Mathematical aspects of catalyst positioning in Lithium/Air Batteries

Lithium/air batteries has been taken interest by many scientists over the last years. The catalyst positioning problem describing the porous cathode during the discharge process is concerned in the research of optimizing the capacity of Lithium/air batteries. During discharge process, there is a critical issue: the discharge oxygen reduction products is insoluble in the organic electrolytes. This clogs the oxygen entrance to the pore to be reacted with Lithium ions and limits the capacity of the batteries by narrowing the active surface inside the pore. The dynamics of the discharge process is described by the initial mixed boundary value problem for two one-dimensional partial differentiable equations. The two variables of the system are the pore radius inside the cathode and the Oxygen concentration at certain coordinate and time. The subject of the thesis is to investigate some catalyst positioning models and to maximize the free volume of the pore after pore clogging by the deposited discharged products. We aim at the following fields: First, we research analytically the forward model describing continuous catalyst positioning in Li/air batteries: well-posedness of the problems, the Fr echet differentiability of the pore radius and the oxygen concentration with respect to catalytic function in some spaces. Second, we present optimization problems and analyze the sensitivity and adjoint method to solve them. Finally, some numerical methods are carried out to solve the forward problems and some numerical approach for solving optimization problem are also examined to illustrate the theoretical results.