Analysis on Overvoltage Relaxation of Lithium Secondary Batteries after Current Interruption
Authors: Ito Tomohiro , Tachibana Kazuhiro , Nishina Tatsuo , Kawahira Takao 
Published: February 2020

Introduction

It is well known that the lithium ion secondary battery (LiSB) is the most promising power source for electric vehicle (EV), the further development is still needed to assure the life and performance prediction. To elucidate this, recent researches are focused on electrochemical impedance spectroscopy (EIS) method. However, these researches were mainly focused on to obtain data itself and resistance component of EIS by using parameter fitting technique with applying constant phase element without any further analysis on reaction kinetics. Especially the attribution of EIS spectra seemed to be miss-understanding since the theoretical consideration and modeling is not enough due to the complicated porous structure of electrode.
There is another technique called as current-rest method1) suggested by Yata et.al. to obtain the internal resistance of LiSB. This technique is based on the measurement of over-potential relaxation after current interruption during the constant current charging/discharging process. However, the theoretical function of potential relaxation process with time is still not derived.
In this paper, we derived the theoretical functions for the current rest method by applying the transmission line model.

Results and Discussions

The electrolyte solution generally used for LiSB is the 1:1 type electrolyte solution without the supporting electrolyte. In such a case, mass transfer by diffusion only should not be applied; we should take into account the migration with the diffusion at the same time. The ion flux can be expressed by the Nernst-Planck Equation. The effect of the convection is unclear up to now, the combination of diffusion and migration should be taken into account. Since the electro-neutrality should be fulfilled in the any part of the electrolyte solution, the familiar Fick’s law is still fulfilled by applying average diffusion coefficient. Thus, transmission line model can be applied for the mathematical derivation.
The derivation of basic equation was carried out by using Laplace’s transform technique with the appropriate initial potential distribution and boundary conditions. In this paper, analysis have been made for the potential relaxation at separator so that the linear distribution was taken as the initial potential distribution. Thus obtained basic function had the series expansion form but it had the following feature.
i) Initial response showed linear response to the square root of the time.
ii) Long time response can be expressed in single exponential function to the time.
iii) Both of the above functions are smoothly connected at dimensionless time T=0.5256 within the 0.2 % accuracy.
Thus derived function was applied to the analysis of the measured voltage relaxation of commercially available LiSB for cellular phone. The voltage relaxation curves were well fitted by derived function. We employed the solver add-in of the Microsoft Excel in the parameter fitting process, where the time constant and the voltage difference was the fitting parameter for single time-constant function. For the case of fresh batteries with medium to high SOC level, showed two time constant system (50 s and 200 s) of which were connected in series. Fitted results were excellent within 1 mV deviation. On the other hand, the additional time constant system in the beginning of voltage relaxation were found for the SOC=0% and degraded battery. Even for such cases, the fitting of voltage relaxation were excellent by adopting three time constant system (0.3 s, 30 s and 250 s) of which were connected in series. We tested several type of LiSB such as cased in Al cans, 18650 type, and Al-laminated package, and the obtained results were almost similar. We concluded that the performance degradation of LiSB would appear in the beginning of the voltage relaxation with the order of magnitude of 0.1 s.
As a conclusion, voltage relaxation measurement after current interruption was the powerful tool to obtain the information of the performance loss of LiSB. This technique may be the best choice for performance monitoring since the measuring time is short and the combination of charging/discharging is quite easy.

References

1) S. Yata, H. Satake, M. Kuriyama, T. Endo, and H. Kinoshita, Evaluation of Positive Electrode Resistance by Current-Rest Method Using Four -electrode Cell, Electrochemistry, 78(5), 400-402 (2010)