A statistical perspective on oxygen diffusion and surface exchange experiments: Sensitivity analysis, parameter estimation and robust optimal experimental design

The accurate determination of the diffusion and the surface exchange coefficients, indicated by k and D respectively, is of primary importance for solid state electrochemical systems because these two quantities directly relate to their performance. In this article methods to enhance the estimation process in isotope exchange depth profiling (IEDP) are presented. They are based on optimal experimental design (OED) and they leverage on an asymptotic evaluation of the covariance matrix of the estimated parameters. In this context OED is used for the determination of conditions that increase the accuracy and that are insensitive (or “robust”) with respect to variations of the physical parameters considered. Numerical simulations of IEDP under the thin film configuration are used to assess the quality of the estimation process, the impact of OED and the robustness of the designs.