Corresponding Author

Qiu-An Huang (qiuan_huang@shu.edu.cn);
Wei-Heng Li (wh_li@shu.edu.cn);
Jiu-Jun Zhang (jiujun.zhang@i.shu.edu.cn)


In recent years, joint time-frequency analysis has once again become a research hotspot. Supercapacitors have high power density and long service life, however, in order to balance between power density and energy density, two key factors need to be considered: (i) the specific surface area of the porous matrix; (ii) the electrolyte accessibility to the intra-pore space of porous carbon matrix. Electrochemical impedance spectra are extensively used to investigate charge penetration ratio and charge storage mechanism in the porous electrode for capacitance energy storage. Furthermore, similar results could be obtained by different methods such as stable-state analysis in the frequency domain and transient analysis in the time domain. In this work, a joint time-frequency analysis method is proposed to study the charge penetration depth and current spatial distribution in the pore. In detail, the following work has been carried out: (i) Excited by a complex sinusoidal current, the analytical solutions in the time domain and the frequency domain for the single pore are resolved, and the time-frequency characteristics describing the charge diffusion behavior are defined. (ii) Using the joint time-frequency method, the influences of the internal and external parameters on the charge penetration ratio in the single pore are quantitatively analyzed, and the evolution trend between the finite and semi-infinite diffusion of the charge inside the single pore is revealed. (iii) Based on the critical value of the penetration rate, the critical value of the internal parameters of the single pore is defined as well, and the semi-infinite diffusion and finite diffusion of the charge inside the pore are judged. Based on the above analyses, it can be seen that the frequency domain analysis regards the single pore as a whole and examines the charge transfer characteristics at different frequencies; however, the time domain analysis regards the single pore as a distributed parameter system, examining the evolution of charges at different spatial locations over time. Joint time-frequency analysis successfully completes information fusion and ultimately achieves the same goal. Furthermore, the joint time-frequency method can improve the reliability of diagnosis for the complicated porous electrode in electrochemical systems. In a word, the joint time-frequency analysis method proposed in this paper can achieve the information fusion for complex physio-chemical processes, which not only achieves the similar insights with different efforts, but also improves the diagnosis reliability for the complicated porous electrode in the electrochemical energy systems.

Graphical Abstract


Joint time-frequency analysis; Single pore; Charge penetration depth; Current spatial distribution; Semi-infinite diffusion; Finite length diffusion

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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