Resonance energy transfer diffusion rates

As long as r > 3R0, the fluorescence decay is close to exponential, the lifetime of the donor fluorescence decreases linearly with increasing concentration of A and fluorescence quenching obeys Stern Volmer kinetics (Section 3.9.8, Equation 3.36). However, the bimolecular rate constants ket of energy transfer derived from the observed quenching of donor fluorescence often exceed the rate constants of diffusion kd calculated by Equation 2.26, because resonance energy transfer does not require close contact between D and A. Finally, when r < 3R0, at high concentrations and low solvent viscosity, the kinetics of donor fluorescence become complicated, but an analysis is possible,109,110 if required. 

The transfers that take place by mechanism 1 are limited by diffusion of molecules in solution and should be affected by the viscosity of the medium. Transfers by mechanism 2, on the other hand, should be much less sensitive to the viscosity of the medium. It was shown by Foster [86] that the rate constant of resonance-energy transfer (mechanism 1), as a function of distance, is ... 

All of the examples of singlet energy transfer we have considered take place via the long-range resonance mechanism. When the oscillator strength of the acceptor is very small (for example, n-> n transitions) so that the Fdrster critical distance R0 approaches or is less than the collision diameter of the donor-acceptor pair, then all evidence indicates that the transfer takes place at a diffusion-controlled rate. Consequently, the transfer mechanism should involve exchange as well as Coulomb interaction. Good examples of this type of transfer have been provided by Dubois and co-workers.(47-49)... 

Diffuse reflectance spectroscopy (DRS) of VO-porphyrins on reduced and sulfided catalysts exhibit shifts in the porphyrinic electronic spectra (Soret, a, (3 bands) to higher frequencies. Adsorption results in modification of the delocalized electronic resonance structure not observed on the oxide form of the catalyst. X-ray photoelectron spectroscopy reveals shifts to higher Mo binding energies on reduced and sulfided catalysts following VO-porphyrin adsorption, consistent with transfer of electrons from Mo electron donor sites to the V02+ ion. Interaction at the electron donor sites is stronger than interaction at electron acceptor sites typical of the oxide catalyst. This gives rise to the possibility of lower VO-porphyrin diffusion rates on sulfided catalysts, but this effect has not been experimentally demonstrated. 

This is the rate of energy transfer by a single-step resonant interaction process plus terms describing the effects of this process on transfer by diffusion. At this point numerical integration must be used to obtain the explicit time dependence of the energy transfer rate. 

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