A Novel Method for Estimating the Charge Equilibrium within the Dendrites of Rechargeable Batteries

The nonuniform formation and growth of microstructures during the electrochemical charging of a battery is the main reason for the short circuit and capacity fade. The charge distribution across the micro-structure is the result of both local and global equilibrium which is a non-convex problem merely due to random placement of the atoms. As such, obtaining the charge equilibrium (QEq) is critical, since the amount of withheldcharge determines the success rate of the bond formation for the ionic species approaching the microstructure which ultimately determines the morphology of the electrochemical deposits. Herein we develop a computationally-affordable method for estimating the charge allocation within such microstructures. The cost function and the span of the charge distribution correlates very closely with the trivial method as well as a conventional method, albeit having significantly less computational cost. The method can be used for optimization in non-convex problems, specially for those of randomly-formed morphology.