Fluorescence lifetimes calculation

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. 

The quantity riV/RT is equal to six times the rotational period. The rotational relaxation time, p, should he shorter than the fluorescence lifetime, t, for these equations to apply. It is possible to perform calculations for nonspherical molecules such as prolate and oblate ellipsoids of revolution, but in such cases, there are different rotational rates about the different principal axes. 

For single exponential fluorescence decay, as is expected for a sample containing just one fluorophore, either the phase shift or the demodulation can be used to calculate the fluorescence lifetime t. When the excitation light is modulated at an angular frequency (o = 2itv, the phase angle f, by which the emission modulation is shifted from the excitation modulation, is related to the fluorescence lifetime by ... 

Once the fluorescence quantum yield has been determined, all that is required to calculate the fluorescence rate constant kf is the fluorescence lifetime rf. Direct measurement of this quantity, like the measurement of the fluorescence quantum yield, is difficult, in this case because of the short lifetime of the fluorescent state (shorter than the normal flash from a flash lamp ). There are, however, several methods which have been developed to determine fluorescence lifetimes and these will be the subject of this section. 

From spectroscopic measurements, we can estimate the fluorescence lifetime, t [. = (PpTi. where the natural lifetime, rN, can be calculated from the Strickler-Berg equation in CGS units [60] ... 

Fig. 22 (a) Comparison of fluorescence lifetime (blue triangles), calculated from (13), and measured by time-resolved fluorescence red circles) as a function of solvent polarity for G19. (b) Fluorescence quantum yield blue squares) and peak ground state absorption wavelength red circles) as a function of solvent polarity given by the percentage of toluene (T) in toluene-ACN mixtures for G19... 

Calculating quantum yields Fluorescence lifetimes, monkeys, and exit doors... 

With some further assumptions, it is possible to use single frequency FLIM data to fit a two-component model, and calculate the relative concentration of each species, in each pixel [16], To simplify the analysis, we will assume that in each pixel of the sample we have a mixture of two components with single exponential decay kinetics. We assume that the unknown fluorescence lifetimes, iq and r2, are invariant in the sample. In each pixel, the relative concentrations of species may be different and are unknown. We first seek to estimate the two spatially invariant lifetimes, iq and t2. We make a transformation of the estimated phase-shifts and demodulations as follows ... 

A second approach with respect to anisotropic flavin (photo-)chemistry has been described by Trissl 18°) and Frehland and Trissl61). These authors anchored flavins in artificial lipid bilayers by means of C18-hydrocarbon chains at various positions of the chromophore. From fluorescence polarization analysis and model calculations they conclude, that the rotational relaxation time of the chromophore within the membrane is small compared to the fluorescence lifetime (about 2 ns74)). They further obtain the surprising result that the chromophore is localized within the water/lipid interface, with a tilt angle of about 30° (long axis of the chromophore against the normal of the membrane), irrespective of the position where the hydrocarbon chain is bound to the flavin nucleus. They estimate an upper limit of the microviscosity of the membrane of 1 Poise. 

Griseofulvin exhibits both fluorescence and luminescence. A report by Neely et al., (7) gives corrected fluorescence excitation (max. 295 nm) and emission (max. 420 nm) spectra, values for quantum efficiency of fluorescence (0.108) calculated fluorescence lifetime (0.663 nsec) and phosphorescence decay time (0.11 sec.). The fluorescence excitation and emission spectra are given in Figure 7. 

The excited-state lifetime calculated for TINS in PVA film is found to be 1.3 + 0.1 ns compared with 44 4 ps found in the case of water (H). This supports the earlier proposal that complexation, which is proposed to occur in protic, hydrogen-bonding solvents, does not occur in this polymer. In the PVP film an intense fluorescence and a long excited-state lifetime, similar to that found for TINS in PVA, is observed and is consistent with the ESIPT process being prevented in this aprotic medium. 

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. 

Many probes are now known that display changes in fluorescence lifetime on complexation of the analyte, photophysical properties some of them are summarized in Table 10.2. While we have listed the lifetimes of the free and the bound forms of the probes, there is no straightforward equation to calculate the analyte concentration using the mean lifetime as was in the case of the absorbance and intensity (Eqs. (10.14) and (10.15)). The mean lifetime depends not only on relative concentration of the probe species (free and complexed) but also on their decay times, quantum yields, and to some extent on the measurement (method or conditions). While the mean lifetime is independent of total probe concentration, this value generally depends not only on analyte concentration but also on excitation and observation wavelengths.03 ... 

The data for the fluorescence lifetime for this system are plotted against temperature in Figure 11.28, together with its relative temperature sensitivities calculated using Eq. (11.4). It shows that the CrLiSAF fluorescence lifetime decreases monotonically with the temperature increase, although it is rather insensitive to temperature variance around 0°C or below. From about 5°C, the fluorescence lifetime drops more and more sharply with temperature increase. This is seen explicitly from the rapid increase in its... 

Another complication in the quantitation of TIRF on cells is the effect of the membrane thickness itself on the profile of the evanescent wave. Reichert and Truskey<105) have calculated that, in theory, the thickness of the membrane should have a negligible effect on the fluorescence and that a simplified theory of three stratified layers (glass/water/cytoplasm) should be adequate. The theory approximates for simplicity that scattering plays a negligible role and that fluorescence intensity versus angle of observation and fluorescence lifetime are not functions of distance to the interface z. Experiments that... 

The fluorescence lifetime of the /2 metastable state of Nd + ions in LaBGeOs (a solid state laser) is 280 /u.s and its quantum efficiency is 0.9. (a) Calculate the radiative and nonradiative rates from this excited state, (b) If the effective phonons responsible for the nonradiative rate have an energy of 1100 cm, use the Dieke diagram to determine the number of emitted effective phonons from the F3/2 excited state, (c) From which three excited states of the Nd + ions in LaBGeOs do you expect the most intense luminescence emissions to be generated ... 

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