Slow, Steady-State Transport with "Loading" and Bulk Reactions: the Mixed Ionic Conductor La$_2$CuO$_{4+\delta}$

TL;DR

This paper analyzes slow, steady-state ionic and electronic transport in La$_2$CuO$_{4+\\delta}$, incorporating surface fluxes, bulk reactions, and resulting voltage profiles, revealing a diffusion-reaction mode that may explain voltage turbulence phenomena.

Contribution

It introduces a comprehensive model for steady-state transport in La$_2$CuO$_{4+\\delta}$, including surface fluxes and bulk reactions, and identifies a diffusion-reaction mode affecting voltage behavior.

Findings

Identification of a quadratic voltage profile in steady-state transport.

Discovery of a diffusion-reaction mode that does not carry current or load the system.

Explanation of voltage turbulence phenomena near electrodes in mixed ionic conductors.

Abstract

We consider slow, steady transport for the normal state of the superconductor La$_2$CuO$_{4+\delta}$ in a one-dimensional geometry, with surface fluxes 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 O$\to$O$^{2-}+2h$, where neutral atoms ($a$) go into ions ($i$) and holes ($h$). For slow, steady transport, the transport equations simplify because the bulk reaction rate density $r$ and the bulk loading rates $\partial_t n$ 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 flux $j_O$ (neutral plus ion) at each surface. One type of surface mode is associated with electrical screening; the other type is associated both with diffusion and drift, and with chemical reaction (the {\it diffusion-reaction mode}). The diffusion-reaction mode is accompanied by changes in the chemical potentials $\mu$, and by reactions and fluxes, but it neither carries current (J=0) nor loads the system chemically ($j_O=0$). Generation of the diffusion-reaction mode may explain the phenomenon of ``turbulence in the voltage'' often observed near the electrodes of other mixed ionic electronic conductors (MIECs).