Introducing Alternative Algorithms for the Determination of the Distribution of Relaxation Times
Tobias G. Bergmann, Nicolas Schlüter
Abstract
Impedance spectroscopy is a powerful characterization method to evaluate the performance of electrochemical systems. However, overlapping signals in the resulting impedance spectra oftentimes cause misinterpretation of the data. The distribution of relaxation times (DRT) method overcomes this problem by transferring the impedance data from the frequency domain into the time domain, which yields DRT spectra with an increased resolution. Unfortunately, the determination of the DRT is an ill-posed problem, and appropriate mathematical regularizations become inevitable to find suitable solutions. The Tikhonov algorithm is a widespread method for computing DRT data, but it leads to unlikely spectra due to necessary boundaries. Therefore, we introduce the application of three alternative algorithms (Gold, Richardson Lucy, Sparse Spike) for the determination of stable DRT solutions and compare their performances. As the promising Sparse Spike deconvolution has a limited scope when using one single regularization parameter, we furthermore replaced the scalar regularization parameter with a vector. The resulting method is able to calculate well-resolved DRT spectra.