Compact Analytical Modeling of Quantum Tunneling Effects in Li-Air Batteries with Organic Electrolyte
Authors: Bevara Vamsci V , Andrei Petru 
Published: February 2020

In the last few years, Lithium air batteries with organic electrolyte have received much attention because of their potential applications in systems requiring large storage elements, such as in renewable energy storage or electric vehicles. Although the theoretical energy density of these batteries is relatively high, the experimental values are usually much lower. This fact is generally attributed to two phenomena: (1) the discharge product (e.g. LiO2, Li2O2, etc.) deposits in the cathode and fills in the pores at the air side, in this way blocking the transport of the oxygen from the outside, and (2) the resistivity of the discharge product is high and the ohmic losses become too large. In this second case, quantum tunneling is believed to be responsible for the transport through the deposit layer when the thickness of this layer is less than 5 -10 nm. In this presentation we develop a new analytical model that takes into account both the Faradaic effects and the resistivity of the discharge layer by employing a quantum approximation of the transport through the discharge layer. A very good agreement is obtained between our analytical approach and the more computationally intensive, finite-element simulations, in which the full transport model is solved, including the diffusion of the oxygen, diffusion and conductivity of the electrolyte ions, electron conductivity, and variation of porosity.
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.