Forster critical transfer distances

The degree of spectral overlap between the absorption spectrum of BDHM and the P2NMA monomer and excimer fluorescence emission, indicates that the BDHM chromophore is capable of acting as an acceptor in a Forster-type energy transfer process from both the monomer and excimer species. The values of the Forster critical transfer distance, Rq, for energy transfer... 

An estimate of Cq for the nonradiative transfer of energy from the excimer to a benzotriazole acceptor can be obtained from the relation Cq = Cq /y. After the substitution of the appropriate values of and y into this equation, a value for Cq of 0.109 M is obtained. Inserting this value for Cq into equation (5) results in a Forster critical transfer distance of 16 A which agrees well with the value estimated from steady-state measurements. This result provides further support for the proposal that the quenching mechanism for the excimer fluorescence from the 2NMA-BDHM copolymers involves one-step Forster energy transfer to a BDHM chromphore. 

Another way to express the rate introduces Rq, the Forster distance or critical transfer distance, at which the EET efficiency is 0.5 ... 

By applying Fermi s golden rule, Forster derived a very important relation between the critical transfer distance R0 and experimentally accessible spectral quantities (Equation 2.35),° 67,68 namely the luminescence quantum yield of the donor in the absence of acceptor A, orientation factor, k, the average refractive index of the medium in the region of spectral overlap, n, and the spectral overlap integral, J. The quantities J and k will be defined below. Equation 2.35 yields remarkably consistent values for the distance between donor and acceptor chromophores D and A, when this distance is known. FRET is, therefore, widely applied to determine the distance between markers D and A that are attached to biopolymers, for example, whose tertiary structure is not known and thus... 

Equation 2.35 ForsteTs equation to calculate the critical transfer distance R0 was erroneously printed with k6 instead ofn5 in the denominator in several papers by Forster. He corrected this misprint in a later publication.69 70 11... 

Thus, in rigid solutions, the critical transfer distance R0 can be determined experimentally either from the observed relative quantum yields of D or A at various concentrations of A (Equation 2.44) or from time-resolved measurement of the fluorescence decay of D (Equation 2.42). The results are in good agreement with those calculated from the Forster Equation 2.37. 

R0 is a critical transfer distance as defined in Forster s theory ... 

Further evidence of Forster-type energy-transfer effects has been obtained for several excited triplet-state donors and several ground-state doublet nitroxyl radicals. Critical transfer distances of the order of 12—20 A were measured and were on good agreement with calculated values. 

Here is Avogadro s number, D and A are as defined above, R° is either the Forster or Perrin critical transfer distance dependent on whether or not the migration is singlet-singlet or triplet-triplet, and kp can be obtained from a modified Stern-Volmer plot. 

In this equation is the fluorescence intensity of the donor emission and is the extinction coefficient of the acceptor at the wavenumber v. The distance between the donor and acceptor species at which excitation transfer and spontaneous deactivation of the donor are of equal probability is known as the critical transfer distance, Rq. An expression for Rq was also derived by Forster [5,6] and is given in equation (3). 

The critical transfer distance between the BDHM chromophore and P2NMA excimers is comparable with the estimated value oM 7 A which has been reported previously for Forster energy transfer between polystyrene (PS) excimers and the 2H5V comonomer [9,10]... 

Note that the transfer efficiency is 50% when the donor-acceptor distance is equal to the Forster critical radius. Equation (4.83) shows that the distance between a donor and an acceptor can be determined by measuring the efficiency of transfer, provided that r is not too different from Ro (which is evaluated by means of Eq. 4.80). 

The sixth power dependence explains why resonance energy transfer is most sensitive to the donor-acceptor distance when this distance is comparable to the Forster critical radius. 

Fig. 9.1. Variations in the transfer efficiency as a function of the ratio donor—acceptor distance/Forster critical radius.

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 ir transitions) so that the Forster critical distance Ro 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. " ... 

Complexadon of a bifluorophore would lead to a much larger increase in transfer efficiency if the interchromophoric distance were larger than the Forster critical radius in the free ligand and lower in the complex. In fact, because of the sixth power of the ratio R/Rq involved in the expression of transfer efficiency (29)... 

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