{"title":"On the futility of the Fuoss-Kirkwood relation","authors":"K.T. Malkow","doi":"10.1016/j.elecom.2024.107731","DOIUrl":null,"url":null,"abstract":"<div><p>The Fuoss-Kirkwood (FK) relation is used to derive analytical expressions for the distribution of uncorrelated relaxation times (DRT), particularly of probed biochemical and electrochemical systems, often without scrutiny. Its futility is proven simply by using the parity of impedance with complex frequencies. However, given the futile nature of the FK relation, these expressions are not suitable for validation of computed DRT spectra. Despite this, the need for such expressions persists. Addressing this need and the oversight of the dependency of the DRT value on the underlying data, the DRT is extended into the complex plane using the Hilbert transform (HT). It makes the DRT universal for any complex-valued quantity to not only quantify the extent of relaxations but also to assess their nature. keyword: distribution; integral transforms; relaxation time; superposition.</p></div>","PeriodicalId":304,"journal":{"name":"Electrochemistry Communications","volume":"164 ","pages":"Article 107731"},"PeriodicalIF":4.7000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1388248124000742/pdfft?md5=b90d63be747b59ed5e41e63eb90c0c30&pid=1-s2.0-S1388248124000742-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electrochemistry Communications","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1388248124000742","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ELECTROCHEMISTRY","Score":null,"Total":0}
引用次数: 0
Abstract
The Fuoss-Kirkwood (FK) relation is used to derive analytical expressions for the distribution of uncorrelated relaxation times (DRT), particularly of probed biochemical and electrochemical systems, often without scrutiny. Its futility is proven simply by using the parity of impedance with complex frequencies. However, given the futile nature of the FK relation, these expressions are not suitable for validation of computed DRT spectra. Despite this, the need for such expressions persists. Addressing this need and the oversight of the dependency of the DRT value on the underlying data, the DRT is extended into the complex plane using the Hilbert transform (HT). It makes the DRT universal for any complex-valued quantity to not only quantify the extent of relaxations but also to assess their nature. keyword: distribution; integral transforms; relaxation time; superposition.
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Electrochemistry Communications is an open access journal providing fast dissemination of short communications, full communications and mini reviews covering the whole field of electrochemistry which merit urgent publication. Short communications are limited to a maximum of 20,000 characters (including spaces) while full communications and mini reviews are limited to 25,000 characters (including spaces). Supplementary information is permitted for full communications and mini reviews but not for short communications. We aim to be the fastest journal in electrochemistry for these types of papers.
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