Mathematical analysis of the lithium ion transport in lithium ion batteries using three dimensional reconstructed electrodes

Abstract

Computational analysis of lithium ion batteries has been improved since Newman and et al. suggested the porous electrode theory. It assumed the electrode as a simple structure of homogeneous spherical particles. Bruggeman relationship which characterizes porous material by a simple equation was adopted in the homogeneous electrode model instead of the electrode morphology. To improve the prediction of a cell performance, the numerical analysis requires the realistic microstructure of the cell.

Based on the experimentally determined microstructure of the positive and negative electrodes of a lithium ion battery (LIB) using x-ray micro/nano-CT technology, three dimensional (3D) simulations have been presented in this research. Tortuosity of the microstructures has been calculated by a linear diffusion equation to characterize the 3D morphology. The obtained tortuosity and porosity results pointed out that the Bruggeman relationship is not sufficiently estimate the tortuosity by the porosity of electrodes.

We studied the diffusion-induced stress numerically based on realistic morphology of reconstructed particles during the lithium ion intercalation process. Diffusion-induced stresses were simulated at different C rates under galvonostatic conditions and compared with spherical particles. The simulation results showed that the intercalation stresses of particles depend on their geometric characteristics. The highest von Mises stress and tresca stress in a real particle are several times higher than the stresses in a spherical particle with the same volume.

With the reconstructed positive electrode structure, local effects in the LIB cathode electrode during galvanostatic discharge process have been studied. The simulation results reported that large current density usually occurs at the joints between cathode active material particles and in the small channels in electrolyte, which will generate high electric joule power. By using the 3D real image of a LIB cathode electrode, numerical simulation results revealed that the spatial distribution of variable fields such as concentration, voltage, reaction rate, overpotential, and etc. in the cathode electrode are complicated and non-uniform, especially at high discharge rates.