Charge hopping percolation process

State conditions. It applies in situations where charge motion may be adequately described by means of mobilities and diffusion coefficients. Thus, certain hopping/percolation processes are excluded . Further, it is assumed that the Einstein relation, D. = (kT/ez.)u 5 holds between diffusion coefficient, D., and mobility, of a charge carrier of valence number z.. 

One way to determine the characteristics of these trajectories is by solving a transport equation with different probabilities of hopping of the charge carrier and the corresponding diffusion parameters of the host droplet. Another way, which we shall use here, is based on a visualization of the equivalent static cluster structure. This approach allows us to interpret the dynamic percolation process in terms of the static percolation. 

Monte Carlo simulation was carried out by Blauch and Saveant based on a percolation process, and Z>app was obtained as shown in Eq. (14-4) considering charge hopping and bounded motion of the redox center [14]. Bounded motion is a kind of local oscillation of redox molecules. In this model, charge transfer by molecular diffusion is not taken into account. 

The Percolation Process for Charge Hopping without Bounded Motion... 

When physical motion is either nonexistent or much slower than electron hopping, charge propagation is fundamentally a percolation process, because the microscopic distribution of redox centers plays a critical role in dictating the rate of charge transport [27-29]. Any self-similarity of the molecular clusters between successive electron hops imparts a memory effect, making the exact adjacent-site cormec-tivity between the molecules important. 

FIGURE 1.4. Schematic representation of charge injection/extraction at the electrode/ polymer interface and the quasi-diffusional charge percolation process (electron hopping) in a surface-immobilized electroactive polymer film. 

When a film is very thin, it may not be continuous, and conduction is subject to the percolation effect, whereby charge migrates by hopping or tunneling between island sites [50,51]. Such a process is activation controlled, and such thin films do not obey Ohm s law. The activation energy can be decreased by the presence of an applied electric field, making development of a rigorous theory difficult. The resistivity can be expressed by the relationship [5]... 

Until now we have considered electron-hopping processes in isolation to other charge percolation phenomena occurring in electroactive polymer films. This of course is not valid We must also consider the... 

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