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Modeling and Simulation of Electrochemical Impedance Spectra in Lithium-Air Batteries

_{2}O

_{2}, and Li-ion transport. The model equations are relatively similar to the ones presented in (2) can be expressed in terms of a small-signal equivalent circuit like in (3). In this presentation we develop a finite element model for computing the impedance spectra of Li-air batteries with organic electrolyte and investigate the accuracy of the analytical model. The new finite element model is based on the theory of concentrated solutions, which we recently applied in (4) to compute the discharge characteristics in Li-air batteries. This model provides a complete description of lithium-ion and oxygen diffusion in the anode, separator and the cathode regions. It also takes into account the following effects: the electron conductivity in the carbon cathode, Butler-Volmer kinetics at anode and cathode, the formation and deposition of the Li

_{2}O

_{2}at the cathode, and the change in porosity as a result of the deposition of the reaction product. The impedance spectra are computed by applying small-signal linear perturbations to the transport equations and solving the final linear system of equations numerically.

The figure below compares the results obtained using the analytical model (symbols) with the more computationally expensive finite element simulations (continuous lines) for three values of the dc discharge current, 0.2mA/cm^{2}, 0.5mA/cm^{2}, and 2mA/cm^{2}. The total value of the discharge current is a superposition of the dc and small-signal ac currents. In figure (a) the simulations were performed by solving only the oxygen diffusion equations, whereas in figure (b) the simulations were performed by solving the equations for oxygen diffusion, lithium-ion drift and diffusion, porosity change, and electron conductivity in the solid cathode phase. A very good agreement between the analytical computations and the finite element simulations is observed at all the dc discharge currents. This suggests that the assumptions used in the development of the analytical model hold true for a wide range of discharge currents. However, in figure (b) we observe a slight disagreement between the two models. It is important to point out that although the curve obtained using finite element simulations is slightly shifted in the positive direction of the real axis, the actual nature (or shape) of both the curves (i.e. analytical and simulation) remains the same for low discharge currents. This shift is due to the finite electric conductivity of the solid phase and electrolyte. For current densities larger than 2mA/cm^{2}, the general shape of the simulation curve deviates from the analytical results. The discrepancy between the analytical and finite element simulations can be explained by the fact that the analytical model does not consider the nonuniform distribution of the porosity throughout the cathode, while the finite element simulations takes this effect into consideration.

The derivation of the finite element model equations, the numerical implementation, more simulations results, and a detailed discussion of the limitations and accuracy of the analytical and finite element simulations will be presented at the conference.

REFERENCES

1. M. Mehta, G. Mixon, J. P. Zheng and P. Andrei, *J. Electrochem. Soc*., 160, A2033 (2013).

2. D. Franceschetti, J. R. Macdonald and R. P. Buck, *J. Electrochem. Soc*., 138, 1368 (1991).

3. R. P. Buck and C. Mundt, *Electrochim. Acta*, 44, 1999 (1999)

4. P. Andrei, J. P. Zheng, M. Hendrickson and E. J. Plichta, *J. Electrochem. Soc*., 157, A1287 (2010).