A Mathematical Model for All Solid-State Lithium Ion Batteries

We present a new model for all solid-state lithium ion batteries that takes into account detailed aspects of ion transport in solid solutions of crystalline metal oxides. More precisely, our model describes transient lithium ion flux through a solid electrolyte, the solid-solid interfaces and an intercalation electrode. The diffuse part of the double layer is dynamically described via the Poisson equation, while the Stern layer potential drop is modeled by a Robin boundary condition. Electrochemical reactions on the electrode/electrolyte interface are modeled via non-linear Neumann boundary conditions. After a detailed derivation of the model equations and boundary conditions, numerical results are presented and discussed.