In electrochemistry "Inductive loops" appear as a small "hook" into the upper half-plane in the low frequency range of the Nyquist plot of the impedance function. This has puzzled scientists for decades because the electrochemical impedance is known to have a purely negative imaginary part. In this dissertation we will show that the lack of time-invariance can be a source of inductive loops. We first introduce a technique for measuring the impedance of a time-invariant electrochemical system. Since circuits of arbitrary complexity can be approximated by an equivalent circuit model consisting of elementary Voigt circuits and possibly a capacitor, we show that this technique gives a reliable approximation of the impedance of an elementary Voigt element and the exact impedance of a capacitor. We then apply the same procedure to systems with time-dependent resistances and capacitances and observe the appearance of inductive loops in the plot of the "impedance function". Finally, we examine electrochemical systems whose properties change on time scales of $1/\Ge$, where $\Ge$ is a small parameter. We derive a formula which permits one to extend the theory of electrochemical impedance spectroscopy to time-dependent systems with slowly changing properties. This formula agrees with the classical theory at high frequencies while being able to capture low-frequency inductive loops. / Mathematics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/9501 |
| Date | 12 1900 |
| Creators | Guynee, Jacob |
| Contributors | Grabovsky, Yury, Grabovsky, Yury, Queisser, Gillian, Seibold, Benjamin, Zdilla, Michael J., 1978- |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 63 pages |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/9463, Theses and Dissertations |
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