An analytical impedance model and a small-signal equivalent circuit are derived for the impedance spectra of Li-air batteries with porous cathodes. The model takes into consideration the effects of the oxygen diffusion, double layer, and faradaic processes in the cathode and can be applied to Li-air batteries with organic and aqueous electrolytes operating under d.c. discharge. It is shown that the cathode of Li-air batteries can create two slightly asymmetrical semicircles on the Nyquist diagram: one at low frequencies, where the oxygen diffusion dominates the operation of the cell and one at medium frequencies due to the combined effects of the double-layer capacitance and faradaic processes. The second semicircle becomes negligibly small at low values of the cathode width or oxygen concentration. Both semicircles can degenerate into one large semicircle when the double layer capacitance is large enough and masks the effects of the faradaic processes, which happens at large values of the specific area of the cathode and double layer capacitance, or when the oxygen diffusion coefficient in the electrolyte is relatively large. They also degenerate into one semicircle when the porosity is decreased, for instance during the final period of the discharge of Li-air batteries with organic

A numerical algorithm is presented for the large-scale optimization of catalyst distribution in proton exchange membrane fuel cells (PEMFCs). The algorithm is based on the evaluation of catalyst sensitivity functions, which show how much the cell voltage or discharge current are increasing when a small amount of catalyst is added at given locations inside the catalyst layers. The catalyst sensitivity functions are evaluated with relatively low computational cost using an adjoint space approach. Using the proposed algorithm one can compute the exact, optimum, three-dimensional (3-D) distribution of platinum particles inside the catalyst layers in order to maximize the overall power density of the cell. It is shown that the optimum distribution depends on the discharge conditions, on the positions of landings and openings, and on the geometry and dimensions of the layers. In general, the optimum catalyst density in the cathode catalyst layer should be larger at the membrane than at the gas diffusion layer interface. In addition, the catalyst density should be slightly larger under the gas channel and smaller under landings.

In this article we present an adjoint method for the optimization of the catalyst distribution in proton exchange membrane fuel cells (PEMFCs). By using the theory of functional analysis we derive analytical equations for the sensitivity functions of the cell voltage with respect to the catalyst distribution in a very general framework, independent on the transport model used to simulate the PEMFC. Then we present an efficient numerical algorithm to calculate the sensitivity functions using the adjoint method. The adjoint method has the advantage that it can be applied to the optimization of systems with a large (>10 4 ) number of optimization variables that are computed simultaneously and independently to maximize the objective function. Finally, we apply the method to the optimization of 2-D platinum distribution in PEMFCs. We show that the optimum platinum distribution varies with the operating conditions, position of landings and openings, cell geometry, and dimensions of the catalyst layers. The method presented in this work can be naturally extended to the optimization of other 2-D and 3-D field variables such as the porosity of catalyst and gas diffusion layers, particle size distribution, or microstructure of the cell. Proton exchange membrane fuel cells (PEMFCs) have attracted the attention of the research community because of their high power density, energy efficiency, and environmentally friendly characteristics. Operating at low temperatures, PEMFCs are suitable for a variety of applications ranging from automotive applications to stationary and portable applications. In the area of automotive applications, PEMFCs have already been introduced commercially or for demonstration purposes by all the major car manufacturing companies; in addition, they are increasingly being used in busses, motorcycles, boats, submarines, and airplanes.1,2 In the area of stationary and portable applications, PEMFCs are employed as emergency power systems, such as uninterrupted power supplies, and have the potential to be used for energy storage in electric grid systems.3 Since the technical feasibility of PEMFCs has already been established, a significant amount of current research focuses on increasing the durability and decreasing the total manufacturing cost, which, at large manufacturing volumes, is mainly given by the cost of the catalyst layers (CLs), bipolar plates, and membrane.4-8 (For instance, the US Department of Energy estimates that 45% of the cost of fuel cell stack fabricated at a volume of 500,000 systems/year is due to the cost of platinum, 27% to bipolar plates, 10% to the cost of membrane 9 ). In this article, we address the problem of decreasing the manufacturing cost of the CLs by presenting a large-scale optimization technique to optimize the platinum deposition in the CLs of PEMFCs. The technique can also be applied to the optimization of other two-dimensional (2-D) and three-dimensional (3-D) field variables, such as porosity distribution and ionomer content, in which the number of optimization p...

An adjoint-space technique is presented for the large-scale optimization (i.e. optimization with over 10 2 design variables) of the catalyst distribution in fuel cells. The algorithm is based on evaluating the catalyst sensitivity functions of the discharge voltage under specified current conditions. The catalyst sensitivity functions are computed efficiently using a gradient maximization algorithm, which requires solving a small number of sparse linear systems of equations to find the Gâtaux derivatives of the discharge current of the cell with respect to the design variables. It is shown that the optimum distribution of the catalyst varies with the discharge conditions, with the positions of landings and openings, as well as with the geometry and dimensions of the layers. It should be noted that our numerical algorithm can be used to describe the complete profile of the optimal catalyst by providing the full (mathematically exact) distribution of platinum particles in the catalyst layer.