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Analytical modeling of Li-ion diffusion in a three-layer electrode-separator-electrode stack with time-dependent current

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Abstract

Li-ion diffusion in electrodes and separator plays a key role in determining the charge/discharge characteristics of a Li-ion cell. Past papers have analyzed solution-phase limitation diffusion in a Li-ion cell for constant current conditions. In the present work, an analytical model is presented for concentration diffusion under solution-phase limitation in a three-layer structure under arbitrary, time-dependent current conditions that may be encountered in practical scenarios. The eigenvalue-based solution is shown to agree well with numerical simulations and may be suitable for implementation in practical battery management systems since only a few eigenvalues are shown to offer excellent accuracy. Computed concentration distributions are analyzed for sinusoidal and step function current profiles. The impact of electrode porosities on concentration distribution is also investigated. This work improves the theoretical understanding of diffusion in Li-ion cells and offers practical tools for modeling and optimization of electrochemical energy conversion and storage devices.

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Data availability

Data and material are available upon request from the corresponding author.

Code availability

Code is available upon request from the corresponding author.

Abbreviations

Brugg :

Bruggeman coefficient

c i :

Concentration in region i (mol m−3)

c i,in :

Initial concentration (mol m−3)

C i :

Dimensionless concentration in region i

C i,in :

Dimensionless initial concentration in region i

c 0 :

Reference concentration (mol m-3)

D :

Diffusion coefficient of lithium ions in the electrolyte (m2 s−1)

D eff,i :

Effective diffusion coefficient of lithium ions in each layer (m2 s−1)

F :

Faraday’s constant (C mol−1)

i app :

Applied current density (A m−2)

J i :

Dimensionless flux density in region i

K :

Ratio of electrode thicknesses

L :

Total width of cell (m)

t :

Time (s)

t + :

Transference number

x :

Position (m)

ε i :

Porosity in region i

γ i :

Dimensionless position at the interface i

λ n :

Eigenvalue

τ :

Dimensionless time

ξ :

Dimensionless position

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Funding

This material is based upon work supported by CAREER Award No. CBET-1554183 from the National Science Foundation. This research was also supported by the Key Project of Science of the Education Bureau of Henan Province (19B460005), the Special Project of Basic Scientific Research Operating Expenses of Henan Polytechnic University (NSFRF180427), and the China Scholarship Council.

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, Henan, China

    Long Zhou

  2. Mechanical and Aerospace Engineering Department, University of Texas at Arlington, 500 W First St, Rm 211, Arlington, TX, 76019, USA

    Long Zhou, Mohammad Parhizi & Ankur Jain

  3. BattGenie, Inc., Seattle, WA, USA

    Manan Pathak

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  1. Long Zhou
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  2. Mohammad Parhizi
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Contributions

Long Zhou – Methodology, formal analysis, investigation, data curation, visualization; Mohammad Parhizi – Methodology, formal analysis, investigation, data curation, visualization; Manan Pathak – Conceptualization, methodology, visualization, funding acquisition; Ankur Jain – conceptualization, methodology, supervision, project administration, visualization, funding acquisition. All authors contributed towards writing original draft and review/editing.

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Correspondence to Ankur Jain.

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Zhou, L., Parhizi, M., Pathak, M. et al. Analytical modeling of Li-ion diffusion in a three-layer electrode-separator-electrode stack with time-dependent current. Ionics 28, 1143–1155 (2022). https://doi.org/10.1007/s11581-021-04332-2

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