Transport site hopping

Transmembrane channels represent a special type of multi-unit effector allowing the passage of ions or molecules through membranes by a flow or site-to-site hopping mechanism. They are the main effectors of biological ion transport. Natural and synthetic peptide channels (gramicidin A, alamethicin) allowing the transfer of cations have been studied [6.66-6.68]. 

Most of the redox centers in a polymer film cannot rapidly come into direct contact with the electrode surface. The widely accepted mechanism proposed for electron transport is one in which the electroactive sites become oxidized or reduced by a succession of electron-transfer self-exchange reactions between neighboring redox sites [22]. However, control of the overall rate is a more complex problem. To maintain electroneutrality within the film, a flow of counterions and associated solvent is necessary during electron transport. There is also motion of the polymer chains and the attached redox centers which provides an additional diffusive process for transport. The rate-determining step in the electron site-site hopping is still in question and is likely to be different in different materials. 

Mobility Scales with Average Inter site Hopping Distance, Gill identified an exponential dependence of electron drift mobility on average TNF intersite hopping distance and noted an associated decrease in hole drift mobility (35). Gilfs subsidiary observation that TNF addition also decreased hole mobility precisely because complexed carbazole is removed as a hole transport site provided evidence for the key role of the discrete carbazole groups in hole transport. 

It should be noted that the conductivity in ionic solids involves ion transport mechanism between coordinating sites (site-to-site hopping) and local structural relaxation. In general, the conductivity measured by ac measurements, can be expressed as a function of the conductivity from dc measurements, and the frequency (Bruce et al., 1983a,b Skinner and Munnings, 2002 Girdauskaite et al., 2006 Khrokunov et al., 2006 Berenov et al., 2007) ... 

Surfaces are heterogeneous on the atomic scale. Atoms appear in flat terraces, at steps, and at kinks. There are also surface point defects, vacancies, and adatoms. These various surface sites achieve their equilibrium surface concentrations through an atom-transport process along the surface that we call surface diffusion. Adsorbed atoms and molecules reach their equilibrium distribution on the surface in the same way. This view of surface diffusion as a site-to-site hopping process leads to the random-walk picture, in which the mean-square displacement of the adsorbed particle along the. r-component of the coordinate is given by... 

For simplicity we consider a Gaussian distribution of hopping sites and assume the same width of CT states and coulombically unbound transport sites. It should be emphasized that the averaging over energy in Eq. (6) is automatically taken care of. It implies that the rate of the first electron transfer event does not depend upon the energy of its target site but is governed by the disorder of the system and the value of b. 

Microporous Membrane and Surface Transport A full treatment of microporous membrane transport by site hopping is found in the hterature (Verweij, 2003 Verweij et al., 2006) and is summarized below. This treatment is also apphcable to the case of surface transport by diffusion hopping on the pore walls of meso- and macroporous stractures. 

Electron-hopping is the main charge-transport mechanism in ECHB materials. There is precedence in the photoconductivity Held for improved charge transport by incorporating a number of redox sites into the same molecule. A number of attempts to adapt this approach for ECHB materials have been documented. Many use the oxadiazole core as the electron-transport moiety and examples include radialene 40 and dendrimer 41. However, these newer systems do not offer significant improvements in electron injection over the parent PBD. 

Besides its temperature dependence, hopping transport is also characterized by an electric field-dependent mobility. This dependence becomes measurable at high field (namely, for a field in excess of ca. 10d V/cm). Such a behavior was first reported in 1970 in polyvinylcarbazole (PVK) [48. The phenomenon was explained through a Poole-ITenkel mechanism [49], in which the Coulomb potential near a charged localized level is modified by the applied field in such a way that the tunnel transfer rale between sites increases. The general dependence of the mobility is then given by Eq. (14.69)... 

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