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Variability Analysis of Discharge Characteristics and Impedance Spectra in Li-Air Batteries

The goal of this presentation is twofold: First, we analyze the effects of intrinsic and extrinsic parameter fluctuations on the discharge characteristics and impedance spectra of Li-air batteries. Second, we develop a small-signal perturbation technique for the characterization of the variability in Li-air batteries. The analysis of the parameter fluctuation induced effects is done using Monte-Carlo methods. For this purpose, we generate a large number of the devices with identical macroscopic but different microscopic configurations and simulate each device independently. In this way we accumulate statistics for the parameters of interest – in our case the discharge curves, specific capacity, and impedance spectra – and compute the average values and standard deviations of these parameters.

The Monte-Carlo method is computationally very expensive because it requires simulating many different devices. If we assume the parameter fluctuations are normally distributed, the error in computing the standard deviation of one parameter of interest is approximately equal to 1/sqrt(2*N*), where *N*is the number of devices simulated. This equation shows that in order to compute the standard deviation of a parameter with an error of less than 5% we need to perform at least 200 device simulations. For this reason, we develop a new technique for the analysis of variability in electrochemical devices based on small-signal perturbations. We assume that the fluctuating parameters that appear in the transport equations are random variables characterized by some average values and given standard deviations. Then, we expand the transport equations in power series and find analytical equations for the average values and fluctuations of the parameters of interest. These equations are then solved either analytically or using finite element models and the results are compared the Monte-Carlo method. The computational complexity of perturbation techniques is much smaller than the complexity of Monte-Carlo methods because perturbations techniques require solving the (nonlinear) transport system of equations once and a few linear systems of equations.

At the conference we will present results for the discharge characteristics obtained using the finite element model presented in (2). The impedance spectra are modeled using both the compact model presented in (3) and the finite element approach presented in (4). Our initial results show a very good agreement between the Monte-Carlo simulations and the linearization approach. A detail discussion of the variability of the discharge characteristics, specific capacity, and impedance spectra in Li-air will be presented at the conference.

** References**

- L. D. Griffith, A. E. S. Sleightholme, J. F. Mansfield, D. J. Siegel and C. W. Monroe,
*ACS Appl. Mater. Interfaces*,**7**, 7670 (2015). - P. Andrei, J. P. Zheng, M. Hendrickson and E. J. Plichta,
*J. Electrochem. Soc.*,**157**, A1287 (2010). - M. Mehta, G. Mixon, J. Zheng and P. Andrei,
*J. Electrochem. Soc.*,**160**, A2033 (2013). - M. Mehta and P. Andrei,
*ECS Trans.*,**61**(15), 39 (2014).