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A.2 Calculation of specific capacities, energy densities and state of charge One can find many slightly different values for the theoretical volumetric and gravi- metric capacities of various cathode materials in the literature. However, since the specific charge is a fundamental material property, there is only one correct value for each material, which can be derived as follows qmax =z·F·M−1 , (A.1) where z is the change in oxidation state, equal to the number of electrons transferred, M is the molar mass of the species, and F is Faraday’s constant. Values of qmax are reported in Tab. A.2 for several systems. The specific capacity qmax can be calculated for either the charged or discharged state; for a fair comparison of different materials the heavier state should be used, as is reported in Tab. A.2. Contrary to this postula- tion, the specific capacity is often reported as Ah/kgsulfur, not Ah/kgLi2S, in this work. This is a minor compromise to improve comparability with other works; the factor for conversion of Ah/kgsulfur to Ah/kgLi2S is 0.698. The specific charge contained in a battery electrode q ̃max equals q ̃max = qmax · mactive material · m−1 , (A.2) where mactive material and melectrode are the total mass of the active material and the entire electrode, respectively. Because qmax is a fundamental property of each material, it is useful to compare different materials, especially from a theoretical point of view. On the other hand, q ̃max takes the composition of the electrode into account and is therefore more popular among experimentalists, because of its technological relevance. ̃ Finally, there is q ̃max, which is based on the system’s weight – a figure popular among ̃ engineers. Of course, q ̃max < q ̃max ≤ qmax always holds. While the capacity of a cell depends on the oxidation state of the active material, the specific energy depends on the standard Gibbs free energy of reaction ∆G: wmax = ∆G · M−1 . (A.3) Again, the value may also be expressed in units of electrode weight w ̃max or system ̃ weight w ̃max. In contrast, the specific energy is determined experimentally by integrat- ing the charge density times the voltage at which it is extracted: 146 wexp = ˆ q=0 q=qmax E (q) dq . (A.4) electrodePDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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