Modeling, of hopping conductivity

The modeling of hopping conductivity of real amorphous dielectrics of limited thickness, with or without the incorporated space charge, has recently been done by Parkhutik and Shershulskii.62... 

The two-level model of hopping conductivity allows calculating from the set of experimental data the fundamental microscopical parameters of hopping conductivity - the electron localization radius and the concentration of localization centers corresponding to the intrinsic and impurity states [3]. 

The change in the dielectric properties of the polymer matrix, mainly of the dielectric constant, leads to a dramatic change in conductance due to the peculiarities of the hopping mechanism. In the course of our research [41] we treated the hopping conduction in polymer-nanocomposites in the framework of the Shklovski-Efros model of hopping conduction in semiconductors. The basic equation which determinies the composite conductivity in this case is ... 

Temperature-dependent conductivity data of q-6T are also inconsistent so far. Vaterlein et al. [326] find an exponential behavior with temperature T (a — gq exp(o r)) for undoped and doped o -6T as well as for EC6T even at low temperatures whereas an Arrhenius fit (cr = uo exp(—with Ep, as activation energy) reveals a large error. This exponential relation does neither fit into the above-mentioned model of hopping conduction nor in the SCLC model with shallow traps. For SCLC from equation 3 and... 

In solid state materials, single-step electron transport between dopant species is well known. For example, electron-hole recombination accounts for luminescence in some materials [H]. Multistep hopping is also well known. Models for single and multistep transport are enjoying renewed interest in tlie context of DNA electron transfer [12, 13, 14 and 15]. Indeed, tliere are strong links between tire ET literature and tire literature of hopping conductivity in polymers [16]. 

Neither of the above theories takes the macrostructure of carbon black into account in any quantitative way, although in practice this is crucial in selecting a material for a particular application. Sheng (1980) was, however, able to develop the first of these theories and extend its range of applicability. He noted the well-established model for hopping conduction by tunnelling... 

X and Y perpendicular distances. Bloch, Weisman, and Varma were the first to point out the significance of disorder for the transport properties of such materials, introducing the so-called "disorder model" and interpreting the temperature-dependence of 6 in terms of hopping conduction. Consider as an example a simple square lattice of molecular stacks withoC = 0 = and X +Y =S, Let S be the minimum distance... 

Friedman (1971) found a solution to this problem. He calculated the Hall mobility jjl using the random phase model which served also as the basis for the mobility expression Eq. (5.7). As in the case of hopping conduction of a small polaron (Holstein and Friedman (1968)) Friedman assumed that the applied magnetic field modifies the phase of the transfer integral between sites. A minimum of three sites, which are mutual nearest... 

As indicated earlier, polymers have a semicrystalline structure that is compatible with a two-phase model of polymer conductivity. A model proposed by Epstein and co-workers [8] describes the polymer sample as a set of metallic islands embedded in the insulating matrix. Conductivity is controlled by hopping of charge carriers between metallic islands. Such a structure may be a result of nonuniform doping as well as of two-phase crystalline-amorphous morphology. Interchain transport is favorable for high-density crystalline packing of macromolecules because... 

The influence of polymer matrix on the behavior nanocomposite system was the drastic increase of composite conductivity caused by absorption of water vapors by polymer matrix. The value of such a change has the sharp extremum corresponding to the range where hopping conduction dominates the system electroconductivity> It was assumed that the influence is primarily realized through the dependence of hopping conductivity (see Eq. (25)) on dielectric constant of polymer matrix, which is drastically changed when absorption of such polar molecules as HjO takes place. The simple theoretical model has been developed (mean field approximation) ... 

The first half of this chapter concentrates on the mechanisms of ion conduction. A basic model of ion transport is presented which contains the essential features necessary to describe conduction in the different classes of solid electrolyte. The model is based on the isolated hopping of the mobile ions in addition, brief mention is made of the influence of ion interactions between both the mobile ions and the immobile ions of the solid lattice (ion hopping) and between different mobile ions. The latter leads to either ion ordering or the formation of a more dynamic structure, the ion atmosphere. It is likely that in solid electrolytes, such ion interactions and cooperative ion movements are important and must be taken into account if a quantitative description of ionic conductivity is to be attempted. In this chapter, the emphasis is on presenting the basic elements of ion transport and comparing ionic conductivity in different classes of solid electrolyte which possess different gross structural features. Refinements of the basic model presented here are then described in Chapter 3. 

When sodium lignosulfonate or sulfur lignin are compounded, for instance, with iodine or bromine, complexes supposedly form (16-17). These systems are conductors with mixed ionic and electronic nature. Presumably they are charge transfer complexes, since the electronic conductivity predominates (18-19). These compounded materials form charge transfer structures (20). Water is supposed to introduce ionic conductivity to the system. Impurities affect conductivity, too (21). In any case, the main models of conductivity are probably based on the band model and/or the hopping model. 

The soliton conductivity model for rrans-(CH) was put forward by Kivelson [115]. It was shown that at low temperature phonon assisted electron hopping between soliton-bound states may be the dominant conduction process in a lightly doped one - dimensional Peierls system such as polyacetylene. The presence of disorder, as represented by a spatially random distribution of charged dopant molecules causes the hopping conduction pathway to be essentially three dimensional. At the photoexitation stage, mainly neutral solitons have to be formed. These solitons maintain the soliton bands. The transport processes have to be hopping ones with a highly expressed dispersive... 

The second necessary condition for crystalline or vitreous solid to have high ionic conductivity is that the mobile ions have a high diffusion coefficient, i.e. it is indeed a fast ion conductor . Much attention has been given to developing models of ionic motion. The simple hopping models applied successfully in the case of defect transport are not appropriate because of the high density of mobile ions in solid electrolytes, and... 

An alternative model considers the carriers to be localized on individual molecules, and that charge transfer occurs by the carrier hopping between these localized centres. The hopping process involves the charge carrier overcoming a potential energy barrier and thus involves an activation energy for conduction.7 The temperature dependence of this conductivity may depend on the dimensionality of the system.8... 

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