Convexification of Charge Equilibrium within the Dendrites of Rechargeable Batteries

The amorphous propagation of microstructures during the electrochemical charging of a battery is the main reason for the capacity decay and short circuit. The charge distribution across the micro-structure is the result of both local and global equilibrium and is non-convex problem merely due to stochastic placement of the atoms. As such, obtaining the charge equilibrium (QEq) is a critical factor, since the amount of charge determines the success rate of the bond formation for the ionic species approaching the microstructure and consequently the ultimate morphology of the electrochemical deposits. Herein we develop a computationally-affordable method for determining 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 environments, specially those of stochastic nature.