{"title":"带串联电阻的恒相元件对线性电压扫描的电气响应的精确解","authors":"Anis Allagui, Ahmed Elwakil, Enrique H. Balaguera","doi":"10.1016/j.jpowsour.2024.234907","DOIUrl":null,"url":null,"abstract":"A resistance in series with a constant phase element (CPE) of frequency-dependent impedance given by the power law function is commonly used for the analysis of steady-state frequency response data exhibiting non-purely capacitive behavior. This is the case in most (bio)(electro)chemical systems including dielectrics, batteries, supercapacitors, capacitive deionization units, biological tissues and bioelectrodes. Passing to the time domain, the current, voltage and charge of the system are governed by differential equations with non-integer, fractional-order operators. The purpose of this study is to provide the exact analytical expressions for the electrical response of an -CPE model under linear sweep voltammetry with the use of the Laplace transform method. The electrical variables are expressed in terms of special functions regularly encountered with fractional calculus such as the Fox’s -function and the Mittag-Leffler function, and can be used for modeling non-ideal devices as well as extracting their characteristic parameters.","PeriodicalId":377,"journal":{"name":"Journal of Power Sources","volume":null,"pages":null},"PeriodicalIF":8.1000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exact solution for the electrical response of a constant phase element with a series resistance to linear voltage sweep\",\"authors\":\"Anis Allagui, Ahmed Elwakil, Enrique H. Balaguera\",\"doi\":\"10.1016/j.jpowsour.2024.234907\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A resistance in series with a constant phase element (CPE) of frequency-dependent impedance given by the power law function is commonly used for the analysis of steady-state frequency response data exhibiting non-purely capacitive behavior. This is the case in most (bio)(electro)chemical systems including dielectrics, batteries, supercapacitors, capacitive deionization units, biological tissues and bioelectrodes. Passing to the time domain, the current, voltage and charge of the system are governed by differential equations with non-integer, fractional-order operators. The purpose of this study is to provide the exact analytical expressions for the electrical response of an -CPE model under linear sweep voltammetry with the use of the Laplace transform method. The electrical variables are expressed in terms of special functions regularly encountered with fractional calculus such as the Fox’s -function and the Mittag-Leffler function, and can be used for modeling non-ideal devices as well as extracting their characteristic parameters.\",\"PeriodicalId\":377,\"journal\":{\"name\":\"Journal of Power Sources\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":8.1000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Power Sources\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1016/j.jpowsour.2024.234907\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Power Sources","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1016/j.jpowsour.2024.234907","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
Exact solution for the electrical response of a constant phase element with a series resistance to linear voltage sweep
A resistance in series with a constant phase element (CPE) of frequency-dependent impedance given by the power law function is commonly used for the analysis of steady-state frequency response data exhibiting non-purely capacitive behavior. This is the case in most (bio)(electro)chemical systems including dielectrics, batteries, supercapacitors, capacitive deionization units, biological tissues and bioelectrodes. Passing to the time domain, the current, voltage and charge of the system are governed by differential equations with non-integer, fractional-order operators. The purpose of this study is to provide the exact analytical expressions for the electrical response of an -CPE model under linear sweep voltammetry with the use of the Laplace transform method. The electrical variables are expressed in terms of special functions regularly encountered with fractional calculus such as the Fox’s -function and the Mittag-Leffler function, and can be used for modeling non-ideal devices as well as extracting their characteristic parameters.
期刊介绍:
The Journal of Power Sources is a publication catering to researchers and technologists interested in various aspects of the science, technology, and applications of electrochemical power sources. It covers original research and reviews on primary and secondary batteries, fuel cells, supercapacitors, and photo-electrochemical cells.
Topics considered include the research, development and applications of nanomaterials and novel componentry for these devices. Examples of applications of these electrochemical power sources include:
• Portable electronics
• Electric and Hybrid Electric Vehicles
• Uninterruptible Power Supply (UPS) systems
• Storage of renewable energy
• Satellites and deep space probes
• Boats and ships, drones and aircrafts
• Wearable energy storage systems