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Investigating Inductive Loops in Electrochemical Impedance Spectroscopy
Guynee, Jacob
Guynee, Jacob
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Thesis/Dissertation
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2022-12
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Mathematics
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http://dx.doi.org/10.34944/dspace/9463
Abstract
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.
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