Theoretical Models of Electron Transport

Theories of electron mobility are intimately related to the state of the electron in the fluid. The latter not only depends on molecular and liquid structure, it is also circumstantially influenced by temperature, density, pressure, and so forth. Moreover, the electron can simultaneously exist in multiple states of quite different quantum character, between which equilibrium transitions are possible. Therefore, there is no unique theory that will explain electron mobilities in different substances under different conditions. Conversely, given a set of experimental parameters, it is usually possible to construct a theoretical model that will be consistent with known experiments. Rather different physical pictures have thus emerged for high-, intermediate- and low-mobility liquids. In this section, we will first describe some general theoretical concepts. Following that, a detailed discussion will be presented in the subsequent subsections of specific theoretical models that have been found to be useful in low- and intermediate-mobility hydrocarbon liquids. 

The electron in a condensed medium is never entirely free, being in constant interaction with the molecules. It is designated quasi-jree when its wave function is delocalized and extends over the medium geometry. Such quasi-free electrons do 

The more incisive calculation of Springett, et al., (1968) allows the trapped electron wave function to penetrate into the liquid a little, which results in a somewhat modified criterion often quoted as 47r/)y/V02 0.047 for the stability of the trapped electron. It should be noted that this criterion is also approximate. It predicts correctly the stability of quasi-free electrons in LRGs and the stability of trapped electrons in liquid 3He, 4He, H2, and D2, but not so correctly the stability of delocalized electrons in liquid hydrocarbons (Jortner, 1970). The computed cavity radii are 1.7 nm in 4He at 3 K, 1.1 nm in H2 at 19 K, and 0.75 nm in Ne at 25 K (Davis and Brown, 1975). The calculated cavity radius in liquid He agrees well with the experimental value obtained from mobility measurements using the Stokes equation p = eMriRr], with perfect slip condition, where TJ is liquid viscosity (see Jortner, 1970). Stokes equation is based on fluid dynamics. It predicts the constancy of the product Jit rj, which apparently holds for liquid He but is not expected to be true in general. 

X = (pc2)-1 in place of its isothermal counterpart, where p is the mass density of the liquid and c is the speed of sound. With this modification, the agreement between theory and experiment improves somewhat yet some fundamental difference remains unexplained. 

In high-mobility liquids, the quasi-free electron is often visualized as having an effective mass m different fron the usual electron mass m. It arises due to multiple scattering of the electron while the mean free path remains long. The ratio of mean acceleration to an external force can be defined as the inverse effective mass. Often, the effective mass is equated to the electron mass m when its value is unknown and difficult to determine. In LRGs values of mVm 0.3 to 0.5 have been estimated (Asaf and Steinberger,1974). Ascarelli (1986) uses mVm = 0.27 in LXe and a density-dependent value in LAr. 

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Why did we introduce this purely experimental material into a chapter that emphasizes theoretical considerations It is because the ability to replicate Tafel s law is the first requirement of any theory in electrode kinetics. It represents a filter that may be used to discard models of electron transfer which predict current-potential relations that are not observed, i.e., do not predict Tafel s law as the behavior of the current overpotential reaction free of control by transport in solution. 

Theoretical Model of Hot Electron Transport and Reaction Probability... 

In crystalline semiconductors, the investigation of electronic transport properties (measured as a function of temperature or electric or magnetic field strength) can provide information on the scattering mechanism, carrier concentration and mobility, Fermi-level position, etc. Yet none of these latter quantities is obtained directly from the experiment Theoretical models for the transport are fitted to the experiment data to obtain transport parameters. The validity of both transport theories and transport parameters is checked by the quality of the fit and by a comparison of parameters obtained from different transport experiments. 

Fig. 6 Basics of the theoretical model for charge transport based on conical intersections (Coins) and the excimer-Hke interaction between the donor and acceptor electronic states of a molecular system formed by 2 monomers (a), PESs of the donor and acceptor electronic states in the adenine-cytosine (AC) heterodimer and the cytosine-cytosine homodimer (b) and scheme of the Coin-based mechanism for charge transport in DNA (c).

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