Energy resonance mechanism

The triplet-triplet energy transfer, which is doubly forbidden by a resonance mechanism, is allowed by an exchange mechanism ... 

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)... 

More convincing proof for a particle-enhanced energy transfer mechanism comes from a study of the concentration dependence of the transfer. Bulk Forster transfer leads to a linear dependence on acceptor concentration with constant donor-to-acceptor ratio. The resonance mechanism would be expected to saturate at (relatively) high concentrations and fall off linearly at very low concentrations. 

To conclude, even if there exist several processes that affect the vibrational line shape it seems probable that when most of them have been sorted out and with the good agreement between theory and experiment, the lifetime broadening for a chemisorbed CO molecule is of the order of a few cm, corresponding to a lifetime of a few ps. The main vibrational energy relaxation mechanism is creation of electron-hole pairs caused by the local charge oscillations between the metal and the 2n molecular resonance crossing the Fermi level. 

For quenching by energy transfer mechanism, the quencher must have suitable energy levels, singlet or triplet, near or below the energy level of the donor molecule. Such a transfer has the greatest probability if there is an approximate resonance between the donor and the acceptor energy levels. 

This is because the low efficiency of such a transfer is compensated by long lifetime. If other modes of triplet deactivation are less competitive, that is, similarly forbidden, intermolccular transfer may occur with reasonable rates. The slow rate of energy transfer is not incompatible with a large value of R0 for transfer by a resonance mechanism (Table 6.8). 

A DETAILED discussion of resonance energy can be found in books on quantum mechanics. A simple problem, the dependence of the energy resonance between two structures on the difference in energy of the structures, is discussed in the following paragraphs. 

A piezoelectric mass sensor is a device that measures the amount of material adsorbed on its surface by the effect of the adsorbed material on the propagation of acoustic waves. Piezoelectric devices work by converting electrical energy to mechanical energy. There are a number of different piezoelectric mass sensors. Thickness shear mode sensors measure the resonant frequency of a quartz crystal. Surface acoustic wave mode sensors measure the amplitude or time delay. Flexure mode devices measure the resonant frequency of a thin Si3N4 membrane. In shear horizontal acoustic plate mode sensors, the resonant frequency of a quartz crystal is measured. 

Fig. 3.7 Pictorial representation of resonance (coulombic) and exchange energy transfer mechanisms...

The Forster equation for the first-order rate constant, ke, for energy transfer by the inductive-resonance mechanism can be written in simplified form... 

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