Distribution of Relaxation Times

The distribution of relaxations times (DRT) is an approach to the analysis of electrochemical impedance spectroscopy (EIS) measurements. EIS is one of the most important electrochemical experimental techniques, which has been applied to solid state materials, solid oxide fuel cells, and Li-ion batteries, but also chemical sensors and biological systems, in order to understand the reaction kinetics and transport phenomena of such systems. The DRT is an useful complementary tool to the traditional equivalent circuit modelling approach to EIS data. In particular, the distribution function of relaxation times describes the time relaxation characteristics of the electrochemical system analysed. The DRT isolates the processes with different time constants, and it gives direct access to the distribution of the timescales, i.e., the relaxation times, of the system under study. Obtaining the DRT from EIS experimental data is a mathematically ill posed problem. In our work, we investigate methods for the optimal regularization of the DRT deconvolution [1], and we study the effect of various discretization methods on the estimated DRT [2]. Further, we take a Bayesan approach to the DRT [3], which not only is more robust than traditional ones, but can be extended to include more informative priors, thus allowing further development of the DRT approach to EIS data.

Finally, we have developed DRTtools, a Matlab GUI that helps you calculate the DRT of your EIS data. The code and a user manual can be found at https://sites.google.com/site/drttools. Our work on the DRT has been the subject of three publications on Electrochimica Acta between 2014 and 2015.


[1] M. Saccoccio, T.H. Wan, C. Chen, and F. Ciucci. Optimal Regularization in Distribution of Relaxation Times Applied to Electrochemical Impedance Spectroscopy: Ridge and Lasso Regression Methods – a Theoretical and Experimental Study. Electrochimica Acta, 147, 470-482 (2014) link

[2] F. Ciucci and C. Chen. Analysis of Electrochemical Impedance Spectroscopy Data Using the Distribution of Relaxation Times: A Bayesian and Hierarchical Bayesian Approach. Electrochimica Acta, 167, 439-454 (2015)link

[3] T.H. Wan, M. Saccoccio, C. Chen, and F. Ciucci. Influence of the Discretization Methods on the Distribution of Relaxation Times Deconvolution: Implementing Radial Basis Functions with DRTtools. Electrochimica Acta, 184, 483–499 (2015) link and code

If you cannot access the code and/or need assistance, please contact us.