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4.2.4 Electrical properties Next, the relationship of the cell’s electrical properties to the chemistry explained above is presented. Since electrons are treated as yet another species (with zero mass), the Faradaic current density iFV in a CV follows directly from reaction kinetics. More precisely, it can be obtained by summing up the electrons produced or consumed at all interfaces: iFV = ∑FAVms ̇electron,m . (4.14) m ”Free” electrons only exist in the electronically conductive materials, which are as- sumed to be in perfect contact with the current collector. The total, externally detected current density is defined as ˆ LCA|AN V V iF+idl dy, (4.15) where LCA|AN is the thickness of the cathode or anode, iFV is the Faradaic, and idVl the double-layer current source term in the CV, which in turn is calculated as iV = AVC ∂(∆φ), (4.16) itot= y=0 dl m dl,m ∂t with Cdl, m being a constant, area-specific capacity of the interface and ∆φ the potential step defined as in Eq. (4.9). Several different effects contribute to the double-layer capacity Cdl,m, see e.g. [213]. Nevertheless, it can be safely treated in this simplified fashion since the influence of its properties besides the amount of capacity are only relevant at time scales much shorter than those studied in this work. Note that in Eqs. (4.15) and (4.16) both electrodes must be considered for the double-layer current as well as for the integration of the local current densities. Per definition, the resulting value of itot is positive while discharging and negative while charging. The total cell voltage E is simply defined as the potential difference between the cathode’s and anode’s conductive bulk material (which are carbon and lithium metal, respectively): E = φCA, elde − φAN, elde . (4.17) At rest, this voltage is identical to the OCV, i.e. the equilibrium Nernst voltage of the electrochemical system [214]. Unlike the potential of the electrolyte φelyte, which is calculated for each CV, φelde is the same for all CVs within one electrode and thus just represented by a number each. Physically, this means that the Ohmic drop due to the electric resistivity within the electrode is negligible. Optionally, however, an 77PDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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