Numerical simulations of cyclic voltammetry for lithium-ion intercalation in nanosized systems: finiteness of diffusion versus electrode kinetics


The voltammetric behavior of Li+ intercalation/deintercalation in/from LiMn2O4 thin films and single particles is simulated, supporting very recent experimental results. Experiments and calculations both show that particle size and geometry are crucial for the electrochemical response. A remarkable outcome of this research is that higher potential sweep rates, of the order of several millivolts per second, may be used to characterize nanoparticles by voltammetry sweeps, as compared with macroscopic systems. This is in line with previous conclusions drawn for related single particle systems using kinetic Monte Carlo simulations. The impact of electrode kinetics and finite space diffusion on the reversibility of the process and the finiteness of the diffusion in ion Li / LiMn2O4 (de)intercalation is also discussed in terms of preexisting modeling.

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  1. 1.

    Vassiliev S, Levin EE, Nikitina VA (2016) Kinetic analysis of lithium intercalating systems : cyclic voltammetry. Electrochim Acta 190:1087–1099.

    CAS  Article  Google Scholar 

  2. 2.

    A.K. Hjelm, G. Lindbergh, A. Lundqvist, Investigation of LiMn2O4 cathodes for use in rechargeable lithium batteries by linear sweep voltammetry - Part I. Theoretical study, J. Electroanal. Chem. 506 (2001) 82–91. doi:

  3. 3.

    Zhang D, Popov BN, White RE (2000) Modeling Lithium intercalation of a single spinel particle under Potentiodynamic control. J Electrochem Soc 147(3):831.

    CAS  Article  Google Scholar 

  4. 4.

    Das SR, Majumder SB, Katiyar RS (2005) Kinetic analysis of the Li+ ion intercalation behavior of solution derived nano-crystalline lithium manganate thin films. J Power Sources 139(1-2):261–268.

    CAS  Article  Google Scholar 

  5. 5.

    Wunde F, Nowak S, Mürter J, Hadjixenophontos E, Berkemeier F, Schmitz G (2017) Ion transport and phase transformation in thin film intercalation electrodes. Int J Mater Res 108:984–998.

    CAS  Article  Google Scholar 

  6. 6.

    Xiao L, Guo Y, Qu D, Deng B, Liu H, Tang D (2013) Influence of particle sizes and morphologies on the electrochemical performances of spinel LiMn2O4 cathode materials. J Power Sources 225:286–292.

    CAS  Article  Google Scholar 

  7. 7.

    Nakayama N, Nozawa T, Iriyama Y, Abe T, Ogumi Z, Kikuchi K (2007) Interfacial lithium-ion transfer at the LiMn2O4 thin film electrode/aqueous solution interface. J Power Sources 174(2):695–700.

    CAS  Article  Google Scholar 

  8. 8.

    Chung MD, Seo JH, Zhang XC, Sastry AM (2011) Implementing realistic geometry and measured diffusion coefficients into single particle electrode modeling based on experiments with single LiMn2O4 spinel particles. J Electrochem Soc 158(4):A371.

    CAS  Article  Google Scholar 

  9. 9.

    Dokko K, Mohamedi M, Umeda M, Uchida I (2003) Kinetic study of Li-ion extraction and insertion at LiMn2O4 single particle electrodes using potential step and impedance methods. J Electrochem Soc 150(4):A425.

    CAS  Article  Google Scholar 

  10. 10.

    Tang SB, Lai MO, Lu L (2008) Study on Li+−ion diffusion in nano-crystalline LiMn2O4 thin film cathode grown by pulsed laser deposition using CV, EIS and PITT techniques. Mater Chem Phys 111(1):149–153.

    CAS  Article  Google Scholar 

  11. 11.

    Zhou HM, Zhu YH, Li J, Sun WJ, Liu ZZ (2019) Electrochemical performance of Al 2 O 3 pre-coated spinel LiMn 2 O 4. Rare Metals 38(2):128–135.

    CAS  Article  Google Scholar 

  12. 12.

    Cheng F, Wang H, Zhu Z, Wang Y, Zhang T, Tao Z, Chen J (2011) Porous LiMn 2O 4 nanorods with durable high-rate capability for rechargeable Li-ion batteries. Energy Environ Sci 4(9):3668–3675.

    CAS  Article  Google Scholar 

  13. 13.

