Unsupported Situations Theoretical Models

Boundary Conditions Adsorption-Reaction Effects. The Macdonald- 

Franceschetti model involves relatively general boundary conditions at the electrodes and so includes the possibility of charge transfer reactions and specific adsorption. Because of its generality, however, the model prediction for Z,((o) is very complicated and, in general, cannot be well represented by even a complicated equivalent circuit. The Z,(m) expression, may, however, be used directly in CNLS fitting. Here, for simplicity, we shall consider only those specific situations where an approximate equivalent circuit is applicable. Idealizations involved in the model include the usual assumption of diffusion coefficients independent of field and position, the use of the simplified Chang-Jaff6 [1952] boundary conditions, and the omission of all inner layer and finite-ion-size effects. Some rectification of the latter two idealizations will be discussed later. 

The Chang-Jaff6 boundary conditions involve the physical assumption that the current arising from the reaction of a charge carrier of a given species is proportional to the excess concentration of that species at the interface, that is for, say, a negatively charged species. 

It proves convenient in the theoretical work to use the dimensionless Chang-Jaff6 rate parameters 

The rate-limiting diffusion of an electrode reaction can also be incorporated into the Chang-Jaffd boundary conditions by a similar approach. In this case, assuming, for example, diffusion through a semiinfinite electrode, the result obtained is 

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It is thus unfortunate that there has been a tendency among some workers in the solid electrolyte field to take over many of the relatively simple theoretical results derived for supported conditions and use them uncritically in unsupported situations, situations where the snpported models and formulas rarely apply adequately. For example the expression for the Warburg impedance for a redox reaction in a supported situation is often employed in the analysis of data on unsupported situations where the parameters involved are quite different (e.g. Sections 2.2.3.2 and 2.2.3.3). 

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