A zero dimensional model of lithium–sulfur batteries during charge and discharge

Lithium–sulfur cells present an attractive alternative to Li-ion batteries due to their large energy density, safety, and possible low cost. Their successful commercialisation is dependent on improving their performance, but also on acquiring sufficient understanding of the underlying mechanisms to allow for the development of predictive models for operational cells. To address the latter, we present a zero dimensional model that predicts many of the features observed in the behaviour of a lithium–sulfur cell during charge and discharge. The model accounts for two electrochemical reactions via the Nernst formulation, power limitations through Butler–Volmer kinetics, and precipitation/dissolution of one species, including nucleation. It is shown that the flat shape of the low voltage plateau typical of the lithium–sulfur cell discharge is caused by precipitation. During charge, it is predicted that the dissolution can act as a bottleneck, because for large enough currents the amount that dissolves becomes limited. This results in reduced charge capacity and an earlier onset of the high plateau reaction, such that the two voltage plateaus merge. By including these effects, the model improves on the existing zero dimensional models, while requiring considerably fewer input parameters and computational resources than one dimensional models. The model also predicts that, due to precipitation, the customary way of experimentally obtaining the open circuit voltage from a low rate discharge might not be suitable for lithium–sulfur. This model can provide the basis for mechanistic studies, identification of dominant effects in a real cell, predictions of operational behaviour under realistic loads, and control algorithms for applications.