Kontinuumsbasierte Modellierung elektrochemomechanischer Phänomene durch einen Variationsansatz mit Anwendung auf Feststoffbatterien
Mathematik
Mechanische Eigenschaften von metallischen Werkstoffen und ihre mikrostrukturellen Ursachen
Theoretische Chemie: Moleküle, Materialien, Oberflächen
Thermodynamik und Kinetik sowie Eigenschaften der Phasen und Gefüge von Werkstoffen
Zusammenfassung der Projektergebnisse
Within the present project, a “generic” variational formulation for the thermodynamically consistent continuum modeling of a wide range of dissipative isothermal multiphysics phenomena has been examined. This formulation is based on the notion of standard dissipative media, supplemented by a careful distinction between the thermodynamic state of the system under consideration and the processes changing this state. Starting from a space-time continuous formulation, a space-time discrete counterpart has been obtained. For this purpose, the finite element method is used for spatial discretization, while finite difference based schemes are used for temporal discretization. Regarding the latter, a novel method has been devised, which is second order accurate and simultaneously preserves the symmetry of the finite element systems. Utilizing the finite element code deal.II, the formulation has been implemented into program code, which is freely available (libraries GalerkinTools and IncrementalFE). The general approach has been specialized to the modeling of electrochemomechanically coupled phenomena in all solid state lithium ion batteries (ASSLBs). In a first step, the influence of space charge accumulation in solid electrolytes has been examined. Contrary to recent literature results, it was found that space charge layers are likely to be nanometer sized. As a consequence, they cannot be explicitly accounted for in continuum models and must rather be ignored or taken into account by suitable interface terms. Consistent with this finding, the socalled local electroneutrality condition has been imposed for three-dimensional finite element computations of charging-discharging cycles of battery cells conducted subsequently. The latter simulations included representations of the electrodes and the separator of a battery on the microstructural level and have been used to demonstrate the efficiency and robustness of the formulation. Finally, the extensibility of the approach with regard to the incorporation of additional physical effects has been exemplified by replacing the single ion conducting inorganic solid electrolyte considered originally by a binary salt polymer electrolyte, with finite deformations of the polymer and dissociation of the salt explicitly taken into account. The generality of the variational approach has further been demonstrated by considering the modeling of hydrogels. In this regard, an existing porous media formulation has been successfully reformulated within the variational framework. However, a thorough investigation indicated that the model is unable to describe the bending of hydrogels in electric fields if realistic material parameters are used. In order to remedy this issue, an extended model has been devised. This model explicitly accounts for (i) a solution bath surrounding the hydrogel, (ii) fluid-structure interaction in a large deformation setting, (iii) advection of ionic species in the solution bath, (iv) dissociation of water, (v) dissociation of the ionic groups fixed to the hydrogel, and (vi) electrolysis reactions at electrodes attached to the solution bath, thus extending the state of the art of the modeling of hydrogels in several respects. In summary, a unified continuum based variational framework has been considered, which can be used in the future for systematic studies of the properties of ASSLBs and the optimization of their properties. Due to the generality of the formulation, its application is however not limited to ASSLBs, as demonstrated by the modeling of the behavior of hydrogels.
