Modeling fractal electrodes for Li-ion batteries

Abstract

This paper presents a first approximation to the theoretical analysis of fractal-like electrodes for lithium-ion batteries, and demonstrates that fractals constitute an optimal electrode configuration for electrochemical energy storage systems. The model considers a generalized description of three-dimensional, non-deterministic branching structures composed of cylindrical elements for the electrode design. Each element is attached to a branch in an iterative process. At every branching step, the “parent” branch divides into N “child” branches ( N being a random variable with a defined probability distribution). At the same time, the dimensions of the radii and lengths of the branches are also determined by a stochastic process. With this model, the charge characteristics of several fractal electrodes corresponding to different geometric configurations are simulated, and the optimal parameters are obtained.