Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling

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Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling ( lithium-sulfur-battery-design-characterization-and-physicall )

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4 Modeling the lithium-sulfur battery – theory and methods 4.1 Background Modeling has become an established, if not essential part of the toolset of electrochem- ical analysis methods. Not only can it save considerable cost and time in the research and development of batteries, but also it enables a more profound understanding than possible by mere experimentation. Therefore, modeling has penetrated all aspects of battery development and design, ranging from system layout to atomistic reaction kinetics [178], see also Fig. 4.1. Small-scale models typically perform ab initio calcu- lations, which make use of quantum mechanics and fundamental physical constants to determine parameters of materials and reactions without experimental input [179]. Despite some simplifying assumptions, this approach is computationally very inten- sive and thus limited by the size of the system (typically to a few dozen atoms). It needs to be complimented by other techniques, e.g. Monte-Carlo simulations, in order to bridge the gap to electrochemical applications [180, 181]. Large scale, system level simulations on the other hand mostly use an equivalent circuit [91] or black box rep- resentation of the battery, which is described by an entirely empirical set of equations, see e.g. Ref. [182]. This approach is computationally inexpensive to the point where the algorithms can be implemented in real-time, embedded battery management sys- tems [183–185]. With regard to the electrochemistry, however, the insight which can be gained by using such a model is very limited as is its extent of validity [186, 187]. An overview of the different types of models can be found in Ref. [188]. For this work, an intermediate level is chosen both in terms of scale and computational complexity: A physically-based continuum approach is taken to model the membrane-electrode assembly (MEA) of the cell in detail. The system is determined by a set of differential algebraic equations describing physical processes such as reaction kinetics, transport, or the evolution of phases on a length scale larger than individual structural details of the electrodes, which is why this type of model is often referred to as continuum model. 68

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