A theory of inductive loops in electrochemical impedance spectroscopy

We demonstrate that failure of time-invariance assumption in the modeling of electrochemical systems by equivalent circuits can lead to the formation of low frequency "inductive loops" that manifest themselves as positive imaginary parts of the impedance function. Assuming that the properties of the equivalent circuits change slowly in time we perform an asymptotic analysis and obtain a new integral representation of the impedance function that reduces to the standard one at high frequencies, while exhibiting inductive loops at low frequencies.