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Effects of concentration-dependent modulus and external loads on Li-ion diffusion and stress distribution in a bilayer electrode

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Abstract

Structural batteries offer a new way to reduce device mass and increase the overall energy density of devices. An important feature of structural batteries is that they are designed to be subjected to external loads, which generally have a significant impact on electrochemical reactions in normal batteries. In the present work, a multi-field coupled model for a bilayer electrode was developed by considering the effects of external loads and concentration-dependent modulus. It was found that a positive external load, which bent the unlithiated electrode toward the active electrode side, accelerated the Li-ion diffusion process, whereas a negative external load, which was applied in the opposite direction to the positive external load, hindered the diffusion of Li ions. The curvature variation of the bilayer electrode was a result of the coupling effect of external loading, Li-ion concentration distribution, and the concentration-dependent modulus. The convex curvature of the bilayer electrode (bending toward the active electrode side) increased the Li-ion binding capacity of the active electrode, and an opposite effect was found for the concave curvature. During the lithiation process, positive external load exerts a greater influence on the stress distribution across the bilayer electrode compared to negative external load. The results of this work can provide theoretical guidance to design structural batteries under external loading.

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References

  1. Zhang, Y.C., et al.: Multifunctional structural lithium-ion battery for electric vehicles. J. Intell. Mater. Syst. Struct. 28, 1603–1613 (2017). https://doi.org/10.1177/1045389X16679021

    Article  Google Scholar 

  2. Thomas, J.P., Qidwai, M.A.: Mechanical design and performance of composite multifunctional materials. Acta Mater. 52, 2155–2164 (2004). https://doi.org/10.1016/j.actamat.2004.01.007

    Article  Google Scholar 

  3. Tan, M.Y., et al.: Concepts and emerging trends for structural battery electrolytes. Chem-Asian J. (2022). https://doi.org/10.1002/asia.202200784

    Article  Google Scholar 

  4. Jin, T.W., et al.: Structural batteries: advances, challenges and perspectives. Mater. Today. 62, 151–167 (2023). https://doi.org/10.1016/j.mattod.2022.12.001

    Article  Google Scholar 

  5. Ladpli, P., et al.: Multifunctional energy storage composite structures with embedded lithium-ion batteries. J. Power Sources. 414, 517–529 (2019). https://doi.org/10.1016/j.jpowsour.2018.12.051

    Article  Google Scholar 

  6. Carlstedt, D., Asp, L.E.: Performance analysis framework for structural battery composites in electric vehicles. Compos Part B-Eng. (2020). https://doi.org/10.1016/j.compositesb.2020.107822

    Article  Google Scholar 

  7. Qi, Y., et al.: Threefold increase in the young’s modulus of graphite negative electrode during lithium intercalation. J. Electrochem. Soc. 157, A558–A566 (2010). https://doi.org/10.1149/1.3327913

    Article  Google Scholar 

  8. Malave, V., et al.: Concentration-dependent chemical expansion in lithium-ion battery cathode particles. J Appl Mech-T ASME. (2014). https://doi.org/10.1115/1.4027833

    Article  Google Scholar 

  9. Yang, F.Q.: Effect of local solid reaction on diffusion-induced stress. J. Appl. Phys. (2010). https://doi.org/10.1063/1.3374471

    Article  Google Scholar 

  10. Ji, L., et al.: Stress induced by diffusion, curvature, and reversible electrochemical reaction in bilayer lithium-ion battery electrode plates. Int. J. Mech. Sci. 134, 599–609 (2017). https://doi.org/10.1016/j.ijmecsci.2017.10.048

    Article  Google Scholar 

  11. Hu, H., et al.: Stress induced by diffusion and local chemical reaction in spherical composition-gradient electrodes. Acta Mech. 231, 2669–2678 (2020). https://doi.org/10.1007/s00707-020-02652-4

    Article  Google Scholar 

  12. Li, Y., et al.: Analysis of large-deformed electrode of lithium-ion battery: Effects of defect evolution and solid reaction. Int. J. Solids Struct. 170, 1–10 (2019). https://doi.org/10.1016/j.ijsolstr.2019.05.001

    Article  Google Scholar 

  13. Gao, Y.F., Zhou, M.: Strong stress-enhanced diffusion in amorphous lithium alloy nanowire electrodes. J. Appl. Phys. (2011). https://doi.org/10.1063/1.3530738

    Article  Google Scholar 

  14. Song, Y.C., et al.: Role of material properties and mechanical constraint on stress-assisted diffusion in plate electrodes of lithium ion batteries. J Phys D Appl Phys. (2013). https://doi.org/10.1088/0022-3727/46/10/105307

    Article  Google Scholar 

  15. Song, X., et al.: A coupled electro-chemo-mechanical model for all-solid-state thin film li-ion batteries: The effects of bending on battery performances. J. Power Sources. (2020). https://doi.org/10.1016/j.jpowsour.2020.227803

    Article  Google Scholar 

  16. Yin, H.F., et al.: Modeling strategy for progressive failure prediction in lithium-ion batteries under mechanical abuse. eTransportation. (2021). https://doi.org/10.1016/j.etran.2020.100098

    Article  Google Scholar 

  17. Pereira, T., et al.: Performance of thin-film lithium energy cells under uniaxial pressure. Adv. Eng. Mater. 10, 393–399 (2008). https://doi.org/10.1002/adem.200700214

    Article  Google Scholar 

  18. Zhu, J.E., et al.: Mechanism of strengthening of battery resistance under dynamic loading. Int. J. Impact Eng. 131, 78–84 (2019). https://doi.org/10.1016/j.ijimpeng.2019.05.003

