Theory of mixed conduction

In part I above, c. Wagner s theory of mixed conduction was reviewed in terms of an equivalent circuit approach. The implications of mixed conduction theory for parabolic scaling of metals in high temperature atmospheres were also detailed. It was pointed out, however, that current interest in mixed conduction theory is no longer motivated by corrosion considerations because far too few systems of practical interest conform to the conditions required for pareibolic oxidation. 

These solid electrolytes do conform to the conditions laid out in Wagner s theory and many important applications cein be foreseen which would require devices based on such solid electrolytes. Some of these applications aire of the open circuit variety such as solid electrolyte emf sensors for high temperature environments where contamination of the electrolyte may be a problem. But many other applications will be of the closed circuit variety and to a large extent this aspect has not been negotiated very rigorously in the traditional theory. Significant extensions of the traditional theory will have to be made before the performance characteristics of fuel cells and high temperature steam hydrolyzers can be successfully analyzed via the theory of mixed conduction in solids. 

Of course the dependence of on x is also required if the integral in Equation 34 is to be evaluated. But determining that dependence is such a complicated matter that no solution can be given here at least for the most general case. For this reason, this matter of evaluating the conductance term defined in Equation 34 is the single most difficult problem here and it always arises when one tries to extend the theory of mixed conduction to non-open circuit conditions. In particular we must not only know how depends on the chemical potential of i or partial... 

It may be helpful at this point to ejcplain why the formidable "central problem" discussed above doesn t show up in the traditional theory of mixed conduction as developed by Wagner. He only treats two situations ion blocking electrode conditons and open circuit conditions. When the electrodes are ion blocking, l vanishes in Equation, 32 (for each ionic species) in which case Equation 32 is easy to integrate. 

Yokota I (1961) On the theory of mixed conduction with special reference to conduction in silver sulfide group semiconductors. J Phys Soc Jpn 16 2213-2223... 

The search for highly conducting low-dimensional materials has been at the forefront of chemical research in the last decade. There are two criteria which have to be satisfied, and which appear naturally from the theories of mixed valence (i) the metal-ligand units should occupy crystallographically similar sites and (ii) they should be mixed-valence units. 

Electrolytical production of metals from chalcogenide (in particular, sulphide) compounds was, in fact, the first problem where the researchers faced the essential effect of mixed conductivity in electrochemical practice. Owing to the studies of Velikanov and his team [1-7], we had got the term polyfunctional conductor (PFC) and the main ideas about physico-chemical properties of this object. According to his theory, the electronic conductance of PFC can undergo the semiconductor to metal transformation (Mott transition), which can be detected from the ccaiductivity-temperature dependency. The possibihty had been found for the enhancement of ionic conductivity and, thus, for the improvement of electrochemical behaviour of the melt. It was achieved by means of so-called heteropolar additives— compounds with ionic chemical bond. 

Chebotin s scientific interests were characterized by a variety of topics and covered nearly all aspects of solid electrolytes electrochemistry. He made a significant contribution to the theory of electron conductivity of ionic crystals in equilibrium with a gas phase and solved a number of important problems related to the statistical-thermodynamic description of defect formation in solid electrolytes and mixed ionic-electronic conductors. Vital results were obtained in the theory of ion transport in solid electrolytes (chemical diffusion and interdiffusion, correlation effects, thermo-EMF of ionic crystals, and others). Chebotin paid great attention to the solution of actual electrochemical problem—first of all to the theory of the double layer and issues related to the nature of the polarization at the interface of the solid electrol34e and gas electrode. 

A systematic study to identify solid oxide catalysts for the oxidation of methane to methanol resulted in the development of a Ga203—M0O3 mixed metal oxide catalyst showing an increased methanol yield compared with the homogeneous gas-phase reaction.1080,1081 Fe-ZSM-5 after proper activation (pretreatment under vacuum at 800-900°C and activation with N20 at 250°C) shows high activity in the formation of methanol at 20°C.1082 Density functional theory studies were conducted for the reaction pathway of the methane to methanol conversion by first-row transition-metal monoxide cations (MO+).1083 These are key to the mechanistic aspects in methane hydroxylation, and CuO+ was found to be a likely excellent mediator for the reaction. A mixture of vanadate ions and pyrazine-2-carboxylic acid efficiently catalyzes the oxidation of methane with 02 and H202 to give methyl hydroperoxide and, as consecutive products, methanol and formaldehyde.1084 1085... 

This is of the same form as Equation 30, but involves the mixed diffusion coefficient, Jci9, instead of the thermal conductivity of the mixture. However, as seen from the kinetic theory of gases, the thermal conductivity is proportional to the diffusion coefficient. Therefore agreement of experimental results with either Equation 30 or 53a is not an adequate criterion for distinguishing between first explosion limits in branching chain reactions and purely thermal limits. It has been reported (52), that, empirically,... 

The transport properties of such disordered materials (see Section II) are difficult to study, for several reasons. One is that the microscopic theory of transport is not clear even for perfectly ordered CPs, as discussed in the reviews mentioned above. Another is that a dc or low-frequency conductivity measurement on an inhomogeneous material can be viewed as measuring several resistances in series, the larger playing the major role. For instance, in a fibrillar material interfibril transport is important, in a mixed crystalline-amorphous medium the amorphous regions may limit... 

In the face of the complicated nature of carbon black it is not surprising that it proves to be difficult to predict theoretically the accurate conductivity of a composite with a given filler concentration. For one thing, the all-important structure is affected by the process of mixing the black into the polymer. Nevertheless, there are two theories which go some way in explaining the behaviour of the composites in certain regimes. 

In the previous section we saw the key roles played by the various partial conductivities—or equivalently the transference numbers—in mixed conduction theory. They appear prominently in the integrands of the formulas for open circuit emf emd scaling rate. Thus, if they exhibit any dependences on partial pressure Px2 which is equivalent to Px2 these dependences will have very... 

Treinsport in a mixed conducting medium is treated here, but only in terms of ion cind electron migration. This avoids unnecessary confusions in connection with defect theory and emphasizes the fact that in xjrtant results can be arrived at quite independently of specific assun tions about the defects involved (19). Any further breakdown of the ions euid electrons into defect species is neither necesseiry nor desirable for most purposes. 

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