Double exponential decay

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. 

Mathematically these are radically different functions. Du Di, and D3 are all double exponential decays, but their preexponential factors deviate radically and the lifetimes differ noticeably. The ratio of preexponentials for the fast and slow components vary by a factor of 16 D has comparable amplitudes, while D2has a ratio of short to long of 4, and D3 has a ratio of short to long of 1/4. D4 is a sum of three exponentials. All five functions vary from a peak of about 104 to 25, and all four functions, if overlaid, are virtually indistinguishable. To amplify these differences, we assume that the Gaussiandistribution, Da, is the correct decay function and then show the deviations of the other functions from Do. These results are shown in Figure 4.10. The double exponential D fits the distribution decay essentially perfectly. Even Dj and Ds are a very crediblefit. >4 matches Do so well that the differences are invisible on this scale, and it is not even plotted. 

Fig. 1. Auto-correlation function of the energy and the best fit for a double exponential decay used to obtain the interval of statistical correlation.

The laser output intensity of the C153 and R6G ORMOSIL gels was studied as a function of the number of laser pump pulses. Both materials could be pulsed for more than 3000 shots with a reduction of the emission amplitude of about a factor of four. Specifically, the C153 gel laser intensity decreased by a factor of 6 after more than 6000 pulses of 500 MW/cmA The plot of the intensity versus number of shots has a double exponential decay. This phenomenon is not yet completely understood, but it could be associated with microscopic phase separation in the medium. The R6G decay plot shows that the intensity undergoes a 90% reduction after 5300 laser pulses. 

Wilkes, Koontz and Cinalli (1996) investigated the emission during 8 to 9 days of low vapor pressure VOCs from water-based paints applied to prepainted gypsumboard. They observed that a double exponential decay model (empirical constants a, b, x, y) fitted the data well ... 

Figure 9. Temperature dependence of the T, and T, BKI relaxation times of a 68% crystalline melt-recrystallized PTFE sample ( ) denote the short-relaxationtime component in a double exponential decay. T,times longer than 100 ms and Ttimes longer than 1 s are not shown since their experimental values could not be determined accurately. The expected temperature dependence below...

The solvation dynamics of bulk water have been well studied. Jarzeba et al. [33] obtained a correlation function with 160 fs (33%) and 1.2 ps (67%), and Jimemez et al. [34] reported an initial Gaussian-type component (frequency 38.5 ps-1 25 fs in time width, 48%) and two exponential decays of 126 fs (20%) and 880 fs (35%). Using Eq. (6), the correlation function we obtained for bulk water, as shown in Fig. 4, is best fitted by double exponential decays integrated with an initial Gaussian-type contribution through a stretched mode c t) = + c2e tlZl, where for a pure Gaussian-type decay, / = 2. The... 

Similarly, we systematically measured the fs-resolved fluorescence transients from the blue to red side. The solvation components for all blue-side transients are well presented by a double-exponential decay with time constants that range... 

Strikingly, the solvation dynamics for all mutants are nearly the same. All correlation functions can be best described by a double exponential decay with time constants of 0.67 ps with 68% of the total amplitude and 13.2 ps (32%) for D60, 0.47 ps (67%) and 12.7 (33%) for D60G, and 0.53 ps (69%) and 10.8 ps (31%) for D60N. Relative to SNase above, the solvation dynamics are fast, which reflects the neighboring hydrophobic environment. We also measured the anisotropy dynamics and, as shown in the inset of Fig. 33, the local structure is very rigid in the time window of 800 ps. This observation is consistent with the inflexible turn (-T30W31-) in the transition from the second /1-sheet and the second x-helix (Fig. 31). Thus, the three mutants, with a charged, polar, or hydrophobic reside around the probe (Fig. 34) but with the similar time scales of... 

All levels affected by predissociation. Early work found two decay components but this is not confirmed by Brzozowksi et al. [119], Shows strong double exponential decay. Shorter component T < 1 /is. 

For insoluble monolayers of cholesterol and dipalmitoyl choline the relaxation at pressures below the collapse point were studied by Joos et al. ), using oscillatory and stress relaxation techniques. They found experimental evidence (and presented theory) for a double-exponential decay, representing two consecutive processes. The longer r s are 0(10 s) and 0(10 s) for cholesterol and the lipid, respectively, so these relaxations are relatively slow and may therefore be overlooked, especicJly in automated apparatus. No molecular mechanism was proposed the two r s did not exhibit a clear relationship with the surface pressure at which the experiments were carried out. 

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