Thermodynamics and Kinetics of Charge Carriers

The statistics of the defects conceived as building elements (i.e., elements that can be 

In thermodynamic equilibrium, the equilibrium condition is Vpj. = 0 as regards the positional coordinate and = 0 (disappearance of the reaction sum of 

As described in Ref. [11], such equations can be symmetrized for local thermal equilibrium to give, for example, for the transport case the relationship 

A special problem consists of dealing with processes that do not lead to successful 

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J. Maier, Solid state electrochemistry I Thermodynamics and kinetics of charge carriers in solids, in Modern Aspects of Electrochemistry Vol. 38, Ed. by B. E. Conway, C. G. Vayenas, R. E. White, and M. E. Gamboa-Adelco Kluwer Academic/Plenum Pubishers, New York, 2005, pp. 1-173. 

Solid State Electrochemistry I Thermodynamics and Kinetics of Charge Carriers in Solids... 

This contribution deals with thermodynamics and kinetics of charge carriers in solids in the case of zero or non-zero electrical or chemical driving forces. It does not intend to repeat well-known electrochemical principles, however, it intends to underline the special situation in solids by, on one hand, emphasizing characteristic aspects due to the solid nature, but on the other hand, stressing the common and generalizing aspects of the picture whenever it appears necessary. This also implies that specific solid state aspects (such as structural details, anisotropies or strain effects) are neglected whenever their influence is not indispensable for the understanding. 

Electrochemistry 1 Thermodynamics and Kinetics of Charge Carriers in Solids, Modem Aspects of Electrochemistry, Vol. 38 (eds B.E. Conway, C.G. Vayenas and R.E. White), Kluwer Academic/Plenum Publishers, New York, pp. 1-173 ... 

Criteria 6 and 7 are important because in order to vary the kinetically relevant parameters such as the spatial distribution of charge carriers and the thermodynamic driving force, semiconductor electrodes with different majority carrier types, doping densities and band gaps must be used. 

As intensive studies on the ECPs have been carried out for almost 30 years, a vast knowledge of the methods of preparation and the physico-chemical properties of these materials has accumulated [5-17]. The electrochemistry ofthe ECPs has been systematically and repeatedly reviewed, covering many different and important topics such as electrosynthesis, the elucidation of mechanisms and kinetics of the doping processes in ECPs, the establishment and utilization of structure-property relationships, as well as a great variety of their applications as novel electrochemical systems, and so forth [18-23]. In this chapter, a classification is proposed for electroactive polymers and ion-insertion inorganic hosts, emphasizing the unique feature of ECPs as mixed electronic-ionic conductors. The analysis of thermodynamic and kinetic properties of ECP electrodes presented here is based on a combined consideration of the potential-dependent differential capacitance of the electrode, chemical diffusion coefficients, and the partial conductivities of related electronic and ionic charge carriers. 

Kinetic or activation overpotential is defined as the potential in excess of the thermodynamic equilibrium ( °) potential of the half-reaction that is necessary to drive the reaction, and often plays an important role in determining overall reaction rates. A means of increasing the reaction rate is to specifically improve the kinetics of the surface reactions by the addition of catalyst materials which can reduce these overpotentials. In metal electrodes, the modification of the surface with a catalyst increases the current at a given applied potential. Similarly in photoelectrodes, addition of a catalyst can ensure efficient catalytic turnover of photogenerated minority charge carriers at the semiconductor-electrolyte interface. 

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