Excited-state decays excitation conditions

FIG. 12 Simulation of fluorescent decays for dye species located in the aqueous phase following laser pulses in TIR from the water-DCE interface according to Eq. (38). A fast rate constant of excited state decay (10 s ) was assumed in (a). The results showed no difference between infinitely fast or slow kinetics of quenching. On the other hand, a much slower rate of decay can be observed for other sensitizers like Eu and porphyrin species. Under these conditions, heterogeneous quenching associated with the species Q can be readily observed as depicted in (b). (Reprinted with permission from Ref 127. Copyright 1997 American Chemical Society.)... 

Figure 15 illustrates the interplay between the time scales of intermediate state decay, final state decay, and dephasing in determining the photon energy dependence of 8s. The final state in Fig. 15 is chosen to satisfy the resonance condition when the intermediate state is resonantly excited, e/ e,- = 2(er — e,). 

Each y-ray energy emission connecting two excited states corresponds to the difference between the disintegration energy associated with the two a decays, which lead to the two limiting excited conditions. 

A related phenomenon is the conversion of single visible photons with the result the quantum efficiency can be higher than 100%. If, for example, 0.1% of Pr + is incorporated in YF3 and excited with the mercury spectral line at 185 nm, the electron from 4f5d states decay non-radiatively to the Sq (4p) State. This system is able to generate two visible photons by So- f6> followed by non-radiative decay to the closely adjacent Po and by transition another photon is emitted by transitions to one of the six /-levels of or F. A condition for this cascade process is that the nephelauxetic effect for inter-shell transitions is sufficiently weakly pronounced for the lowest 4/5d state to be above Sq (Reisfeld and Jbrgensen 1977). 

It is probably appropriate to note at this point that Stern-Volmer type of analysis of luminescence data obtained using modern gated spectrometers (such as the Perkin-Elmer LS5) follows different mathematical expressions than those used for data obtained under continuous irradiation conditions. This is true even for homogeneous systems where the excited state decays with simple monoexponential behaviour. 

Figure 5-16. State decay of DABCO/ether cluster (2p3s) Rydberg state observed through origin excitation. The conditions and conclusions are the same as described for Figure 5-15. 

The fluorescence signal can be used in a number of ways. Most simply it provides a measure of the population of the excited state or states through Equation 1. In addition, if a relationship can be found between the number density of all the quantum states under excitation conditions, then the total number density of the species can be deduced. Unfortunately, collisional decay process can cause redistribution of population from the excited level, complicating interpretation. 

Figure 6e, f show the experimentally relevant case in which a mixture of mechanisms occurs, i. e., E 0 and Wetu 0- The parameters have been chosen such that under steady-state excitation conditions 40% of the upconversion is generated by GSA/ESA, and 60% by GSA/ETU. Panel e shows that following a short pulse the properties of both panels a and c can be identified. Specifically, a nonzero N2 is observed at time = 0, but a delayed maximum and a long decay time are also observed. This provides a way to identify intensity involving both GSA/ESA and GSA/ETU contributions. This transient curve is triexponential, involving the decay of the GSA/ESA population, and the rise and decay of the GSA/ETU population (dashed lines). The analogous square-wave transient is shown in Fig. 6f. Termination of the square pulse leads to a simple biexponential decay curve, with a fast component corresponding to the natural decay rate of the upper state, and a slow component corresponding to twice the decay rate of the intermediate state (dashed lines). Again, a small deviation from pure biexponential behavior is observed at short times due to the effect of k2- The relative contributions of each mechanism, in this case 40 60, can be determined from the decay curve as shown in Fig. 6f. This information can be introduced directly into Eq. (10) for data simulation.

Case 2 Decay of excited states is much faster than the dynamic processes. This situation is most frequently encountered for excited singlet states, and the condition applies when [H] and kp are much smaller than Aq and k. The system can be viewed as having two populations of excited probe molecules which do not interchange during the excited state lifetime. Thus, no information on the dynamics of the probe can be obtained by directly following the decay of the excited states rather, each population of probe reports on their respective environments. 

The formal reduction of this transient state to a time-dependent resonance state whose initial condition is set at f = 0 presupposes the normally occurring situation that the duration of its preparation is much smaller than its lifetime, in which case the assumption of decoupling between excitation and decay is valid. Otherwise, when the time-scales of preparation and decay are comparable, it is necessary to resolve the coherent time evolution by solving the TDSE in the range -oo < f < oo, e.g.. Ref. [76] and Chapter 6. 

The lowest vibronic levels may be treated in terms of the weak-coupling case, as sparsely spaced, quasi-stationary v states nearly identical (except for an accidental degeneracy) with zero-order n states. In view of the low vibronic-level density, the conditions for a single-resonance excitation are easily fulfilled so that the excited, radiant v> ( s state decays by emission of the resonance fluorescence. This is the case for benzene, aniline, etc. 

It has to be stated that this simple fragmentation model cannot explain any energy dependence of the recorded data. For other excitation conditions, e.g. as used by Gerber and coworkers in their experiments on Na, the model might lose its validity. For example, Gerber and coworkers [71, 132] excited Nas close to four surface plasmon resonances at 2.39eV (518nm). Therefore, several ultrashort decay processes are involved simultaneously, instead of one in the case discussed here. 

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