Critical distance for energy transfer

Suppose we have a pH indicator like Phenol Red whose absorption spectrum is pH-sensitivewith pKa = 7.6 (Figure 10.12). Phenol Red displays two distinct absorption spectra for protonated form (pH 2.5) and for unprotonated form (pH 10.4). One of the possible donors is an Eosin which displays an emission spectrum that overlaps with the absorption spectra of the protonated and unprotonated forms (acceptors) of Phenol Red (Figure 10.12). The critical distances for energy transfer (R0),(32) calculated from spectral properties of Eosin and Phenol Red, are 28.3 and 52.5 A for protonated and unprotonated forms of Phenol Red, respectively. For randomly distributed acceptors in three dimensions with no diffusion, the donor decay is... 

Comparison of Experimentally Determined Rate Constants and Critical Distances for Energy Transfer with Those Calculated Using Forster s Theory1 ... 

Over what distances can energy be transferred in this way To answer this question it is important to realize that S has. several ways to decay to the ground state energy transfer with a rate P a, and radiative decay with a rale Ps (the radiative rate). We neglect nonradiative decay (but it can be included in Ps). The critical distance for energy transfer (R ) is defined as the distance for which P a equals Ps, i.e. if S and A are separated by a distance R, the transfer rate equals the radiative rate. For R > Rc radiative emission from S prevails, for R < R energy transfer from S to A dominates. 

In this equation the distance must be expressed in A. When A centres also are present the probability of emission from S and the probability of transfer from S to A are equal to one another if = 27 A, an appreciable distance. This distance, called the critical distance for energy transfer is denoted by the symbol / a. For > Tsa the emission is almost exclusively in S. For energy... 

TABLE 29 Experimental deactivation rates (see text for definitions), calculated energy transfer efficiencies, Eq. (153), and critical distances for 50% transfer (J ) in microcrystalline samples of [RM(L36)3]" helicates (M = Cr ", Ru") (data from Torelli et al., 2005)... 

The unwanted Dq - F emission of the Ss site is suppressed in the commercial 3% Eu samples by the occurrence of energy traiLsfcr from Eu +(S6) to Eu (C2). The critical distance for this transfer amounts to about 8 A and exchange as well as dipole-quadrupole interaction seem to play a role [IS]. 

The tendency for energy transfer between a pair of molecules in resists is characterized by a critical distance Rq at which the rate of energy transfer and the rate of spontaneous deactivation of the donor are equal. This leads to a con-... 

In the molecular model of Fig. 8.34a the potential curves V(/ ) are considered for the collision pairs A + B and A + B. At the critical distance the energy difference = V(AB ) — F(A B) may be equal to fuo. Resonant absorption of a photon by the collision pair A + B at the distance Rc results in a transition into the upper potential curve V(AB ), which separates into A + B. The whole process (8.42) then leads to an energy transfer from A to B, where the initial and final kinetic energy of the collision partners depends on the slope dV/dR of the potential curves and the internuclear distance Rq where photon absorption takes place. 

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... 

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-> n transitions) so that the Fdrster critical distance R0 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.(47-49)... 

The penetration depth of waves is defined as the distance from the surface of the material at which the power drops to 1 /e from its value at the surface. The penetration depth of microwaves is equal to 15 mm for water at 20 °C. The electromagnetic energy transfer is ensured by matched alumina windows. The propagated mode within the reactor is theoretically the TEn mode. The interest of this system is to make very specific chemical reaction such as oxidation in aqueous medium under critical conditions. 

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