Apparent lifetimes

Jablonski (48-49) developed a theory in 1935 in which he presented the now standard Jablonski diagram" of singlet and triplet state energy levels that is used to explain excitation and emission processes in luminescence. He also related the fluorescence lifetimes of the perpendicular and parallel polarization components of emission to the fluorophore emission lifetime and rate of rotation. In the same year, Szymanowski (50) measured apparent lifetimes for the perpendicular and parallel polarization components of fluorescein in viscous solutions with a phase fluorometer. It was shown later by Spencer and Weber (51) that phase shift methods do not give correct values for polarized lifetimes because the theory does not include the dependence on modulation frequency. 

It is important to note that if a mixture of fluorophores with different fluorescence lifetimes is analyzed, the lifetime computed from the phase is not equivalent to the lifetime computed from the modulation. As a result, the two lifetimes are often referred to as apparent lifetimes and should not be confused with the true lifetime of any particular species in the sample. These equations predict a set of phenomena inherent to the frequency domain measurement. 

Spectral FLIM involves measuring the apparent lifetimes in a preparation at many wavelengths with the assistance of a spectrograph or a series of filters (see also Chapter 4, Figs. 4.7 and 4.8 depicting hyperspectral FLIM in the time domain). The goal of the measurement is similar to that of the multifrequency approach ... 

Xanthylidene also does not react measurably with 02. The lifetime of XA is the same in 02-saturated cyclohexane as it is in solutions which have been deoxygenated. Bearing in mind that triplet carbenes react with 02 at nearly the diffusion limited rate, if 3XA were in rapid equilibrium with XA, then 02 should shorten the apparent lifetime of the singlet by reacting with the triplet. 

Molecular emission is referred to as luminescence or fluorescence and sometimes phosphorescence. While atomic emission is generally instantaneous on a time scale that is sub-picoseconds, molecular emission can involve excited states with finite, lifetimes on the order of nanoseconds to seconds. Similar molecules can have quite different excited state lifetimes and thus it should be possible to use both emission wavelength and emission apparent lifetime to characterize molecules. The instrumental requirements will be different from measurements of emission, only in detail but not in principles, shared by all emission techniques. 

The noise-free Stern-Volmer lifetime plots are clearly curved, which indicates a failure of a two discrete site model. However, this is a difficult nonlinear least-squares fitting problem, and the unquenched apparent lifetimes are within a factor of two of each other. Thus, for real data, it is much more difficult to pick up on the nonlinearities and exclude a discrete two-site model. For distributions with smaller R s, of course, fitting becomes too difficult for reliable model testing at least at 104 counts in the peak channel. 

The apparent lifetimes calculated by these expressions are the true lifetimes only if the fluorophore obeys single exponential decay kinetics. In the case of a single exponential decay, the apparent lifetimes as determined from the two equations should be the same. If the apparent phase and modulation lifetimes are not equal, more than one decay process is indicated. 

The time (symbolized by t) needed for a concentration of a molecular entity to decrease, in a first-order decay process to e of its initial value. In this case, the lifetime (sometimes called mean lifetime) is equal to the reciprocal of the sum of rate constants for all concurrent first-order decompositions. If the process is not first-order, the term apparent lifetime should be used, and the initial concentration of the molecular entity should be provided. The terms lifetime and half-life should not be confused. See Half-Life Fluorescence... 

The reaction of 02 with cytochrome c oxidase to form the oxygenated species A (Fig. 18-11) is very rapid, occurring with apparent lifetime T (Eq. 9-5) of -8-10 is.139 Study of such rapid reactions has depended upon a flow-flash technique developed by Greenwood and Gibson.136/140/141 Fully reduced cytochrome oxidase is allowed to react with carbon monoxide, which binds to the iron in cytochrome a3 just as does 02. In fact, it was the spectroscopic observation that only half of the... 

The (pyrazolyl)borate coligand was established to effect a blue-shift of ca. 20-30 nm in the absorption spectra of 488 and 489, relative to that in [K2-C2,N-phenylpyridine)Pt(dpm)] (dpm = 2,2,66-tetramethyheptanedio-nate), though apparently has little effect upon the luminescent emission. These complexes do, however, possess significantly longer apparent lifetimes (5.7 and 8.6 ps) than related dpm compounds (2.6 ps), though the... 

