Hopping mechanism model

As mentioned in Sec. 1.3, the electrochemical potential of electrons in condensed phases corresponds to the Fermi level of electrons in the phases. There are two possible cases of electron ensembles in condensed phases one to which the band model is applicable (in the state of degenera< where the wave functions of electrons overlap), and the other to which the band model cannot apply (in the state of nondegeneracy where no overlap of electron wave functions occurs). In the former case electrons or holes are allowed to move in the bands, while in the latter case electrons are assumed to be individual particles rather than waves and move in accord with a thermal hopping mechanism between the a4jacent sites of localized electron levels. 

For an adequate description of the temperature behavior of electric resistivity of complex salts [N-CH3-Pz](MTCNQ)2 and [N-C2H5-Pz](MTCNQ)2 we use a model based on a conductivity hopping mechanism possibly conditioned by the structural peculiarities of the ARS ... 

The general concepts as they were derived in the previous section apply only to theoretical models and/or idealized systems. In real systems, both superexchange and hopping mechanisms through modular bridges require a more sophisticated treatment. In fact, both mechanisms are omnipresent in charge-transfer reactions and interplay with each other. 

The DNA bases most easily reduced are T and C, the reduction potentials of which are very similar [26]. It is therefore expected that excess electron migration through DNA occurs via a hopping mechanism involving all base pairs (C-G and T-A) and the radical anions C and T as stepping stones. We focused our work on 5-pyrenyl-2 -deoxyuridine (Py-dU) and 5-pyrenyl-2 -deoxycytidine (Py-dC) as nucleoside models for ET in DNA. Photoexcitation of the pyrenyl group results in... 

As announced above these findings are in astonishing agreement with the heuristic pictures of the diffusion mechanism discussed in the framework of some microscopic diffusion models. But, besides being free of the conceptual drawbacks (the ad hoc assumptions) of the classical diffusion models, the MD method of computer simulation of diffusion in polymers makes it possible to get an even closer look at the diffusion mechanism and explain from a true atomistic level well known experimental findings. For example the results reported in (119,120) on the hopping mechanism reveal the following additional features. 

Concerning the slow dynamics below the crossover temperature Tc, the predictive power of the theory seems to be rather limited. In particular, the emergence of intrinsic slow secondary processes, which seems to be associated with the dynamic crossover in the experimental spectra, is not contained even in the extended versions of the theory consequently, the slow dynamics spectrum is not reproduced correctly. In this respect, the extended theory introducing the hopping mechanism for describing the susceptibility minimum below Tc is misleading. On the other hand, the most prominent prediction of MCT below Tc is the anomaly of the nonergodicity parameter, which, as discussed, is found by different model-independent approaches. However, within the framework of MCT, this anomaly is closely connected with the appearance of a so-called knee feature in the spectral shape of the fast dynamics spectrum below Tc. This feature, however, has not been identified experimentally in molecular liquids, and only indications for its existence are observed in colloidal systems [19]. In molecular systems, merely a more or less smooth crossover to a white noise spectrum has been reported in some cases [183,231,401]. Thus, it may be possible that the knee phenomenon is also smeared out. 

Finally, the data of electrical conductivity and thermopower of Lai xSrxMn03.5 at elevated temperature has been treated by a hopping mechanism for x < 0.2, and by a band model for the semi-metallic behaviour observed at x > 0.3 by Mizusaki [161]. On the other hand, to explain their results of Laj. Sr MnOs and Lai. rxMn03 5 for compositions with 0.30 < x 0.80, Stevenson et al. [209] included the thermally activated charge disproportionation of Mn " into Mn " and Mn " pairs. 

Gileadi et al. [22], in their study of the conductivity characteristics of certain salts, namely AlBr3-LiBr and AlBr3-KBr, in toluene, have observed a behavior similar to that found by Fuoss and Kraus. The model proposed by them is based on a hopping mechanism of ionic species from one cluster to another. 

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