Statistical Analysis of Li-Oxygen Batteries
Authors: Andrei Petru , Zhu Chen 
Published: February 2020

The reported values of the specific capacity and energy and power densities of Li-oxygen batteries vary from battery to battery even when the they are fabricated using the same technological processes and when much care is given to produce identical cells. In addition, the practical discharge curves of Li-air batteries are significantly different from one battery to another even when these curves are measured under the same discharge conditions. In this presentation, we introduce a mathematical model to analyze the statistical variability of the discharge characteristics in Li-air batteries with organic and aqueous electrolyte. In this model, the variability of the discharge curves is due to microscopic variations of the cathode structure that result in random local values of the porosity, specific area, and reaction rates. It is shown that microscopic variations of the cathode microstructure from one location to another inside the same battery as welll as from one battery to another result in large variations of the discharge characteristics. These variations can explain in part the large variability of the discharge curves reported in the literature for Li-air/oxygen batteries.
The basic idea of our mathematical model is to write the transport model equations into the form of a system of stochastic partial differential equations, and to solve this system using Monte-Carlo techniques. In the case of Li-oxygen batteries, the transport model equations can be written as a system of five partial differential equations that include the migration and diffusion of the electrolyte, oxygen diffusion, local porosity variation, and electron conductivity equation (1, 2). These equations are discretized on a finite element grid and a solved self-consistently to compute the discharge voltage as a function of the specific capacity. Due to the stochastic nature of the transport system, the solution of the transport equations will also be stochastic and will vary from battery to battery.
In order to perform a comprehensive statistical analysis of the discharge curves in Li-oxygen batteries, we generate a large number of the batteries with identical macroscopic characteristics (i.e. identical geometrical dimensions, average porosity, and specific area) but with different microscopic structures and simulate each battery independently. In this way we accumulate statistics for the parameters of interest – in our case for the discharge curves, the specific capacity, and the energy density – and compute the average values and standard deviations of these parameters. We observe that the standard deviation of the specific capacity decreases with increasing the d.c. discharge current, however, the relative variability, defined as the standard deviation of the specific capacity divided by the mean value of the specific capacity, increases dramatically.
Finally, we investigate the sensitivity of the discharge characteristics to variations of the structural properties of the battery by performing a sensitivity analysis of the discharge voltage as a function of the local values of the porosity and reaction kinetic constant. We observe that initial local variations of the porosity at the air side increase the variability of the discharge voltage curves more than variations of the porosity at the separator side. Unlike variations of the porosity, variations of the reaction kinetic constant do not influence the discharge characteristics significantly. More details about the numerical implementation of our method as well as simulation results for the variability of the discharge characteristics, specific capacity, and energy density will be presented at the conference.
1. P. Andrei, J. P. Zheng, M. Hendrickson and E. J. Plichta, “Some Possible Approaches for Improving the Energy Density of Li-Air Batteries”, Journal of the Electrochemical Society, 157, A1287 (2010).
2. M. Mehta and P. Andrei, “Variability Analysis of Discharge Characteristics and Impedance Spectra in Li-Air Batteries”, 228 ECS Meeting, Phoenix, AZ, 2015.