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Modeling ionic intercalation and solid-state diffusion using typical descriptors of batteries

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Abstract

Mathematical models can predict the performances of batteries, such as their state of charge and state of health. Among physicochemical governing equations, Fick’s first and second laws describe ionic intercalation and solid-state diffusion in electrode particles, respectively. Conventionally, molar concentration and current density are the main descriptors for ionic intercalation and solid-state diffusion in the electrochemical models. However, more relevant and typical descriptors for rechargeable batteries are intercalation quantity (i.e., x in LixC6) and C-rate. Herein, we translate the governing equations of Fick’s laws based on intercalation quantity and C-rate, instead of the molar concentration and current density. The new governing equations enabled faster computation of the electrochemical models, benefited by the intrinsically dimensionless properties of the descriptors. Moreover, the newly derived equations provide a practical insight to design the morphology of particles for the improved rate capability. Implementing the newly derived governing equations to a single-particle model demonstrated faster, efficient, and reliable simulation to investigate the effects of particle size, diffusivity, and C-rate on lithium-ion batteries performances. These new governing equations can be implemented in various models for batteries in general, enabling an efficient computation and facilitated communication among researchers investigating energy storage.

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Abbreviations

t :

Time [s]

D :

Solid-state chemical diffusion coefficient (or, diffusivity) [cm2 s−1]

n :

Orthonormal vector on the electrode–electrolyte boundary for ion intercalation (positive direction: from electrode to electrolyte)

C-rate:

Ratio of charging/discharging current to current that charges/discharges the intercalation host in one hour [h−1]

C-rate :

Dimensionless C-rate, which is equivalent to C-rate [h−1] × 1 [h]

V :

Volume of an intercalation host [cm3]

S :

Microscopic surface area into which ions can intercalate [cm2]

c :

Local concentration of ions in the host [mol cm−3]

z :

Ion charge number

F :

Faraday’s constant, 96,485 [C mol−1]

R :

Universal gas constant, 8.3145 [J mol−1 K−1]

T :

Temperature [K]

ρ :

Density of intercalation host [g cm−3]

Q :

Theoretical specific capacity of intercalation host [C g−1]

x :

Intercalation quantity, x = czF/ρQ

v :

Intercalation velocity [cm s−1] = \(- D\nabla x\), which can be regarded as the propagation vector of the intercalation quantity

i :

Current density [A cm−2]

i 0 :

Exchange current density [A cm−2]

η ct :

Charge transfer overpotential [V]

α :

Charge transfer coefficient

U(x):

Open-circuit potential [V] as a function of x

V(x):

Cell voltage [V]

ESR:

Equivalent series resistance [Ω cm2]

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Acknowledgements

This work was supported by the National Research Foundation (NRF-2018R1C1B6004808 and NRF-2018R1A5A1025594) of the Korean Ministry of Science and ICT. The authors are grateful to Mr. Fuead Hasan for the careful proofreading of the manuscript.

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  1. Department of Chemistry and Chemical Institute for Functional Materials, Pusan National University, Busan, 46241, Republic of Korea

    Jinhong Kim, Sangram Keshari Mohanty & Hyun Deog Yoo

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Kim, J., Mohanty, S.K. & Yoo, H.D. Modeling ionic intercalation and solid-state diffusion using typical descriptors of batteries. J Appl Electrochem 51, 703–713 (2021). https://doi.org/10.1007/s10800-021-01530-8

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