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
收稿日期: 2023-03-22
修回日期: 2023-05-31
录用日期: 2023-06-05
网络出版日期: 2023-06-08
基金资助
国家自然科学基金项目(22078190);中国国家重点研发计划项目(2020YFB1505802)
Joint Time-Frequency Analysis: taking Charge Penetration Depth and Current Spatial Distribution in the Single Pore as An Example
Received date: 2023-03-22
Revised date: 2023-05-31
Accepted date: 2023-06-05
Online published: 2023-06-08
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。
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, 2024 , 30(2) : 2303141 . DOI: 10.13208/j.electrochem.2303141
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.
| [1] | González A, Goikolea E, Barrena J A, Mysyk R. Review on supercapacitors: technologies and materials[J]. Renew. Sust. Energ. Rev., 2016, 58: 1189-1206. |
| [2] | Raza W, Ali F, Raza N, Luo Y, Kim K H, Yang J, Kumar S, Mehmood A, Kwon E E. Recent advancements in supercapacitor technology[J]. Nano Energy, 2018, 52: 441-473. |
| [3] | Salanne M, Rotenberg B, Naoi K, Kaneko K, Taberna P L, Grey C P, Dunn B, Simon P. Efficient storage mechanisms for building better supercapacitors[J]. Nat. Energy, 2016, 1(6): 16070. |
| [4] | Jadhav P R, Suryawanshi M P, Dalavi D S, Patil D S, Jo E A, Kolekar S S, Wali A A, Karanjkar M M, Kim J Hyeok, Patil P S. Design and electro-synthesis of 3-D nanofibers of MnO2 thin films and their application in high performance supercapacitor[J]. Electrochim. Acta, 2015, 176: 523-532. |
| [5] | Sonai Muthu N, Gopalan M. Polyethylene glycol-assisted growth of Ni3S4 closely packed nanosheets on Ni-foam for enhanced supercapacitor device[J]. J. Solid State Electrochem., 2019, 23(10): 2937-2950. |
| [6] | Wang H, Forse A C, Griffin J M, Trease N M, Trognko L, Taberna P L, Simon P, Grey C P. In situ NMR spectroscopy of supercapacitors: Insight into the charge storage mechanism[J]. J. Am. Chem. Soc., 2013, 135(50): 18968-18980. |
| [7] | Chen J, Lee P S. Electrochemical supercapacitors: From mechanism understanding to multifunctional applications[J]. Adv. Energy Mater., 2021, 11(6): 2003311. |
| [8] | Kurzweil P, Chwistek M. Electrochemical stability of organic electrolytes in supercapacitors: Spectroscopy and gas analysis of decomposition products[J]. J. Power Sources, 2008, 176(2): 555-567. |
| [9] | Lin Z, Taberna P L, Simon P. Advanced analytical techniques to characterize materials for electrochemical capacitors[J]. Curr. Opin. Electrochem., 2018, 9: 18-25. |
| [10] | Ciucci F. Modeling electrochemical impedance spectroscopy[J]. Curr. Opin. Electrochem., 2019, 13: 132-139. |
| [11] | Bi S, Banda H, Chen M, Niu L, Chen M Y, Wu T Z, Wang J S, Wang R X, Feng J M, Chen T Y, Dinc? M, Kornyshev A A, Feng G. Molecular understanding of charge storage and charging dynamics in supercapacitors with MOF electrodes and ionic liquid electrolytes[J]. Nat. Mater., 2020, 19(5): 552-558. |
| [12] | Zhang L Y, Shi D W, Liu T, Jaroniec M, Yu J G. Nickel-based materials for supercapacitors[J]. Mater. Today, 2019, 25: 35-65. |
| [13] | Lazanas A Ch, Prodromidis M I. Electrochemical impedance spectroscopy─A tutorial[J]. ACS Meas. Sci. Au, 2023, 3 (3): 162-193. |
| [14] | Allagui A, Fouda M E, Elwakil A, Psychalinos C. Time-domain response of supercapacitors using their impedance parameters and fourier series decomposition of the excitation signal[J]. J. Electroanal. Chem., 2023, 947: 117751. |
| [15] | Barsoukov E, Macdonald R J. Impedance spectroscopy: Theory, experiment, and applications[M]. USA: Wiley-Interscience, 2005. |
| [16] | Lasia A. Electrochemical impedance spectroscopy and its applications[M]. New York: Springer, 2014. |
| [17] | Wang X X, Zhou Z Z, Shan Q, Zhang Z M, Huang J, Liu Y W, Chen S L. Porous-electrode theory of lithium ion battery: old paradigm and new challenge[J]. J. Electrochem., 2020, 26(5): 596-606. |
