Computational Study on the Na Storage Mechanism in Carbon Anodes Based on Bilayer Graphene Nanoribbons with Zigzag and Armchair Edges

Hard carbon (HC) is one of the most promising anode materials for sodium-ion batteries (SIBs). Yet its sodiation mechanism—particularly the origin of the sloping and plateau regions in the voltage–capacity curve—remains debated. In this work, first-principles density functional theory (DFT) calculations are employed to systematically investigate the sodium storage mechanism at the edges and within the interlayer ultramicropores of bilayer graphene nanoribbons (BGNRs) with zigzag (BGNRs-Z) and armchair (BGNRs-A) terminations. A series of edge models, including hydrogenated, dehydrogenated (dangling bond), monovacancy (MV), and divacancy (DV) defects, were constructed to elucidate the effects of edge type and defect species on Na adsorption and intercalation. Our results demonstrate that Na ions preferentially adsorb at the edges rather than in the interior interlayer regions. The zigzag edge exhibits stronger binding affinity toward Na than the armchair edge. Progressive Na intercalation gradually opens the edge interlayer spacing. It reduces the interlayer angle toward a parallel configuration and accompanies a stacking transition from AB to AA at higher Na concentrations. Edge dangling bonds significantly enhance Na binding and drive the initial separation of edge carbon layers, whereas surface MV and DV defects contribute to Na adsorption at lower binding strengths. The calculated voltage–capacity relationships reveal that the first sloping region (>1.0 V) is primarily associated with Na adsorption at zigzag and defective edges, the second sloping region (0.1–1.0 V) can be rationalized by combined surface defect adsorption and interlayer intercalation, and the low-voltage plateau (<0.1 V) is thermodynamically linked to Na filling of narrow slit pores with optimized interlayer distances (~4.0 Å for zigzag and ~4.3–5.8 Å for armchair edges). These findings establish a direct structure–property correlation between carbon microstructure (edge type, defect architecture, and pore geometry) and the electrochemical voltage profile, offering atomic-level insights for the rational design of high-performance carbon-based anodes for SIBs.