Electron Hopping a More Detailed View

Intersite Electron Hopping a More Detailed View 

The process of intersite electron hopping has been discussed in terms of a quasi-diffusional process. We now take a more detailed view of the intersite electron transfer reaction in a fixed-site redox polymer. The approach adopted here is due to Fritsch-Faules and Faulkner. These researchers developed a microscopic model to describe the electronhopping diffusion coefficient Z e in a rigid three-dimensional polymer network as a function of the redox site concentration c. The model takes excluded volume effects into consideration, and it is based on a consideration of probability distributions and random-walk concepts. The microscopic approach was adopted by these researchers to obtain parameters that could be readily understood in the context of the polymer s molecular architecture. A previously published related approach was given by Feldberg.  

In the Fritsch-Faulkner model, it is assumed that redox centers are immobilized. This of course rules out electron transfer via physical diffusion of the center. The model is based on the notion of extended electron transfer. It is also assumed that the concentration, and therefore the spatial distribution of redox sites, affects the diffusion coefficient D. A notable feature of the analysis is the explicit consideration of the finite volume of the redox center, which for simplicity is assumed to be a rigid sphere. Excluded volume effects are important when the redox site concentration is high (recall that a typical value is in the range of 0.1-1 M). 

Since it is well-known that in a microscopic sense, diffusion can be modeled in terms of a random walk, then in three dimensions, the electron-hopping diffusion coefficient can be expressed as follows 

All redox centers are assumed to be identical, immobile, noninterac-tive hard spheres, which are randomly distributed throughout a rigid three-dimensional homogeneous network. An individual electron-hopping event is pictured as follows. The central site is in the reduced form, and it may donate its electron only by extended electron transfer to one of a number of neighboring oxidized sites. In contrast for hole hopping, an oxidized site can donate its hole to any one of several neighboring reduced sites. 

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