Summary A 1D model is developed for the Li‐S cell to predict the effect of critical cathode design parameters—carbon‐to‐sulfur (C/S) and electrolyte‐to‐sulfur (E/S) ratios in the cathode—on the electrochemical performance. Cell voltage at 60% depth of discharge corresponding to the lower voltage plateau is used as a metric for calculating the cell performance. The cathode kinetics in the lower voltage plateau is defined with a single electrochemical reaction; thus, the model has a single apparent kinetic model parameter, the cathode exchange current density (i0,pe). The model predicts that cell voltage increases considerably with increasing carbon content until a C/S ratio of 1 is attained, whereas the enhancement in the cell voltage at higher ratios is less obvious. The model can capture the effect of the C/S ratio on the cathode kinetics by expressing the electrochemically active area in the cathode in carbon volume fraction; the C/S ratio in the cathode does not affect i0,pe in the model. On the other hand, the electrolyte amount has a significant impact on the kinetic model parameter such that increasing electrolyte amount improves the cell voltage as a result of increasing i0,pe. Therefore, in the model, i0,pe needs to be defined as a function of the electrolyte volume fraction, which is known to have a crucial effect on reaction kinetics.

Summary Lithium‐sulfur batteries have attracted much research interest because of their high theoretical energy density and low‐cost raw materials. While the electrodes are composed of readily available materials, the processes that occur within the cell are complex, and the electrochemical performance of these batteries is very sensitive to a number of cell processing parameters. Herein, a simple electrochemical model will be used to predict, with quantitative agreement, the electrochemical properties of lithium‐sulfur cathodes with varying carbon to sulfur ratios. The discharge capacity and the polarization were very similar for the lowest sulfur loadings, while above 23.2 wt% sulfur the gravimetric capacity dropped significantly, and there was an increase in the cell polarization. In addition, a transition in the electrode morphology, from well dispersed to aggregated sulfur at the surface, will be reflected in the change in a critical model parameter demonstrating the sensitivity and functionality of even this simple model in predicting complex behavior in the lithium‐sulfur cells.

In lithium-sulfur (Li-S) batteries, the discharge performance depends greatly on a number of cell design parameters because of the complex reaction mechanisms in the cathode. Electrolyte-to-sulfur (E/S) ratio and carbon-to-sulfur (C/S) ratio in the cell are key examples of these critical design factors that define the Li-S battery performance. Here, a 1-D electrochemical model is reported to calculate the dependence of the discharge behavior of a Li-S battery on the E/S and C/S ratios. Proposed model describes the complex kinetics through two electrochemical and two dissolution/precipitation reactions. Concentration variations in the cathode are also taken into account in the model. Characteristic aspects of the discharge profile of a Li-S battery-the two distinct voltage plateaus and the voltage dip in between-are captured in the predicted voltage curve. Similar trends on the discharge performance of the Li-S cell with varying E/S and C/S ratios are projected; both voltage and discharge capacity of the Li-S battery are improved substantially with increasing C/S or E/S ratio up to a certain point, whereas, the dependence of the discharge performance on these factors is less substantial at higher ratios. This model offers a mechanistic interpretation of the influence of cell design on the Li-S battery performance.

Lithium-Sulfur (Li-S) batteries are one of the most promising energy storage systems beyond Li-ion batteries because of the high specific capacity (1675 mAh/g), low cost, natural abundance and non-toxicity of sulfur [1-3]. Although Li-S batteries have many attractive characteristics, they are facing major problems that are required to be solved to improve the cycle life and capacity retention; the precipitation of the insulating solids on the cathode (S, Li2S), infinite charging due to the polysulfide shuttle mechanism and the instability of the lithium anode [1-3]. Carbon to sulfur ratio in the cathode is one of the most critical design parameters in a Li-S battery [1-3]. Because of the insulating nature of both S and Li2S, Li-S cathodes typically require high C:S ratios [1-3]. As this ratio increases, cathode kinetics are improved due to an enhancement in both electronic conductivity and active surface area. However, techno-economic model predictions in a previous study show that too much increase in the C:S ratio results in a significant decrease at the system-level energy density [1]. Therefore, thoughtful selection of the C:S ratio in the cathode is critical to achieve high-energy density Li-S batteries. In this study, the effect of carbon to sulfur ratio in the cathode on the electrochemical performance of a Li-S cell is modeled. For this purpose, a one-dimensional, concentration-independent electrochemical model for an isothermal, constant-current discharge of a Li-S cell is developed based on a previous model [1, 4]. In the model, the current-voltage relationship is predicted using Butler-Volmer kinetics in the anode, Ohm’s Law in the porous separator and the porous electrode model by Newman and Tobias in the cathode [5]. The effect of C:S ratio in the cathode on the electrochemical performance is investigated at 60% depth of discharge by feeding the model with the experimental cell design parameters from the literature (i.e. carbon to sulfur ratio and electrolyte to sulfur ratio in the cathode, anode, separator and cathode thicknesses and current density in references [2, 3]). Consequently, cell voltage at 60% DOD for different C:S ratios are predicted by the model proposed and compared with the experimental data. Cell voltage at 60% DOD predicted by the model as a function of C:S ratio for two different current densities is shown in Figure 1. It can be seen that the cell voltage increases significantly with increasing C:S ratio, especially up to a C:S ratio of 1. Further increase in the carbon content leads to a less apparent increase in the cell voltage for both current densities. This may suggest that the cell is limited by the kinetics at C:S ratios lower than 1 whereas the improvement on the cathode kinetics is less significant at higher ratios. The model predictions are also validated with the experimental data [2] as shown in the figure. It is clear that the model predictions show close agreement with the experimental data. Figure 1. The effect of C:S ratio in the cathode on the cell voltage at 60% DOD predicted by the model for two different Li-S cell designs [2, 3]. The comparison of the model predictions with the experimental data [2] is also presented. References [1] Eroglu D., Zavadil K.R., Gallagher K.G., J. Electrochem. Soc., 162 (6), A982-A990 (2015). [2] Xu R., Li J.C., Lu J., Amine K., Belharouak I., Journal of Materials Chemistry A, 3(8), 4170-4179 (2015). [3] Ding N., Chien S.W., Hor T.A., Liu Z., Zong Y., Journal of Power Sources, 269, 111-116 (2014). [4] Erensoy S.C., Eroglu D., Meeting Abstracts. No. 5. The Electrochemical Society, (2016). [5] Newman J.S., Tobias C.W., Journal of The Electrochemical Society, 109 (12), 1183-1191 (1962). Figure 1