联合时频分析：以单孔中电荷穿透深度和电流空间分布为例

doi:10.13208/j.electrochem.2303141

摘要/Abstract

摘要：

近年来，联合时频分析再次成为研究热点。超级电容器功率密度高和寿命长，但为了优化平衡功率密度和能量密度，需考虑两个关键因素：（1）多孔基质的比表面积；（2）孔内空间电解质可抵达性。本文采用联合时频分析方法，研究孔内电荷穿透深度及电流空间分布。具体开展了如下工作：（i）在复正弦电流激励下，推导单孔的时域响应和频域响应解析解，由此定义了描述电荷扩散行为的时频特征。（ii）采用联合时频方法，分析了内部参数和外部参数对孔内电荷穿透率的影响，揭示了孔内电荷有限扩散和无限扩散之间的演变规律。（iii）基于穿透率临界值，定义了孔内部参数的临界值，由此判断孔内电荷半无限扩散和有限扩散。本文提出联合时频分析方法，实现了多孔电极中复杂物理化学过程的信息融合，联合时频分析最终殊途同归，并提高诊断可靠性。

关键词: 联合时频分析, 单孔, 电荷穿透深度, 电流空间分布, 半无限扩散, 有限长度扩散

Abstract:

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.

Key words: Joint time-frequency analysis, Single pore, Charge penetration depth, Current spatial distribution, Semi-infinite diffusion, Finite length diffusion

王南, 黄秋安, 李伟恒, 白玉轩, 张久俊. 联合时频分析：以单孔中电荷穿透深度和电流空间分布为例[J]. 电化学（中英文）, 2024, 30(2): 2303141.

Nan Wang, Qiu-An Huang, Weiheng Li, Yuxuan Bai, Jiujun Zhang. Joint Time-Frequency Analysis: taking Charge Penetration Depth and Current Spatial Distribution in the Single Pore as An Example[J]. Journal of Electrochemistry, 2024, 30(2): 2303141.

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链接本文: https://electrochem.xmu.edu.cn/CN/10.13208/j.electrochem.2303141

https://electrochem.xmu.edu.cn/CN/Y2024/V30/I2/2303141

图/表 19

图1.

表1.

图2.

图3.

图4.

图5.

表2.

图6.

图7.

表3.

图8.

图9.

表4.

单孔时频EIS特征及电荷在孔中穿透率随σ的演变趋势

σ/σ₀	3	1	1/3	1/9
R_L/Ω	8.19×10⁸	2.46×10⁹	7.37×10⁹	2.21×10¹⁰
C_LF/F	6.79×10^-14	6.79×10^-14	6.79×10^-14	6.79×10^-14
f₀/Hz	$2424$	808	269.3	89.8
τ₀/s	4.13×10^-4	1.24×10^-3	3.71×10^-3	1.11×10^-2
l_p/m	4.15×10^-7	2.39×10^-7	1.38×10^-7	7.98×10^-8
$α$	0.69	0.40	0.23	0.13

表4.

图10.

图11.

表5.

图12.

图13.

表6.

参考文献 54

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Parameter	Default value	Unit	Reference
Interface capacitance per unit area C_dl	C₀=1	F·m^-2	[36,37]
Liquid electrolyte conductivity σ	σ₀=8×10^-2	S·m^-1	[16,38]
Pore length L	L₀=6×10^-7	m	[22,39]
Pore diameter d	d₀=36×10^-9	m	[22,40]
Observed frequency f_O	10³	Hz	[41,42]
Current density j_a	j_a0=3×10³	A·m^-2	[43-49]

C_dl/C0	1/4	1	4	16
R_L/Ω	2.46×10⁹	2.46×10⁹	2.46×10⁹	2.46×10⁹
C_LF/F	1.70×10^-14	6.79×10^-14	2.71×10^-13	1.03×10^-12
f₀/Hz	3232	808	202	50.5
τ₀/s	3.09×10^-4	1.23×10^-3	4.95×10^-3	1.98×10^-2
l_p/m	4.79×10^-7	2.40×10^-7	1.20×10^-7	5.98×10^-8
α	0.80	0.40	0.20	0.10

L/L₀	1/6.25	1/2.50	1.0	2.50
R_L/Ω	3.93×10⁸	9.82×10⁸	2.46×10⁹	6.14×10⁹
C_LF/F	1.09×10^-14	2.71×10^-14	6.79×10^-14	1.70×10^-13
f₀/Hz	3.16×10⁴	5.05×10³	8.08×10²	1.29×10²
l_p/m	3.17×10^-5	1.98×10^-4	1.23×10^-3	7.73×10³
l_p/m	2.39×10^-7	2.39×10^-7	2.39×10^-7	2.39×10^-7
α	2.49	1	0.40	0.16