Mechanistic Understanding of Physical Processes in Lithium-Sulfur Batteries through Experiments and Modeling
Authors: Dai Yiling , Wang Jing-Yang , Ai Guo , Liu Gao , Srinivasan Venkat 
Published: February 2020

Lithium-Sulfur (Li-S) batteries are very promising as next-generation high-energy and low-cost energy storage devices for electric vehicle and stationary applications. However, Li-S batteries presently suffer from low cyclability, low sulfur utilization and high self-discharge. A better understanding of physical processes in Li-S batteries is critical and necessary to improving performance. Here, we have combined experimental and modeling efforts to gain better insight into Li-S batteries.
Figure 1 shows first-cycle discharge curves from Li-S coin cells at different C-rates (1C=1680 mAh/g). Comparison of the different discharge curves shows that the difference in the capacity between C-rates stems from the lower plateau rather than higher one. This suggests that the limiting process during discharge at these C-rates is the reduction of short-chain polysulfide (PS) to final solid product. Accordingly, we have performed electrochemical impedance spectroscopy (EIS) to probe the dynamic process corresponding to the lower plateaus of the discharge curves. As shown in Figure 2, the radius of the semi-circle in the EIS grows dramatically at the end of discharge, compared to that at the beginning of discharge. The EIS experiment was repeated in the same solution after cleaning the electrode surface. The EIS spectrum acquired from the cleaned electrode was very close to that at the beginning of discharge, indicating that the effect of change in the Li electrode and the electrolyte, if any, on the EIS spectra is minimal. This also suggests that the discharge process is not limited by chemical reaction, because cleaning the electrode surface should not have any effect on the reaction kinetics. Instead, this suggests that the increasing resistance arises from the formation of passivating film on the electrode surface. Furthermore, we discharged cells containing different concentrations of PS solution, using one of two types of electrodes with different reaction surfaces. Figure 3 shows that the specific capacity obtained using non-porous glassy carbon was much lower than that obtained using porous carbon at all concentrations, due to the limited surface area of glassy carbon. On the other hand, for both types of electrodes, the capacity (proportional to the product of concentration and specific capacity) obtained when using a high concentration solution was higher than that obtained with a low concentration solution. This suggests that transport of redox species through the film could be limiting.
A mathematical model was developed based on the assumption that the transport of PS species through the film is indeed limiting. It was assumed that the film porosity is constant, and that ionic diffusion through the film follows Fick’s law:
∂C/∂t=Deff(∂2C/∂x2)
Deff=Dεbrugg

where D is bulk diffusion coefficient, and brugg is Bruggeman exponent. Good agreement between model and experimental results can be obtained, only if the Bruggeman exponent is dependent on the thickness of the film. This suggests that the film growing process is more complicated than a simple increase in film thickness.
Figure captions:
Figure 1. Rate performance of Li/S batteries.
Figure 2. EIS spectra obtained from Au/Li/Li cell. The EIS spectra were recorded at the beginning of discharge, at the end of discharge (1.5 V), and after cleaning of the discharged electrode surface
Figure 3.Specific capacity as a function of concentration for carbon paper (porous) and glassy carbon (non-porous)

Figure 1