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with internal self-discharge. Therefore, the slowest regular cycling data (with a dis- charge rate of C/50 and a charge rate of C/20) was used for the calibration of the offset in Fig. 5.13. The best fit is obtained for ∆g0 = 220 kJ · mol−1. Because of the different charge and discharge rates in the reference data, the calibration is difficult and even the best result looks slightly off-center. Diffusion constants. Diffusion constants for different species are expected to be dif- ferent in reality. Unfortunately, in the literature there is no direct measurement or even a clue to the values of Dn for all dissolved species n. The values chosen by Refs. [196, 198, 199] may serve as guidance values. However, they lack experimental references themselves and are assumed for different electrolytes. To handle this situ- ation, all ten diffusion constants are assumed identical so that only one value needs to be fitted. In this study, the diffusion constants are varied in the range of 10−10– 10−12 m2 · s−1, which has been reported for ionic liquid based electrolytes [175, 261] and compared with cycling and impedance data in Figs. 5.14 and 5.15, respectively. While the impact of the speed of diffusion is obvious in general, it is difficult to quantitatively distinguish between the data sets with smaller diffusion constants in Fig. 5.14. Therefore, impedance spectra are analyzed additionally. More precisely, the high-frequency intercept of the spectra with the x-axis is evaluated. This feature is related to the electrolyte’s ionic conductivity, which in turn depends on the diffusion constants according to Eqs. (4.3) and (4.4). EIS results are presented in Fig. 5.15. Note that the shape of the Nyquist plots does not match very well since the reaction rates are not yet calibrated. The effect of the diffusion constants on the Z′ intercept is clearly visible. While there is a lot of variation in the reference data (cf. section 3.2.4), the plot still shows a clear trend and the diffusion constants can be calibrated to at least the right order of magnitude much more easily than on the basis of discharge profiles. The best agreement is obtained for Deff = 1.0 · 10−11 m2 · s−1. 111PDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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