Recently, we have proposed an adjoint method to numerically optimize electrochemical systems with a large number of degrees of freedom [2,3]. This method was initially developed by the applied mathematics community to solve optimization problems in fluid dynamics, climate, and heat transfer problems but, more recently, the method was used by other research communities to solve optimization problems in magnetics, model parameter determination, and semiconductor devices . In the case of electrochemical systems, the adjoint method can be used to evaluate the catalyst sensitivity functions ΥPt(r), which show how sensitive the parameters of the cell are to the platinum density at location r. For instance, the catalyst sensitivity function of the cell voltage, ΥPt,V(r), shows how much the cell voltage is increasing by adding 1 mg of platinum at a given location inside the catalyst layer (by operating at the same current density). Since the catalyst sensitivity functions measure the sensitivity of cell parameters to the local platinum content, they are instrumental in the design of PEFMC.
In this presentation we formulate the optimization problem in matrix form, appropriate for 2-D and 3-D finite element simulations of PEMFCs, in which the number of optimization parameters is over 106. Optimization results for low and large platinum loadings will be presented for unconstrained and constrained optimizations (when the amount of platinum is fixed). Our numerical results show that the optimum platinum distribution function, ρ(r), depends on operating current, temperature, and humidity. In general, at low operating currents, the platinum can be distributed approximately uniformly inside the cathode catalyst layer, however, at large operating currents, it is more efficient to increase the platinum content in the region close to the membrane and under the oxygen channels. The technique can also be extended to the optimization of GDL porosity ε(r), particle size, and ionomer content. More details about the numerical implementation of the method in the case of multiscale transport models and the computational efficiency will be presented in the full paper.
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 P. Andrei, G. Mixon, M. Mehta, and V. Bevara, "Design of the catalyst layers in PEMFCs using an adjoint sensitivity analysis approach," ECS Transactions 66(8), 91-128, 2015.
 P. Andrei, I. Mayergoyz, “Quantum mechanical effects on random oxide thickness and random doping induced fluctuations in ultrasmall semiconductor devices”, Journal of Applied Physics, 94, 7163-7172, 2003.