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a galvanostatic discharge. When looking at the total amount of sulfur present in the cell (black line), this relation is perfectly fulfilled. The colored lines, however, which represent the amount of sulfur at various positions in the cell, do not follow the same pattern. The closer a control volume (CV) is to the negative electrode, the faster the conversion of sulfur in that CV. Close to the separator, the electrode is devoid of solid sulfur long before the end of discharge. 0.5 0.4 0.3 0.2 0.1 0.0 total 40 μm 35 μm 30 μm 25 μm 20 μm 15 μm 10 μm 5μm 0 5 10 15 20 Time / h Figure 5.2: Changes in the distribution of solid sulfur during one cycle. Colors denote the position in the electrode: 0 μm = separator; 40 μm = current collector. When charging, the situation is reversed: the region closer to the separator is recharged more quickly. This process is not perfectly balanced, however, so that the distributions of S8 and Li2S across the cell are slightly different after each cycle. The effect adds up over time, leading to an increasingly non-uniform composition of the cell. Due to the diffusion overpotential, the local electrochemical potential depends on the position in the positive electrode. Because of this and the sulfur redistribu- tion, a slightly higher voltage is needed each cycle to access all the sulfur deposited in the previous cycle. When using a standard cycling protocol that enforces a constant charge/discharge cutoff voltage, the sulfur utilization is decreased during each cycle. This can be best observed when looking at the average volume fractions of active mate- rial plotted over time, see Fig. 5.3. The utilization of active material decreases rapidly, causing faster, but more shallow cycling. Since there is no physical or chemical mechanism in this model which could cause irreversible degradation, the effect discussed above is naturally reversible. While less and less material is cycled over time, none of the S8 or Li2S is actually lost. Running a 93 Sulfur volume fractionPDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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