Physical interpretation of the electrochemical impedance spectroscopy (EIS) characteristics for diffusion-controlled intercalation and surface-redox charge storage behaviors

AC impedance response is an important criteria in characterizing the electrochemical performance of metal ion batteries, including sodium ion batteries (SIBs) and lithium ion batteries (LIBs). This work investigates the electrochemical impedance spectroscopy (EIS) of diffusion-controlled intercalation in LIBs and surface-redox charge storage in SIBs. To do so, a first-principle based physical modeling was performed for a nanoparticle of TiO${}_2$ immersed in lithium ion or sodium ion electrolytes. Nyquist plots showed typical charge transfer resistance, diffusion impedance, and capacitive behaviors for lithium ion storage. The diffusion impedance was absent for sodium ion storage. Similarly, the radial distribution of ion concentration response showed significant slope jump for lithium ion storage, also absent for sodium ion storage. In addition, the charge transfer resistance first remained constant then increased with the increase in bias potential for both lithium ion storage and sodium ion storage, both numerically and experimentally. This corresponded to the Faradaic and capacitive regimes in the CV curves. Furthermore, distribution of relaxation time (DRT) analysis showed two distinct peaks, corresponding to the charge transfer process and the diffusion process. Finally, the resistances of lithium ion storage increased with the increase in electrode nanoparticle diameter, due to the increase in diffusion pathways. On the other hand, sodium ion intercalation was independent of the size of the electrode nanoparticle. This investigation offered insights in distinguishing extrinsic pseudocapacitance from intrinsic pseudocapacitance through EIS analysis.