Exchange mechanism of energy transfer

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

This formula was first derived in ref. 6 when calculating the kinetics of donor luminescence decay in the presence of the randomly, i.e. chaotically, located acceptors under the condition n N and on the assumption of the resonance exchange mechanism of energy transfer. Similar equations were later used for the analysis of experimental data on the kinetics of electron tunneling reactions obtained under conditions of the chaotic distribution of the reagents and at n < N. As a rule, only the first term of the exponent in eqn. (23) has been taken into account, which is equivalent to employing the previously mentioned (see Sect. 2.1) stepwise approximation of the function 0(R,t) = exp[- 1V(jR)(]. In this case, one obtains... 

It is worth noting that while Dexter s name became synonymous with the exchange mechanism of energy transfer, the main body of his seminal paper is devoted to spin-allowed EET mediated by the various multipole terms of the Coulomb interaction. 

The Dexter or electron exchange mechanism of energy transfer. 

Figure 3.36 The Dexter mechanism of energy transfer through simultaneous electron exchange.

On cooling films of pure polystyrene to 77K the ratio Ie/Im goes to almost zero (14). Assuming that excimer traps are preformed in the TTlm when cast, the population of such traps will remain constant, once the film is formed. Neither the exchange nor the dipole-dipole mechanism of energy transfer is particularly sensitive to temperature and thus it is difficult to see why the traps should not be populated at very low temperatures, if indeed the mechanism of population is by e.e.m. into the traps. 

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. 

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. 

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 ... 

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 ... 

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

Another evident mechanism for energy transfer to activated ions may be by bimolecular collisions between water molecules and solvated ion reactants, for which the collision number is n(ri+ r2)2(87tkT/p )l/2> where n is the water molecule concentration, ri and r2 are the radii of the solvated ion and water molecule of reduced mass p. With ri, r2 = 3.4 and 1.4 A, this is 1.5 x 1013 s"1. The Soviet theoreticians believed that the appropriate frequency should be for water dipole librations, which they took to be equal 10n s 1. This in fact corresponds to a frequency much lower than that of the classical continuum in water.78 Under FC conditions, the net rate of formation of activated molecules (the rate of formation minus rate of deactivation) multiplied by the electron transmission coefficient under nonadiabatic transfer conditions, will determine the preexponential factor. If a one-electron redox reaction has an exchange current of 10 3 A/cm2 at 1.0 M concentration, the extreme values of the frequency factors (106 and 4.9 x 103 cm 2 s 1) correspond to activation energies of 62.6 and 49.4 kJ/mole respectively under equilibrium conditions for adiabatic FC electron transfer. 

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