Distribution of relaxation times as a method of separation and identification of complex processes measured by impedance spectroscopy

Impedance spectroscopy is one of the most commonly performed measurements to characterize electronic and electrochemical systems. Impedance spectra have limited resolution and many different processes may overlap what could be the reason of obstructions in its proper later analysis. Up to date, there are three approaches to solve this problem: examining impedance spectra itself, fitting spectra with equivalent circuits, and calculating the distribution of relaxation times (DRT). The latter method does not require any model or further knowledge about the system. As a result of DRT calculation, a plot containing relatively narrow peaks related to relaxation process of measured system is obtained. Namely, the position of the peak is related to time constant of the process, while the area under the peak to relaxation resistance. The aim of this work is to test available fitting functions to calculate area under a peak for previously prepared model containing different equivalent circuit elements. Obtained results are validated using exact formulas describing distribution of relaxation times for mentioned elements.