A Nonlinear Model for Analyzing the Electrical Conductivity Relaxation Data of Mixed Ionic Electronic Conductors

Abstract

Mixed ionic electronic conductors (MIECs) are materials able to conduct both ions and electrons and are used in many applications including solid oxide fuel cells, electrolyzers, and oxygen sensors. The performance of these materials can be assessed using electrical conductivity relaxation (ECR) technique. This technique is used to obtain two physical parameters related to the diffusivity and activity of the MIEC namely, \U0001d437chem and \U0001d458chem. The analytical model usually used to fit the ECR data is obtained from a linear partial differential equation for the oxygen transport with a linearized surface reaction rate as the boundary condition. In this work, we extend the linear approach and develop a nonlinear ECR simulation framework. The latter is based on a nonlinear partial differential equation that models the transport of oxygen defects and nonlinear surface reaction rates. Our approach also considers the influence of extrinsic factors, namely the impact of testing-chamber’s size and the gas-feed flow-rates on the ECR response. We show that the nonlinear model is able to model ECR well beyond the limits of the typical linear analytical models, i.e., when the final partial pressures inside the testing chamber are low. Further, we also show that, under certain conditions, the exchange of oxygen between the MIEC and the testing chamber can significantly affect the ECR response.