Linearized Tracking of Dendritic Evolution in Rechargeable Batteries

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.