A Simple, One-Dimensional Electrochemical Model for the Lithium-Sulfur Battery
Authors: Can Erensoy Sevgi , Eroglu Damla 
Published: February 2020

The use of rechargeable batteries in electric and hybrid vehicles would not only reduce the carbon emission significantly but also decrease the dependence on foreign oil. In addition, the use of rechargeable batteries in grid storage would be beneficial for the storage of renewable energy sources such as solar and wind energy which are normally intermittent. Therefore, developing high energy density and low cost rechargeable batteries will play a critical role in overcoming many of the energy-related challenges. Lithium-sulfur (Li-S) batteries have gained significant attention in recent years due to their very high theoretical specific energy [1-6]. However for the commercial use of the Li-S battery, its capacity retention and cycle life must be improved [1-6]. Electrochemical modeling coupled with electrochemical characterization is essential to have a better understanding of the reaction and degradation mechanisms in these batteries in order to improve the battery performance and life.
In this study, a simple one-dimensional electrochemical model for a Li-S cell is developed based on a previous model by Eroglu et al [1]. The Li-S cell in the model is composed of the lithium-metal anode, a porous separator and the porous sulfur-carbon cathode filled with the electrolyte. The concentration gradients in the cell as well as the polysulfide shuttle mechanism are neglected in the model. The model predicts the current-voltage relationship for each charge transfer step for an isothermal discharge of the Li-S cell. In the electrochemical model, anode kinetics is defined with the Butler-Volmer kinetics. The Ohmic losses from the transport of Li+ through the porous separator are also considered in the model using Ohm’s Law. The cathode is treated with the one-dimensional concentration-independent porous electrode model by Newman and Tobias [7]. The cathode kinetics is defined with a single reaction step, simplifying the multiple-step redox reactions for the sulfur cathode. By simplifying the sulfur reaction in the cathode into a single reaction, the cathode kinetics in the electrochemical model can be defined by a single kinetic parameter, exchange current density for the cathode (i0,pe).
The electrochemical model of the Li-S cell is supported with the Electrochemical Impedance Spectroscopy (EIS) data from the literature [2-6]. The exchange current density for the cathode kinetics is estimated as a function of depth of discharge (Figure 1) by comparing the total cell resistance measured by the EIS data in the literature with the area-specific impedance (ASI) predicted by the model. It is seen in Figure 1 that the exchange current density for the cathode kinetics in a Li-S cell increases with depth of discharge (DOD) until 60% where it reaches a maximum. Further increase at DOD results in lower i0,pe. This could be explained by the increasing electronic conductivity of the sulfur cathode at the beginning of the discharge due to the consumption of insulating sulfur. However at higher DODs, the accumulation of the insoluble Li2S at the cathode surface becomes significant, decreasing the charge transfer rate.
Figure 1. Exchange current density for the cathode kinetics predicted by the electrochemical model as a function of depth of discharge.

References

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Figure 1