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physicochemical model, including detailed chemistry and transport, without the use of equivalent circuits [191]. 4.3.2 Parametrization and validation techniques This section deals with the third step of the modeling process as defined on page 69: the determination of the parameters introduced by the previously discussed governing equations. From a theoretical point of view, there are three kinds of parameters: a) those which are ultimately based on natural constants and for which only one true value exists, e.g. the diffusion coefficient of Li+ in a certain solvent or the enthalpy of formation of Li2S, b) those which define morphological or technical properties, e.g. the porosity or the discharge current, and may take any (reasonable) value, and c) parameters that are not part of the physical description itself, such as the size of a control volume or the solver tolerances. In principle, parameters in group a) can be looked up or determined by independent measurements, those in group b) need to match the conditions of a given experiment and those in group c) just need to be set “right”, i.e. in a way that the simulation results do not heavily depend on the value chosen, cf. section 4.3.3. From a practical point of view, however, it makes sense to group the parameters differently, to be specific: according to their source. The model needs lots of input to determine all parameters and thus one has to make use of every possible independent source. Three categories can be formed which do not necessarily correlate with those mentioned above: i) parameters known from literature with sufficient accuracy. This includes dedi- cated scientific measurements as collected in the CRC handbook [238], but also other modeling efforts, e.g. of 3D-resovled microstructures [239] or ab initio calculations [143]. ii) parameters determined from dedicated experiments. This includes trivial param- eters such as the dimensions and composition of the electrodes, but also more complex ones like the conductivity of the liquid electrolyte including all dissolved ions. Often, the parameters detected experimentally are not exactly the ones that are required as input by the model. In such cases, the relationship of the parameters needs to be analyzed to establish a rule for conversion. iii) fitted parameters. For statistical reasons, this category should be kept as small as reasonably possible [240, chap. 8]. Since the model’s behavior is strongly prede- termined by the governing equations, its parametrization is not to be confused with a polynomial fit. Still, fitting too many free parameters significantly reduces the ex- planatory power of the model. Also, finding the optimal set of parameters becomes more and more difficult as the number of parameters increases [240, chap. 8.2]. In 87PDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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