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5.3.2 Parameters calculated from experimental data Many parameters can be obtained from the experimental setup and results, either because they can – at least in principle – be chosen freely within reasonable constraints or because they can be easily measured, extracted, or calculated from the experimental results. All the macroscopic geometric parameters, the choice of materials, and the electrode composition fall into this category. A full list can be found in Tab. 5.1. In addition, the following parameters are readily extracted from experimental data: • Volume fractions of all solids in the electrodes are calculated from the volume of the electrode, the known composition of solids (see Tab. 5.1), and their densities. In the (hypothetical) fully charged state they are for the positive electrode: 12.1 % for S8, 0.0 % for Li2S, 3.2 % for total carbon, 2.8 % for the binder, 70.9 % for the liq- uid electrolyte. The remaining 10.0 % are filled with non-reactive, compressible Argon gas in the model, as discussed in section 4.2.6 on page 81. • The concentration of the LiTFSI conducting salt is 1.0 mol · l−1; that of the LiNO3 additive is 0.5 mol · l−1 according to the standard recipe, cf. section 2.3.3. • The total surface area of the active material can be derived assuming that all ball-milled Li2S particles are spherical with an average diameter of 1.1μm (cf. section 3.1). Their total surface area is calculated to be 1.20 · 106 m2 · m−3. Further assuming that the number of particles does not change when the material is converted to S8, the surface area of all sulfur particles is 1.40 · 106 m2 · m−3. • The electrochemically active surface area, i.e. the carbon|electrolyte interface, was measured to be 1.1 · 107 m2 · m−3 in Ref. [P4] by Krypton BET. Since the electrodes used for this work are very similar in carbon content and structure, the same value is used here. • The radius of the carbon black particles in Eq. (4.27) is estimated to be 40 nm based on SEM images (see e.g. Fig. 3.1b). 5.3.3 Parameters determined by equilibration More parameters can be determined without fitting by making smart use of the model: Only the composition of solids is known from experiments, not the composition of the electrolyte. The equilibrium concentrations of dissolved species, however, are readily obtained by simulating a cell at rest for a long time. Starting with volume fractions derived from the composition of the solid material (see Tab. 5.1) and an electrolyte with virtually no dissolved polysulfides, a simulation is run with itot = 0 for t = 109 s (several years). After this time, the cell is perfectly equilibrated and the final values 106PDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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