Rate of triplet energy transfer

Cundall has done extensive work on benzene231,237 and acetone243 sensitized isomerizations of the 2-butenes, and in every case reported a photostationary or radiostationary trans/cis ratio of 1.27-1.37. Sato, however, has measured a value of unity for the benzene photosensitized isomerization.510 With higher homologs, from 2-pentene to 2-octene, benzene-sensitized isomerizations yield trans/cis ratios of 1.0,238 while acetone-sensitized isomerization of the 2-pentenes in solution yields a ratio of 1.65.244 At present no explanation is possible for the differences between 2-butene and 2-pentene. Until much more information is gathered relating to rates of triplet energy transfer as functions of olefin structure, sensitizer, and medium, the natural decay ratios of each olefin s common triplet cannot be deduced from photostationary trans/cis ratios. 

Figure 3. Correlation between the experimentally measured rates of triplet energy transfer and the scaled product of the appropriate electron and hole transfer rates [41]. The straight line indicates the slope of unity which corresponds to = fSy. ...

The rate of triplet energy transfer in the original Dexter formulation is given by... 

There was a marked difference in the rate of triplet energy transfer for 24 and 26. In a benzene solution of 24, the carotenoid triplet species had a rise time of ca. 2/is and decayed in ca. lO s. Concomitant with the rise of the carotenoid triplet absorbance at 550 nm, the porphyrin triplet absorbance at 440 nm decayed with a time constant of 2/js. There was no appreciable change in these parameters when 24 was dissolved in a rigid plastic matrix [73]. For 26 the triplet energy transfer was much faster. In 1981, we reported it as faster than 30 ns, which was the limit of our instrumentation [91]. Measurements with greater time resolution were made in 1983, but it remained difficult to separate the carotenoid triplet rise time from the instrument response time [73]. In any case, under conditions ranging from solution to solid plastic to a glass at 10 K, the rise time of triplet carotene in 26 was < 5 ns. 

The nature of the lowest-lying excited states of the fullerenes has been difficult to identify with much certainty. From Shpol skii-type luminescence spectra recorded at 1.5 K it has been concluded that the first-excited singlet state in C70 is of A 2 character. The origins of the lowest energy transitions in Ceo, namely Si(T]g) and S2(Gg), have been assigned on the basis of fluorescence and excitation spectra, supported by theoretical calculations. " The luminescence properties and relaxation dynamics of single crystals of Qo have been described while related measurements have been made for solid films of Ceo " Similar studies have reported the luminescence spectral properties of 50 trapped inside the cavities of NiY zeolites. An analysis of the fine structure of electron-vibrational spectra has been made for 50 and its derivatives in a solid toluene matrix. The rate of triplet energy transfer between fullerenes in toluene solution has been measured as a function of temperature and used to derive thermodynamic parameters for the transfer process. ... 

In several cases, dependent on the donor, the electron transfer triplet energy transfer from the triplet state of the fullerenes to the donor was observed. For example, excitation of C6o/perylene (Pe) mixtures leads to 3Pe and C6o in a fast reaction ((1.4 0.1) X 109 M 1 s-1). The electron transfer from Pe to 3C o occurs with a rate one-third of triplet energy transfer [127]. Ito et al. investigated the photoexcitation of mixed system of C6o and (3-carotene [141], They observed triplet energy transfer from 3C o to (3-carotene in polar as well as in nonpolar solvents besides electron transfer from (3-carotene to 3C o However, the electron transfer rate constant increases with solvent polarity while the energy transfer is only less effected by the change of solvent polarity (Table 5). 

In the case of triplet energy transfer where electron exchange is the dominant interaction, Dexter has expressed the transfer rate as... 

TABLE 3. Rate Constants Of Triplet Energy Transfer. ... 

Fig. /. The four-state model used for the description of triplet energy transfer in the RC according to Angerhofer (1997). For detailed explanation, see text. The filled arrows denote the rates that have been observed and described in the literature. The broken arrows depict rates that are either unknown (from and to BS) or speculative (k3 -i for bypass reaction, and k4 -2 for tunneling). The rates defined by arrows between different molecules (P, B, and Car) are in reality second order rates, i.e. they depend on the ground state concentrations of the molecule the excited state of which they point to. In the case of low excitation densities, i.e., when double excitation of the RCs can be neglected these rates can be assumed to be first order as for example done by Frank et al. (1996b).

Figure 9.37 Rate constant versus driving force AC of triplet ET from 140biacetyl to aryl (%) and alkene (O) acceptors and theoretical curves generated using the semiclassical Marcus-jortner formalism of triplet energy transfer. Reprinted with permission from [115]. Copyright 1998 American Chemical Society...

State intensity and lifetime of the trimetallic complex are equal to the corresponding data for Gd meaning that the rate of the energy transfer process in [Yb2(105)] is at least one order of magnitude smaller than the decay rate of the triplet state (i.e., <10 s ). This points to an electron transfer mechanism for the excitation of the Yb( F5/2) state, the lifetime of which amounts to 18.2 0.8 ps in dmso-fie (Klink et al. 2000c, 2002). 

The triplet state of the hgand has to be located not too far in energy from one of the excited state of the lanthanide ions, in order to have an optimal rate of the energy transfer yet not too close to avoid energy back transfer from the lanthanide excited state to the triplet state, which would drastically decrease the luminescence intensity. 

Since S -T - energy gaps in organic molecules vary considerably, it is easy to find acceptor-donor pairs in which only triplet excitation transfer is energetically feasible. Such systems have been extensively exploited for study of the factors which influence the efficiency of Reaction (8). Three methods have been used to measure rates of triplet excitation transfers in solution. The first involves measurement of the phosphorescence lifetimes of the donor molecule as a function of the concentration of the acceptor molecule (Sandros and Backstrom, 1962). The general applicability of this method is severely limited by the fact that few molecules phosphoresce in solution. The second, more generally applicable, method uses the flash... 

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