Charge transfer kinetics, site dependence

The EIS response depends on the flhn thickness and morphology, applied potential, and, obviously, the nature of the components of the hybrid system. The hydro-phobic nature of the polymer, the level of doping within the film, and the size of ions in contact with the polymer surface are factors to be considered for studying the response of such materials. In short, the kinetics of the overall charge transfer process should take into account (1) electron hopping between adjacent redox sites (Andrieux et al., 1986) usually described in terms of a Warburg diffusion impedance element (Nieto and Tucceri, 1996) and (2) double-layer charging at the metal-flhn interface, represented in terms of a double-layer capacitance element. 

All solid surfaces exhibit structural features that can have significant effects on the kinetics of charge transfer reactions and on the stability of the interfacial region. In the case of metals, the most significant structural features for "smooth" surfaces are emergent dislocations, kink sites, steps, and ledges. It has long been known, for example, that the kinetics of some electrodissolution and electrodeposition reactions depend on the density of such sites at the surface, but the exact mechanisms by which the effects occur have not been established. The role of "adion" in these processes is also unclear, as is the sequence of the dehydration-electronation-adsorption-diffusion-incorporation processes, even for the simplest of metals. 

Eor very high exchange current densities (i.e., rapid reactions), a linearized form of Eq. 27 can often be used. For very slow reaction kinetics, either the anodic or cathodic term dominates the kinetics, and so the other term is often ignored, yielded what is known as a Tafel equation for the kinetics. Often, more complicated expressions than that of Eq. 27 are used. For example, if the elementary reaction steps are known, one can write down the individual steps and derive the concentration dependence of the exchange current density and the kinetic equation. Other examples include accounting for surface species adsorption or additional internal or external mass transfer to the reaction site [9]. All of these additional issues are beyond the scope of this chapter, and often an empirically based Butler-Volmer equation is used for modeling the charge transfer in porous electrodes. 

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