Effect of prestress on the stability of electrode–electrolyte interfaces during charging in lithium batteries

We formulate a model of the growth of electrode–electrolyte interfaces in lithium batteries in the presence of an elastic prestress. The model accounts for the kinetics of Li+ transport through a solid electrolyte and, within the interface, for the kinetics of Li+ adsorption by the anode, electrostatics, and the elastic field. We specifically account for the effect of the elastic field through an asymptotic analysis of a nearly flat interface between two semi-infinite elastic bodies. We use the model as a basis for assessing the effect of prestress on the stability of planar growth and the potential of prestress as a means of suppressing the formation of deleterious dendrites. We present a linear stability analysis that results in explicit analytical expressions for the dependence of growth rates, and of the critical unstable wavelength for the interfacial roughening, on the state of prestress and on fundamental parameters such as surface diffusivities, surface energy, deposition kinetics, and elastic moduli. Finally, we examine the model in the light of experimental observations concerned with the effect of applied pressure on a lithium/dioxolane-dimethoxy ethane electrolyte systems. With reasonable choices of parameters and some calibration, the model accounts for the observation that a modest applied pressure indeed results in a substantial reduction in the roughening of the lithium surface during cycling.