Simulating Hard Carbon for Sodium-Ion Batteries with the DFN Model
Authors: Wikner Evelina , Gond Ritambhara 
Published: February 2024

The development of Sodium-ion battery technologies and materials is moving rapidly forward, and several companies are on the verge of commercialising their products. An important question is what knowledge and synergies that can be drawn from Lithium-ion batteries. 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. Previous work indicates that this should be the case [2]–[4].
It has been shown that the insertion process of sodium in hard carbon does not follow the same process as for lithium in hard carbon [5]. The sodium insertion 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. As a first step in investigating the above assumption, an additional assumption made is that the needed parameters can be extracted using similar methods as for Li-ion batteries. With this starting point, a parameter sensitivity analysis is made for simulating mobile sodium in hard carbon with the DFN model.

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.