Solid state batteries are gaining increasing attention due to their potential for high energy densities and their enhanced safety properties when using a solid electrolyte separator with a metal anode such as Lithium or Sodium. The solid electrolyte can be designed as a single ion conductor or as a solid solvent with both mobile anions and cations. Especially for the description of the latter case, the influence of mechanics on ion transport and reaction kinetics cannot be neglected or treated in a simplified manner as is usually done for liquid electrolytes, see e.g. [1]. In this contribution we present a coupled electro-chemo-mechanical modeling framework for ion transport in solid electrolytes and investigate the influence of mechanics on both ion transport and reaction kinetics.

Drawing on ideas from Bucci et al. [2], we formulate a fully coupled large strain theory for ionic transport in terms of electric field, mechanical deformation and anion and cation concentrations. We derive suitable constitutive relations based on the Helmholtz energy and thermodynamic restrictions for the species fluxes of the different ionic constituents as done in the context of liquid electrolytes e.g. by Dreyer et al. [3]. We propose a constitutive formulation that allows the calculation of the electrochemical transport in the deformed state and consistently predicts the coupling between species transport and gradients of stress and material properties based on the choice of the Helmholtz energy, similar to e.g. lithium diffusion in active particles [4] or the swelling of polymeric gels [5].

Using the framework of the newly derived transport theory, we investigate the effect of mechanics on the interfacial kinetics at the metal anode/solid electrolyte interface. Based on energetic considerations as presented in [6] or [7], we propose a modified Butler-Volmer relation that not only establishes a relation between the exchange current density and potential/concentration differences across the interface but also takes into account the mechanical state of both solid electrolyte and metal anode.

To illustrate the features of the model and to highlight cases where the electro-chemo-mechanical coupling plays an important role for ion transport and kinetics, we show numerical examples for a Lithium symmetric solid state cell with binary solid electrolyte.

[1] NEWMAN, J. S.; THOMAS-ALYEA, K. E. [2004]: Electrochemical systems. J.Wiley, Hoboken, N.J., 3rd ed Edition.

[2] BUCCI, G.; CHIANG, Y.-M.; CARTER, W. C. [2016]: Formulation of the coupled electrochemical mechanical boundary value problem, with applications to transport of multiple charged species. Acta Materialia, 104:33–51.

[3] DREYER, W.; GUHLKE, C.; MÜLLER, R. [2013]: Overcoming the shortcomings of the Nernst–Planck model. Physical Chemistry Chemical Physics, 15(19):7075.

[4] BOHN, E.; ECKL, T.; KAMLAH, M.; MCMEEKING, R. [2013]: A model for lithium diffusion and stress generation in an intercalation storage particle with phase change. Journal of the Electrochemical Society, 160(10):A1638–A1652.

[5] HONG, W.; ZHAO, X.; ZHOU, J.; SUO, Z. [2008]: A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids, 56(5):1779–1793.

[6] BOCKRIS, J. O.; REDDY, A. K. N.; GAMBOA-ALDECO, M. [2000]: Modern Electrochemistry 2A: Fundamentals of Electrodics.

[7] MONROE, C.; NEWMAN, J. [2004]: The effect of interfacial deformation on electrodeposition kinetics. Journal of The Electrochemical Society, 151(6):A880.