Electrochemical impedance spectroscopy of mixed conductors under a chemical potential gradient: a case study of Pt|SDC|BSCF

The AC impedance response of mixed ionic and electronic conductors (MIECs) exposed to a chemical potential gradient is derived from first principles. In such a system, the chemical potential gradient induces a gradient in the carrier concentration. For the particular system considered, 15% samarium doped ceria (SDC15) with Ba_(0.5)Sr_(0.5)Co_(0.8)Fe_(0.2O3-) (BSCF) and Pt electrodes, the oxygen vacancy concentration is a constant under the experimental conditions and it is the electron concentration that varies. The resulting equations are mapped to an equivalent circuit that bears some resemblance to recently discussed equivalent circuit models for MIECs under uniform chemical potential conditions, but differs in that active elements, specifically, voltage-controlled current sources, occur. It is shown that from a combination of open circuit voltage measurements and AC impedance spectroscopy, it is possible to use this model to determine the oxygen partial pressure drop that occurs between the gas phase in the electrode chambers and the electrode|electrolyte interface, as well as the interfacial polarization resistance. As discussed in detail, this resistance corresponds to the slope of the interfacial polarization curve. Measurements were carried out at temperatures between 550 and 650 °C and oxygen partial pressure at the Pt anode ranging from 10^(-29) to 10^(-24) atm (attained using H_2/H_2O/Ar mixtures), while the cathode was exposed to either synthetic air or neat oxygen. The oxygen partial pressure drop at the anode was typically about five orders of magnitude, whereas that at the cathode was about 0.1 atm for measurements using air. Accordingly, the poor activity of the anode is responsible for a loss in open circuit voltage of about 0.22 V, whereas the cathode is responsible for only about 0.01 V, reflecting the high activity of BSCF for oxygen electro-reduction. The interfacial polarization resistance at the anode displayed dependences on oxygen partial pressure and on temperature that mimic those of the electronic resistivity of SDC15. This behavior is consistent with hydrogen electro-oxidation occurring directly on the ceria surface and electron migration being the rate-limiting step. However, the equivalent resistance implied by the oxygen partial pressure drop across the anode displayed slightly different behavior, possibly indicative of a more complex reaction pathway

Chordal Graphs are Fully Orientable

Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let m and M denote the minimum and the maximum of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly d dependent arcs for every d satisfying m <= d <= M. A graph G is called chordal if every cycle in G of length at least four has a chord. We show that all chordal graphs are fully orientable.Comment: 11 pages, 1 figure, accepted by Ars Combinatoria (March 26, 2010