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existing implementations of Li/S models shall be discussed. The selection presented here is strictly limited to Li/S continuum models. A rigorous derivation of nonequi- librium thermodynamics of porous electrodes can be found in Ref. [193]; a more com- prehensive overview of battery modeling literature can be found in Refs. [188] or [194, chap. 2.5]. Despite this restriction, there are several noteworthy works whose achieve- ments (and shortcomings) shall be analyzed in the following. One of the early protagonists in the recent advancement of Li/S batteries is Sion Power Corporation [45], which started developing a model of the Li/S cell as early as 2003 [51]. In this model, the chemistry of the cell is described by only two electro- chemical reactions, implemented as a Nernst equation each. Only during charging, the polysulfide shuttle is described by one additional phenomenological parameter, the so-called shuttle constant ks, which is in effect a measure of the speed of the reac- tions responsible for the shuttle relative to the charge/discharge reactions. This rather simple zero-dimensional model does not include any description of transport, double- layer capacity, or phase changes and only a very simple temperature dependence. In a joint project of the same company with the group of R. E. White at the University of South Carolina, a more detailed model was developed in 2007 [195, 196]. This model is, by design, similar to the work presented here. It differs, however, at the choice of processes to be included in the model as well as at the formulation of the governing equations. It does include a physically-based one-dimensional description of the transport in the liquid electrolyte as well as electrochemical reactions among the dissolved polysulfides and the evolution of phases. However, the model does not treat the negative electrode explicitly, but just as a boundary condition (a source of Li+ ions). For this reason, the model cannot accommodate processes like the polysulfide shuttle or degradation mechanisms, which require additional chemical reactions at the lithium electrode. Also, the model does not include a description of the Helmholtz double layer nor a sophisticated representation of the electrodes’ microstructure. It does not include any side or disproportionation reactions and the publications do not report anything on the impedance of the cell, the charging process, cycling, or degradation. Finally, the end of discharge cannot be explained conclusively. Nevertheless, Ref. [197] rightfully states that this is the first reasonably complete model of the Li/S cell. Only recently (2014), another effort was started to model the Li/S cell by the group of P. Chen at the University of Waterloo [198, 199]. This model is conceptually very similar to the model presented in [196]. In fact, only a few parameters were chosen dif- ferently. Instead of advancing the model itself, the merit of this two-part publication is that it presents lots of simulation results, including a rather comprehensive sensitivity analysis of the model. Unfortunately, the report is still limited to the discharge only. A third part was announced, but never published. 70PDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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