Mixed Conductor Model

Limitations of Bulk, ID Transport Models for Porous Mixed Conductors... 

The significance of this length parameter A can be understood by examining the predicted steady-state vacancy concentration profile in the porous electrode as shown in Figure 26a. At steady state, the model predicts that the mixed conductor will be reduced by an amount that decays exponentially with distance... 

Figure 26. Predictions of the Adler model shown in Figure 25 assuming interfacial electrochemical kinetics are fast, (a) Predicted steady-state profile of the oxygen vacancy concentration ( ) in the mixed conductor as a function of distance from the electrode/electrolyte interface, (b) Predicted impedance, (c) Measured impedance of Lao.6Cao.4Feo.8-Coo.203-(5 electrodes on SDC at 700 °C in air, fit to the model shown in b using nonlinear complex least squares. Data are from ref 171.

Figure 28. Svensson s macrohomogeneous model for the i— 1/characteristics of a porous mixed-conducting electrode, (a) The reduction mechanism assuming that both surface and bulk diffusion are active and that direct exchange of oxygen vacancies between the mixed conductor and the electrolyte may occur, (b) Tafel plot of the predicted steady-state i— V characteristics as a function of the bulk oxygen vacancy diffusion coefficient. (Reprinted with permission from ref 186. Copyright 1998 Electrochemical Society, Inc.)...

Bulk path at moderate to high overpotential. Studies of impedance time scales, tracer diffusion profiles, and electrode microstructure suggest that at moderate to high cathodic over potential, LSM becomes sufficiently reduced to open up a parallel bulk transport path near the three-phase boundary (like the perovskite mixed conductors). This effect may explain the complex dependence of electrode performance on electrode geometry and length scale. To date, no quantitative measurements or models have provided a means to determine the degree to which surface and bulk paths contribute under an arbitrary set of conditions. 

M. Kleitz and T. Kloidt, Dessemondt, Conventional oxygen electrode reaction facts and models, in F.W. Poulsen, J.J. Bentzen, T. Jacobsen, E. Skou, M.J.L. OstergSrd (Eds.), High Temperature Electrochemical Behaviour of Fast Ion and Mixed Conductors. Rise National Laboratory, Denmark, 1993, pp. 89-116. 

However, in order to fit the data accurately in the instances in which biofilms spanned the gap, it was necessary to add an extra resistor, representing an additional conductive pathway, in parallel to the RC model that described the controls without biofilms (Fig. 7.6b dotted line). This equivalent circuit method has been previously employed to measure conductivity of nanostructured films [51, 52] and conducting polymers [53] and serves to separate electronic and ionic conductivity in mixed conductors [49]. The need to include this extra conductance in the circuit model demonstrates that the biofilm is electronically conductive. Additional experiments in the absence of acetate further confirmed that the measured conductance is an intrinsic property of biofilm and does not arise from the charge transfer occurring at the biofilm/anode interface. 

AC impedance spectroscopy measurements further confirmed that the measured electron transport is electronic in nature. The necessity to include an additional current path to the ionic resistance shown in the equivalent circuit model of the control setup showed that the biofilm possesses significant electronic conductivity. This method has been employed successMly for mixed conductors [49]. 

J. Jamnik and J. Maier, Treatment of the impedance of mixed conductors equivalent circuit model and explicit approximate solutions, /. Electrochem. Soc. 146, 1999, 4183-4188. 

J. Jamnik, J. Maier and S. Pejovnik A Powerful Electrical network Model for the Impedance of Mixed Conductors Electrochim. Acta, 44 (1999) 4139. The figure is reprinted from this reference. Copyright 1989, with permission from Elsevier. 

A mixed ion conductor, BaSnO, has also been tested as a contact layer on a Schottky sensor [90]. The BaSnOj/SiC sensor showed a response to oxygen and this was most pronounced at 400°C. The sensor was tested from 200°C to 700°C. Operated at 700°C, the sensor showed a negative resistance peak at a bias of 2V (Figure 2.8). This peak was accounted for by the tunneling or Esaki effect [91]. Up to an operation temperature of 400°C, thermionic emission was proposed to explain its behavior. At higher temperatures, a resistance connected in series with a Schottky diode can model the device [5, 73]. At temperatures of 500-600°C, the BaSn03 shows a mixed behavior of electronic and ion conduction, and the Nernst potential [92] can be added to the model. The complete proposed model is given in (2.9). 

Hitherto we have dealt with model FICs that are mostly useful as solid electrolytes. The other class of compounds of importance as electrode materials in solid state batteries is mixed electronic-ionic conductors (with high ionic conductivity). The conduction arises from reversible electrochemical insertion of the conducting species. In order for such a material to be useful in high-energy batteries, the extent of insertion must be large and the material must sustain repeated insertion-extraction cycles. A number of transition-metal oxide and sulphide systems have been investigated as solid electrodes (Murphy Christian, 1979). 

When sodium lignosulfonate or sulfur lignin are compounded, for instance, with iodine or bromine, complexes supposedly form (16-17). These systems are conductors with mixed ionic and electronic nature. Presumably they are charge transfer complexes, since the electronic conductivity predominates (18-19). These compounded materials form charge transfer structures (20). Water is supposed to introduce ionic conductivity to the system. Impurities affect conductivity, too (21). In any case, the main models of conductivity are probably based on the band model and/or the hopping model. 

This expression is independent of molecular chain length and so is suitable for use with polymers of mixed molecular weight. The turn molecular rotation contribution can be obtained from either of the models for optical rotation we have presented 12-14), either as a sum of contributions from four-atom units or by use of helical conductor equation (Eq. 1) ... 

Similar approaches are used for most steady-state measurement techniques developed for mixed ionic-electronic conductors (see -> conductors and -> conducting solids). These include the measurements of concentration-cell - electromotive force, experiments with ion- or electron-blocking electrodes, determination of - electrolytic permeability, and various combined techniques [ii-vii]. In all cases, the results may be affected by electrode polarization this influence should be avoided optimizing experimental procedures and/or taken into account via appropriate modeling. See also -> Wagner equation, -> Hebb-Wagner method, and -> ambipolar conductivity. 

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