Electrical Conductivity Relaxation in the Nonlinear Regime

Abstract

Electrical Conductivity Relaxation (ECR) is an experimental procedure used to assess the chemical diffusion and reaction coefficients (i.e. Dchem and kchem) of mixed ionic electronic conductors (MIECs). The analytical model usually employed to fit the ECR data is based on linear physics. In fact, it is obtained from a linear partial differential equation for the oxygen diffusion with a linearized surface reaction rate as the boundary condition. In this article, we extend the linear approach and develop a novel 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, such as the 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.