Solid Electrolyte Interphase elastic instability in Li-ion battery anodes

Mechanical instabilities of the solid electrolyte interphase (SEI) layer can lead to battery degradation phenomena. Rubbery-based electrodes, during lithiation and delithiation, being subject to large volumetric changes impose large deformations to the SEI layer which, in turn, can lead to interphase mechanical instabilities. We investigate a typical instability which gives rise to the formation of wrinkling patterns. To account for large deformations, we consider the theory of nonlinear elasticity and we apply a standard perturbative theory to search for possible wavy solutions. By varying the geometrical and the constitutive parameters of interest we compute the critical radius of the electrode at which the instability can occur. We first describe the SEI as a homogeneous layer and we then incorporate in the model the well-established heterogeneity hypothesis of a bilayer SEI, whose inner and stiffer part includes mostly inorganic species whilst the outer and softer sublayer includes mostly the organic species. We show a nontrivial transition in passing from the former to the latter hypothesis and we derive general conditions where two theories can or cannot be considered both valid. Through our simulations, we then warn of the possible errors that a predicting model can exhibit by neglecting the microstructure of the shell layer. Furthermore, conditions for preventing the wrinkling patterns formation and/or for designing optimal artificial SEI can be deduced from some illustrative numerical examples.