Compact Analytical Modeling of Li-Air Batteries with Organic Electrolyte at Low Discharge Currents
The model developed gives a compact analytical solution for the discharge curves and specific capacity of Li-air batteries with organic electrolyte, as a function of the galvanostatic discharge current. The model uses the oxygen diffusion equation at the cathode and an approximate Butler-Volmer equation to obtain an expression for overpotential as a function of time. This overpotential can be used to derive an equation for change in porosity as a function of time, which leads to a closed-form expression for the discharge voltage as a function of the specific capacity and other parameters of the battery. The final equation will be presented in detail at the conference.
The resistance of the deposit layer is approximated to vary exponentially with the thickness of the layer in agreement with Wentzel-Kramers-Brillouin (WKB) theory of quantum tunneling. As the discharge progresses and the thickness of the deposit layer grows, the electron resistivity increases, and the voltage drop across the deposit layer increases drastically. We show that when the thickness of the deposit layer reaches a critical value the tunneling resistance is too large and the battery is discharged. The derivation of our model, a comparison between the analytical and more accurate finite-element simulations, and different loss mechanisms in the deposit layer will be discussed at the conference. Sample results obtained, assuming quantum tunneling using our compact model are presented in the figure.
Comparison between the ohmic and the tunneling phenomenon will be presented along with a comparison between the compact model and a finite-element model. The compact model derived assumes low discharge currents and narrow cathode widths.
Figure 1 depicts discharge curves obtained using the compact model, assuming quantum tunneling to be the charge transfer phenomenon through the deposit layer. Figure 1a shows discharge curves for different values of critical tunneling length, d0. Figure 1b shows discharge curves for different values of the galvanostatic discharge currents, I.