Lifetime amplitude-averaged

The definition used depends on the phenomenon under study. For instance, the intensity-averaged lifetime must be used for the calculation of an average colli-sional quenching constant, whereas in resonance energy transfer experiments, the amplitude-averaged decay time or lifetime must be used for the calculation of energy transfer efficiency (see Section 9.2.1). 

Table 2. Fluorescence lifetimes, Tn(n = 1,2,3) and their amplitudes, An for the donor - spacer(Cn) - acceptors (C12NC12 and C18NC8) films, together with the average lifetimes < t > = Z, ...

Figure 1.4. Fluorescence decay parameters of 3-(p-hydroxyphenyI)propionic acid as a function of pH. The filled squares indicate the association between the shorter lifetime and its amplitude the open squares that between the longer lifetime and its amplitude. The solid lines running through the relative amplitudes express the theoretical Henderson-Hasselbach relationship for a pK of 4.5. The solid lines connecting the lifetimes represent their average value. (Reprinted from Ref. 38 with the permission of the American Chemical Society.)...

The mean lifetime can be compared with the commonly used average (amplitude-weighted) lifetime, defined by... 

Amplitudes, A, and time constants, Xj, obtained from a triexponential fit to the fluorescence decay of the acceptors in DMA and average lifetime, Tav. 

The lifetime of the film depends on pfei) hence it decreases for interfaces with low bending moduli (less rigid interfaces are likely to fluctuate with a larger amplitude and thus can reach easier the maximum ofthe enthalpy). Therefore, while the undulation repulsion increases the average thickness of the film at a given external pressure (Figure 6a), it decreases its stability (Figure 5). 

This has been explained through the fact that the scattering amplitude is proportional to the optical anisotropy correlation function, a quantity which the breaking of a hydrogen bond modulates in time, a process that affects the optical anisotropy of water. We see, therefore, that the linewidth is the inverse of the average lifetime of the hydrogen bond. 

Figure 15 shows how the average fatigue lifetime of PS depends on frequency for two different stress amplitudes. The variation appears to be a linear one on this log-log plot, with the number of cycles to fracture increasing with increase of frequency, and at essentially the same rate for both stress amplitudes. For the rubber modified HIPS the fatigue endurance is plotted as a function of frequency in Fig. 16. Here too the lifetime increases with increase of test frequency and again the variation is a linear one on a log-lot plot. The slope of these curves is also essentially independent of stress...

Fatigues tests have been run on a series of ABS samples under reversed tension-compression at a stress amplitude of 27.6 MPa, at four different frequencies, viz. 0.02, 0.2, 2, and 21 Hz. The average fatigue lifetime as a function of frequency is shown in Fig. 46 and, for comparison purposes, the data for HIPS obtained at 17.2 MPa is also shown. The average fatigue life-time of ABS increases in a linear manner with frequency on this log-log plot. The rate of increase, however, is reduced compared to that of HIPS, or of PS (Fig. 15). The reduced frequency sensitivity is perhaps a result of a reduced magnitude of the p-transition in the SAN copolymer compared to that in PS. A reduced frequency sensitivity of FCP rate in ABS vs. a HIPS-modified PPO has also been noted... 

Having determined = the remaining task is to try to learn the extent of vibrational excitation in the NO. When the NO/I fluorescence amplitude ratios are (1) measured as a function of NO pressure (2) corrected for detector response, filter transmission, and radiative lifetime and (3) extrapolated to zero NO pressure to correct for any NO selfabsorption, a ratio of 3.4 0.7 is obtained. Generalization of the kinetic scheme to the case where = 4 shows that this fluorescence ratio should be equal to the average number of NO quanta excited per... 

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