A finite strain electro-chemo-mechanical theory for ion transport with application to binary solid electrolytes

Abstract

An electro-chemo-mechanical formulation of ion transport in solid electrolytes, in particular for binary systems, is presented. Starting with conservation laws and the second law of thermodynamic, we state a consistent Helmholtz-energy-based framework taking electrostatics, component transport and nonlinear elastic mechanical interaction into account. With the help of finite strain continuum mechanics, we include the effect of geometry changes on ion transport. Changes of local concentration cause swelling and shrinkage and hence stress assisted diffusion. Further coupling originates via an osmotic pressure. Since binary systems are of special interest in battery applications, we formulate both, a fully resolved and an electroneutral model for ion transport. The latter turns out to be an extended version of Newman’s concentrated solution theory taking mechanical effects into account. We demonstrate the importance of these mechanical effects by means of double layers adjacent to blocking electrodes and concentration profiles during galvanostatic charging. Further, we investigate the effect of external deformation as, e.g. found in dendrite growth.