Fluctuation induced tunnelling model

Fluctuation-induced tunneling model for highly doped polyacetylene (Ref. 9)... 

CNTs in polymer-CNT composites are efficiently debundled and isotropically dispersed in polymer matrices, the efficient interaction between CNT and polymer provides good dispersion and a low percolation threshold, but only relatively low conductivity near and above percolation, frequently around 10 s cm is achieved at close to 2wt% CNT loading [70, 71], The polymer layer in the intemanotube connections is supposed to be the highest resistance section in the electrical pathway. This polymer layer is a barrier to efficient carrier transport between CNTs, and models for conductivity based on fluctuation-induced tunneling have been proposed [72]. A power law related to percolation theory can be used to model conductivity in the following form ... 

Figure 1.40. Temperature dependence of the d.c. conductivity of heavily (iodine) doped polyacetylene and fit of the model of fluctuation-induced tunnelling. Solid curve theoretical fit. (Reprinted with permission from ref 84)...

Figure 3.12. Sheng s model considers the effect of fluctuation-induced tunneling through potential barriers between extended highly conducting regions. In a model circuit the barriers can be treated as capacitances with charging resistances [22b].

It seems plausible that the inter-fibre resistance behaves similarly to that between metallic grains in evaporated thin films or metallic particles in insulting polymer matrices. For this case a model of fluctuation-induced tunneling has been successfully applied /13/. It also fits perfectly to the temperature dependence of highly doped polyacetylene /lU,9/ (Fig. I8). We assume... 

Equation (1.6) accounts for both the Arrhenius regime and the temperature-independent low-temperature behavior, as described by the fluctuation-induced tunneling conductivity model. Each of the terms in curly brackets include a description of the forward current density component, in the direction of the applied electric field and a backflow current density in the opposite direction. The first term corresponds to the net current in the low-temperature limit, with an abrupt change in the density of states at the Fermi energy, while the other terms are corrections caused by expansion of the Fermi-Dirac distribution to first order in temperature. 

The temperature conductivity data of iodine doped PMQ3 (1.14 I per repeat from element analysis and weight gain.)(Figure 14) can be fitted not only with Equation 4, but also to a model of fluctuation-induced carrier tunneling (Equation 5). Either of them can be expected only when the metallic domain concentration increases to above the percolation threshold from broken paths. ... 

The realization that tunneling might be driven by thermally induced vibrations [48] in the protein scaffold (that is a thermally fluctuating energy surface), as described by the theoretical model of Kuznestov and Ulstrup [31] (analogous to electron transfer theory [49]) and illustrated in Fig. 13.1, has been a major step forward in recent years. This model has been adopted by Knapp and Klinman [14, 30], and is of the form ... 

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