Hierarchical Porous Electrode Impedance Model Based on Diffusion Dynamics and the Electrode Morphology and Prediction of Electric Double-Layer Structures

The capacitance performance of a hierarchical porous carbon (HPC) electrode mainly depends on the dipole storage capacity and the rate of electric double-layer (EDL) reorganization. However, it is difficult to directly measure the effect of microscopic changes of pores and electrolytic characteristics on the internal ionic mechanism of the EDL. Therefore, a model is proposed to easily and accurately describe both the diffusion and EDL dynamics of the HPC electrode. In general, diffusion in the mesoporous channel can be characterized in the middle-frequency region (5-500 Hz) and in the micropore in the low-frequency region (0.05-5 Hz). What is more, we have proven that the diffusion layer thickness is inversely proportional to the electrolytic concentration and positively proportional to the mesoporous size, microporous depth, and surface roughness. In particular, the thicker diffusion layer makes it easier for ions diffusing into micropores and a better EDL recombination in mesoporous channels. However, the thinner diffusion layer means a better EDL recombination in micropores. The low-frequency region (0.01-0.05 Hz) characterized the compact layer dynamics, which shows the constant phase element behavior obviously. Moreover, the compact layer thickness is inversely proportional to the surface heterogeneity, thus determining the dipole storage capacity. The model offers a general framework for impedance analysis and EDL prediction of HPC.