Critical interaction distance

Since any quenching action is a bimolecular process, it is essential that the molecules M and Q should be in relatively close contact, but not necessarily in hard sphere (van der Waals) contact. Theoretical models lead to the distance dependence of the quenching rate constants as exponentials or sixth powers of r, the centre-to-centre distance of M and Q. Since these distance dependences are very steep, it is convenient to define a critical interaction distance r at which the quenching efficiency is, this being the distance at which 50% of the molecules M decay with emission of light (or undergo a chemical reaction) and 50% are quenched by some nearby molecule Q. 

At this point it is convenient to introduce the critical interaction distance defined as... 

Thus, the critical interaction distance is the sensitizer-activator separation for which the transfer rate is equal to the intrinsic decay rate. 

From the preceding section it is clear that certain important questions must be answered in characterizing host sensitized energy transfer in a specific material. The first question is whether the transfer is a single-step or multistep process. If it is a single-step process, the type of interaction mechanism must be identified and the strength of the interaction determined. The latter is usually characterized by the critical interaction distance Rq. Finally, it is important to determine whether the energy transfer is a resonant or phonon-assisted process. If the transfer is a multistep process, two distinct sets of parameters must be determined ... 

This is due to the fact that the emission of the tantalate group in YTa04 is at such hi energies (viz. 30000 cm" )> the spectral overlap is no longer with the forbidden narrow absorption lines of the rare earth ions, but with allowed, broad bands. The critical interaction distance, Rq, has been estimated to be 10 A in the case of tantalate to terbium transfer. 

Luminescence kinetics studies of host-sensitized energy transfer in Eu -doped Cap2 crystals have also been reported and both radiative transfer and exciton diffusion have been found to contribute to the results. The diffusion distance is found to be about 25 A at low temperatures and increases by about an order of magnitude at high temperatures. Single-step electric dipole-dipole interaction also contributes to the energy transfer with the critical interaction distance calculated to be about 16 A. 

Here pis the quantum efficiency of the sensitizer (ti = Tp/xp = l/3forpentacene)in the O4 site of p-terphenyl at 4 K, n is the index of refraction (n = 1.7 for the p-terphenyl crystal), and Na is the Avogadro s number. The integral in (H9) is calculated from the normalized fluorescence spectrum/(v) and the decadic molar extinction coefficient e(v) of pentacene at O4 site. The critical interaction distance is the sensitizer-activator separation for which the transfer rate is equal to the intrinsic decay time. Although derived for low temperatures. Equation H9 is also vaUd for arbitrary temperatures. In fact, the temperature dependence of the resonant energy transfer rate is contained in the spectral overlap integral. 

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