    Xia H, Luo Z, Xie J (2012) Nanostructured LiMn2O4 and their composites as high-performance cathodes for lithium-ion batteries. Prog Nat Sci Mater Int 22(6):572–584.

    Article  Google Scholar 

  14. 14.

    Nie XJ, Xi XT, Yang Y, Ning QL, Guo JZ, Wang MY, Gu ZY, Wu XL (2019) Recycled LiMn2O4 from the spent lithium ion batteries as cathode material for sodium ion batteries: electrochemical properties, structural evolution and electrode kinetics. Electrochim Acta 320:134626.

    CAS  Article  Google Scholar 

  15. 15.

    Tao B, Yule LC, Daviddi E, Bentley CL, Unwin PR (2019) Correlative electrochemical microscopy of Li-ion (De)intercalation at a series of individual LiMn2O4 particles. Angew Chemie - Int Ed 58(14):4606–4611.

    CAS  Article  Google Scholar 

  16. 16.

    Mürter J, Nowak S, Hadjixenophontos E, Joshi Y, Schmitz G (2018) Grain boundary transport in sputter-deposited nanometric thin films of lithium manganese oxide. Nano Energy 43:340–350.

    CAS  Article  Google Scholar 

  17. 17.

    E.M. Gavilán-Arriazu, O.A. Pinto, B.A. López De Mishima, D.E. Barraco, O.A. Oviedo, E.P.M. Leiva, Kinetic Monte Carlo applied to the electrochemical study of the Li-ion graphite system, Electrochim. Acta. 331 (2020). doi:

  18. 18.

    E.M. Gavilán-Arriazu, M.P. Mercer, O.A. Pinto, O.A. Oviedo, D.E. Barraco, H.E. Hoster, E.P.M. Leiva, Effect of temperature on the kinetics and thermodynamics of electrochemical insertion of Li-ions into a graphite electrode, J. Electrochem. Soc. 167 (2020) 013533. doi:

  19. 19.

    Leiva EPM, Perassi E, Barraco D (2017) Shedding light on the entropy change found for the transition stage II→stage I of Li-ion storage in graphite. J Electrochem Soc 164(1):A6154–A6157.

    CAS  Article  Google Scholar 

  20. 20.

    M. Otero, A. Sigal, E.M. Perassi, D. Barraco, E.P.M. Leiva, Statistical mechanical modeling of the transition Stage II → Stage I of Li-ion storage in graphite. A priori vs induced heterogeneity, Electrochim. Acta. 245 (2017) 569–574. doi:

  21. 21.

    Mercer MP, Otero M, Ferrer-Huerta M, Sigal A, Barraco DE, Hoster HE, Leiva EPM (2019) Transitions of lithium occupation in graphite: a physically informed model in the dilute lithium occupation limit supported by electrochemical and thermodynamic measurements. Electrochim Acta 324:134774.

    CAS  Article  Google Scholar 

  22. 22.

    Gavilán Arriazu EM, López de Mishima BA, Oviedo OA, Leiva EPM, Pinto OA (2017) Criticality of the phase transition on stage two in a lattice-gas model of a graphite anode in a lithium-ion battery. Phys Chem Chem Phys 19(34):23138–23145.

    Article  PubMed  Google Scholar 

  23. 23.

    Gavilán-Arriazu EM, Pinto OA, de Mishima BAL, Leiva EPM, Oviedo OA (2018) Grand canonical Monte Carlo study of Li intercalation into graphite. J Electrochem Soc 165(10):A2019–A2025.

    CAS  Article  Google Scholar 

  24. 24.

    Perassi EM, Leiva EPM (2016) A theoretical model to determine intercalation entropy and enthalpy: application to lithium/graphite. Electrochem Commun 65:48–52.

    CAS  Article  Google Scholar 

  25. 25.

    Gavilán-Arriazu EM, Pinto OA, López de Mishima BA, Barraco DE, Oviedo OA, Leiva EPM (2018) The kinetic origin of the Daumas-Hérold model for the Li-ion/graphite intercalation system. Electrochem Commun 93:133–137.

    CAS  Article  Google Scholar 

  26. 26.

    Aoki K, Tokuda K, Matsuda H (1984) Theory of linear sweep voltammetry with finite diffusion space. Part I. J Electroanal Chem 160(1-2):33–45.

    CAS  Article  Google Scholar 

  27. 27.

