Modeling the Cathode Area to Predict Lithium-Sulfur Battery Performance as a Function of Materials and Cell Design

Beyond lithium-ion batteries have attracted significant attraction recently. The lithium-sulfur (Li-S) battery is perhaps the most commonly investigated example as it has a significantly high theoretical energy density. Furthermore, sulfur, which is the active material in the cathode, is an abundant, cheap, and environmentally friendly material. The design of lithium-sulfur batteries affects the performance significantly; both materials properties, such as the conductivity and surface area of the carbon, and cell design factors, such as the carbon-to-sulfur ratio, electrolyte-to-sulfur ratio, and sulfur loading, play an essential role in the discharge performance of the Li-S batteries.<br/>There is an immense effort to model the electrochemical performance of the Li-S batteries in the literature. However, the importance of defining the electrochemically active cathode area has not been considered in the previous reports. This study offers a one-dimensional model for the Li-S battery projecting the initial discharge profile. In the model, the electrochemically active cathode area is defined in a novel way based on the weight fraction of the carbon in the cathode and a reference porosity. The effect of key materials and cell design parameters on the discharge performance is captured successfully by employing this novel area definition. The results of the model are compared with that of two different models, which use two different electrochemically active area formulas. Furthermore, a mechanistic explanation of the effect of critical design parameters on the battery performance is proposed by investigating the change of the electrochemically active cathode area with carbon properties, carbon-to-sulfur ratio, electrolyte-to-sulfur ratio, and sulfur loading.<br/>The model predictions for the effect of the carbon-to-sulfur ratio on the discharge profile of a Li-S cell present that increasing the carbon-to-sulfur ratio increases the discharge capacity and cell voltage up to a point. However, a further increase in the carbon-to-sulfur ratio does not affect the cell voltage and diminishes the discharge capacity. Considering the experimental findings in the literature, the model successfully predicts the effect of the carbon-to-sulfur ratio on the discharge profile due to the proposed definition of the electrochemically active area. As a result of including a reference porosity in the description of the electrochemically active cathode area in the model, we observe the following trend. The electrochemically active cathode area increases with increasing carbon-to-sulfur ratio up to a point; however, due to the decreasing porosity with increasing carbon-to-sulfur ratio, the increase in the active area stops at high C loadings. This expected trend can only be captured with the proposed cathode area. Similarly, the model successfully projects the impact of electrolyte-to-sulfur ratio and sulfur loading on the discharge behavior of a Li-S cell with the proposed cathode area definition.<br/>The properties of carbon in the cathode have a determinative influence on the discharge performance of the Li-S battery. The offered model can successfully capture the impact of both the carbon surface area and electronic conductivity on the discharge behavior. The carbon surface area controls the electrochemically active area in the model; consequently, the predicted discharge capacities are highly sensitive to this property.<br/><br/><b>Acknowledgments </b><br/>Busra Abdulkadiroglu acknowledges support from the Scientific and Technological Research Council of Turkey (TUBITAK) 2209-A National/International Research Projects Fellowship Programme for Undergraduate Students, Application No: 1919B012000712.