Electrical conductivity relaxation measurements: Statistical investigations using sensitivity analysis, optimal experimental design and ECRTOOLS

Abstract

Abstract Mixed ionic and electronic conductors (MIECs) can be found in many applications of interest to solid state ionics, ranging from separation membranes, to solid oxide fuel cells and oxygen sensors. The performance of such MIEC-based devices is closely linked to fundamental transport and electrocatalytic properties such as the oxygen diffusion coefficient D and oxygen exchange rate k , which can be estimated using electrical conductivity relaxation (ECR). In this article, the statistical quality of k and D obtained using ECR is studied via asymptotic statistical methods. In particular, optimal experimental design (OED) is used to design experiments, which minimize the uncertainty on the estimated k and D , by selecting optimal sample size and experimental time span. Furthermore, robust OED is introduced as a tool to reduce the uncertainty on the estimated k and D when some prior information on the two quantities is available such as their literature values or their bounds in a given temperature range. In addition, it is shown that the sensitivity analysis can be used as a graphical tool to investigate the measurability of k and D and that the parameters governing the sensitivity are linked to the Biot number, the diffusion and reaction timescales. Similarly, flush time limitations can be linked to the Biot number and the ratio between the characteristic timescale of the flush process. All calculations are carried out with ECRTOOLS a freely available MATLAB toolbox which allows the estimation of k and D from ECR data, the evaluation of the quality of the estimated parameters and OED.