Rate constant nonradiative energy transfer

Ln-L distance, energy transfer occurs as long as the higher vibrational levels of the triplet state are populated, that is the transfer stops when the lowest vibrational level is reached and triplet state phosphorescence takes over. On the other hand, if the Ln-L expansion is small, transfer is feasible as long as the triplet state is populated. If the rate constant of the transfer is large with respect to both radiative and nonradiative deactivation of T, the transfer then becomes very efficient ( jsens 1, eqs. (11)). In order to compare the efficiency of chromophores to sensitize Ln - luminescence, both the overall and intrinsic quantum yields have to be determined experimentally. If general procedures are well known for both solutions (Chauvin et al., 2004) and solid state samples (de Mello et al., 1997), measurement of Q is not always easy in view of the very small absorption coefficients of the f-f transitions. This quantity can in principle be estimated differently, from eq. (7), if the radiative lifetime is known. The latter is related to Einstein s expression for the rate of spontaneous emission A from an initial state I J) characterized by a / quantum number to a final state J ) ... 

The rate constant for nonradiative energy transfer via a dipole-dipole mechanism, k j, was derived by Forster [5,6] and is given in equation (1). 

Nonradiative processes (knr) can occur with a wide range of rate constants. Molecules with high knr values display low quantum yields due to rapid depopulation of the excited state by this route. The measured lifetime in the absence of collisional or energy transfer quenching is usually referred to as To, and is given by to = (kr + knr). ... 

Adams and Cherry (78) have investigated the effects of stilbene substitution on the behavior of their excited complexes with fumaronitrile and find that the rate constants for fluorescence and nonradiative decay are insensitive to substitution, but that the rate constant for intersystem crossing is increased by electron-donating substituents (lower stilbene oxidation potential). This trend is attributed to a decrease in the energy gap between the excited complex and locally excited 3t (Fig. 4). The observed energy gap dependence of the exciplex lifetime could also account for the absence of fluorescence (or cycloadduct formation, see Section IV-B) from the excited charge-transfer complexes of t-1 with stronger electron acceptors such as maleic anhydride (76) or tetracyanoethylene (85). 

In a typical SM-FRET experiment, one photoexcites the donor dye at a rate of kex 108.s. The photoexcited donor either fluoresces back to the ground state, with a rate constant kD ( 109.s ), or is quenched by nonradiatively transferring its energy to the acceptor, with a rate constant Uet (Cf. Fig. 1). In the case where energy transfer (ET) from donor to acceptor takes place, emission of a fluorescence photon by the excited acceptor, with rate constant ka ( 109.s ), follows. The fluorescence photon from the donor is typically blue-shifted relative to that from the acceptor, so that they can be detected in a selective manner. While the rate constants kn and are typically insensitive to the conformational state of the macromolecule, the ET rate constant ksT is strongly dependent on the conformational state of the macromolecule at the time when ET takes place (Cf. Eq. (1)). The probability per excitation event for quenching via ET is given by ... 

Figure 3. Energy level diagram and restrictions on kinetic parameters for the series of chromo-phores C, C2, C3. k C ) represents the intrinsic decay rates for C , regardless the radiative or nonradiative nature of the processes k and k2 are energy transfer rate constants.

In a molecular crystal the fluorescence decay reflects the sum of the rate constant for radiative and nonradiative decay of the excited state of the crystal. Information on energy transfer requires a fluorescent or nonfluorescent dopant that depletes the exciton reservoir. In a disordered system, in which the excited state is inhomo-geneously broadened a fluorescence decay study does yield information without requiring an excitation scavenger provided that the emission is spectrally resolved [see Section 3.2.3.1]. When measuring the decay within a spectrally narrow detection window one monitors the relaxation across the spectrally assessed energy slice of the EDOS. Such experiments were first done on films of PPV [70]. 

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