The Forster energy transfer

It is useful in discussion of weak coupling between nanostructures to remember the nonradiative mechanism of Forster resonant energy transfer from an excited molecule (a donor) to some other molecule (an acceptor) which can be in the ground or in an excited state. The probability of such a transfer is determined by the Coulomb nonretarded (instantaneous) dipole-dipole interaction between molecules and is proportional to Rp/R6 where Rp is the Forster radius and R is the distance between molecules. For organic materials the Forster radius is usually about several nanometers and strongly depends on the overlapping 

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Another major energy transfer process, the so-called Forster transfer mechanism is based on a dipole-dipole interaction between the host excited state and the guest ground state (Figure 4.2) [24], It does not include the transfer of electrons and may occur over significantly larger distances. The rate constant of the Forster energy transfer is inversely proportional to the sixth power of the distance R between the molecules ... 

Using the Forster energy transfer equations (16), one can calculate that Co2+ and Tb3+ are 13.7 A apart, in excellent agreement with the value of 13.7 A from the protein x-ray structure. This technique should be valuable for future applications to other multimetal ion binding proteins and enzymes. 

The self-assembled diad Zn P-PH2P consisting of a zinc porphyrin donor and a free base porphyrin acceptor (Scheme 7.4) was studied by time-resolved fluorescence [21]. The driving force of the assembly is the site selective binding of an imidazole connected to a free base porphyrin. Evidence for Forster back transfer was obtained from the analysis of the fluorescence decay (Fig. 7.8) and the relevant rate was quantitatively evaluated for the first time. The transfer efficiency [13] is 0.98, and the rate constants for direct and back transfer were found to be 24.4 x 10 s and 0.6 X 10 s respectively. These values are consistent with the Forster energy transfer mechanism. 

The rates of the Forster energy transfer and Dexter energy transfer depend on the separation distance between the donor and the acceptor, shown qualitatively in Fig. 1.1. The former decreases as the inverse sixth power of the distance, whereas the latter falls off exponentially as the distance increases. Therefore, the Forster energy transfer is able to occur over very large distances, while Dexter energy transfer will give much greater rates at short distances and close contacts. 

The real disadvantage of the Forster energy transfer is that it is proportional to r. Therefore, the decrease of the energy transfer as a function of distance occurs so rapidly that only two cases can be discerned the distance is either smaller or larger than the Forster radius. However, the measurement of the real distance between the photodonor and acceptor is virtually impossible. A typical Forster radius is 5 + 1 nm. 

The Forster energy transfer is a non-radiative transfer of electronic excitation from a donor molecule D to an acceptor molecule A, according to... 

The rate constant of energy transfer kj between the donor molecule and the acceptor molecule in the Forster energy transfer mechaitism can be described by the following equation ... 

The rod-coil copolymer was varied by the number of methylene groups in the coil segments that resulted in a changed supramolecular structure and directly affected the Forster energy transfer efficiency (an increase for this efficiency for 12 methylene units as compared to 7 methylene units) [131]. 

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