Hierarchical\nPorous\nElectrode Impedance Model Based\non Diffusion Dynamics and the Electrode Morphology and Prediction\nof Electric Double-Layer Structures

The capacitance performance of a\nhierarchical porous\ncarbon (HPC)\nelectrode mainly depends on the dipole storage capacity and the rate\nof electric double-layer (EDL) reorganization. However, it is difficult\nto directly measure the effect of microscopic changes of pores and\nelectrolytic characteristics on the internal ionic mechanism of the\nEDL. Therefore, a model is proposed to easily and accurately describe\nboth the diffusion and EDL dynamics of the HPC electrode. In general,\ndiffusion in the mesoporous channel can be characterized in the middle-frequency\nregion (5–500 Hz) and in the micropore in the low-frequency\nregion (0.05–5 Hz). What is more, we have proven that the diffusion\nlayer thickness is inversely proportional to the electrolytic concentration\nand positively proportional to the mesoporous size, microporous depth,\nand surface roughness. In particular, the thicker diffusion layer\nmakes it easier for ions diffusing into micropores and a better EDL\nrecombination in mesoporous channels. However, the thinner diffusion\nlayer means a better EDL recombination in micropores. The low-frequency\nregion (0.01–0.05 Hz) characterized the compact layer dynamics,\nwhich shows the constant phase element behavior obviously. Moreover,\nthe compact layer thickness is inversely proportional to the surface\nheterogeneity, thus determining the dipole storage capacity. The model\noffers a general framework for impedance analysis and EDL prediction\nof HPC.