Predicting Active Material Utilization in LiFePO4 Electrodes Using a Multiscale Mathematical Model

A mathematical model is developed to simulate the discharge of a LiFePO 4 cathode. This model contains three size scales, which match with experimental observations present in the literature on the multiscale nature of LiFePO 4 material. A shrinking core is used on the smallest scale to represent the phase transition of LiFePO 4 during discharge. The model is then validated against existing experimental data and this validated model is then used to investigate parameters that influence active material utilization. Specifically, the size and composition of agglomerates of LiFePO 4 crystals is discussed, and we investigate and quantify the relative effects that the ionic and electronic conductivities within the oxide have on oxide utilization. We find that agglomerates of crystals can be tolerated under low discharge rates. The role of the electrolyte in limiting (cathodic) discharge is also discussed, and we show that electrolyte transport does limit performance at high discharge rates, confirming the conclusions of recent literature.

[1]  J. Crank.  Free and moving boundary problems , 1984 .

[2]  Peter R. Slater,et al.  Atomic-Scale Investigation of Defects, Dopants, and Lithium Transport in the LiFePO4 Olivine-Type Battery Material , 2005 .

[3]  Primary Alkaline Battery Cathodes: A Simplified Model for Porous Manganese Oxide Particle Discharge , 2005 .

[4]  Takashi Ida,et al.  Isolation of Solid Solution Phases in Size‐Controlled LixFePO4 at Room Temperature , 2009 .

[5]  Xincun Tang,et al.  Investigation on diffusion behavior of Li+ in LiFePO4 by capacity intermittent titration technique (CITT) , 2009 .

[6]  Robert Dominko,et al.  Is small particle size more important than carbon coating? An example study on LiFePO4 cathodes , 2007 .

[7]  L. Nazar,et al.  Nano-network electronic conduction in iron and nickel olivine phosphates , 2004, Nature materials.

[8]  John R. Owen,et al.  How the electrolyte limits fast discharge in nanostructured batteries and supercapacitors , 2009 .

[9]  Haoshen Zhou,et al.  The design of a LiFePO4/carbon nanocomposite with a core-shell structure and its synthesis by an in situ polymerization restriction method. , 2008, Angewandte Chemie.

[10]  François Weill,et al.  C-containing LiFePO4 materials — Part II: Electrochemical characterization , 2008 .

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

[12]  Shinichi Komaba,et al.  Emulsion drying synthesis of olivine LiFePO4/C composite and its electrochemical properties as lithium intercalation material , 2004 .

[13]  Palani Balaya,et al.  Anisotropy of Electronic and Ionic Transport in LiFePO4 Single Crystals , 2007 .

[14]  Y. Marcus,et al.  Standard partial molar volumes of electrolytes and ions in nonaqueous solvents. , 2004, Chemical Reviews.

[15]  C. Please,et al.  Primary Alkaline Battery Cathodes A Three‐Scale Model , 2000 .

[16]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[17]  Moving Boundary Model for the Discharge of a LiCoO2 Electrode , 2007 .

[18]  Yet-Ming Chiang,et al.  Electronically conductive phospho-olivines as lithium storage electrodes , 2002, Nature materials.

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

[20]  M. Gaberšček.  Towards optimized preparation of cathode materials: How can modeling and concepts be used in practice , 2009 .

[21]  Frédéric Bernard,et al.  Characteristics of LiFePO4 obtained through a one step continuous hydrothermal synthesis process working in supercritical water , 2009 .

[22]  P. Sweby.  High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws , 1984 .

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

[24]  M. Behm,et al.  Electrochemical characterisation and modelling of the mass transport phenomena in LiPF6–EC–EMC electrolyte , 2008 .

[25]  K. S. Nanjundaswamy,et al.  Phospho‐olivines as Positive‐Electrode Materials for Rechargeable Lithium Batteries , 1997 .

[26]  Linda F. Nazar,et al.  Approaching Theoretical Capacity of LiFePO4 at Room Temperature at High Rates , 2001 .

[27]  Jinbao Zhao,et al.  Novel electrolytes based on aliphatic oligoether dendrons , 2009 .

[28]  Pedro E. Arce,et al.  Discharge Model for LiFePO4 Accounting for the Solid Solution Range , 2008 .

[29]  John Newman,et al.  Measuring the Salt Activity Coefficient in Lithium-Battery Electrolytes , 2008 .

[30]  Nathalie Ravet,et al.  On the electronic conductivity of phospho-olivines as lithium storage electrodes , 2003, Nature materials.

[31]  Pedro E. Arce,et al.  A Discharge Model for Phase Transformation Electrodes: Formulation, Experimental Validation, and Analysis , 2007 .

[32]  C. Delmas,et al.  Lithium deintercalation in LiFePO4 nanoparticles via a domino-cascade model. , 2008, Nature materials.

[33]  T. R. Jow,et al.  Analysis of the FePO4 to LiFePO4 phase transition , 2008 .

[34]  Carol S. Woodward,et al.  Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers , 2020, ACM Trans. Math. Softw..

[35]  Guangchuan Liang,et al.  LiFePO4 doped with magnesium prepared by hydrothermal reaction in glucose solution , 2008 .

[36]  Sai-Cheong Chung,et al.  Optimized LiFePO4 for Lithium Battery Cathodes , 2001 .

[37]  Linda F. Nazar,et al.  Proof of Supervalent Doping in Olivine LiFePO4 , 2008 .

[38]  Jing-ying Xie,et al.  A PVB-based rheological phase approach to nano-LiFePO4/C composite cathodes , 2008 .

[39]  C. Kelley.  Solving Nonlinear Equations with Newton's Method , 1987 .

[40]  Byoungwoo Kang,et al.  Battery materials for ultrafast charging and discharging , 2009, Nature.

[41]  Igor O. Golosnoy,et al.  Numerical solutions of diffusion-controlled moving boundary problems which conserve solute , 2005 .

[42]  Prashant N. Kumta,et al.  Surfactant based sol–gel approach to nanostructured LiFePO4 for high rate Li-ion batteries , 2007 .

[43]  Venkat Srinivasan,et al.  Design and Optimization of a Natural Graphite/Iron Phosphate Lithium-Ion Cell , 2004 .

[44]  Charles Delacourt,et al.  Study of the LiFePO4/FePO4 Two-Phase System by High-Resolution Electron Energy Loss Spectroscopy , 2006 .

[45]  D. Uskoković,et al.  A review of recent developments in the synthesis procedures of lithium iron phosphate powders , 2009 .

[46]  Akiko Nakashima,et al.  Preparation of dense LiFePO4/C composite positive electrodes using spark-plasma-sintering process , 2005 .

[47]  E. Teller,et al.  ADSORPTION OF GASES IN MULTIMOLECULAR LAYERS , 1938 .

[48]  Thomas J. Richardson,et al.  Electron Microscopy Study of the LiFePO4 to FePO4 Phase Transition , 2006 .

[49]  A. Yamada,et al.  Experimental visualization of lithium diffusion in LixFePO4. , 2008, Nature materials.

[50]  Karim Zaghib,et al.  Unsupported claims of ultrafast charging of LiFePO4 Li-ion batteries , 2009 .

[51]  Robert Dominko,et al.  Wired Porous Cathode Materials: A Novel Concept for Synthesis of LiFePO4 , 2007 .