Decay single exponential

The copolymer with the structure shown in Figure 16-15 displays a behavior similar to that of Ooct-OPV5-CN. In solution, one finds a fast double-exponential decay, while in a polysulfonc matrix single-exponential decay with a time constant of l. 7 ns is observed. We attribute this behavior to the same conformational phenomena. 

Figure 3.18. Time dependence of the peak position of the 1570 cm Raman band of Sj trans-stilbene in chloroform solution (filled triangle). The time dependence of the anti-Stokes/Stokes intensity ratio is also shown with open circles. The best fit of the peak position change with a single-exponential function is shown with a solid curve, while the best fit of the anti-Stokes/Stokes intensity ratio is shown with a dotted curve. The obtained lifetime for both single-exponential decay functions was 12ps. (Reprinted with permission from reference [78]. Copyright (1997) American Chemical Society.)...

Final resolution of these problems, particularly the complications from multiple matrix sites, came from investigations using spectroscopic methods with higher time resolution, viz. laser flash photolysis. Short laser pulse irradiation of diazofluorene (36) in cold organic glasses produced the corresponding fluorenylidene (37), which could be detected by UV/VIS spectroscopy. Now, in contrast to the results from EPR spectroscopy, single exponential decays of the carbene could be observed in matrices... 

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 ... 

Ballew, R. M. and Demas, J. N. (1989). An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays. Anal. Chem. 61, 30-3. 

For 8,9,10,11-tetrahydro-BA the lifetimes measured with and without DNA are the same within experimental error ( 2 nsec). Without DNA the decay profile of trans-7,8-dihydroxy-7,8-dihydro-BP follows a single-exponential decay law. With DNA the decay profile has a small contribution from a short-lived component (x = 5 nsec) which arises from DNA complexes. This indicates that Equation 1 is not strictly valid. However, the analysis of the decay profile with DNA also indicates that the short lifetime component contributes less than 11% to the total emission observed at [POa ] 5 x 10 M. Under these conditions Equation 1 still yields a good approximate value to the association constant for intercalation. 

Fluorescence Lifetimes. The fluorescence decay times of TIN in a number of solvents (11.14.16.18.19), low-temperature glasses (12.) and in the crystalline form (15.) have been measured previously. Values of the fluorescence lifetime, Tf, of the initially excited form of TIN and TINS in the various solvents investigated in this work are listed in Table III. Values of the radiative and non-radiative rate constants, kf and knr respectively, are also given in this table. A single exponential decay was observed for the room-temperature fluorescence emission of each of the derivatives examined. This indicates that only one excited-state species is responsible for the fluorescence in these systems. 

In the case of a single exponential decay with time constant % (excited-state lifetime), the steady-state anisotropy is given by... 

If data analysis with a single exponential decay is not satisfactory, a double exponential can be used, but such a decay must be considered as a purely mathematical model. 

General relations for single exponential and multi-exponential decays For a single exponential decay, the b-pulse response is... 

Note that the measurement of a decay time is fast (a fraction of a second) for a single exponential decay because a single frequency is sufficient. Note also that a significant difference between the values obtained by means of Eqs (6.35) and (6.36) is compelling evidence of non-exponentiality of the fluorescence decay. 

The time of data collection depends on the complexity of the (5-pulse response. For a single exponential decay phase fluorometry is more rapid. For complex 5-pulse responses, the time of data collection is about the same for the two techniques in pulse fluorometry, a large number of photon events is necessary, and in phase fluorometry, a large number of frequencies has to be selected. It should be emphasized that the short acquisition time for phase shift and modulation ratio measurements at a given frequency is a distinct advantage in several situations, especially for lifetime-imaging spectroscopy. 

In the case of a single exponential decay, the lifetime can be rapidly calculated by either the phase shift modulation ratio M by means of Eqs (6.25) and (6.26) established in Chapter 6 (Section 6.2.3) ... 

Our simplest continuous microheterogeneous model assumes that the luminophore exists in a distribution of spectroscopically different environmental sites. For a tractable, yet plausible, model each site is assumed to be quenched by normal Stem-Volmer quenching kinetics. For luminescence decays each individual component is assumed to give a single exponential decay with the following impulse response ... 

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. 

A solution of a pure fluorophore may reasonably be expected to display a single exponential decay time. The emission from fluorophore-protein conjugates, on the other hand, may be best characterized by two or three exponential decay times (Table 14.2). In labeling proteins with fluorophores, a heterogeneity of labeled sites results in fluorophore populations that have different environments, and hence different lifetimes. The lifetime distribution of a fluorophore-protein conjugate in bulk solution may vary further when immobilized on a solid support (Table 14.2). 

The single-exponential decay kinetics, described by the equation... 

The field TCP can be calculated on the basis of Brownian motion theory. Its initial time dependence is in every case described by a single exponential decay... 

Fig. 11. Triplet-state decay traces for the [ZnCcP, Fe Cc] complex above (295 K), below (168 K), and near Tmid = 234 K. The solid lines are fits to a single-exponential decay. Conditions 30% EG/10 mM KP, buffer pH = 6 at 4°C...

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