Metal coupled-currents approach

In all cases of electron transport, whether it be hopping, thermal emission, or quantum tunneling, the effect of the electric field in the oxide film is extremely important. In fact, the electric field effect on ion motion is the primary reason the electronic species must be considered at all in most real metal oxidation reactions. This can be understood better when we discuss the coupled-currents approach [10,11] in Sect. 1.15. 

We can think of the coupled-currents approach to metal oxidation in terms of the following logical sequence. 

This completes our development of the thick-film parabolic growth law. This particular theory has been presented in some detail because it is an extremely important domain of metal oxidation. In addition, it provides an excellent example of the way the coupled-currents approach [10,11] can be used to obtain oxide growth kinetics and built-in voltages in thermal oxidation. 

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

Much work has been directed towards the synthesis of thiophene oligomers and polymers. This is due to the current interest in research on conducting polymers and molecular electronics (92CRV711). Two main approaches have been used for making such polymers (i) chemical (e.g. FeCl3) or electrochemical oxidation of monomeric thiophenes and (ii) transition metal-catalyzed cross-coupling reactions. 

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