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Lithium iron phosphate electrode semi-empirical performance model

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Abstract

The galvanostatic performance of a pristine lithium iron phosphate (LFP) electrode is investigated. Based on the poor intrinsic electronic conductivity features of LFP, an empirical variable resistance approach is proposed for the single particle model (SPM). The increasing resistance behavior observed at the end of discharge process of LFP batteries can be justified by the increased ohmic resistance, a resistive-reactant feature of LFP as the positive electrode active materials. The model is validated for two different laboratory made Li/LFP coin cells: a high-energy and a high-power configuration. Comparisons between the experimental results and the model predictions reveal that a variable resistance is successful to tackle the increasing overpotential.

Graphical Abstract

Schematic of the coated LFP active material particles in (a) beginning of discharge with well-connected particles, (b) end of discharge with poor-connected particles

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Abbreviations

\(c_{{s,k}}^{{\max }}\) :

Maximum concentration of Li+ in the particle of positive electrode (mol m−3)

\({D_{s,p}}\) :

Li+ diffusion coefficient in the particle of positive electrode (m2 s−1)

\(F\) :

Faraday’s constant (C mol−1)

\(I\) :

Applied current density, (A m−2)

\({K_k}\) :

Reaction rate constant of electrode k (k = p,n), (m2.5 mol−0.5 s−1)

P:

Unknown parameter vector

\(R\) :

Universal gas constant (J mol−1 K−1)

\({R_p}\) :

Radius of the particles of positive electrode (m)

\({S_k}\) :

Total electroactive area of electrode k (k = p,n) (m2)

\(SO{C_p}\) :

State of charge of positive electrode

\(SO{C_{p,ini}}\) :

Initial state of charge of positive electrode

\(t\) :

Time (s)

\(T\) :

Absolute temperature (K)

\({U_p}\) :

Open-circuit potential of positive electrode (V)

\({V_p}\) :

Total volume of positive electrode (m3)

\({{\text{V}}_{cell}}\) :

Model’s estimation of the cell potential (V)

\({\varepsilon _p}\) :

Volume fraction of active material

\({\delta _p}\) :

Dimensionless flux of lithium ion at positive electrode

\({\lambda _k}\) :

The kth eigenvalue

\(ini\) :

Initial state

\(p\) :

Positive electrode

\(n\) :

Negative electrode

\(s\) :

Solid phase

References

  1. Ravet N, Goodenough JB, Besner S, Simoneau M, Hovington P, Armand M (1999) In 96th Meeting of the Electrochemical Society, Vol. 99–2, Abstract, # 127, Hawai

  2. Ravet N, Chouinard Y, Magnan JF, Besner S, Gauthier M, Armand M (2001) Electroactivity of natural and synthetic triphylite. J Power Sources 97:503–507

    Google Scholar 

  3. Yamada A, Chung SC, Hinokuma K (2001) Optimized LiFePO4 for lithium battery cathodes., J Electrochem Soc 148(3):A224-A229

    Google Scholar 

  4. Delacourt C, Poizot P, Levasseur S, Masquelier C (2006) Size effects on carbon-free LiFePO4 powders the key to superior energy density. Electrochem. Solid-State Lett 9:A352–A355

    CAS  Google Scholar 

  5. Islam MS, Driscoll DJ, Fisher CA, Slater PR (2005) Atomic-scale investigation of defects, dopants, and lithium transport in the LiFePO4 olivine-type battery material. Chem Mater 17(20):5085–5092

    CAS  Google Scholar 

  6. Morgan D, Van der Ven A, Ceder G (2004) Li conductivity in Li x MPO 4 (M = Mn, Fe, Co, Ni) olivine materials. Electrochem Solid-State Lett 7(2):A30–A32

    Google Scholar 

  7. Chen G, Song X, Richardson TJ (2006) Electron microscopy study of the LiFePO4 to FePO4 phase transition. Electrochem Solid-State Lett 9(6):A295–A298

