A compact model is developed for the discharge curves and specific capacity of Li-air batteries with organic electrolyte as a function of the galvanostatic discharge current and specific capacity. The Li_2O_2 deposit layer formed in the cathode is modeled using two approaches: as a resistive layer and as a quantum barrier. In each case the voltage drop across the deposit layer is computed analytically. The model considers Butler-Volmer reaction kinetics at anode and cathode to obtain expressions for the anode and cathode overvoltages as functions of time. The solution for the porosity change equation, the rate equation for deposition of the discharge product, and the solutions for the overvoltages at anode and cathode are used to obtain a closed-form expression for the discharge voltage as a function of the specific capacity and other parameters of the battery.
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