Energy Forster mechanism

More recently Andrews and Juzeliunas [6, 7] developed a unified tlieory that embraces botli radiationless (Forster) and long-range radiative energy transfer. In otlier words tliis tlieory is valid over tire whole span of distances ranging from tliose which characterize molecular stmcture (nanometres) up to cosmic distances. It also addresses tire intennediate range where neitlier tire radiative nor tire Forster mechanism is fully valid. Below is tlieir expression for tire rate of pairwise energy transfer w from donor to acceptor, applicable to transfer in systems where tire donor and acceptor are embedded in a transparent medium of refractive index ... 

The occurrence of energy transfer requires electronic interactions and therefore its rate decreases with increasing distance. Depending on the interaction mechanism, the distance dependence may follow a 1/r (resonance (Forster) mechanism) or e (exchange (Dexter) mechanisms) [ 1 ]. In both cases, energy transfer is favored by overlap between the emission spectrum of the donor and the absorption spectrum of the acceptor. 

Self-assembly of functionalized carboxylate-core dendrons around Er +, Tb +, or Eu + ions leads to the formation of dendrimers [19]. Experiments carried out in toluene solution showed that UV excitation of the chromophoric groups contained in the branches caused the sensitized emission of the lanthanide ion, presumably by an energy transfer Forster mechanism. The much lower sensitization effect found for Eu + compared with Tb + was ascribed to a weaker spectral overlap, but it could be related to the fact that Eu + can quench the donor excited state by electron transfer [20]. 

In these dye-functionalized dendrimers, light absorbed by the numerous peripheral coumarin-2 units is funneled to the coumarin-343 core with remarkably high efficiency (toluene solution 98% for the first three generations 93% for compound 8). Given the large transition moments and the good overlap between donor emission and acceptor absorption, energy transfer takes place by Forster mechanism [34]. 

If the conditions for Forster transfer are not applicable, then the theory must be extended. There is recently experimental evidence that coherent energy transfer participates in photosynthesis [74, 75], In this case, the participating molecules are very close together. The excited state of the donor does not completely relax to the Boltzmann distribution before the energy can be shared with the acceptor, and the transfer can no longer be described by a Forster mechanism. We will not discuss this case. There has been active discussion of coherent transfer and very strong interactions in the literature for a longer time [69], and references can be found in some more recent papers [70-72, 76, 77],... 

Swager and co-workers have observed that energy transfer from conjugated polymers to other fluorophores does not always go by a Forster mechanism. 

Murphy CB, Zhang Y, Troxler T, Ferry V, Martin JJ, Jones WE Jr (2004) Probing Forster and Dexter energy-transfer mechanisms in fluorescent conjugated polymer chemosensors. J Phys Chem B 108 1537-1543... 

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. 

As well as returning to the ground state by radiative or radiationless processes, excited states can be deactivated by electronic energy transfer. The principal mechanisms for this involve dipole-dipole interactions (Forster mechanism) or exchange interactions (Dexter mechanism). The former can take place over large distances (5 nm in favourable cases) and is expected for cases where there is good overlap between the absorption spectrum of the acceptor and the emission spectrum of the donor and where there is no change in the spin... 

Dipole-dipole interaction the Forster mechanism (Figure 3.37). This is in fact the interaction of the transition moments of the excitation Q — Q and the deactivation M — M. As the excited electron of M falls to the lower orbital of M there is a change in dipole moment which produces an electric field this field is proportional to the transition moment M and to the inverse cube of the distance. An electron in the molecule Q therefore experiences a force proportional to M/r3, and as it moves towards a higher orbital it produces its own electric field which results in a force being applied on the electron in molecule M. In this way the downward motion of the electron in M and the upward motion of the electron in Q are coupled by their electric fields, the rate constant for energy transfer being... 

Figure 3.37 The Forster mechanism of energy transfer through transition dipole interaction.

Forster mechanism Energy transfer by dipole-dipole interactions... 

A non-radiative energy transfer solely by dipole-dipole interactions - without recourse to electron exchange - from energy donor to an acceptor (Fig. 5.4) is described by the Forster mechanism. 

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