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Multi-step reaction mechanism. To overcome the limitations of the global mecha- nism, two modifications are needed: First, lithium sulfide needs to be allowed to dis- solve into and precipitate from the liquid electrolyte. Second, a more detailed imple- mentation of the sulfur redox chemistry is needed. Ref. [192] discusses why there need to be at least three electrochemical reduction steps to reproduce the two-plateau dis- charge profile often detected experimentally. Various publications, however, suggest that there are at more or different intermediate steps, see e.g. Refs. [138, 142, 220, 221]. Our multi-step reaction mechanism consists of a linear chain of reactions involving several dissolved polysulfide intermediates: (4.23) S8(s) S8(ds) 1/2S +e− 1/2S2− 8(ds) 8 3/2S2−+e− 2S2− 86 S2− + e− 3/2 S2− 64 1/2S2−+e− S2− 42 1/2S2−+e− S2− 2 S2− + 2 Li+ Li2S(s) Opposed to the mechanism presented in [196], the only solid products in the cell are sulfur and lithium sulfide, which is backed by X-ray diffraction and transmission X-ray microscopy studies [155, 156]. Surface areas are modeled to depend on the solid phases as ε 32 AVS8|elyte = S8 , and (4.24) (4.25) V ALi2S|elyte = ε0,S8 εLi2S 32 . ε0,Li2S Here, ε0, n denotes the reference volume fraction of a phase, equal to either the initial or the maximum value of εn. These expressions represent as the surfaces of homoge- neously expanding and shrinking particles. Since the initial volume fraction of Li2S in the charged state is very low, this naturally generates a situation where particle growth of Li2S is severely inhibited due to the very small AVLi2S|elyte until a certain amount of Li2S is precipitated. This can be interpreted as an implicit, yet effective implementation of a nucleation phenomenon. Multi-step reaction mechanism, revised. In order to reproduce experimental results more faithfully, a revised version of the multi-step model was prepared. Besides a rigorous reparametrization, described in section 5.3, two new phases are introduced: 81PDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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