Hopping, rate constant

Eq 5 reveals at a glance the two major components of the desired rate constant the primary electron-hopping rate constant, ke (r), which involves quantum and statistical mechanics associated with both heavy atom and electronic motion, on... 

The energy differences among nearby sites are altered by the presence of an electric field, and, therefore, so are the hopping rate constants. It is plausible, if not entirely obvious, that energetic disorder should generally make the mobility more strongly field-dependent. 

The diffusion of H and D atoms in the molecular crystals of hydrogen isotopes was explored with the EPR method. The atoms were generated by y-irradiation of crystals or by photolysis of a dopant. In the H2 crystals the initial concentration of the hydrogen atoms 4x 10 mol/cm is halved during 10 s at 4.2 K as well as at 1.9 K [Miyazaki et al. 1984 Itskovskii et al. 1986]. The bimolecular recombination (with rate constant /ch = 82cm mol s ) is limited by diffusion, where, because of the low concentration of H atoms, each encounter of the recombinating partners is preceded by 10 -10 hops between adjacent sites. 

Energy hopping among the peryleneimide chromophores, revealed by anisotropy decay times [30], occurs with a rate constant of 4.6x10 s E When three peryleneimide and one terryleneimide chromophores are attached to the dendrimer rim, energy transfer from the former to the latter units takes place with... 

Secondly, Fig. 5 shows that the polymeric rate constants parallel values of heterogeneous rate constants that have been observed for the electrochemical reactions of solutions of the corresponding dissolved porphyrin monomers. (The slope of the line is 0.5). This re-emphasizes what was said above, that measurements of electron hopping in polymers can give rate constants that are meaningful in the context of the metalloporphyrin s intrinsic electron transfer chemistry. 

We have also investigated the transient spectroscopy of hairpins such as 4GAGAGG (Fig. 9), which possess two hopping steps [40]. While a long lived-component of Sa transient decay can be observed, it is not possible to obtain the rate constants from a fit of the transient decay curves. 

The major part of the reports discussed above provides only a qualitative description of the catalytic response, but the LbL method provides a unique opportunity to quantify this response in terms of enzyme kinetics and electron-hopping diffusion models. For example, Hodak et al. [77[ demonstrated that only a fraction of the enzymes are wired by the polymer. A study comprising films with only one GOx and one PAH-Os layer assembled in different order on cysteamine, MPS and MPS/PAH substrates [184[ has shown a maximum fraction of wired enzymes of 30% for the maximum ratio of mediator-to-enzyme, [Os[/[GOx[ fs 100, while the bimolecular FADH2 oxidation rate constant remained almost the same, about 5-8 x 10 s ... 

Using a simple electrostatic interaction-based model factored into reaction rate theory, the energy barrier for ion hopping was related to the cation hydration radius. The conductance versus water content behavior was suggested to involve (1) a change in the rate constant for the elementary ion transfer event and (2) a change in the membrane microstructure that affects conduction pathways. 

Fig. 20 Charge carrier mobility in P3HT as a function of the charge carrier concentration. Squares refer to an experiment performed on a field effect transistor while circles refer to experiments done on an electrochemically doped sample. In the latter case the mobility is inferred from the steady state current at a given doping level. Solid and dashed lines have been fitted using the theory of [101]. The fit parameters are the site separation a, the prefactor Vq in the Miller-Abrahams-type hopping rate, the inverse wavefunction decay parameter y and the dielectric constant e. From [101] with permission. Copyright (2005) by the American Institute of Physics...

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