Time window, excited-state lifetime

Quantitative information can be obtained only if the time-scale of rotational motions is of the order of the excited-state lifetime r. In fact, if the motions are slow with respect to r(r ro) or rapid (r 0), no information on motions can be obtained from emission anisotropy measurements because these motions occur out of the experimental time window. 

Dynamic quenching of fluorescence is described in Section 4.2.2. This translational diffusion process is viscosity-dependent and is thus expected to provide information on the fluidity of a microenvironment, but it must occur in a time-scale comparable to the excited-state lifetime of the fluorophore (experimental time window). When transient effects are negligible, the rate constant kq for quenching can be easily determined by measuring the fluorescence intensity or lifetime as a function of the quencher concentration the results can be analyzed using the Stern-Volmer relation ... 

PPE signals give direct information on the density of states of the unoccupied states which is obtained only indirectly with other optical methods. One drawback is that since the excited electrons are detected, the observation time window is limited to the lifetime of the excited electrons. The excited state lifetimes at metal surfaces are typically less than a few hundreds of femtoseconds and much shorter than vibrational relaxation times. Hence the information is limited to that in the very beginning of the nuclear wavepacket motion, right after the photoexcitation. 

In the study of protein electron transfer (ET), radiolytic and photochemical techniques have indeed proven highly complementary. Between them, these techniques provide a range of reaction types and reaction free energies [cf. Zn porphyrin triplets (F° - 0.8 V) versus Fe porphyrins ( ° - 0 V)], Of particular interest in the current study is the different dynamic range(s) of the techniques. Photochemistry is subject to a natural time window set by the excited state lifetime only reactions faster than the excited state decay can be observed. Conversely, the bimolecular nature of radiolysis sets an upper hmit on the observed rates that is often determined by the rate of electron capture. 

The main features of the early kinetics could be reproduced using a five-level rate equation which included convolution with the pump and probe pulse shapes. These levels represent five locations, or time windows (L1-L5), describing five discrete time zones in the evolution of the Cr(CO)6 excited state and ultimate formation of Cr(CO)5 and Cr(CO)4 in the gas phase. These levels are consecutively populated and differ in the nature and ratio of the fragment ions they produce. Their populations are modeled by rate equations providing the lifetimes (x. for Li) and the ionization-dissociation cross section ("a. for Cr(CO)n+) for a particular fragment in Li. This five-level model is represented in Fig. 12 and Table 2 contains the optimized... 

The determination of the rate constants for photoinduced processes in supramolecular systems is possible via time-resolved fluorescence techniques [16] provided that the characteristic times of these processes fall into the experimental time window that is defined by the lifetime of the involved excited states. 

The chemical exchange rate(s) between two or more vanadium species can lie in about the same time window as the relaxation rates (lifetime of an excited state in an NMR... 

In order to optimise the manifold design of the flow system, the lifetimes of the excited states of the molecules should be considered, because the processed sample is in motion. In the situation of too high a flow rate and too small a flow cell, a fraction of the excited molecules could exit the flow cell without emitting light. On the other hand, if the flow rate is too low, a significant fraction of the molecules may emit radiation before reaching the flow cell. Both situations can lead to a decrease in the analytical sensitivity. This feature can be considered as a "time window" in flow analysis and the effect is more pronounced in phosphorimetric methods where light emission is slow relative to fluorimetric methods [65]. This is also true for chemiluminescence and bioluminescence, as discussed in the next section. 

For a realistic value of X = 0.5 eV and at room temperature this gives ket = 3.6xl08(HDA)2(ket in s" in cm ). Practical lower limits to kg for detection of intramolecular electron-transfer are either set by the lifetime of the electronically excited state from which it occurs (i.e. for photoinduced electron-transfer) or by competition of intermolecular electron- transfer, which is often occurring at a diffusion controlled rate. The former typically limits the time window for observation of kgj to < 10 ns, while at high dilution ( 10" mol/1) the latter does not produce problems if the intramolecular electron transfer proceeds significantly within < 10 ps. These constraints thus require kg values 10 s and S 10 s" corresponding to > 0.5 cm" and S 0.017 cm for photoinduced and thermal electron-transfer respectively, while the latter can be expanded to still much lower values if diffiisional encounter is avoided e.g. in solid matrices or for D/A pairs encapsulated in large protein envelopes. 

The ultimate single molecule detection limit is set by the probability with which a typical chromophore can emit a photon within a sub-picosecond time window. Even for the best chromophores with large transition dipoles and correspondingly high radiative rates this probability is low. The instantaneous brightness of a fluorophore is determined by the coefficient of spontaneous emission and hence by the extinction coefficient of the molecule. For an excellent molecular emitter with a radiative lifetime of 1 ns, such as for example the S2 state of porphyrins (smax = 600 000), the probability of emission within the initial 100 fs following excitation is only approximately 0.1%. Therefore, the molecule must be excited approximately 1000-times in order for one photon to be emitted with the specified 100 fs time window. Naturally, more than one photon must be collected in order to determine the dynamics of the system of interest and the collection efficiency of even the best microscope is far from 100%. 

Figure 30 Calculated state-resolved dissociation rates for NO2. The symbols indicate well converged (open circles) and less well converged (black dots) results. The smooth solid line indicates the quantum mechanical average (within windows of AE = 200 cm ). The points above the dashed line correspond to lifetimes shorter than the ballistic time for ejecting one of the 0 atoms. The solid stepped line is the SACM dissociation rate. The triangles represent the experimental average rates obtained by Kirmse et al. [35] and the shaded circles are the rates of Ionov et al. [34]. The hatched box a,t E = 0 shows the range of rates extracted from the energy-resolved spectroscopic experiment by Abel et al. [137]. The shaded boxes AE = 200 cm ) indicate the ranges of resonance states excited by the pump pulses with Apu — 396, 387, and 383 nm, respectively. Reprinted, with permission of the American Chemical Society, from Ref. 35.

---