Energy transfer exchange mechanism

Figure 4 Orbital scheme illustrating the quenching of a photo-excited fluorophore FI by a nearby metal centre M via an electronic energy transfer (ET) mechanism. A simultaneous exchange of two electrons takes place, one from FI to M, one from M to FI. Following this circular electron motion, FI is deactivated. The excited M centre which is obtained can emit and relax to its ground state, but in most cases undergoes a non-radiative decay.

Thennal equilibrium means free transfer (exchange) of energy in the fonn of heat, mechanical (liydrostatic) equilibrium means free transfer of energy in the fonn of pressure-volume work, and material equilibrium means free transfer... 

C3.4.6 EXCHANGE MECHANISM OF ENERGY TRANSFER IN FORBIDDEN TRANSITIONS... 

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. 

Ivey, H. J., and D. J. Morris, 1962, On the Relevance of the Vapor Liquid Exchange Mechanism for Subcooled Boiling Heat Transfer at Higher Pressure, Rep. AEEW-R-137, UK Atomic Energy Authority, Winfrith, England. (2)... 

The triplet-triplet energy transfer, which is doubly forbidden by a resonance mechanism, is allowed by an exchange mechanism ... 

When energy transfer takes place via an exchange mechanism, the system obeys Wigner s spin rule.(32) If and xs are the initial spin quantum numbers... 

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)... 

In addition, it can be shown for the concentration range of the 4,4 -BPDC used, assuming each molecule occupies a spherical volume, the average radius of this volume is about 108 a. This calculation predicts, on the average, the probability of an excited DMT molecule having a 4,4 -BPDC molecule within the required 15 A for energy transfer to occur by the exchange mechanism, which would be spin allowed, is small. 

The conclusion from the monomer solvent studies is that, in nearly equal molar solutions, DMT and 4,4 -BPDC compete for absorption of the 298 nm radiation. However, the results also show that, even in equal concentrations, the DMT emission, when excited by 298 nm light, is several times as intense as the 4,4 -BPDC emission at 472 nm. It must be emphasized that these studies do not preclude the existence of energy transfer from excited DMT to 4,4 -BPDC. From the volume calculation used above, it can be shown that a concentration of v 0.1 M 4,4 -BPDC is needed to assume an occupied volume with radius of 15 8, the required distance for the exchange mechanism. 

Based on luminescence studies, we postulated triplet-triplet energy transfer by electron exchange as the mechanism of photostabilization and we calculated an active quenching sphere with a radius, R0, of 19.7 A for 2,6-ND. Because the value of R0 is larger than 15 A, we postulated that energy migration was occurring. 

The rate of energy transfer at a very short donor-acceptor separation R by the exchange mechanism has been given by Dexter (1953) as follows ... 

Ehrenfest dynamics with the MMVB method has also been applied to the study of intermolecular energy transfer in anthryl-naphthylalkanes [85]. These molecules have a naphthalene joined to a anthracene by a short alkyl —(CH)n— chain. After exciting the naphthalene moiety, if n = 1 emission is seen from both parts of the system, if n = 3 emission is exclusively from the anthracene. The mechanism of this energy exchange is still not clear. This system is at the limits of the MMVB method, and the number of configurations required means that only a small number of trajectories can be run. The method is also unable to model the zwitterionic states that may be involved. Even so, the calculations provide some mechanistic information, which supports a stepwise exchange of energy, rather than the conventional direct process. 

Figure 23. Two principal mechanisms of excitation energy transfer (EET). (a) The Forster dipole-dipole mechanism, in which the active electrons, one and two, remain, respectively, on D and A throughout the process, (b) In the (Dexter) exchange mechanism, electrons one and two exchange locations.

Understand that triplet-triplet energy transfer by the dipole mechanism is forbidden, but that the application of the Wigner spin rule shows that it can occur by the exchange mechanism. 

Table 6.1 Some energy-transfer processes by the electron-exchange mechanism allowed according to the Wigner spin conservation rule...

Energy transfer by the exchange mechanism will occur provided the spin states before and after overlap obey the Wigner spin conservation rule that is, provided the overall spin states before and after overlap have common components (Table 6.1). 

According to the Dexter theory of energy transfer, the distance dependence of energy transfer by the exchange mechanism falls off rapidly and is given by ... 

Figure 6.15 Electron movements occurring in short-range triplet-triplet energy transfer by the exchange mechanism. Note that an electron initially on D moves to A and an electron initially on A moves to D ...

Fig. 4.14. Schematic representation of the (A) Coulombic and (B) exchange mechanisms of excitation energy transfer. Cl Coulombic interaction EE electron exchange.

Dexter s formulation of exchange energy transfer (very weak coupling) In contrast to the inverse sixth power dependence on distance for the dipole-dipole mechanism, an exponential dependence is to be expected from the exchange mechanism. The rate constant for transfer can be written as... 

Because the energy rate does not imply the transition moments in the exchange mechanism, triplet-triplet energy transfer is possible ... 

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