Analytical Electrochemical Impedance Modeling of Li-Air Batteries under D.C. Discharge

Abstract

An analytical impedance model and a small-signal equivalent circuit are derived for the impedance spectra of Li-air batteries with porous cathodes. The model takes into consideration the effects of the oxygen diffusion, double layer, and faradaic processes in the cathode and can be applied to Li-air batteries with organic and aqueous electrolytes operating under d.c. discharge. It is shown that the cathode of Li-air batteries can create two slightly asymmetrical semicircles on the Nyquist diagram: one at low frequencies, where the oxygen diffusion dominates the operation of the cell and one at medium frequencies due to the combined effects of the double-layer capacitance and faradaic processes. The second semicircle becomes negligibly small at low values of the cathode width or oxygen concentration. Both semicircles can degenerate into one large semicircle when the double layer capacitance is large enough and masks the effects of the faradaic processes, which happens at large values of the specific area of the cathode and double layer capacitance, or when the oxygen diffusion coefficient in the electrolyte is relatively large. They also degenerate into one semicircle when the porosity is decreased, for instance during the final period of the discharge of Li-air batteries with organic electrolyte, when the cathode is partly clogged with the deposit reaction products. The elements of the small-signal equivalent circuit are expressed in terms of the oxygen diffusion coefficient, oxygen concentration, discharge current, and other material and kinetic parameters, which make our model instrumental for extracting information about the material structure, reaction processes, and diffusion in the cathode. Based on the derived analytical results, we also propose a method to extract the effective value of the oxygen diffusion coefficient and reaction rate constant from the experimental impedance spectra of the cells. A simplified small-signal equivalent circuit model is also presented. This model contains only elementary components such as resistors and capacitors and can be implemented numerically in circuit simulators.