Transfer distance, critical

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

TaUe 4. Critical transfer distance (Ro) for poly(VBP), poly(VBP-co-St)s and poly(VBP-co-MMA)s against benzophenone (BP) [23,24]... 

Perrin Model. At the other extreme, Perrin (16) considered the case where the donor and acceptor molecules are immobile, and energy transfer occurs Instantaneously when the two molecules lie within a critical transfer distance, R, and does not occur at all at large intermolecular separations. 

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. 

We need not be concerned with the quantum mechanical treatment of electron exchange. All we need to know is that triplet energy transfer by electron exchange, the Dexter mechanism, requires appreciable overlap between the molecular orbitals of D and A, so that the critical transfer distance becomes essentially equal to the sum of the van der Waals radii of D and A. 

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

The critical transfer distance, R0, for which the excited energy transfer occurs within the fluorescence lifetime of the excited state is given by Eq. (1.155) where 0a is the quantum yield of fluorescence. 

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. 

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