Energy intrinsic lifetimes

Here t. is the intrinsic lifetime of tire excitation residing on molecule (i.e. tire fluorescence lifetime one would observe for tire isolated molecule), is tire pairwise energy transfer rate and F. is tire rate of excitation of tire molecule by the external source (tire photon flux multiplied by tire absorjDtion cross section). The master equation system (C3.4.4) allows one to calculate tire complete dynamics of energy migration between all molecules in an ensemble, but tire computation can become quite complicated if tire number of molecules is large. Moreover, it is commonly tire case that tire ensemble contains molecules of two, tliree or more spectral types, and experimentally it is practically impossible to distinguish tire contributions of individual molecules from each spectral pool. 

FRET interactions are typically characterized by either steady-state or transient fluorescence emission signals from the donor or acceptor species. Efficient nonradiative energy transfer results in donor PL loss associated with acceptor gain in photoluminescence intensity (if the acceptor is an emitter). The rate of this energy transfer is related to the intrinsic lifetime of the isolated donor and depends strongly on the donor-acceptor separation distance ... 

Figure 16-4. Scheme proposed, based on CASPT2 calculations, for the main decay pathways of adenine (A), measured in molecular beams with intrinsic lifetimes t, < 100 fs and t2 1 ps. Energies in kcal mol-1 referred to the lowest conical intersection. A similar scheme is proposed for guanine (G). (Reproduced from Ref. [50] with permission from Wiley-VCH Verlag)... 

The situation when the gas is isotopically scrambled, however, is very different and indeed the experimentally observed measured quantity is also very different. When the gas is isotopically scrambled, one does not measure these specific ratios of rate constants. Instead, a statistical steady-state, such as Q -F OO QOO QO + O and in the above example O + QQ OQQ OQ + Q, exists at all energies, and now the energy distribution of the vibrationally excited intermediates is that which is dictated by the steady-state equations for the above reactions, and not by that of a vibrationally hot intermediate formed solely via one channel. Under such conditions all energies of the intermediate are statistically accessible, if not from one side of the reaction intermediate then from the other. Phrased differently, the isotopic composition of the collisionally stabilized product Q3 or QO2 or will typically differ from that of the vibrationally excited species Q or QO2, since the intrinsic lifetime of the latter is isotope-dependent, as discussed in [15]. The usual RRKM-type pressure-dependent rate expression and conventional isotope effect results, modified by the nonstatistical effect discussed earlier [15]. 

The energy transfer rate can be determined in several ways. One is by comparing the luminescence lifetime of the sensitizer in the presence of energy transfer with the intrinsic lifetime when no activators are present for energy transfer r ... 

Further confirmation of this assignment comes from time-resolved phosphorescence measurements. Figure 11.10 shows the phosphorescence decay curves of the PtOEP in MeLPPP, without and with benzil codoped at a concentration of 20 wt.%. In both cases, fast and slow components are observed. The decay time of the fast component agrees with the intrinsic lifetime of the triplet state of PtOEP (70-100 p,s). Obviously, the fast component is due to porphyrin molecules excited as a result of the singlet-singlet energy transfer from the polymer. 

Figure A3.12.2. Relation of state occupation (schematically shown at constant energy) to lifetime distribution for the RRKM theory and for various actual situations. Dashed curves in lifetime distributions for (d) and (e) indicate RRKM behaviour, (a) RRKM model, (b) Physical counterpart of RRKM model, (c) Collisional state selection, (d) Chemical activation, (e) Intrinsically non-RRKM. (Adapted from [9].)...

The experimental results for 6 were very encouraging. Excitation at 590 nm populates the two porphyrin excited singlet states, but steady state and time resolved fluorescence measurements revealed that singlet energy transfer from the Pzn to the free base P occurs with a time constant of ca. 40 ps and an efficiency of 90% (step 1 in Fig. 7), resulting in the excitation being localized on P. This result confinned the expectation that the added porphyrin would act as an antenna for the system. In a model dyad consisting of just the PZn-P species, the intrinsic lifetime of the firee base... 

Figure A3,12.2(a) illnstrates the lifetime distribution of RRKM theory and shows random transitions among all states at some energy high enongh for eventual reaction (toward the right). In reality, transitions between quantum states (though coupled) are not equally probable some are more likely than others. Therefore, transitions between states mnst be snfficiently rapid and disorderly for the RRKM assumption to be mimicked, as qualitatively depicted in figure A3.12.2(b). The situation depicted in these figures, where a microcanonical ensemble exists at t = 0 and rapid IVR maintains its existence during the decomposition, is called intrinsic RRKM behaviour [9].

Definitive examples of intrinsic non-RRKM dynamics for molecules excited near their unimolecular tluesholds are rather limited. Calculations have shown that intrinsic non-RRKM dynamics becomes more pronounced at very high energies, where the RRKM lifetime becomes very short and dissociation begins to compete with IVR [119]. There is a need for establishing quantitative theories (i.e. not calculations) for identifying which molecules and energies lead to intrinsic non-RRKM dynamics. For example, at thenual... 

The width and shape of the energy loss peaks in HREELS are usually completely determined by the relatively poor instrumental resolution. This means that no information can be obtained from HREELS about such interesting chemical physics questions as vibrational energy transfer, since the influence of the time scale and mechanism of vibrational excitations at surfaces on the lifetimes, and therefore the line widths and shapes, is swamped. (Adsorbates on surfaces have intrinsic vibra-... 

The lifetime, therefore, depends not only on the intrinsic properties of the fluorophore but also the characteristics of the environment. For example, any agent that removes energy from the excited state (i.e., dynamic quenching by oxygen) shortens the lifetime of the fluorophore. This general process of increasing the nonradiative decay rates is referred to as quenching. 

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