Excitation of the Lnm ion by a d-transition metal ion is an alternative to chromophore-substituted ligands, and proof of principle has been demonstrated for several systems. The lack of quantitative data, however does not allow an evaluation of their real potential, except for their main advantage, which is the control of the luminescent properties of the 4f-metal ion by directional energy transfer. In this context, we note the emergence of self-assembly processes to build new edifices, particularly bi-metallic edifices, by the simultaneous recognition of two metal ions. This relatively unexplored area has already resulted in the design of edifices in which the rate of population, and therefore the apparent lifetime, of a 4f-excited state can be fine-tuned by energy transfer from a d-transition metal ion (Torelli et al., 2005). 

Figure 6 shows a snapshot of the molecular structure of the tripeptide Lysine-Tryptophan-Lysine (KWK) in water with 2-ns MD simulations. Both 7r-cation and hydrophobic interactions are clearly present in this folded structure in recognition. The original idea was to examine 7r-cation interaction and solvation dynamics around this structural motif. Figure 7 shows fluorescence temporal behaviors of tryptophan in tripeptide-KWK, and the overall decay dynamics are similar to that of tryptophan in the same buffer [49]. Besides the two apparent lifetime contributions, three exponential decays were used to represent the solvation dynamics. At the blue side, the three decays occur in 0.22-0.4,1.8-3.4,... 

The establishment of such an equilibrium should have two effects after a short flash the apparent lifetime of the radical-pair should vary with n (because of the 5ns lifetime, at most, of Chi and of the occurrence of other traps in the antenna), and the amount of radical-pair should decrease while excitation resides in the antenna. To check that hypothesis we have varied n, measuring the amount of biradical state and its lifetime in several PS-II preparations with a different antenna size (n=5 to 200) (Hansson et al., 1987). 

Thus the ratio of the true lifetime to the apparent lifetime at any time is given by... 

Lifetime (t) The lifetime of a molecular entity which decays in a first-order process is the time needed for a concentration of the entity to decrease to 1/e of its original value. Statistically, it represents the life expectation of the entity. It is equal to the reciprocal of the sum of the (pseudo)unimolecular rate constants of all processes which cause the decay. Lifetime is used sometimes for processes which are not first order. However, in such cases, the lifetime depends on the initial concentration of the entity, or of a quencher and therefore only an initial or a mean lifetime can be defined. In this case it should be called apparent lifetime, instead. Occasionally, the term half-life (T1/2) is used, representing the time needed for the concentration of an entity to decrease to one half of its original val-... 

The average results of regions I and IE are represented by a linear fit in Fig. 3. The middle section with an apparent lifetime inversion is roughly matched with a curved line through the data, connecting the ends of both other fits. 

Hence, the apparent lifetime of the composition with the added regrind is decreased by 15%. Of course, the real lifetime of the composition in the held would be determined by the temperatnre factor, and the above calculations give only a rough estimate of the effect of a regrind on oxidative degradation of composites. 

Though the apparent lifetime of the final formulation is still lower (by almost 20%) compared to that without added regrind, the final OTT is high enough to make the composite serve in the field for quite a long time, probably, well over the warranty time period. 

Fig. 7-5. Coagulation behavior of particles produced by nucleation. [Adapted from Walter (1973).] A continuous generation of embryos with 1.2x 10 3 pm radius is assumed. Left Variation of the distribution function with time in the absence of preexisting particles production rate q = 106 cm" s"1. Right Steady-state distributions for different concentrations of preexisting large particles (r > 0.1 pm) production rate q = 102 cm 3 s-1 number density of preexisting large particles N0 = 270/3. The dashed curve (for /3 = 1) is obtained from the steady-state distribution 12 h after terminating the source of embryos. The apparent lifetime of Aitken particles for coagulation is here greater than that indicated in Fig. 7-4 because of the smaller number density of particles.

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