Physical interpretations of diffusion-controlled intercalation and surface-redox charge storage behaviors

Pseudocapacitance shows emerging properties to achieve both high capacity and high-rate performance simultaneously, including lithium ion and sodium ion storage systems. Herein, this work investigated the insightful mechanisms of pseudocapacitive lithium ion and sodium ion storage of anatase titanium dioxide anode. A transient two-dimensional continuum electrochemical modeling was performed for electrodes consisting of a single TiO₂ nanoparticle immersed in the electrolyte. The process of intrinsic surface-redox pseudocapacitance showed a uniform ion concentration across the electrochemical-active amorphous layer without hysteresis. By contrast, typical hysteresis and concentration gradients in the electrode were observed in the process of extrinsic intercalation pseudocapacitance, which enlarged with the increase in nanoparticle size or scan rate. The results indicated that sodium ion storage in TiO₂ was a surface-redox pseudocapacitive reaction. Design guidelines for sodium ion storage in TiO₂ electrodes was proposed by dimensional analysis. The dimensionless capacity for sodium ion storage remained nearly constant when the dimensionless scan rate was less than a critical value. This provided the guidance for the design and synthesis of the TiO electrode to enhance sodium ion storage by balancing nanoparticle size, thickness of Na_xTiO₂ surface layer, and effective diffusion coefficient of the electrode. Furthermore, such surface-redox pseudocapacitive sodium ion storage model could be extended to analyze other electrode materials.