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Research Papers

A Linearized Model for Lithium Ion Batteries and Maps for their Performance and Failure

[+] Author and Article Information
Rajlakshmi Purkayastha

Materials Department,  University of California, Santa Barbara, CA 93106

Robert M. McMeeking

Materials Department andDepartment of Mechanical Engineering, University of California, Santa Barbara, CA 93106; School of Engineering Aberdeen University, King’s College Aberdeen AB24 3UE, Scotland;  INM - Leibniz Institute for New Materials, D-66123 Saarbrücken, Germany

J. Appl. Mech 79(3), 031021 (Apr 05, 2012) (16 pages) doi:10.1115/1.4005962 History: Received September 04, 2011; Revised November 18, 2011; Posted February 13, 2012; Published April 04, 2012; Online April 05, 2012

A linearized model is developed for lithium ion batteries, relying on simplified characterizations of lithium transport in the electrolyte and through the interface between the electrolyte and the storage particles of the electrodes. The model is valid as a good approximation to the behavior of the battery when it operates near equilibrium, and can be used for both discharge and charging of the battery. The rate of extraction of lithium from and to the electrode storage particles can be estimated from the results of the model, information that can be used in turn to estimate the shrinkage and swelling stresses that develop in the particles. Given specified rates of extraction for spherical particles, maps of the resulting shrinkage and swelling stresses can be developed connecting their values to battery parameters such as particles size, diffusion coefficient, lithium partial molar volume, and particle elastic properties. Since a constant rate of extraction can only be achieved for a limited period of time until the concentration of lithium at the particle perimeter constrains the lithium mass transport, plots of the average state of charge in the particle versus time are also produced.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of a Li-ion battery showing the main components, namely the current collectors, the electrodes, anode and cathode, and the separator. The electrodes are composed of active storage particles, binder, and filler, with electrolyte filling the pores within the particulate structure.

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Figure 2

Plot of the open circuit potential (OCP) versus the state of charge (SOC) for an electrode having ideal thermodynamics

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Figure 3

Three-dimensional stress maps generated for (a) Ω̂=1500, (b) Ω̂=150, and (c) Ω̂=10, where Ω̂ is the normalized lithium partial molar volume. The peak maximum principal stress during galvanostatic extraction followed by potentiostatic extraction is shown as a function of the normalized lithiation strain ɛLimax and the normalized extraction rate Î.

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Figure 4

Lithium concentration profile in a storage particle at specific times for particular values of the normalized extraction rate Î, the normalized lithium partial molar volume Ω̂, and the normalized lithiation strain ɛLimax: (a) Î=15, Ω̂=1500, ɛLimax=1.0; (b) Î=15, Ω̂=10, ɛLimax=1.0; and (c) Î=15, Ω̂=1500, ɛLimax=0.01

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Figure 5

Histories of maximum principal stress (a)–(d) and average lithium concentration (SOC) (e)–(h) in a storage particle during galvanostatic extraction followed by potentiostatic extraction. The normalized extraction rate is Î=15 and results are shown for four values of the normalized lithium partial molar volume Ω̂. Within each plot results for different values of the normalized lithiation strain ɛLimax are provided. (a) Maximum principal stress for Ω̂=1500; (b) maximum principal stress for Ω̂=150; (c) maximum principal stress for Ω̂=10; (d) maximum principal stress for Ω̂=0; (e) SOC for Ω̂=1500; (f) SOC for Ω̂=150; (g) SOC for Ω̂=10; and (h) SOC for Ω̂=0.

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Figure 6

Histories of maximum principal stress (a)–(c) and average lithium concentration (SOC) (d)–(f) in a storage particle during galvanostatic extraction followed by potentiostatic extraction. The normalized extraction rate is Î=15 and results are shown for three values of the normalized lithiation strain ɛLimax. Within each plot results for different values of the normalized lithium partial molar volume Ω̂ are provided. (a) Maximum principal stress for ɛLimax=1.0; (b) maximum principal stress for ɛLimax=0.1; (c) maximum principal stress for ɛLimax=0.01; (d) SOC for ɛLimax=1.0; (e) SOC for ɛLimax=0.1; and (f) SOC for ɛLimax=0.01.

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Figure 7

Histories of maximum principal stress in a storage particle during galvanostatic extraction followed by potentiostatic extraction. The normalized extraction rate is Î=1.0 and results are shown for two values of the normalized lithium partial molar volume Ω̂ and two values of the normalized lithiation strain ɛLimax. In the plot for a given value of Ω̂ results are shown for various values of ɛLimax, and vice versa. (a) Maximum principal stress for Ω̂=1500; (b) maximum principal stress for Ω̂=150; (c) maximum principal stress for ɛLimax=1.0; and (d) maximum principal stress for ɛLimax=0.1.

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