Galilean Bulk-Surface Electrothermodynamics and Applications to Electrochemistry.

In this work, the balance equations of non-equilibrium thermodynamics are coupled to Galilean limit systems of the Maxwell equations, i.e., either to (i) the quasi-electrostatic limit or (ii) the quasi-magnetostatic limit. We explicitly consider a volume Ω, which is divided into Ω+ and Ω- by a possibly moving singular surface S, where a charged reacting mixture of a viscous medium can be present on each geometrical entity (Ω+,S,Ω-). By the restriction to the Galilean limits of the Maxwell equations, we achieve that only subsystems of equations for matter and electromagnetic fields are coupled that share identical transformation properties with respect to observer transformations. Moreover, the application of an entropy principle becomes more straightforward and finally helps estimate the limitations of the more general approach based the full set of Maxwell equations. Constitutive relations are provided based on an entropy principle, and particular care is taken in the analysis of the stress tensor and the momentum balance in the general case of non-constant scalar susceptibility. Finally, we summarise the application of the derived model framework to an electrochemical system with surface reactions.

Mathematical modeling of intercalation batteries at the cell level and beyond.

Mathematical modeling of lithium ion batteries is a key feature for a profound understanding of the whole spectrum of phenomena occurring in such electrochemical systems. Due to their inherent multi-scale nature, batteries cannot be described with a single equation. It is necessary to couple the physical chemistry, reaction kinetics, ion flow, heat generation, et cetera, appropriately to obtain a coupled set of equations (a model) which has predictive efficiency. To adapt ideas and expertise obtained in the field of modeling to future type of batteries, new electrode or electrolyte materials or to improve the model reliability, a universal basis is desirable. In this sense, we carefully derive the commonly used set of equations based on the most general form of linear non-equilibrium thermodynamics. Due to chemical and physical assumptions the set of equations is reduced to facilitate numerical computations. Transport equations for a general electrolyte are derived and different electroneutrality assumptions are applied to obtain Poisson-Nernst-Planck-type equations or a generalized Ohmic law. Electrodes are described with single and many particle models, e.g. for phase separating materials, and the transition to porous electrode theory is given. A mathematical treatment of the intercalation reaction is finally presented, based on surface charge densities and electrode potentials.

An advanced model framework for solid electrolyte intercalation batteries.

Recent developments of solid electrolytes, especially lithium ion conductors, led to all solid state batteries for various applications. In addition, mathematical models sprout for different electrode materials and battery types, but are missing for solid electrolyte cells. We present a mathematical model for ion flux in solid electrolytes, based on non-equilibrium thermodynamics and functional derivatives. Intercalated ion diffusion within the electrodes is further considered, allowing the computation of the ion concentration at the electrode/electrolyte interface. A generalized Frumkin-Butler-Volmer equation describes the kinetics of (de-)intercalation reactions and is here extended to non-blocking electrodes. Using this approach, numerical simulations were carried out to investigate the space charge region at the interface. Finally, discharge simulations were performed to study different limitations of an all solid state battery cell.