Simulating Sodium-Ion Batteries with the DFN Model
Authors: Wikner Evelina , Tesfamhret Yonas 
Published: December 2024

Commercial sodium-ion battery (SIB) technologies have reached the market. The SIBs hold the potential to achieve higher safety and sustainability compared to today's lithium-ion batteries (LIBs). The SIB can today reach an energy density on par with LFP. An important question is; what knowledge and synergies can be drawn from LIBs? Utilising similar equipment and processes during production has made it possible to draw benefits from the development of lithium-ion batteries (LIBs), speeding up the development of SIBs. This work has investigated whether the Doyle-Fuller-Newman model (DFN model) [1] can be used for simulating the insertion and extraction of mobile sodium ion in hard carbon and Prussian White. Previous work indicates the possibility of this [2]–[4].
However, Prussian White has, to the authors knowledge, yet not been characterised for DFN models. In addition, the insertion of sodium in hard carbon does not follow the same process as for lithium in hard carbon [5]. Insertion of sodium in hard carbon is suggested to be a combination of capacitive adsorption, intercalation and nanopore filling [6]–[8]. Hence, the question is if capacitive adsorption and nanopore filling can be simulated as an intercalation process. In addition, the sodium-ion has a lower charge density than lithium-ion, leading to different properties for the electrolyte and the interfacial species [9], [10].
One of the issues with the DFN model is to measure, calculate or estimate the material and electrode properties needed. In this work, a DFN model for hard carbon and Prussian White has been set up using material parameters estimated from intermittent current interruption (ICI) on three electrode cells.

References

[1] M. Doyle, T. Fuller, and J. Newman, “Modeling of galvanostatic charge and discharge of the lithium/ polymer/insertion cell,” J. Electrochem. Soc., vol. 140, no. 6, pp. 1526–1533, 1993, doi: 10.1149/1.2221597.
[2] K. Chayambuka, M. Jiang, G. Mulder, D. L. Danilov, and P. H. L. Notten, “Physics-based modeling of sodium-ion batteries part I: Experimental parameter determination,” Electrochim. Acta, vol. 404, p. 139726, Feb. 2022, doi: 10.1016/J.ELECTACTA.2021.139726.
[3] K. Chayambuka, G. Mulder, D. L. Danilov, and P. H. L. Notten, “Physics-based modeling of sodium-ion batteries part II. Model and validation,” Electrochim. Acta, vol. 404, p. 139764, Feb. 2022, doi: 10.1016/J.ELECTACTA.2021.139764.
[4] C. M. Doyle, “Peer Reviewed Title: Design and Simulation of Lithium Rechargeable Batteries,” 2010. Accessed: Feb. 01, 2021. [Online]. Available: http://www.escholarship.org/uc/item/6j87z0sp
[5] H. D. Asfaw, C. W. Tai, M. Valvo, and R. Younesi, “Facile synthesis of hard carbon microspheres from polyphenols for sodium-ion batteries: insight into local structure and interfacial kinetics,” Mater. Today Energy, vol. 18, p. 100505, Dec. 2020, doi: 10.1016/j.mtener.2020.100505.
[6] J. Y. Hwang, S. T. Myung, and Y. K. Sun, “Sodium-ion batteries: Present and future,” Chemical Society Reviews, vol. 46, no. 12. Royal Society of Chemistry, pp. 3529–3614, Jun. 21, 2017. doi: 10.1039/c6cs00776g.
[7] D. Chen et al., “Hard carbon for sodium storage: mechanism and optimization strategies toward commercialization,” Energy Environ. Sci., vol. 14, no. 4, pp. 2244–2262, Apr. 2021, doi: 10.1039/D0EE03916K.
[8] C. Bommier, T. W. Surta, M. Dolgos, and X. Ji, “New Mechanistic Insights on Na-Ion Storage in Nongraphitizable Carbon,” Nano Lett., vol. 15, no. 9, pp. 5888–5892, Sep. 2015, doi: 10.1021/ACS.NANOLETT.5B01969/ASSET/IMAGES/LARGE/NL-2015-01969W_0002.JPEG.
[9] R. Mogensen, S. Colbin, and R. Younesi, “An attempt to formulate non‐carbonate electrolytes for sodium‐ion batteries,” Batter. Supercaps, p. batt.202000252, Dec. 2020, doi: 10.1002/batt.202000252.
[10] L. A. Ma, A. J. Naylor, L. Nyholm, and R. Younesi, “Strategies for Mitigating Dissolution of Solid Electrolyte Interphases in Sodium-Ion Batteries,” Angew. Chemie - Int. Ed., 2020, doi: 10.1002/anie.202013803.