    Aoki K, Tokuda K, Matsuda H (1984) Theory of linear sweep voltammetry with finite diffusion space. Part II. Totally irreversible and quasi-reversible cases. J Electroanal Chem 160(1-2):33–45

    CAS  Article  Google Scholar 

  28. 28.

    Guin SK, Ambolikar AS, Das S, Poswal AK (2020) Advantage of fractional-calculus based hybrid-theoretical-computational-experimental approach for alternating current voltammetry, Electroanalysis.

    Google Scholar 

  29. 29.

    Zeng Y, Albertus P, Klein R, Chaturvedi N, Kojic A, Bazant MZ, Christensen J (2013) Efficient conservative numerical schemes for 1D nonlinear spherical diffusion equations with applications in battery modeling. J Electrochem Soc 160(9):A1565–A1571.

    CAS  Article  Google Scholar 

  30. 30.

    Britz D, Strutwolf J (2016) Digital Simulation in Electrochemistry.

  31. 31.

    Mehrer H (2007) Diffusion in solids. Springer, Berlin, Heidelberg.

    Google Scholar 

  32. 32.

    Levi M, Aurbach D (1999) Frumkin intercalation isotherm—a tool for the description of lithium insertion into host materials: a review. Electrochim Acta 45(1-2):167–185.

    CAS  Article  Google Scholar 

  33. 33.

    Mercer MP, Finnigan S, Kramer D, Richards D, Hoster HE (2017) The influence of point defects on the entropy profiles of Lithium ion battery cathodes: a lattice-gas Monte Carlo study. Electrochim Acta 241:141–152.

    CAS  Article  Google Scholar 

  34. 34.

    Schlueter S, Genieser R, Richards D, Hoster HE, Mercer MP (2018) Quantifying structure dependent responses in Li-ion cells with excess Li spinel cathodes: matching voltage and entropy profiles through mean field models. Phys Chem Chem Phys 20(33):21417–21429.

    CAS  Article  PubMed  Google Scholar 

  35. 35.

    B.E. Conway, two-dimensional and quasi-two-dimensional isotherms for Li intercalation and UPD processes at surfaces, Electrochim. Acta. 38 (1993) 1249–1258. doi:

  36. 36.

    A.K. Hjelm, G. Lindbergh, A. Lundqvist, Investigation of LiMn2O4 cathodes for use in rechargeable lithium batteries by linear sweep voltammetry - Part II. Experimental study using thin films, single particles and composite electrodes, J. Electroanal. Chem. 509 (2001) 139–147. doi:

  37. 37.

    Tian L, Yuan A (2009) Electrochemical performance of nanostructured spinel LiMn2O4 in different aqueous electrolytes. J Power Sources 192(2):693–697.

    CAS  Article  Google Scholar 

  38. 38.

    Tang W, Yang X, Liu Z, Kasaishi S, Ooi K (2002) Preparation of fine single crystals of spinel-type lithium manganese oxide by LiCl flux method for rechargeable lithium batteries. Part 1. LiMn2O4. J Mater Chem 12(10):2991–2997.

    CAS  Article  Google Scholar 

  39. 39.

    Geder J, Hoster HE, Jossen A, Garche J, Yu DYW (2014) Impact of active material surface area on thermal stability of LiCoO 2 cathode. J Power Sources 257:286–292.

    CAS  Article  Google Scholar 

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E.P.M. Leiva acknowledges grants PIP CONICET 11220150100624CO, PUE/2017 CONICET, FONCYT PICT-2015-1605 and SECyT of the Universidad Nacional de Córdoba. Support by CCAD-UNC and GPGPU Computing Group, Y-TEC and an IPAC grant from SNCAD-MinCyT, Argentina, are also gratefully acknowledged. M.P. Mercer and H.E. Hoster thank the Faraday Institution (; EP/S003053/1), grant number FIRG003, for funding.

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Correspondence to E.M. Gavilán-Arriazu or E.P.M. Leiva.

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This article is dedicated to Prof. Fritz Scholz on the occasion of his 65th birthday. Es ist ein Vergnügen, mit so einem Chefredakteur zusammenzuarbeiten.

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Gavilán-Arriazu, E., Mercer, M., Pinto, O. et al. Numerical simulations of cyclic voltammetry for lithium-ion intercalation in nanosized systems: finiteness of diffusion versus electrode kinetics. J Solid State Electrochem (2020).

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