Distinguishing sodium-ion penetration and sustained transport in realistic hard carbon nanostructures
Hard carbons are promising anodes for sodium-ion energy storage, yet the relationship between their heterogeneous microstructure and sodium transport remains poorly understood. Here, we combine machine-learning-generated hard-carbon structures with molecular dynamics simulations of explicit 1 M NaPF6 in ethylene carbonate/dimethyl carbonate electrolyte to investigate sodium storage and transport across carbon structures with densities from 0.5 to 2.0 g cm-3. Increasing carbon density produces less accessible pore networks and greater graphitic local ordering, allowing the influence of microstructure on electrochemical response and Na+ transport to be examined systematically. Sodium uptake increases with applied potential but decreases strongly with carbon density, while electrode charging persists even in the densest structure, where Na+ uptake remains very small. Coordination analysis shows increasing interaction with the carbon framework under applied potential, while Na+ retains a partially solvated environment. Three-dimensional trajectory analysis reveals heterogeneous, predominantly tortuous transport pathways, with the more open HC-C1 structure supporting broader penetration and greater sustained displacement. Maximum penetration depth and retained displacement are not equivalent: ions can transiently reach deep regions of denser carbon structures before returning towards the electrolyte interface. Potential-of-mean-force analysis further shows that deep penetration occurs across a range of projected free-energy changes and cannot be described by a single energetic criterion. These results show that Na+ storage and transport are governed by the interplay between electrostatic driving force, electrolyte solvation, pore accessibility and confinement, highlighting carbon microstructure as a key determinant of sustained ionic penetration.