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since it does not affect either the transport in the electrolyte or the electrochemistry. A detailed, fully consistent treatment of Eq. (4.21) would require the introduction of convection in the model as proposed in Ref. [216] as well as a description of mechanical stress in the electrode’s particles as proposed in Refs. [217–219]. The special case, where the gaseous phase becomes zero in a CV receives no special treatment, since it did never occur in any simulation reported here. However, if no gaseous phase is considered at all, e.g. for the global model, Eq. (4.21) is enforced by adjusting the volume fraction of the liquid electrolyte εelyte to fill the remaining space in each CV. Since there is no convection in the liquid electrolyte (cf. section 4.2.2), no material may enter or leave the CV and hence the number of molecules in the electrolyte phase remains constant. If the solid phases grow, this causes a compression of the electrolyte, resulting in an increase of the concentrations of all species (including the solvent’s). Considering the low compressibility of liquids, this assumption may not seem justified at a first glace. However, the pressure itself is not considered in this model and the resulting concentrations quickly equilibrate with the neighboring compartments by means of diffusion. Once the volume fractions are determined, they can be used to calculate specific surface areas of each interface m according to AVm = AVm εp (4.22) and, in the case of the liquid electrolyte, effective diffusion coefficients Dn,eff of all dissolved species according to Eq. (4.4). This way, a feedback of the volume fractions in each CV on the chemical kinetics and transport is established. The functional relation of AVm and the volume fractions represents the electrode’s geometry, e.g. AVm = const. for a film, AVm ∝ ε3/2 for an electrode consisting of spherical particles which grow or shrink at the same rate, or AVm ∝ ε for particles which are consumed one after the other. As required, these expressions may be modified to include additional effects such as explicit nucleation or surface passivation. 4.2.6 Reaction mechanisms Once the governing equations are defined, one still needs to plug in a reaction mech- anism. The requirements for this mechanism are rather simple: It needs to provide at least one reaction generating or consuming electrons and one reaction generating or consuming dissolved ions in the liquid electrolyte at both the cathode and anode side. In this work, two different reaction mechanisms will be discussed. Both share the same reaction at the negative electrode, 79PDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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