An effective model for sodium insertion in hard carbons

Sodium ion batteries (NIBs) are a potential alternative to Lithium ion batteries (LIBs) because of their lower cost and greater availability. As anodes, hard carbons (HCs) seem to be the most promising candidates for NIBs. Previous numerical theoretical research studies have focussed on the general conditions for Na insertion in HCs, while experiments have shown that the properties of Na insertion in HCs depend strongly on specific material properties of HCs. Our target is building an effective model based on experimental data and the volume expansion phenomenon as a base for constructing chemical potentials and free energies efficiently as the starting point for continuum modeling of intercalation in HCs. In our effective model, HC is treated implicitly, while Na is simulated in a confined space, created by the HC. To reproduce the complex intercalation behavior of Na, different intercalation sites at different energy levels must be introduced. The results show good agreement with the experimental data and clarify the contribution of different Na insertion sites and the exchange between different sites of Na to the open circuit voltage as well as their contribution to the reversible and irreversible capacity of Na in HCs.