Linearized Tracking of Dendritic Evolution in Rechargeable Batteries

Abstract

The formation of the dendritic microstructures during the electrodeposition is a complex process depending on several physical/chemical parameters. We establish an analytical framework for tracking the one dimensional dendritic interface based on the asynchronous developments in the concentration C and the electric potential V. Comparing the dynamics of the interface vs the ions, we establish linearized forms of the concentration C and the electric potential V during the quasi-steady-state evolution. Subsequently, we investigate the potentiostatic (V 0) and galvanostatic (i 0) conditions, where we have analytically attained the dependent parameters (i or V) and justified their respective variations in the binary electrolyte. Consequently, we have quantified the role of original concentration C 0, the inter-electrode potential V 0, the electrolyte diffusivity D and the inter-electrode separation l on the value and the growth rate of the dendritic interface. In particular, for the given infinitesimal dendritic growth, we have shown a higher efficacy for the electromigration than the diffusion, especially during the instigation period of the electrodeposition.