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5.5.4 Microstructure Since the model does not include an explicit description of the microstructure, the following section is rather short. The composition of the cell was already analyzed in section 5.5.2 above. Besides the trivial expressions in Eqs. (4.24) and (4.25), represent- ing the S8|electrolyte and Li2S|electrolyte interfaces, there is only one feature in the model dealing with the microstructure: the formation of a passivating Li2S film on the positive electrode’s carbon matrix. This film is studied in Fig. 5.27. Once Li2S starts to precipitate, the film grows almost linearly with time, reaching close to 10 nm at the end of discharge. This nicely matches the experimental findings presented in Fig. 3.8d on page 43. The film thickness cannot be measured directly in the SEM images, but it can be estimated: The smallest structures visible in the electrode without the film (Fig. 3.8c) are about 20 nm across. After deposition of the film, the smallest structures are about 100 nm in size. This means that the precipitated Li2S can fill gaps of several tens of nanometers, but not hundreds. Therefore, a thickness 10 nm, as suggested by the simulations, is within the right order of magnitude. In contrast to the film thickness, its resistivity does not grow initially, but remains very small as long as the film is thinner than the threshold set by ξ2 in Eq. (4.26). Beyond that value, the resistivity increases sharply, causing a correspondingly high overpotential toward the end of discharge. 15 1000 800 film thickness (left axis) film resistivity (right axis) ξ2 threshold 10 5 600 400 200 00 0 50 100 150 200 250 Capacity / Ah/kgS Figure 5.27: Thickness of the Li2S film on the carbon matrix in the positive electrode and corresponding resistivity during a C/20 discharge. 128 Film thickness / nm Film resistivity / Ω · mPDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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