Nonexponential

Jarzeba W, Walker G C, Johnson A E and Barbara P F 1991 Nonexponential solvation dynamics of simple liquids and mixtures Chem. Phys. 152 57-68... 

The pathway model makes a number of key predictions, including (a) a substantial role for hydrogen bond mediation of tunnelling, (b) a difference in mediation characteristics as a function of secondary and tertiary stmcture, (c) an intrinsically nonexponential decay of rate witlr distance, and (d) patlrway specific Trot and cold spots for electron transfer. These predictions have been tested extensively. The most systematic and critical tests are provided witlr mtlrenium-modified proteins, where a syntlretic ET active group cair be attached to the protein aird tire rate of ET via a specific medium stmcture cair be probed (figure C3.2.5). 

To lessen experimental time, the null-point method may be employed by locating the pulse spacing, tnun, for which no magnetization is observed after the 180°-1-90° pulse-sequence. The relaxation rate is then obtained directly by using the relationship / , = 0.69/t n. In this way, a considerable diminution of measuring time is achieved, which is especially desirable in measurements of very low relaxation-rates, or for samples that are not very stable. In addition, estimates of relaxation rates for overlapping resonances can often be achieved. However, as the recovery curves for coupled spin-systems are, more often than not, nonexponential, observation of the null point may violate the initial-slope approximation. Hence, this method is best reserved for preliminary experiments that serve to establish the time scale for spin-lattice relaxation, and for qualitative conclusions. 

Nonexponential blinking kinetics of single CdSe quantum dots A universal power law behavior. J. Chem. Phys., 112, 3117-3120. 

Kuno, M., Fromm, D. P., Hamarm, H. F., Gallagher, A. and Nesbitt, D. J. (2000) Nonexponential blinking kinetics of single CdSe quantum dots A universal power law behavior. J. Chem. Phys., 112, 3117-3120. 

Invariably, measurements of decay of reactive molecules in solid glasses are found to be nonexponential, that is, first-order plots of ln[intensity] versus time are upwardly curved, as shown in Figure 10.3. 

It is generally understood that the reactive intermediates are generated in a random distribution of different microenvironments, each with its own energy barrier. The complex decay of this dispersion of rates leads to the nonexponential kinetics. Thus, disappearance plots are dominated at early times by reaction of those species in fast sites , which have lower energy barriers. As these sites are cleared, the distribution of rates over time becomes more reflective of sites with higher barriers. Finally, at longer times, the decay curves are dominated by the slowest sites. It is often observed that plots of In [intensity] versus or are approximately linear. It... 

Figure 10.3. First-order plots of ln[Intensity] versus time, showing idealized exponential decay (dotted line), and nonexponential decay from statistical distribution of matrix sites (solid line).

Laser flash irradiation of diazofluorene in perdeuterated matrices, in contrast, gave severely nonexponential decay of the carbene spectra. Analyses of the products formed in the low-temperature matrices showed that, as with the EPR studies, the carbene was not undergoing D-abstraction. LFP of the diazo compound 36 in CFCl3-CF2BrCF2Br glasses gave linear first-order decays, and linear Arrhenius plots, which were attributed to classical Cl and Br abstractions. 

There are, however, problems associated with this method of determining fluorescence lifetimes. First, the phase method is not generally applicable for nonexponential signals and, as we shall see later, there are many cases where the observed fluorescence decay is indeed nonexponential. Second, the method... 

Possibly the most easily observable process is the phosphorescence decay.<17) While at 77°K the decay is exponential, at 1.6°K the observed decay for compounds like pyrazine is nonexponential and is composed of three first-order decays. Thus one can determine the values of kx, ky, and kz from this decay. Typical values are shown in Table 6.2. 

In the trajectory study of Cl-—CHjCl complex formation by Cl" + CH3C1 association, the number of complexes with a lifetime t, i.e. N(t), was evaluated for different Cl" + CH3C1 initial conditions.36,37 The resulting plots of N(t) are highly nonexponential and plots of N(t)/N(0) were fit with the biexponential function... 

The switch between discrete emitter forms with fixed but different lifetimes corresponding to free (F) and bound (B) forms of the sensor. Belonging to the same dye, these two forms can be excited at the same wavelength. When excited, they emit light independently, and the observed nonexponential decay can be deconvolved into two different individual decays with lifetimes xF and x6 (Fig. 2b). The ratio of preexponential factors aF and aB will determine the target concentration [18] ... 

Fluctuations, Relaxation, Heterogeneity, and Nonexponential Fluorescence Decay... 

Liu T, Callis PR, Hesp BH, de Groot M, Buma WJ, Broos J (2005) Ionization potentials of fluoroindoles and the origin of nonexponential tryptophan fluorescence decay in proteins. J Am Chem Soc 127(11) 4104-4113... 

Fluorescence Rise and Decay Curves. Both monomer and excimer fluorescence decay curves of the unirradiated film are nonexponential and the excimer fluorescence shows a slow rise component. This behavior is quite similar to the result reported for the PMMA film doped with pyrene. (23) A delay in the excimer formation process was interpreted as the time taken for the two molecules in the ground state dimer to form the excimer geometry. Dynamic data of the ablated area observed at 375 no (monomer fluorescence) and 500 nm (exciner fluorescence) are shown in Figure 5. When the laser fluence increased, the monomer fluorescence decay became slower. The slow rise of the excimer fluorescence disappeared and the decay became faster. 

Alternatively, the white-noise processes W(f) could be replaced by colored-noise processes. Since the latter have finite auto-correlation times, the resulting Lagrangian correlation functions for U and would be nonexponential. However, it would generally not be possible to describe the Lagrangian PDF by a Fokker-Planck equation. Thus, in order to simplify the comparison with Eulerian PDF methods, we will use white-noise processes throughout this section. 

The fluorescence lifetime was determined to be 1124ps for 35a, 785 ps for 35b, and 831 ps for 43 in dichloromethane, whereas in the corresponding amorphous films a nonexponential decay with shorter time constants was observed [118, 119]. These lifetimes are similar to the parent oligophenyls but different from fluorene (10 ns) [120, 121]. When applying oligophenyls as luminescent films, however, we must consider that photooxidation may occur if molecular oxygen is present [122, 123], The proposed pathway for the decomposition is... 

Persistent microheterogeneity exists when the luminescence and quenching decay are fast compared to conformational-environmental rearrangement. Excited molecules can then emit and be quenched in distinctly different chemical environments. Decays can then be nonexponential, multiple emissions may be present, and simple Stern-Volmer kinetics can break down. 

The luminescence decays are somewhat nonexponential for the ionically bound metal complexes nonexponentiality is exacerbated by the presence of 02.We suggest that nonexponential decays reflect a persistent microheterogeneity around the complex. This was our first clear evidence of spectroscopically different binding sites. In this case, oxygen enhances heterogeneity detection by differentially quenching different sites. 

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