Forster interactions

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. 

Inasmuch as the interaction energy can be related to the transition moments, Forster has been able to develop a quantitative expression for the rate of energy transfer due to dipole-dipole interactions in terms of experimental parameters<4 aB-30) ... 

For dilute solutions of essentially independent donor and acceptor molecules the Forster or resonance interaction is quite important in molecular aggregrates and in molecular crystals exciton interactions are likely to be important. When the interaction is strong the excitation is not localized on the donor or acceptor but is spread over both. If larger aggregrates are involved, the excitation can be spread over many molecules/33-3 This can easily be seen for the case of a dimer where the donor and acceptor are... 

Forster, A. M., J. Chem. Soc., Dalton Trans., 1984, 2827 Interaction in absence of a solvent is explosive at ambient temperature. 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

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],... 

FRET is a nonradiative process that is, the transfer takes place without the emission or absorption of a photon. And yet, the transition dipoles, which are central to the mechanism by which the ground and excited states are coupled, are conspicuously present in the expression for the rate of transfer. For instance, the fluorescence quantum yield and fluorescence spectrum of the donor and the absorption spectrum of the acceptor are part of the overlap integral in the Forster rate expression, Eq. (1.2). These spectroscopic transitions are usually associated with the emission and absorption of a photon. These dipole matrix elements in the quantum mechanical expression for the rate of FRET are the same matrix elements as found for the interaction of a propagating EM field with the chromophores. However, the origin of the EM perturbation driving the energy transfer and the spectroscopic transitions are quite different. The source of this interaction term... 

The lifetime of the excited state of fluorophores may be altered by physical and biochemical properties of its environment. Fluorescence lifetime imaging microscopy (FLIM) is thus a powerful analytical tool for the quantitative mapping of fluorescent molecules that reports, for instance, on local ion concentration, pH, and viscosity, the fluorescence lifetime of a donor fluorophore, Forster resonance energy transfer can be also imaged by FLIM. This provides a robust method for mapping protein-protein interactions and for probing the complexity of molecular interaction networks. 

Energy transfer, as described by Forster [78], requires a long range dipole-dipole interaction between the donor and the acceptor fluorophore. This energy transfer is possible at distances between 2 and 10 nm. Contrary to what happens in collisional quenching, there is no need for physical contact between the two molecules. 

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 ... 

The interest in these block copolymer micelles arises from the polyelectrolyte coronal block whose intrinsic properties are strongly influenced by many parameters including pH, salt concentration, and polar interactions. Moreover, they provide a unique model to mimic polyelectrolyte brushes at a high segment concentration, as noted by Forster [15]. 

Energy transfer can result from different interaction mechanisms. The interactions may be Coulombic and/or due to intermolecular orbital overlap. The Coulombic interactions consist of long-range dipole-dipole interactions (Forster s... 

The magnitude of the interaction is even more important than its nature, and it is thus convenient to make a distinction, as proposed by Forster, between three main classes of coupling (strong, weak and very weak), depending on the relative values of the interaction energy (U), the electronic energy difference between D and A (AE), the absorption bandwidth (Aw) and the vibronic bandwidth (As) (Figure 4.15). 

By substituting Eq. (B4.4.5) into Eq. (B4.4.7), we obtain the Forster rate constant kjl (Eq. 4.78 in the text) for energy transfer in the case of long-range dipole-dipole interaction, and substitution of Eq. (B4.4.6) into Eq. (B4.4.7) leads to the Dexter rate constant k fl (Eq. 4.85 in the text) for the short-range exchange interaction. 

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