Our DFT calculations confirm that the defect-assisted intercalation is energetically more favorable than conventional intercalation, which explains why defect-assisted intercalation occurs at higher potential in the potential-capacity curve. The wide range of intralayer defect sites with varying adsorption energies results in a sloping potential region. During the plateau region, the average interlayer spacing increases for each HC, signifying continued intercalation of sodium ions between the graphene layers. Note that for HC-2000, no decrease in the d-spacing is observed in the slope region; we speculate that this is because HC-2000 has fewer available surface defects and a lower surface area, consistent with the comparatively small initial slope region (below 5% SoS). Thus, sodium ions must intercalate to reach intralayer defect sites, resulting in observed increase in d002.