Application of Diluted Electrode Method to Sodium-ion Insertion into Hard Carbon Electrode (Supporting Information)

Herein, the diluted-electrode method is applied to a hard carbon (HC) electrode to estimate sodium-ion (Na⁺) insertion kinetics. As metallic nickel (Ni) particles do not accommodate Na⁺ ions in the potential range of 0–2.0 V vs. Na⁺/Na, the HC powder electrode is diluted by adding inert Ni particles, enabling the adjustment of the HC concentration while maintaining the composite electrode structure. By examining the rate capabilities of the HC electrodes with different dilutions, we confirm that the Na⁺ insertion rate for the highly diluted electrode is 10 times higher than that for the undiluted electrode. These improved kinetics can be attributed to the alleviation of Na⁺ depletion, which results in insignificant concentration polarization under dilute conditions. For a highly diluted electrode, the Na⁺ insertion kinetics must be controlled by the Na⁺ mobility in the HC particles and across the HC/electrolyte interface. Therefore, our study reveals that the inherent kinetics of Na⁺ insertion into HC are very high and provides a basis for developing high-power Na-ion batteries.