Electron-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... 

With these data in hand, the maximum value of the electron hopping diffusion constant, D = 1.8 x 10 cm s , can be interpreted to yield the unimolecular rate constant (Ai) of electron transfer between adjacent Os(DPP)3 sites according to the following equation ... 

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. 

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 ... 

It is to be expected that the radiative rate constants for spontaneous emission of exciplexes and electroplexes will resemble those for excimer and electromers [see discussion of Eqs. (20) and (21) in Sec. 2.3.1)]. This implies that, dependent on the intermolecular configuration, the fluorescence lifetimes of exciplexes range between 10 and 200 ns, and that the emission lifetime of electroplexes is limited by the intermolecular electron hopping time. Though there are no at present direct lifetime measurements on electroplexes, the measurements on a series of donor-acceptor species in solid-state solutions of PC prove these predictions for exciplexes (Table 1). 

In the Miller-Abrahams expression, the hopping rates are a product of a prefactor v0, an electron overlap quantity Wy = Wji9 and the term exp[-(ey - zj)/kT when y > e, and unity for the case where ey < e7. For a pair of sites separated Ry in an isotropic medium, Wy = exp(-2yft7y). where y is an inverse wavefunction decay constant. To incorporate positional or off-diagonal disorder, Pautmeier et al. (1988, 1990) assumed that sites / and j make independent contributions as... 

When the appropriate equilibrium constants are not extremely small, direct electron (or hole) transfer to bridge units may occur and the electron (or hole) may then hop from moiety-to-moiety (randomly) along the bridge. When this happens, the electron-transfer rate will decrease only slowly with bridge length. This behavior has been treated in terms of standard nonadiabatic electron-transfer theory. ... 

This formula is applicable to both exothermic reactions, with AG < 0, and endothermic ones, with AG > 0. In fact, the rate constant for reverse electron transfer, from acceptor to donor, can be obtained by simply replacing AC with —AG in Eq. 25. It can easily be checked that they obey the principle of chemical equilibrium in Eq. 15. A special case of Eq. 25, for AG = 0, was obtained in conjunction with hopping rates of small polarons on a deformable lattice [11]. 

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