Radiative lifetime, fluorescence quantum yield

Table 7.11 Fluorescence quantum yield

The oscillator strength of the longest wavelength absorption band of BMPC (1.1, [25]) is very similar to those of two previously studied carbocyanines (DOC and DTC) [45] so that we can expect that, for BMPC as well as for EK)C and DTC, the radiative constant (kp) is equal to 2-3x10 s". Combining this value with the fluorescence quantum yield of BMPC in methanol, 4)p= 5.3x10", we can estimate its room-temperarnre fluorescence lifetime to be = 2 ps. 

As seen from (1) and (2), intermolecular processes may reduce essentially the lifetime and the fluorescence quantum yield. Hence, controlling the changes of these characteristics, we can monitor their occurrence and determine some characteristics of intermolecular reactions. Such processes can involve other particles, when they interact directly with the fluorophore (bimolecular reactions) or participate (as energy acceptors) in deactivation of S) state, owing to nonradiative or radiative energy transfer. Table 1 gives the main known intermolecular reactions and interactions, which can be divided into four groups ... 

The dependence of the fluorescence quantum yields and lifetimes of these stabilizers on the nature of the solvent suggests that the excited-state, non-radiative processes are affected by solvation. In polar, hydroxylic solvents, values of the fluorescence quantum yield for the non proton-transferred form are significantly lower, and the fluorescence lifetimes are shorter, than those calculated for aprotic solvents. This supports the proposal of the formation, in alcoholic solvents, of an excited-state encounter complex which facilitates ESIPT. The observed concentration dependence of the fluorescence lifetime and intensity of the blue emission from TIN in polymer films provides evidence for a non-radiative, self-quenching process, possibly due to aggregation of the stabilizer molecules. 

Herein, F is the radiative decay rate and km is the nonradiative decay rate, which comes from quenching. It has been demonstrated that silica nanomatrixes can change the fluorescence quantum yield and lifetime of fluorophores. Several groups have reported that both quantum yield and lifetime of fluorophores increased in DDSNs [27, 28, 52, 65-67]. However, the mechanisms regarding this enhancement were reported differently. 

Using the radiative lifetime, as previously defined, the fluorescence quantum yield can also be written as... 

It is interesting to note that when the fluorescence quantum yield and the excited-state lifetime of a fluorophore are measured under the same conditions, the non-radiative and radiative rate constants can be easily... 

Generally, an increase in temperature results in a decrease in the fluorescence quantum yield and the lifetime because the non-radiative processes related to thermal agitation (collisions with solvent molecules, intramolecular vibrations and rotations, etc.) are more efficient at higher temperatures. Experiments are often in good agreement with the empirical linear variation of In (1/Op — 1) versus 1/T. 

In the case of radiative transfer between identical molecules, the fluorescence decays more slowly as a result of successive re-absorptions and re-emissions. A simple kinetic model has been proposed by Birks (1970). It is based on the assumption of a unique value for the average probability a that an emitted photon is absorbed, i.e. without distinction between the generations of photons (a photon of generation n is emitted after n successive re-absorptions). This model leads to the following expressions for the effective lifetime and the macroscopic fluorescence quantum yield ... 

We have obtained additional evidence supporting the electron transfer mechanism of fluorescence quenching in 2 and 2 from picosecond transient absorption and fluorescence measurements. The fluorescence lifetimes of 1-2 in butyronitrile are reported in Table II. These lifetimes are proportional to the observed fluorescence quantum yields of these compounds and therefore indicate that the observed fluorescence quenching is not due simply to a change in the radiative rate for emission. 

The lifetimes of molecular fluorescence emissions are determined by the competition between radiative and nonradiative processes. If the radiative channel is dominant, as in the anthracene molecule, the fluorescence quantum yield is about unity-and the lifetime lies in the nanosecond range. In molecular assemblies, however, due to the cooperative emission of interacting molecules, much shorter lifetimes—in the picosecond or even in the femtosecond range—can theoretically be expected an upper limit has been calculated for 2D excitons [see (3.15) and Fig. 3.7] and for /V-multilayer systems with 100 > N > 2.78 The nonradiative molecular process is local, so unless fluorescence is in resonance by fission (Section II.C.2), its contribution to the lifetime of the molecular-assembly emission remains constant it is usually overwhelmed by the radiative process.118121 The phenomenon of collective spontaneous emission is often related to Dicke s model of superradiance,144 with the difference that only a very small density of excitation is involved. Direct measurement of such short radiative lifetimes of collective emissions, in the picosecond range, have recently been reported for two very different 2D systems ... 

We can provide the following summary for the decay behavior of simple aliphatic aldehydes and ketones with little or no vibrational excitation energy on the Sp manifold under "isolated" molecule conditions at room temperature. A typical fluorescence decay time (tp) measured by a single-photon time-correlated lifetime apparatus (248) is 2-5 ns (42,101,102). A typical fluorescence quantum yield (ketones measured by fluorescence excitation spectroscopy is 10-, but the value is somewhat lower for aliphatic aldehydes (101,102). These values indicate that the radiative process (kp) is lO -lO s-1, three orders of magnitude slower than the total rate of nonradiative processes (kpjp) of 10 10 s-1. A typical radiative lifetime (tr) is 0.1 0.5 ps for aliphatic aldehydes and 0.1 ps for aliphatic ketones. 

Energy-dependent (but not state-dependent) lifetime and quantum yield data are available for some of the more complex carbonyls. With reference to those molecules for which the appropriate data do exist, it can be seen in Table 11 that the radiative lifetime is virtually unaffected over a wide range of energies. This is in sharp contrast to the observed behavior of formaldehyde. The tr values for acetone might be less reliable than the others listed they are calculated using the fluorescence lifetime data of Breuer and Lee (42) and the fluorescence quantum yield data of Heicklen (105). It can be seen that there is no substantial change in tr the apparent (perhaps the real) trend is in the direction opposite that observed for formaldehyde. The values for perfluorocyclobutanone have been calculated using the rp and relative quantum yield values of Lewis and Lee (141) and the absolute fluorescence yield of 0.021 as measured by Phillips (187) as a standard. 

Note that if the radiative rate kf can be calculated, then the fluorescence decay rate and fluorescence lifetime follow from the fluorescence quantum yield (jy. Of course, the situation is often more complex. As will be described below, fluorescence decays for proteins often do not follow the single exponential decay model of Equation 2. The fluorescence quantnm yield and Equation 3 then provide an average fluorescence lifetime. 

The electronic coupling elements between the lowest excited CT state and the ground state (Fq) or the locally excited state lying most closely in energy V ) can be estimated from the CT absorption and fluorescence investigations [14, 54, 57], Applying a simple kinetic model of an irreversible excited CT state formation (with 100 % efficiency) the radiationless (k r) and radiative (kf) rate constants can be determined from the CT fluorescence quantum yields Of and lifetimes r ... 

In a very new report, Fujino et al. challenge the two-isomerization-mechanism concept on the basis of their time-resolved and time-integrated femtosecond fluorescence measurements of B-azobenzene following excitation of the (7t,7t ) State. They use the extremely weak fluorescence (cf. Figure 1.8) as an indicator for the population of the emitting state. From the ratios of their measured fluorescence lifetimes (S2 0.11 ps Sp 0.5 ps) and the radiative lifetimes deduced from the (absorption-spectra-based) oscillator strengths, they determine the fluorescence quantum yields 2.5310 for the emission and 7.5410" for the Si—>So emission. By comparison... 

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