    Google Scholar 

  8. Munakata H, Takemura B, Saito T, Kanamura K (2012) Evaluation of real performance of LiFePO4 by using single particle technique. J Power Sources 217:444–448

    CAS  Google Scholar 

  9. Huang H, Yin SC, Nazar LF (2001) Approaching theoretical capacity of LiFePO4 at room temperature at high rates. Electrochem Solid-State Lett 4(10):A170–A172

    CAS  Google Scholar 

  10. Laffont L, Delacourt C, Gibot P, Wu MY, Kooyman P, Masquelier C, Tarascon JM (2006) Study of the LiFePO4/FePO4 two-phase system by high-resolution electron energy loss spectroscopy. Chem Mater 18(23):5520–5529

    CAS  Google Scholar 

  11. Laffont NN, Nikolowski K, Baehtz C, Bramnik KG, Ehrenberg H (2007) Phase transitions occurring upon lithium insertion-extraction of LiCoPO4. Chem Mater 19(4):908–915

    Google Scholar 

  12. Brunetti G, Robert D, Bayle-Guillemaud P, Rouviere JL, Rauch EF, Martin JF, Colin JF, Bertin F, Cayron C (2011) Confirmation of the domino-cascade model by LiFePO4/FePO4 precession electron diffraction. Chem Mater 23(20):4515–4524

    CAS  Google Scholar 

  13. Chueh WC, Gabaly FE, Sugar JD, Bartelt NC, McDaniel AH, Fenton KR, Zavadil KR, Tyliszczak T, Lai W, McCarty KF (2013) Intercalation pathway in many-particle LiFePO4 electrode revealed by nanoscale state-of-charge mapping. Nano Lett 13(3):866–872

    CAS  PubMed  Google Scholar 

  14. Nelson Weker J, Li Y, Shanmugam R, Lai W, Chueh WC (2015) Tracking non-uniform mesoscale transport in LiFePO4 agglomerates during electrochemical cycling. ChemElectroChem 2(10):1576–1581

    CAS  Google Scholar 

  15. Padhi AK, Nanjundaswamy KS, Goodenough JB (1997) Phospho-olivines as positive-electrode materials for rechargeable lithium batteries., J Electrochem Soc 144(4):1188–1194

    CAS  Google Scholar 

  16. Yamada A, Koizumi H, Sonoyama N, Kanno R (2005) Phase change in LixFePO4. Electrochem. Solid-State Lett 8(8):A409–A413

    CAS  Google Scholar 

  17. Srinivasan V, Newman J (2004) Discharge model for the lithium iron-phosphate electrode. J Electrochem Soc 151:A1517

    CAS  Google Scholar 

  18. Kasavajjula US, Wang C, Arce PE (2008) Discharge model for LiFePO4 accounting for the solid solution range., J Electrochem Soc 155(11):A866–A874

    Google Scholar 

  19. Dargaville S, Farrell TW (2010) Predicting active material utilization in LiFePO4 electrodes using a multiscale mathematical model. J Electrochem Soc 157(7):A830–A840

    Google Scholar 

  20. Singh GK, Ceder G, Bazant MZ (2008) Intercalation dynamics in rechargeable battery materials: general theory and phase-transformation waves in LiFePO4. Electrochim Acta 53(26):7599–7613

    CAS  Google Scholar 

  21. Burch D, Singh G, Ceder G, Bazant MZ (2008) Phase-transformation wave dynamics in LiFePO4. Solid State Phenom 139:95–100

    CAS  Google Scholar 

  22. Burch D, Bazant MZ (2009) Size-dependent spinodal and miscibility gaps for intercalation in nanoparticles. Nano Lett 9(11):3795–3800

    CAS  PubMed  Google Scholar 

  23. Delmas C, Maccario M, Croguennec L, Le Cras F, Weill F (2008) Lithium deintercalation in LiFePO4 nanoparticles via a domino-cascade model., Nat Mater 7(8):665–671

