The principle and application of relaxation time distribution

Electrochemical impedance spectroscopy (EIS) is an electrochemical measurement method that uses a small amplitude sine wave potential or current as a disturbance signal. With the development of impedance measurement instrument technology, the test and application of EIS are becoming more and more extensive. Nowadays EIS is widely used in energy, corrosion and life sciences. The interpretation of EIS data usually relies on the equivalent circuit model (ECM) fitting techniques. Researchers use ECM to simulate electrochemical systems and fit circuit parameters using non-linear least squares method. However, ECM fitting techniques require prior knowledge of the electrochemical system, such as the number of polarization processes, which is not readily available for those complex systems. In addition to this, ECM fitting techniques also have other problems. For example, for the same EIS data, ECMs are non-uniqueness, meaning that multiple ECMs can fit into the same EIS data equally well. In addition, for complex electrochemical system which ECM has too many circuit parameters makes the fitting process difficult. Finally, in order for the fitting to converge, it is necessary to choose appropriate initial values of circuit parameters, but it is still not easy. In order to solve the above problems with ECM fitting techniques, the distribution of relaxation time (DRT) method came into being. The core of the DRT method is the transformation of EIS data in the frequency domain into the time domain. The advantage of the DRT method is that polarization processes with close relaxation times can be distinguished and no prior knowledge is required. As such, DRT method has been widely used in complex electrochemical systems such as fuel cells, secondary batteries, and electrolyzers. The present review first introduces the theory of the DRT method, including the theoretical derivation of DRT function, the solution method of DRT function, the characteristics and information of DRT plot, and the scope of application of DRT method. Then, we mainly review applications of the DRT method in practical electrochemical systems such as proton exchange membrane fuel cell and lithium-ion battery. The DRT method was used in these systems for the separation and attribution of polarization processes, as well as the pre-identification and secondary testing of ECM. Then, for the EIS data of some electrochemical systems is beyond the scope of application of DRT methods, we introduce several extensions of DRT method such as distribution of differential capacity (DDC) method, distribution of diffusion times (DDT) method and generalized distribution of relaxation times (GDRT) method. Finally, we summarize and prospect the DRT method. In general, the DRT method can well solve the shortcomings of ECM fitting techniques in complex electrochemical systems. And the advantages of high resolution and the absence of no prior knowledge make it have a wide range of application prospects. However, there are still some problems with the DRT method. For example, there are currently multiple calculation methods for DRT functions, such as regularization, Fourier transformation, maximum entropy and genetic programming method. However, there is still controversy over which method is more accurate for calculation. And regardless of the calculation method, there is a problem of overfitting or underfitting, and how to avoid it is still unclear. Finally, DRT method is a powerful EIS data analysis method, and it is believed that with the improvement of the accuracy and stability of electrochemical impedance data measurement and the refinement of mathematical methods for DRT function calculation, it can be more widely used in more electrochemical systems.