Application Of Kramers-Kronig Relation To Electrochemical Impedance Spectroscopy Of Lithium Batteries

In materials with ions as charge carriers(such as lithium-ion batteries),due to the large mass charge ratio of ions,the response time in the process of electric field polarization is long.When making electrochemical impedance spectroscopy measurements on such samples,the measurement frequency should be low enough(e.g.,1m Hz)to allow the sample to undergo a complete polarization process.During the measurement process(from a few minutes to tens of minutes),the temperature and humidity of the sample environment,the bias electric field,the intensity and frequency of the excitation signal may change.Therefore,the measurement results may be mixed with the system response of other physical quantity changes besides the excitation signal frequency.Therefore,the reliability of electrochemical impedance spectroscopy data is particularly important for the impedance measurement of lithium batteries.Kramers-Kronig(K-K for short)transformation can be used to analyze the relationship between the real part and the imaginary part of impedance data,so as to verify the reliability of impedance measurement data.First of all,the project needs to realize the numerical calculation of K-K transformation,which mainly has three problems.First,the integral function in the K-K relation has singularity within the integral range.Second,the k-k relation requires that the integral be a continuous integral;And finally,the k-k relationship requires the integral from zero to infinity.The actual impedance spectra are discontinuous data points in a limited frequency range.In view of the above problems,the final treatment method is given by comparing several methods :(1)adding the integral singularity of the perturbation term into the K-K integral formula;(2)The cubic spline interpolation curve algorithm is used to process the discrete impedance data with approximate continuous integration.(3)The equivalent circuit model was established according to the electrochemical impedance spectrum of lithium battery,and the impedance data outside the frequency domain was calculated and measured using the equivalent circuit model.Secondly,the error results between the real part and the imaginary part of the K-K transformation value and the measured value can be used as an auxiliary parameter to judge the matching degree between the equivalent circuit model and the measured lithium battery sample material itself.In this paper,according to the internal mechanism of lithium batteries,and referring to the impedance model established in other researchers work,the impedance data measured by the instrument are fitted through the professional electrochemical analysis software Zview.However,in practical applications,it is found that different equivalent circuits can be used to describe the same measured sample,and the errors between the K-K transformation values and the measured values from the data outside the measured frequency domain obtained from these different equivalent circuit models are different.By comparing the residuals normalized between the real part and the imaginary part of the data,it can be used as an auxiliary parameter to judge the matching degree between the equivalent circuit model and the measured lithium battery sample material itself.