Slow steady transport with loading and bulk reactions: The mixed ionic conductor La2CuO4+delta
Academic Article
Overview
Research
Identity
Additional Document Info
Other
View All
Overview
abstract
We consider slow, steady transport for the normal state of the superconductor La2CuO4+ in a one-dimensional geometry. The fluxes at the sample ends are sufficiently general to permit oxygen to be driven into the sample (loaded) either by electrochemical means or by high oxygen partial pressure. We include the bulk reaction OO 2-+2h, where neutral atoms (a) go into ions (i) and holes (h). This system is a mixed ionic electronic conductor. For slow steady transport, the transport equations simplify because the bulk reaction rate density r and the bulk loading rates tn then are uniform in space and time. All three fluxes j must be specified at each surface, which for a uniform current density J corresponds to five independent fluxes. These fluxes generate two types of static modes at each surface, and a bulk response with a voltage profile that varies quadratically in space, characterized by J and the total oxygen fluxes jO (neutral plus ion) at the surfaces. One type of surface mode is associated with electrical screening; the other type is associated both with diffusion plus drift, and with chemical reaction (the diffusion-reaction mode). The diffusion-reaction mode is accompanied by changes in the chemical potentials , and by reactions and fluxes, but it neither carries current (J =0), nor loads the system chemically (jO=0). Generation of the diffusion-reaction mode leads to exponentially varying spatial profiles near electrodes. Within the bulk, the local fluxes satisfy a relation that is independent of the applied fluxes. As a consequence, the bulk response alone cannot match arbitrary values for the five independent input fluxes; matching occurs by generating appropriate amounts of the diffusion-reaction mode at each surface. The bulk response is completely responsible for steady loading and typically possesses a voltage profile that varies quadratically in space, as for the lead-acid cell. Seven macroscopic parameters (three /n's, three diffusion constants D, and a reaction rate constant ) characterize the theory. We indicate which measurements provide information about these parameters. In voltage profile measurements, only the characteristic length L of the diffusion-reaction mode depends on the reaction rate constant.
