Sodium-ion batteries (SIBs) are emerging as a sustainable and cost-effective alternative to lithium-ion batteries. Now, with the integration of a physics-based SIB model into PyBaMM, researchers and developers have a new tool to accelerate SIB optimization and innovation. This blog post explores the history of SIBs, the intricacies of the new PyBaMM model, and the exciting possibilities it unlocks for the future of energy storage.

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A brief history of sodium ion batteries

Sodium ion batteries (SIBs) are a promising up-and-coming alternative to lithium ion (LIBs); 

Sodium ion is a good candidate for energy storage for multiple reasons. Sodium is much cheaper and 1000 times more earth-abundant than lithium, and the available cathodes also use earth-abundant materials, moving away from the supply chain risks of nickel and cobalt in LIBs. Sodium ion chemistry is intercalation-based just like LIBs; the sodium ions travel back and forth between the anode and cathode transporting charge and energy. The similarity to LIBs mechanistically and in performance and manufacturing has allowed for simplified knowledge transfer and expedited development and commercialization. Current SIBs have a lower energy density than lithium ion batteries, making them a viable candidate for large scale stationary energy storage systems.

Both lithium and sodium ion cathodes were discovered around the same time. However, sodium ion research was hindered by the lack of a suitable intercalation anode. Around 2000, the discovery of hard carbon (HC) as an anode material sparked renewed interest in SIBs. The 2010s saw rapid growth most likely due to the push for LIB alternatives, resulting in the development of new cathode materials, assembly of full cells, and several startups focused on commercialization. The first 18650 cylindrical SIBs were assembled in 2015 with a Na₃V₂(PO₄)₂F₃ (NVPF) cathode and HC anode through the collaboration of several institutions under the French network for electrochemical storage (R2SE). Commercialization efforts have resulted in 1-5 Ah pouch cells from Faradion, the first company to commercialize SIBs; a claim of 10,000 SIBs produced by Tiamat, the startup that came out of R2SE; and an announcement of a 100 kWh battery installment for energy arbitrage from the Chinese company HiNa. Physics-based modeling can play a unique and important role in the ongoing development of SIBs.

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Modeling the intercalation of Na⁺ and beyond

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The first physics-based, pseudo-two-dimensional (P2D) model for sodium ion batteries was published in 2022 by Chayambuka et. al. The model uses the generalized framework of the Doyle-Fuller-Newman P2D model for lithium ion batteries, which predicts the performance and dynamics of intercalation batteries. The modeling work was coupled with experiments on a sodium battery with a cathode made of NVPF particles, an HC anode, and 1 M NaPF6 EC 0.5 : PC0.5 (w/w) electrolyte. The reaction for NVPF is

Na₃V^III₂(PO₄)₂ <--> F₃  NaV^IV₂ (PO₄)₂F₃ + 2Na⁺ + 2e⁻

where 2 Na⁺ are transferred for every unit of NVPF, resulting in a capacity of 128 mAh/g. HC is a non-graphite carbon with a complex structure: they have graphene-like layers within an amorphous microporous phase. Charge transfer happens through adsorption on graphene layers and filling of the meso- and nanopores. There are multiple proposed mechanisms for HC, which may depend on the precursor and structural properties, and this remains an active area of research. The specific capacity of HC is about 300 mAh/g, similar to that of graphite in LIBs.

Parameterization of models can be difficult and involved but remains a key component of ensuring accurate battery models. To create an experimentally-predictive baseline parameter set, the authors of the SIB P2D model used experimental techniques and parameter estimation on half- and full-cell GITT and cycling data, as well as electrolyte measurements and statistics mechanics simulations for transport properties. The schematic for the sodium ion battery can be found in the figure above taken directly from their work. A 3-electrode setup with a Na ion reference electrode was used to individually measure the electrode voltages, and the model output was optimized to that instead of the total battery voltage to minimize error. The relevant parameters and process details can be found in their experimental and modeling papers (Refs. 1 and 2).

This work highlights the power of properly-parameterized physics-based models; the model predictions for rates from 0.1C to 1.4C were under 2% error compared to experimental curves and less than 50 mV absolute error. The authors found that the contact resistance becomes important at higher rates for accurate predictions. Additionally, the high rate performance was hindered by poor mass transport in both electrodes and the electrolyte. The results suggest that reducing the particle size in the HC electrode will improve high rate performance while the diffusion within the NVPF particles was found to limit mass transport.

The figure below reproduces the C-rate study from Chayambuka et al. The model and parameter set is now available in PyBaMM for anyone to use!

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References

1. https://doi.org/10.1016/j.electacta.2021.139764
2. https://doi.org/10.1016/j.electacta.2021.139726
3. https://github.com/pybamm-team/PyBaMM/blob/develop/docs/source/examples/notebooks/models/sodium-ion.ipynb
4. doi:10.1002/aenm.202001310.
5. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10095715/
6. https://www.comsol.com/model/1d-isothermal-sodium-ion-battery-117341

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