Effects of Pore Size Distribution on the Discharge Characteristics of Li-Air Batteries with Organic Electrolyte
The transport model that we introduce here is a generalization of our previous model presented in , in which all the pores were assumed to have the same size. Unlike in , the new model considers the exact form of the pore size distribution function, f(r), where r is the radius of the pore which is assumed to be cylindrical with nonuniform radius. (For instance, with these notations, f(r)*dr is the number of pores per unit area of the cathode with radius between r and r+dr). The model is based on the theory of concentrated solutions developed by Newman  and takes into consideration the transport of lithium-ions and oxygen diffusion inside the cell, the electron conductivity of the carbon cathode, and the formation and deposition of lithium peroxide at the cathode. The model accurately describes the porosity change inside the cathode by carefully adjusting the PDF of the pores inside the cathode during the discharge of the battery. The reaction rates at the anode and cathode are described by Butler-Volmer equations. The transport equations consist of a system of four partial differential equations (two for the Li-ions, one for the oxygen diffusion and one for the electron transport), which are coupled with differential equations for the local change in porosity, the specific surface area (which is computed as an integral involving the pore size distribution function), and the resistance of the deposit layer (Li2O2 or Li2O). Since the electron transport mechanism in the deposit layer is still under investigation in the literature we consider a combination of two different conduction processes: (1) the deposit layer is treated as an oxide with relatively high resistivity and (2) the transport through the conduction layer is governed by quantum tunneling. In this later case, we derive approximate expressions for the voltage drop across the deposit layer and solve it self-consistently with the full systems of transport equations.
The transport equations are solved throughout the whole volume of the battery, including cathode, anode protective layer, and separator. We also assume organic binary monovalent electrolyte and no convection in the battery. The final system of equations is discretized on a finite element mesh and solved numerically in RandFlux . The effect of the pore size distribution function on the discharge curves, specific capacity, and state-of-charge will be discussed at the conference and in the full article.
 P. Andrei, J. P. Zheng, M. Hendrickson, and E. J. Plichta, " Journal of the Electrochemical Society, vol. 159, pp. A770-A780, 2012.
 J. Newman and K. Thomas-Alyea, Electrochemical Systems, 3rd Edition ed.: John Wiley&Sons, 2004.
 RandFlux: User's manual v.0.6, Florida State University, http://www.eng.fsu.edu/ms/RandFlux.