    Article  Google Scholar 

  19. Sahraei, E., et al.: Calibration and finite element simulation of pouch lithium-ion batteries for mechanical integrity. J. Power Sources. 201, 307–321 (2012). https://doi.org/10.1016/j.jpowsour.2011.10.094

    Article  Google Scholar 

  20. Wang, X.Q., et al.: Transient analysis of diffusion-induced stress for hollow cylindrical electrode considering the end bending effect. Acta Mech. 232, 3591–3609 (2021). https://doi.org/10.1007/s00707-021-03014-4

    Article  MathSciNet  Google Scholar 

  21. Zhou, W.B.: Effects of external mechanical loading on stress generation during lithiation in li-ion battery electrodes. Electrochim. Acta. 185, 28–33 (2015). https://doi.org/10.1016/j.electacta.2015.10.097

    Article  Google Scholar 

  22. Xuan, F.Z., et al.: Coupling effects of chemical stresses and external mechanical stresses on diffusion. J Phys D Appl Phys. (2009). https://doi.org/10.1088/0022-3727/42/1/015401

    Article  Google Scholar 

  23. Capraz, O.O., et al.: Electrochemical stiffness changes in lithium manganese oxide electrodes. Adv. Energy Mater. (2017). https://doi.org/10.1002/aenm.201601778

    Article  Google Scholar 

  24. Siegel, J.B., et al.: Expansion of lithium ion pouch cell batteries: Observations from neutron imaging. J. Electrochem. Soc. 160, A1031–A1038 (2013). https://doi.org/10.1149/2.011308jes

    Article  Google Scholar 

  25. Ratchford, J.B., et al.: Young’s modulus of polycrystalline li22si5. J. Power Sources. 196, 7747–7749 (2011). https://doi.org/10.1016/j.jpowsour.2011.04.042

    Article  Google Scholar 

  26. Shenoy, V.B., et al.: Elastic softening of amorphous and crystalline li-si phases with increasing li concentration: A first-principles study. J. Power Sources. 195, 6825–6830 (2010). https://doi.org/10.1016/j.jpowsour.2010.04.044

    Article  Google Scholar 

  27. He, Y.L., et al.: Effects of concentration-dependent elastic modulus on the diffusion of lithium ions and diffusion induced stress in layered battery electrodes. J. Power Sources. 248, 517–523 (2014). https://doi.org/10.1016/j.jpowsour.2013.09.118

    Article  Google Scholar 

  28. Zhang, K., et al.: Effects of concentration-dependent elastic modulus on li-ions diffusion and diffusion-induced stresses in spherical composition-gradient electrodes. J. Appl. Phys. (2015). https://doi.org/10.1063/1.4930571

    Article  Google Scholar 

  29. Guo, Z.S., et al.: Effects of hydrostatic pressure and modulus softening on electrode curvature and stress in a bilayer electrode plate. Comput. Mater. Sci. 94, 218–224 (2014). https://doi.org/10.1016/j.commatsci.2014.04.019

    Article  Google Scholar 

  30. Prado, A.Y.R., et al.: Electrochemical dilatometry of si-bearing electrodes: Dimensional changes and experiment design. J. Electrochem. Soc. (2020). https://doi.org/10.1149/1945-7111/abd465

    Article  Google Scholar 

  31. Michael, H., et al.: A dilatometric study of graphite electrodes during cycling with x-ray computed tomography. J. Electrochem. Soc. (2021). https://doi.org/10.1149/1945-7111/abd648

    Article  Google Scholar 

  32. Zhang, K., et al.: A free volume-based analytical model for plastic flow in thin-walled silicon structures of lithium-ion batteries. Acta Mech. 233, 561–578 (2022). https://doi.org/10.1007/s00707-021-03121-2

    Article  Google Scholar 

  33. Zhuang, Y., et al.: Understanding the li diffusion mechanism and positive effect of current collector volume expansion in anode free batteries. Chin. Phys. B. (2020). https://doi.org/10.1088/1674-1056/ab943c

    Article  Google Scholar 

  34. Zhang, J.: Screening and confirmation methods of the major urinary metabolite of finasteride–carboxy-finasteride by liquid chromatography–mass spectrometry and liquid chromatography–tandem mass spectrometry. Acta Pharmaceutica Sinica B. 2, 220–226 (2012). https://doi.org/10.1016/j.apsb.2012.01.007

    Article  Google Scholar 

  35. Yang, B., et al.: Effects of composition-dependent modulus, finite concentration and boundary constraint on li-ion diffusion and stresses in a bilayer cu-coated si nano-anode. J. Power Sources. 204, 168–176 (2012). https://doi.org/10.1016/j.jpowsour.2012.01.029

    Article  Google Scholar 

  36. Li, D.W., Wang, Y.K.: In-situ measurements of mechanical property and stress evolution of commercial graphite electrode. Mater. Des. (2020). https://doi.org/10.1016/j.matdes.2020.108887

    Article  Google Scholar 

  37. Sepulveda, A., et al.: Bending impact on the performance of a flexible li4ti5o12-based all-solid-state thin-film battery. Sci. Technol. Adv. Mater. 19, 454–464 (2018). https://doi.org/10.1080/14686996.2018.1468199

    Article  Google Scholar 

Download references

Acknowledgements

K.Z. thanks the support from the Natural Science Foundation of Shanghai under grant No.23ZR1468600, and the Fundamental Research Funds for the Central Universities, Tongji University under grant No. 22120210527.

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Correspondence to Bailin Zheng.

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Geng, S., Zhang, K., Zheng, B. et al. Effects of concentration-dependent modulus and external loads on Li-ion diffusion and stress distribution in a bilayer electrode. Acta Mech 235, 191–201 (2024). https://doi.org/10.1007/s00707-023-03726-9

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  • DOI: https://doi.org/10.1007/s00707-023-03726-9

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