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. Li-air batteries have attracted much attention in the last years particularly because of their high energy densities and specific capacities. 1-3 Depending on the type of the battery, the specific capacity is estimated to vary between 1,000-3,840 mAh/g, 4-6 which is a few times to more than one order of magnitude larger than the energy density of Li-ion batteries. This high specific capacity is mostly due to the fact that Li-air batteries use oxygen from the air instead of storing it internally and lithium metal at the anode instead of a composite material. Additionally, Li-air batteries are environmental safe and provide an oil-independent source of energy, which make them attractive in a broad area of applications including transportation, portable electronic devices, and green energy storage. Impedance analysis methods are often employed as convenient, nondestructive ways to analyze and predict the performance of batteries and other energy storage devices. 7 These methods can be used to extract information about the reaction and diffusion processes inside electrochemical devices, as well as about the state-of-charge, state-of-health, ohmic losses, and reliability of these devices. For instance, in the case of Li-ion batteries, one can predict the voltage and monitor the state-of-charge of the cells, 8,9 diagnose and investigate the electrochemical properties and determine the values of the Li diffusion coefficient, reaction rate, and other parameters using impedance spectroscopy. 16 In this article we develop an electrochemical impedance spectra model for Li-air batteries and relate the characteristics of the * Electrochemical Society Active Member. z E-mail: [email protected] spectra of these batteries to their geometrical dimensions, kinetic parameters, diffusion coefficient, porosity, and pore structure. 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. The results for the impedance spectra are derived under relatively general assumptions of the structure and type of the battery, by looking at the oxygen diffusion and faradaic processes in the porous cathode. Since the operation of Li-air batteries is dominated by these processes the effects of other phenomena such as the anode reaction rate or ion transport though the electrolyte can be neglected. We expect this model to be valid for a large number of Li-air or Li-oxygen systems, in which the oxygen diffusion-reaction plays a limiting factor. In particular, the model can be applied to primary and secondary Li-air batteries with organic and aqueous electrolytes as we will also discuss in the next section. Most of the existing work on the theoretical modeling of impedance spectra of electrochemical system is related to the study of Li-ion, other metal-ion or metal batteries, and electrocapacitors, which are dominated by Warburg diffusion or various versions and improvements the Warburg diffusion model (e.g. bounded Warburg models). These models are usually represented in the form of small-signal transmission line circuit models. They are relatively accurate for systems that can be modeled with a semi-infinite or bounded diffusion region and where the reaction takes place on the boundary of this region
