. Newman,et al.  Porous‐electrode theory with battery applications , 1975 .

[6]  R. Newnham,et al.  Electrical Resistivity of Composites , 1990 .

[7]  M. Bazant,et al.  Diffuse-charge dynamics in electrochemical systems. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  P. M. Heertjes,et al.  Analysis of diffusion in macroporous media in terms of a porosity, a tortuosity and a constrictivity factor , 1974 .

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

[10]  J. Maier,et al.  Current Equation for Hopping Ions on a Lattice under High Driving Force and Nondilute Concentration , 2009 .

[11]  Gerbrand Ceder,et al.  Electrochemical modeling of intercalation processes with phase field models , 2004 .

[12]  Anton Van der Ven,et al.  Lithium Diffusion in Layered Li x CoO2 , 1999 .

[13]  Juan Bisquert,et al.  Physical electrochemistry of nanostructured devices. , 2008, Physical chemistry chemical physics : PCCP.

[14]  M. Doyle,et al.  Simulation and Optimization of the Dual Lithium Ion Insertion Cell , 1994 .

[15]  D. Aurbach,et al.  Frumkin intercalation isotherm — a tool for the description of lithium insertion into host materials: a review , 1999 .

[16]  R. Buck.  Kinetics of bulk and interfacial ionic motion: microscopic bases and limits for the nernst—planck equation applied to membrane systems☆ , 1984 .

[17]  Yet-Ming Chiang,et al.  Spatially Resolved Modeling of Microstructurally Complex Battery Architectures , 2007 .

[18]  Ann Marie Sastry,et al.  A review of conduction phenomena in Li-ion batteries , 2010 .

[19]  Long-Qing Chen.  Phase-Field Models for Microstructure Evolution , 2002 .

[20]  Richard P. Buck,et al.  Numerical solution of the Nernst-Planck and poisson equation system with applications to membrane electrochemistry and solid state physics , 1978 .

[21]  Norman Epstein,et al.  On tortuosity and the tortuosity factor in flow and diffusion through porous media , 1989 .

[22]  J. Tarascon,et al.  Comparison of Modeling Predictions with Experimental Data from Plastic Lithium Ion Cells , 1996 .

[23]  Venkat Srinivasan,et al.  Discharge Model for the Lithium Iron-Phosphate Electrode , 2004 .

[24]  Richard P. Buck,et al.  Transmission line equivalent circuit models for electrochemical impedances , 1981 .

[25]  Wei Lai,et al.  Thermodynamics and kinetics of phase transformation in intercalation battery electrodes – phenomenological modeling , 2010 .

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

[27]  R. D. Levie,et al.  On porous electrodes in electrolyte solutions: I. Capacitance effects☆ , 1963 .

[28]  Ralph E. White,et al.  Governing Equations for Transport in Porous Electrodes , 1997 .

[29]  Wei Lai,et al.  Electrochemical impedance spectroscopy of mixed conductors under a chemical potential gradient: a case study of Pt|SDC|BSCF. , 2008, Physical chemistry chemical physics : PCCP.

[30]  J. Newman,et al.  Theoretical Analysis of Current Distribution in Porous Electrodes , 1962 .

[31]  Keld West,et al.  Modeling of Porous Insertion Electrodes with Liquid Electrolyte , 1982 .

[32]  Marc Doyle,et al.  The Use of Mathematical-Modeling in the Design of Lithium Polymer Battery Systems , 1995 .

[33]  Ralph E. White,et al.  Mathematical modeling of secondary lithium batteries , 2000 .

[34]  Ming Tang,et al.  Model for the Particle Size, Overpotential, and Strain Dependence of Phase Transition Pathways in Storage Electrodes: Application to Nanoscale Olivines , 2009 .

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

[36]  Allen J. Bard,et al.  Electrochemical Methods: Fundamentals and Applications , 1980 .

[37]  S. Selberherr.  Analysis and simulation of semiconductor devices , 1984 .

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

[39]  Joachim Maier,et al.  Generalised equivalent circuits for mass and charge transport: chemical capacitance and its implications , 2001 .

[40]  V. Subramanian,et al.  Efficient Macro-Micro Scale Coupled Modeling of Batteries , 2005 .

[41]  R. Buck,et al.  Origins of finite transmission lines for exact representations of transport by the Nernst–Planck equations for each charge carrier , 1999 .

[42]  Dennis W. Dees,et al.  Electrochemical Modeling of Lithium-Ion Positive Electrodes during Hybrid Pulse Power Characterization Tests , 2006 .

[43]  Anton Van der Ven,et al.  Nondilute diffusion from first principles: Li diffusion in Li x TiS 2 , 2008 .

[44]  Michael J. Martínez,et al.  Measurement of MacMullin Numbers for PEMFC Gas-Diffusion Media , 2009 .

[45]  Ralph E. White,et al.  Semi-empirical modeling of charge and discharge profiles for a LiCoO2 electrode , 2007 .

[46]  M. Verbrugge,et al.  Mathematical modeling of high-power-density insertion electrodes for lithium ion batteries , 2002 .

[47]  Sossina M. Haile,et al.  Impedance Spectroscopy as a Tool for Chemical and Electrochemical Analysis of Mixed Conductors: A Case Study of Ceria , 2005 .

[48]  Thomas O. Mason,et al.  Evaluating Dielectric Impedance Spectra using Effective Media Theories , 2000 .

[49]  R. S. Eisenberg,et al.  Computing the Field in Proteins and Channels , 2010, 1009.2857.