Structural descriptors controlling pore-filling mechanism in hard carbon electrode during sodiation

Abstract

Sodiation mechanism in hard carbons, despite their ambiguous structures, is widely understood to involve three stages: adsorption at defects and edges, intercalation between graphene layers, and nano-pore filling. Among these, nano-pore filling might be the most important sodiation stage with its characteristic low-voltage plateau (∼0.1 V) observed over an extended capacity range. To investigate the pore filling mechanism, we introduce a representative nanopore model based on zeolite-templated carbon (ZTC), which consists of mainly sp²-bonded carbon sheets curved into well-defined interconnected nanopores, facilitating well-defined pore descriptors. Three ZTC models with pore sizes of 8.8 Å, 10.1 Å, and 11.2 Å were selected to represent the ideal nanopore features in hard carbon. A pore-filling algorithm, along with density functional theory (DFT) and ab initio molecular dynamics (AIMD) calculations, was used to investigate the sodiation process within the nanopores. Simulations reveal that the pore filling starts from Na absorption near the carbon walls via ionic bonding. As Na filling progresses towards the center, the bonding character gradually transitions to more metallic. Consequently, smaller pores exhibit higher sodiation voltage than larger pores, agreeing with experimental observations. Notably, the ZTC structure with 11.2 Å pores has a plateau voltage that aligns closer to the experimentally observed 0.1 V. The theoretical capacity with favorable formation energies can reach up to NaC₃ (∼470 mAh g⁻¹), more than the theoretical capacity of LiC₆. Comparing the pore filling of ZTC with carbon nanotubes suggests that the presence of non-6-carbon rings in ZTC facilitates charge transfer from Na to carbon, forming ionic bonds. Together, these descriptors – pore size, specific volume, and carbon topology offer design guidelines to quantify carbon electrode design for sodium-ion batteries.