Assessing the identifiability of k and D in electrical conductivity relaxation via analytical results and nonlinearity estimates

• Assessing the quality of estimation of k and D in ECR with analytical solutions
• Covariance matrix as a function of the sample geometries and Biot number
• Comparison on quality of estimation for different sample geometries
• Nonlinearities inherent to the estimation of k and D

The electrical conductivity relaxation (ECR) technique is a common experimental method for determining the surface reaction rate k and the bulk diffusion coefficient D of mixed ionic and electronic conductors (MIECs). The reliability of estimating k and D using ECR is often questioned. In this article, we utilize an asymptotic statistical method to assess the quality of the two estimated parameters for different sample geometries. Furthermore, we develop analytical expressions that allow us to generalize the expression of the covariance matrix of the combined k and D estimates as a function of two sets of generalized parameters. Those include the Biot number, the ratio between the diffusion and the reaction time scales, and a term that is proportional to the ratio between experimental noise level and the total number of data points. We also highlight the importance of considering higher order nonlinearities when determining the confidence region and assessing the identifiability of the estimates. This is particularly useful in assessing the predicted distribution of the parameter estimates when the level of noise in the measurement is large and/or the Biot number deviates significantly from unity.