Energy transfer overlap

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]. 

Et /ZG AG -0.2 V fluorescence quenching correlates with CT driving force no spectral overlap for energy transfer no Zs in injection site or intervening sequence k = 2 x 1011 s 1 observed up to 20 A in time-resolved and steady-state experiments shallow dependence of CT yield between 6-24 A (y = 0.2-0.3) no dependence of kci between 10-17 A strong efficiency and distance dependence of CT yield vary with Z flanking sequence and intervening mismatches... 

When D and A are similar molecules emission-reabsorption cannot be very important due to the usually small overlap of the emission and absorption spectra. Also, this mechanism should not be important for triplet-triplet energy transfer because of (a) low phosphorescence quantum yields in fluid solutions and (b) the low oscillator strengths for singlet-triplet absorption. 

It is possible to estimate the rate of vertical singlet energy transfer (9.31) and (9.33) (when Forster-type energy transfer is negligible, spectral overlap integral is very small) from the relation... 

Is the UV-stabilization only due to the screening effect (or more precisely light absorbing effect in a spectral region where the absorption spectra of polymer and UV-stabilizer overlap) of the UV-stabilizers and/or can it be enhanced by an energy transfer from the excited polymer to the stabilizer molecule ... 

FRET can take place if the emission spectrum of the donor overlaps with the absorption spectrum of the acceptor and they are located at separation distances within 1-10 nm from each other. The efficiency of energy transfer E can be defined... 

Takakusa H, Kikuchi K, Urano Y, Kojima H, Nagano T (2003) A novel design method of ratiometric fluorescent probes based on fluorescence resonance energy transfer switching by spectral overlap integral. Chemistry 9 1479-1485... 

Nonradiative transfer of excitation energy requires some interaction between donor and acceptor molecules and occurs if the emission spectrum of the donor overlaps the absorption spectrum of the acceptor, so that several vibronic transitions in the donor must have practically the same energy as the corresponding transitions in the acceptor. Such transitions are coupled, i.e., they are in resonance, and that is why the term resonance energy transfer (RET) or electronic energy transfer (EET) are often used. 

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... 

If the charge distributions of the D and A overlap than a new class of interactions has to be considered, namely the exchange interaction between the electrons on D and on A. This type of energy transfer is called Dexter transfer [80, 96,98], Here we briefly outline the physical principles involved. 

In previous chapters it was shown that FRET can be reliably detected by donor fluorescence lifetime imaging. Here, we will focus on what is perhaps the most intuitive and straightforward way to record FRET imaging of sensitized emission (s.e., that is, the amount of acceptor emission that results from energy transferred by the donor through resonance) by filterFRET. While simple in principle, determinations of s.e. are complicated by overlap of excitation and emission spectra of the donors and acceptors, and by several imperfections of the recording optics, light sources and detectors. 

Sensitized emission (/ ), as defined in Eq. (7.8), reliably measures the relative amount of energy transfer occurring in each pixel (Fig. 7.2, lower right panel). Iss is corrected for spectral overlap (i.e., Problem 1 has been taken care of) however, unlike E, it is not a normalized measure for interaction nor is it quantitative in absolute terms. It depends on the specific biological question which of the two yields the most relevant information. 

Thus, E is defined as the product of the energy transfer rate constant, ku and the fluorescence lifetime, xDA, of the donor experiencing quenching by the acceptor. The other quantities in Eq. (12.1) are the DA separation, rDA the DA overlap integral, / the refractive index of the transfer medium, n the orientation factor, k2 the normalized (to unit area) donor emission spectrum, (2) the acceptor extinction coefficient, eA(k) and the unperturbed donor quantum yield, QD. 

In contrast to the dipole-dipole interaction, the electron-exchange interaction is short ranged its rate decreases exponentially with the donor-acceptor distance (Dexter, 1953). This is expected since, for the electron exchange between D and A, respective orbital overlap would be needed. If the energy transfer is envisaged via an intermediate collision complex or an exciplex, D + A—(D-------A)- D + A, then Wigner s rule applies there must be a spin com-... 

Fluorescence resonance energy transfer (FRET) has also been used very often to design optical sensors. In this case, the sensitive layer contains the fluorophore and an analyte-sensitive dye, the absorption band of which overlaps significantly with the emission of the former. Reversible interaction of the absorber with the analyte species (e.g. the sample acidity, chloride, cations, anions,...) leads to a variation of the absorption band so that the efficiency of energy transfer from the fluorophore changes36 In this way, both emission intensity- and lifetime-based sensors may be fabricated. 

An increase in sensitivity and reliability of chip analysis can also be achieved by using fluorescence resonance energy transfer (FRET). For this purpose both the probe and the target are labeled with a fluorophor. When the emission spectrum of the donor, e.g. Cy5, overlaps with the absorption spectrum of the acceptor, e.g. Cy5.5, and the donor and the acceptor are at a certain distance from each other, energy is transferred from the donor to the acceptor on excitation of the donor fluorophor. 

Next we shall show that the electronic energy transfer rate can be put into the spectral overlap form. Notice that by ignoring the super-exchange term we have... 

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