    CAS  PubMed  Google Scholar 

  24. Sasaki T, Ukyo Y, Novák P (2013) Memory effect in a lithium-ion battery. Nat Mater 12(6):569–575

    CAS  PubMed  Google Scholar 

  25. Thomas-Alyea KE (2008) Modeling resistive-reactant and phase-change materials in battery electrodes., ECS Trans 16(13):155–165

    CAS  Google Scholar 

  26. Safari M, Delacourt C (2011) Mathematical modeling of lithium iron phosphate electrode: galvanostatic charge/discharge and path dependence. J Electrochem Soc 158:A63

    CAS  Google Scholar 

  27. Safari M, Delacourt C (2011) Modeling of a commercial graphite/LiFePO[sub 4] Cell. J Electrochem Soc 158:A562–A571

    Google Scholar 

  28. Thorat IV (2009) Understanding performance-limiting mechanisms in Li-ion batteries for high-rate applications. Brigham Young University, ProQuest Dissertations Publishing

  29. Farkhondeh M, Delacourt C (2012) Mathematical modeling of commercial LiFePO4 electrodes based on variable solid-state diffusivity. J Electrochem Soc 159(2):A177–A192

    Google Scholar 

  30. Farkhondeh M, Safari M, Pritzker M, Fowler M, Han T, Wang J, Delacourt C (2014) Full-range simulation of a commercial LiFePO4 electrode accounting for bulk and surface effects: a comparative analysis. J Electrochem Soc 161:A201

    CAS  Google Scholar 

  31. Andersson AS, Thomas JO (2001) The source of first-cycle capacity loss in LiFePO4. J Power Sources 97:498–502

    Google Scholar 

  32. Dreyer W, Jamnik J, Guhlke C, Huth R, Moškon J, Gaberšček M (2010) The thermodynamic origin of hysteresis in insertion batteries. Nat Mater 9(5):448–453

    CAS  PubMed  Google Scholar 

  33. Dreyer W, Guhlke C, Herrmann M (2011) Hysteresis and phase transition in many-particle storage systems. Continuum Mech Thermodyn 23, 3:211–231

    CAS  Google Scholar 

  34. Farkhondeh M, Pritzker M, Fowler M, Safari M, Delacourt C (2014) Mesoscopic modeling of Li insertion in phase-separating electrode materials: application to lithium iron phosphate. Phys Chem Chem Phys 16(41):22555–22565

    CAS  PubMed  Google Scholar 

  35. Farkhondeh M, Pritzker M, Fowler M, Delacourt C (2017) Mesoscopic modeling of a LiFePO4 electrode: experimental validation under continuous and intermittent operating conditions. J Electrochem Soc 164(11):E3040–E3053

    CAS  Google Scholar 

  36. Wang J, Sun X (2015) Olivine LiFePO4: the remaining challenges for future energy storage. Energy Environ Sci 8(4):1110–1138

    CAS  Google Scholar 

  37. Doyle M, Fuller M, Newman J (1993) Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. J Electrochem Soc 140(6):1526–1533

    CAS  Google Scholar 

  38. Delacourt C, Safari M (2011) Analysis of lithium deinsertion/insertion in LiyFePO4 with a simple mathematical model. Electrochim Acta 56(14):5222–5229

    CAS  Google Scholar 

  39. Maheshwari A, Dumitrescu MA, Destro M, Santarelli M (2016) Inverse parameter determination in the development of an optimized lithium iron phosphate-Graphite battery discharge model. J Power Sources 307:160–172

    CAS  Google Scholar 

  40. Prada E, Di Domenico D, Creff Y, Bernard J, Sauvant-Moynot V, Huet F (2012) Simplified electrochemical and thermal model of LiFePO4-graphite Li-ion batteries for fast charge applications. J Electrochem Soc 159:A1508–A1519