| [18] | Ji W X, Wang G W, Wang Q, Bai L J, Qu D Y. Porous electrodes in electrochemical energy storage systems[J]. J. Electrochem., 2020, 26(5): 576-595. |
| [19] | Li X, Huang Q A, Li W H, Bai Y X, Wang J, Liu Yang, Zhao Y F, Wang J, Zhang J J. Fundamentals of electrochemical impedance spectroscopy for macrohomogeneous porous electrodes[J]. J. Electrochem., 2021, 27(5): 467-497. |
| [20] | De Levies R. On porous electrodes in electrolyte solutions[J]. Elecrrochim. Acta, 1963, 8(10): 751-780. |
| [21] | De Levies R. On porous electrodes in electrolyte solutions-IV[J]. Electrochim. Acta, 1964, 9(9): 1231-1245. |
| [22] | Candy J P, Fouilloux P, Keddam M, Takenouti H. The characterization of porous electrodes by impedance measurements[J]. Electrochim. Acta, 1981, 26(8): 1029-1034. |
| [23] | Keiser H, Beccu K D, Gutjahr M A. Absch?tzung der porenstruktur por?ser elektroden aus impedanzmessungen[J]. Electrochim. Acta, 1976, 21(8): 539-543. |
| [24] | Linneen N, Delnick F, Islam S Z, Deshmane V G, Bhave R. Application of the macrohomogeneous line model for the characterization of carbon aerogel electrodes in capacitive deionization[J]. Electrochim. Acta, 2019, 301: 1-7. |
| [25] | Paasch G, Micka K, Gersdorf P. Theory of the electrochemical impedance of macrohomogeneous porous electrodes[J]. Electrochim. Acta, 1993, 38(18): 2653-2662. |
| [26] | Song H K, Hwang H Y, Lee K H, Dao L H. The effect of pore size distribution on the frequency dispersion of porous electrodes[J]. Electrochim. Acta, 2000, 45(14): 2241-2257. |
| [27] | Yoo H D, Jang J H, Ryu J H, Park Y, Oh S M. Impedance analysis of porous carbon electrodes to predict rate capability of electric double-layer capacitors[J]. J. Power Sources, 2014, 267: 411-420. |
| [28] | Li W H, Huang Q A, Li Y, Bai Y, Wang N, Wang J, Hu Y M, Zhao Y F, Li X F, Zhang J J. Capacitive energy storage from single pore to porous electrode identified by frequency response analysis[J]. J. Energy Chem., 2023, 77: 384-405. |
| [29] | El Brouji H, Vinassa J M, Briat O, Bertrand N, Woirgard E. Ultracapacitors self discharge modelling using a physical description of porous electrode impedance[C]. El Brouji H, IEEE Vehicle Power and Propulsion Conference, China: IEEE, 2008, 1-6. |
| [30] | Meyers J P, Doyle M, Darling R M, Newman J. The impedance response of a porous electrode composed of intercalation particles[J]. J. Electrochem. Soc., 2000, 147(8): 2930. |
| [31] | Siroma Z, Fujiwara N, Yamazaki S, Asahi M, Nagai T, Ioroi T. Mathematical solutions of comprehensive variations of a transmission-line model of the theoretical impedance of porous electrodes[J]. Electrochim. Acta, 2015, 160: 313-322. |
| [32] | Zhuang Q C, Yang Z, Zhang L, Cui Y H. Research progress on diagnosis of electrochemical impedance spectroscopy in lithium ion batteries[J]. Prog. Chem., 2020, 32(06): 761-791. |
| [33] | Johnson A M, Newman J. Desalting by means of porous carbon electrodes[J]. J. Electrochem. Soc., 1971, 118(3): 510-517. |
| [34] | Gomadam P M, Weidner J W, Zawodzinski T A, Saab A P. Theoretical analysis for obtaining physical properties of composite electrodes[J]. J. Electrochem. Soc., 2003, 150(8): E371. |
| [35] | Huang Q A, Li W H, Tang Z P, Zhang F Z, Li A J, Zhang J J. Fundamentals of electrochemical impedance spectroscopy[J]. Chin. J. Nat., 2020, 42(1): 12-26. |
| [36] | Nguyen T T, Demortière A, Fleutot B, Delobel B, Delacourt C, Cooper S J. The electrode tortuosity factor: Why the conventional tortuosity factor is not well suited for quantifying transport in porous Li-ion battery electrodes and what to use instead[J]. npj Comput. Mater., 2020, 6(1): 123. |
