Lithium–sulfur batteries (LSBs) have attracted attention due to their high theoretical energy density. This and various other advantages, such as the availability and non-toxicity of sulfur, raise interest in LSBs against the background of the energy revolution. However, a polysulfide shuttle mechanism can adversely affect the electrochemical performance of the cell. The sulfur redox properties are influenced, for example, by the electrolyte and the cathode material. Here, a computational study of the discharge process of an LSB with sulfurized poly(acrylonitrile) (SPAN) as the cathode material in combination with a carbonate electrolyte is presented. The nucleation of produced solid Li₂S is compared to soluble Li₂S. Dominating species are determined by comparing the Gibbs free energy of several species. We found that multiple lithiation steps occur before each Li₂S detachment, preventing longer-chain polysulfide cleavage and a polysulfide shuttle. Through nucleating on the nitrogen-rich backbone of SPAN, Li₂S units are stabilized by interactions with each other and with the nitrogen atoms. Experimental data show a potential drop and plateau during discharge, which is consistent with the calculated discharge profiles of SPAN with both soluble and nucleated Li₂S, and hints at a direct solid–solid transition in the Li-SPAN cell during discharge when using carbonate-based electrolytes.