Final Report Summary - FASTCELL (Multiscale Methods for Segregation Phenomena in Solid Oxide Fuel Cell Materials) Solid oxide fuel cells (SOFCs) are among the most promising devices for clean and efficient fuel generation and electric power production from both traditional and renewable energy sources. In particular, SOFCs are known to be the most efficient devices for the direct conversion of the chemical energy stored in a fuel into electrical energy.The goal of the project is to study advanced methods for the study of segregation of impurities in SOFC cathodes. Dopant segregation at the surface is significant in fuel cell applications because it can affect the surface electrochemical reactions and the local transport properties and hereby impacts their performance. This is in turn closely linked to the objectives of the proposal:1. Understanding the elementary steps of oxygen reactions at the cathode and its link with impurity or dopant segregation in order to develop high power density of SOFC cells using novel high-performance cathodes.2. Searching and designing novel cathode materials and optimizing microstructures by developing “fast” first-principle algorithms. In particular our work brought a clearer understanding on the chemisorption on surfaces, on the identification of relevant processes in electrochemical spectroscopy experiments and it has elucidated the nature of the reactions occurring in materials on the nanoscale.In particular we have introduced several novel tools for the identification and reduction of errors in parameters estimated with electrochemical impedance spectroscopy experiments used in fuel cells; we have bridged the gap between classical Poisson Boltzmann theory for chemisorption and differential capacitance in a novel multidimensional Schroedinger-Poisson setting. Our results showed the dependence of the chemisorbed charge and the differential capacitance on oxygen partial pressure. In our most important contribution, titled “Measuring oxygen reduction/evolution reactions on the nanoscale” published in Nature Chemistry, we studied the physical chemistry of the reactions in a fuel cell occurring on a nanoscale tip. We have linked the displacement of the tip to the reactivity of the sample by studying a set of complex partial differential equations, this has led to physical chemical insight on the reactions with unprecedented space sensitivity. More work is underway on this topic.The impact of this work is not limited to SOFC technology but it extends to two other fields: Applied Mathematics of Multiscale Problems and Catalysis of Materials. Hence, this work is of interest to workers electrochemistry, materials science and applied mathematics as well as to industry.