    Google Scholar 

  41. Jokar A, Rajabloo B, Désilets M, Lacroix M, An inverse method for estimating the electrochemical parameters of lithium-ion batteries, part A: methodology (2016) J Electrochem Soc 163(14):A2876-A2886

    Google Scholar 

  42. Rajabloo B, Jokar A, Désilets M, Lacroix M (2016) An inverse method for estimating the electrochemical parameters of lithium-ion batteries, Part II: implementation, J Electrochem Soc. https://doi.org/10.1149/2.0221702jes

    Article  Google Scholar 

  43. Delacourt C, Laffont L, Bouchet R, Wurm C, Leriche JB, Morcrette M, Tarascon JM, Masquelier C (2005) Toward understanding of electrical limitations (electronic, ionic) in LiMPO4 (M = Fe, Mn) electrode materials. J Electrochem Soc 152(5):A913–A921

    Google Scholar 

  44. Dominko R, Gaberscek M, Drofenik J, Bele M, Pejovnik S, Jamnik J (2003) The role of carbon black distribution in cathodes for Li ion batteries. J Power Sources 119:770–773

    Google Scholar 

  45. Marcicki J (2012) Modeling, parametrization, and diagnostics for lithium-ion batteries with automotive applications, Dissertation, The Ohio State University

  46. Santhanagopalan S, Guo Q, Ramadass P, White RE (2006) Review of models for predicting the cycling performance of lithium ion batteries. J Power Sources 156(2):620–628

    CAS  Google Scholar 

  47. Doyle M, Newman J, Gozdz AS, Schmutz CN, Tarascon J (1996) Comparison of modeling predictions with experimental data from plastic lithium ion cells., J Electrochem Soc 143(6):1890–1903

    Google Scholar 

  48. Fuller TF, Doyle M, Newman J (1994) Relaxation phenomena in lithium-ion-insertion cells. J Electrochem Soc 141(4):982–990

    CAS  Google Scholar 

  49. Atlung S, West K, Jacobsen T (1979) Dynamic aspects of solid solution cathodes for electrochemical power sources., J Electrochem Soc 126(8):1311–1321

    CAS  Google Scholar 

  50. Haran BS, Popov BN, White RE (1998) Determination of the hydrogen diffusion coefficient in metal hydrides by impedance spectroscopy., J Power Sources 75(1):56–63

    CAS  Google Scholar 

  51. Guo M, Sikha G, White RE (2011) Single-particle model for a lithium-ion cell: thermal behavior., J Electrochem Soc 158(2):A122–A132

    Google Scholar 

  52. Arora P, Doyle M, Gozdz AS, White RE, Newman J (2000) Comparison between computer simulations and experimental data for high-rate discharges of plastic lithium-ion batteries., J Power Sources 88(2):219–231

    CAS  Google Scholar 

  53. Paxton B, Newman J (1996) Variable diffusivity in intercalation materials a theoretical approach. J Electrochem Soc 143(4):1287–1292

    CAS  Google Scholar 

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Acknowledgements

The authors are very grateful to Hydro-Québec and to the Natural Sciences and Engineering Council of Canada (NSERC) for their financial support.

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Authors and Affiliations

  1. Department of Chemical and Biotechnological Engineering, Université de Sherbrooke, 2500, boul. de l’Université, Sherbrooke, Canada

    B. Rajabloo, A. Jokar & M. Désilets

  2. Department of Chemistry, Université de Sherbrooke, Sherbrooke, Canada

    W. Wakem & G. Brisard

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  1. B. Rajabloo
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  2. A. Jokar
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Correspondence to B. Rajabloo.

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Rajabloo, B., Jokar, A., Wakem, W. et al. Lithium iron phosphate electrode semi-empirical performance model. J Appl Electrochem 48, 663–674 (2018). https://doi.org/10.1007/s10800-018-1189-z

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