| [37] | Honda K, Rao T N, Tryk D A, Fujishima A, Watanabe M, Yasui K, Masuda H. Impedance characteristics of the nanoporous honeycomb diamond electrodes for electrical double-layer capacitor applications[J]. J. Electrochem. Soc., 2001, 148(7): A668. |
| [38] | Siroma Z, Sato T, Takeuchi T, Nagai R, Ota A, Ioroi T. AC impedance analysis of ionic and electronic conductivities in electrode mixture layers for an all-solid-state lithium-ion battery[J]. J. Power Sources, 2016, 316: 215-223. |
| [39] | Bisquert J, Garcia-Belmonte G, Fabregat-Santiago F, Compte A. Anomalous transport effects in the impedance of porous film electrodes[J]. Electrochem. Commun., 1999, 1(9): 429-435. |
| [40] | Wang D W, Li F, Liu M, Lu G Q, Cheng H M. Mesopore-aspect-ratio dependence of ion transport in rodtype ordered mesoporous carbon[J]. J. Phys. Chem. C, 2008, 112(26): 9950-9955. |
| [41] | Huang Q A, Li Y, Tsay K C, Sun C, Changping Yang, Zhang L, Zhang J. Multi-scale impedance model for supercapacitor porous electrodes: Theoretical prediction and experimental validation[J]. J. Power Sources, 2018, 400: 69-86. |
| [42] | Musiani M, Orazem M, Tribollet B, Vivier V. Impedance of blocking electrodes having parallel cylindrical pores with distributed radii[J]. Electrochim. Acta, 2011, 56(23): 8014-8022. |
| [43] | Huang J, Zhang J. Theory of impedance response of porous electrodes: simplifications, inhomogeneities, non-stationarities and applications[J]. J. Electrochem. Soc., 2016, 163(9): A1983-A2000. |
| [44] | Yuan X, Wang H, Colinsun J, Zhang J. AC impedance technique in PEM fuel cell diagnosis—A review[J]. Int. J. Hydrogen Energy, 2007, 32(17): 4365-4380. |
| [45] | Tang Y, Zhang J, Song C, Liu H, Zhang J, Wang H, Mackinnon S, Peckham T, Li J, Mcdermid S, Kozak P. Temperature dependent performance and in situ AC impedance of high-temperature PEM fuel cells using the Nafion-112 membrane[J]. J. Electrochem. Soc., 2006, 153(11): A2036. |
| [46] | Wagner N, Gülzow E. Change of electrochemical impedance spectra (EIS) with time during CO-poisoning of the Pt-anode in a membrane fuel cell[J]. J. Power Sources, 2004, 127(1-2): 341-347. |
| [47] | Brett D J L, Atkins S, Brandon N P, Vesovic V, Vasileiadis N, Kucernak A. Localized impedance measurements along a single channel of a solid polymer fuel cell[J]. Electrochem. Solid-State Lett., 2003, 6(4): A63. |
| [48] | Iranzo A, Mu?oz M, Pino Fco J, Rosa F. Non-dimensional analysis of PEM fuel cell phenomena by means of AC impedance measurements[J]. J. Power Sources, 2011, 196(9): 4264-4269. |
| [49] | Jang J H, Oh S M. Complex capacitance analysis of porous carbon electrodes for electric double-layer capacitors[J]. J. Electrochem. Soc., 2004, 151(4): A571. |
| [50] | Li Y, Yang W M, Huang Q A, Li W H, Li X F, Zhang J J. Simulation of warburg impedance spectra under finite diffusion boundary conditions for porous energy electrode materials[J]. J. Xi'an Univ. Technol., 2019, 35(2): 138-146. |
| [51] | Jang J H, Yoon S, Ka B H, Jung Y H, Oh S M. Complex capacitance analysis on leakage current appearing in electric double-layer capacitor carbon electrode[J]. J. Electrochem. Soc., 2005, 152(7): A1418. |
| [52] | Taberna P L, Simon P, Fauvarque J F. Electrochemical characteristics and impedance spectroscopy studies of carbon-carbon supercapacitors[J]. J. Electrochem. Soc., 2003, 150(3): A292. |
| [53] | Itagaki M, Suzuki S, Shitanda I, Watanabe K. Electrochemical impedance and complex capacitance to interpret electrochemical capacitor[J]. Electrochemistry, 2007, 75(8): 649-655. |
| [54] | Huang J, Gao Y, Luo J, Wang S, Li C, Chen S, Zhang J. Editors’ Choice-Review-Impedance response of porous electrodes: Theoretical framework, physical models and applications[J]. J. Electrochem. Soc., 2020, 167(16): 166503. |
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