On the stabilization and extension of the distribution of relaxation times analysis

The Distribution of Relaxation Times (DRT) is a useful technique to provide an improved insight into the interpretation of Electrochemical Impedance Spectroscopy (EIS) data. Despite its capability to distinguish the characteristic frequencies of the processes involved in an electrochemical system, the DRT solution is an ill-posed problem that requires a regularization method. Tikhonov regularization is one of the most commonly adopted methods for DRT analysis. Nevertheless, the domain discretization, needed to solve the original continuous problem, introduces errors in DRT evaluation. This problem is quite relevant when the impedance is not sufficiently resolved at boundary frequency range (imaginary part of impedance does not approach 0), affecting the edges of the DRT spectrum and the internal part. Here, the zero-padding technique is applied to overcome this issue. The results show how this approach, frequently used in the signal theory but not in DRT, improves DRT evaluation quality with Tikhonov regularization. It consists of an extension of the experimental frequency domain, reducing the errors due to the frequency truncation. The extended algorithm, named ED-DRT, is compared with the conventional Tikhonov method on both simulated and real impedance data. The new approach increases the quality of DRT results, providing higher stability and accuracy in evaluating characteristic frequencies and global polarization resistance even with noisy EIS data.