Overpotential analysis of Na-ion batteries through physics-based electrochemical modeling

Sodium-ion batteries (SIBs) are candidate post-lithium technologies for grid-scale storage and electric-vehicle applications; however, their high-rate performance is strongly limited by kinetic and transport overpotentials. Here, we compare three physics-based electrochemical models, namely the Doyle–Fuller–Newman (DFN) model, the Single-Particle Model with electrolyte (SPMe), and the Single-Particle Model (SPM), for a hard-carbon | NaPF 6 (EC:PC) | N a 3 ⁢ V 2 ⁢ ( P O 4 ) ⁢ 2 ⁢ F 3 (NVPF) full cell. Simulated discharge voltage curves are evaluated against literature data at current densities of 1 to 12 A m -2 . Parameters are adopted from the literature, and the analysis is restricted to transport and kinetic polarization within porous electrodes and the electrolyte (i.e., contact resistances and interphase-growth effects are not explicitly modeled). Across the conditions examined, DFN yields the smallest deviations, whereas SPMe and SPM deviate more at higher rates due to their reduced resolution of electrolyte and solid-phase concentration gradients. Using DFN, we further decompose the total cell overpotential into solid-phase concentration, electrolyte concentration, charge-transfer, and ohmic contributions and quantify how each term evolves with C-rate. Finally, we assess the effects of cathode thickness and porosity during 1 C discharge. Higher C-rates increase polarization, while thicker cathodes amplify transport-related losses by extending diffusion pathways. Cathode porosity modifies internal resistance and electrolyte transport, thereby changing concentration and ohmic overpotentials in the electrolyte. Quantitatively, the hard-carbon solid-state diffusion overpotential increases with the rate and reaches approximately 1.0 V at 1.2 C; from 1.2 C to 1.4 C, electrolyte depletion contributes roughly -0.20 V to -0.15 V. The cathode overpotential features, including mid-discharge excursions, are consistent with phase-transition features in the NVPF equilibrium potential. Overall, the analysis provides quantitative guidance for improving high-rate performance via coordinated optimization of electrode microstructure and electrolyte transport.