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4 1 0.4 1 ms 1 s 1 h 1 year Time / h Figure 5.10: Initial equilibration. Time trace of a simulation with itot = 0 (in the fully charged state). For selected quantities, the relative deviation from the final values is reported. The latter are considered to be the true equilibrium values and are used as a starting point for subsequent simulations. of this simulation are used as the starting values for all subsequent simulations of the same cell. The actual equilibration run is presented in Fig. 5.10. 5.3.4 Parameters fitted to experimental data After making use of all known independent sources, many parameters are still un- known. In total, there are 26 parameters left, including the Gibbs free energy of formation of solvated species in the electrolyte ∆g0, ten diffusion constants, and ten forward reaction rate constants as well as ξ1 and ξ2 in the expression for the surface resistivity, Eq. (4.26), and finally, the fraction of activated Li2S. These parameters need to be fitted to experimental data, which will be discussed in the following. Originally, it was planned to fit several parameters at once using a multidimensional optimization algorithm, cf. section 4.30. Because of the large number of parameters to be fitted on the one hand as well as the very different types of reference data on the other hand (single data points, sets of data points, x-y-curves, parameters of a family of curves), this turned out to be a futile approach. Instead, the parameters were grouped and each group was adjusted manually within a reasonable range. In the following, the fitting results are complemented by parameter variation plots and corresponding discussions. In all plots, circles represent experimental data, lines simulation results. cell voltage cLi+ cS8 cS2− 8 εS8 107 Relative deviation from equilibriumPDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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