Energy decay curve

Computations done in imaginary time can yield an excited-state energy by a transformation of the energy decay curve. If an accurate description of the ground state is already available, an excited-state description can be obtained by forcing the wave function to be orthogonal to the ground-state wave function. 

Schroeder has shown that this averaging is unnecessary [Schroeder, 1965], The true energy decay curve can be obtained by integrating the impulse response of the room as follows ... 

Relaxation times for the total energy were calculated for each of the three samples as a function of temperature by integrating the scaled, shifted energy decay curve as described in Section V.C.2. The master equation was solved analytically by matrix diagonalization (Section III.D) using two different starting distributions. The results in Figure 1.37a were obtained... 

Fig. 12.3 Normalized energy decay curve for systole (up) and diastole (down) - Pathology type aortic stenosis (discontinued line) as compared to normal heart (continued line)...

Figure 9-17. Photoinduced absorption in s-LPPP al 0.26 eV versus temperature (filled squares). Full lines represent the model results (lower curve for two activation energies, higher curve for one). The doited lines represent the decay rates for the 0.12eV (a) and 0.37 eV (b) activated processes the dash-dolled horizontal line represents the temperature-independent part E.

The "add-to-memory" signal averaging method currently available to us distorts fluorescence intensity versus time plots when the fluorescence intensity is a non-linear function of incident laser energy and the laser energy varies from shot to shot. For this reason we have not attempted detailed kinetic modelling of the observed fluorescence intensity decay curves recorded at high 532 nm laser fluence. 

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... 

According to Ludwig (1968), there is a some similarity between UV- and high-energy-induced luminescence in liquids. In many cases (e.g., p-ter-phenyl in benzene), the luminescence decay times are similar and the quenching kinetics is also about the same. However, when a mM solution of p-terphenyl in cyclohexane was irradiated with a 1-ns pulse of 30-KeV X-rays, a long tail in the luminescence decay curve was obtained this tail is absent in the UV case. This has been explained in terms of excited states produced by ion neutralization, which make a certain contribution in the radiolysis case but not in the UV case (cf. Sect. 4.3). Note that the decay times obtained from the initial part of the decay are the same in the UV- and radiation-induced cases. Table 4.3 presents a brief list of luminescence lifetimes and quantum yields. 

Several authors have made restricted comparisons between experiment and calculations of diffusion theory. Thus, Turner et al. (1983, 1988) considered G(Fe3+) in the Fricke dosimeter as a function of electron energy, and Zaider and Brenner (1984) dealt with the shape of the decay curve of eh (vide supra). These comparisons are not very rigorous, since many other determining experiments were left out. Subsequently, more critical examinations have been made by La Verne and Pimblott (1991), Pimblott and Green (1995), Pimblott et al. (1996), and Pimblott and LaVeme (1997). These authors have compared their... 

Energy transfer. Energy acceptors can be the substrate 23 as well as suitable adsorbates. 24,25 In both cases the decay curves become nonexponential and, especially in the initial part, much steeper than the spontaneous decay. 

In order to avoid complications caused by excitation energy transfer between tryptophan residues, most investigations have been performed with proteins containing one tryptophan residue per molecule. When studying protein solutions, there are difficulties in separating the effects of rotation of entire protein molecules and of the chromophores themselves relative to their environment in the protein matrix. It is usually assumed that intramolecular motions are more rapid and manifest themselves as short-lived components of anisotropy decay curves or in depolarization at short emission lifetimes. 

Table II presents the vadues of v, the rate constant for the electron transfer reaction with the donor and acceptor in contact, calculated by deconvolution of the fluorescence decay curves for a number of excited porphyrin-cOkyl halide systems. It appears that the rate parauneter depends strongly on the calculated exothermicity for these reactions. Parauneter i/ contadns information about the Framck-Condon factor of the electron-tramsfer reaction, which is in itself dependent on the reaction exothermicity and reorgauiization energy (22.23). Whether the rate constauit for the electron-transfer reactions depends on the exothermicity in the manner predicted by theory, that is with a simple Gaussian dependence (22), cannot be ainswered at present because of the uncertainties in the energetics of the particular reactions studied here.

The decay time of the Cr " band of approximately 150 ns is very short for such emission. Radiative energy transfer may not explain it because in such a case the decay curves of each of the ions are independent of the presence of the other. Thus non-radiative energy transfer may also take part, probably via multipolar or exchange interactions. In such cases the process of luminescence is of an additive nature and the lifetime of the sensitizer from which the energy is transferred is determined, apart from the probability of emission and radiationless transitions, by the probability of the energy transfer to the ion activator. 

Our study of time-resolved luminescence of diamonds revealed similar behavior (Panczer et al. 2000). Short-decay spectra usually contain N3 luminescence centers (Fig. 4.71d 5.69a,b) with decay time of r = 30-40 ns. Despite such extremely short decay, sometimes the long-delay spectra of the same samples are characterized by zero-phonon lines, which are very close in energy to those in N3 centers. At 77 K Aex = 308 nm excitation decay curve may be adjusted to a sum of two exponents of ti = 4.2 ps and i2 = 38.7 ps (Fig. 5.69c), while at 300 K only the shorter component remains. Under Aex = 384 nm excitation an even longer decay component of 13 = 870 ps may appear (Fig. 5.69d). The first type of long leaved luminescence may be ascribed to the 2.96 eV center, while the second type of delayed N3 luminescence is ascribed to the presence of two metastable states identified as quarfef levels af fhe N3 cenfer. 

Weller24 has estimated enthalpies of exciplex formation from the energy separation vg, — i>5 ax of the molecular 0"-0 and exciplex fluorescence maximum using the appropriate form of Eq. (27) with ER assumed to have the value found for pyrene despite the doubtful validity of this approximation the values listed for AHa in Table VI are sufficiently low to permit exciplex dissociation during its radiative lifetime and the total emission spectrum of these systems may be expected to vary with temperature in the manner described above for one-component systems. This has recently been confirmed by Knibbe, Rehm, and Weller30 who obtain the enthalpies and entropies of photoassociation of the donor-acceptor pairs listed in Table XI. From a detailed analysis of the fluorescence decay curves for the perylene-diethyl-aniline system in benzene, Ware and Richter34 find that... 

The line shapes for the vibrational levels, and specifically that of v = 20 of the excited surface 1 are much narrower than the energy level spacing therefore, all the resonances are isolated as in the atomic case discussed above. The decay curves resulting from coupling the a) = v = 20) with the b) = v = 30) are shown in Figure 9.13. Again the method is very successful in completely suppressing the decay. 

CMS and Polystyrene Solutions in Cyclohexane. Both monomer and excimer fluorescences were observed in the pulse radiolysis of polystyrene solution in cyclohexane. The decay curves of monomer and excimer fluorescences at 287 and 360 nm are shown in Figures 7(a) and (b), respectively. Energy migration on the polymer chain has been discussed elsewhere (15). The dependences of the decay of monomer fluorescence and the rise of excimer fluorescence on the... 

The decay curves of the 5D0 state were found to reveal a measurable rise time that was about the same order of magnitude as the decay time of the SD state. No rise was found for the 5 >i state, however. The authors thus conclude that the energy transferred from the organic radical to the 5D0 state goes via the SDX state. This appears to be quite justified. 

The rate of recovery is normally highest at the start of an isothermal annealing cycle because the driving force is largest at that time. As recovery continues, the driving force diminishes as the available strain energy is used up and the rate of recovery falls continuously toward zero. A plot of the rate of recovery as a function of time yields a curve that is somewhat similar in appearance to an exponential decay curve. The rate of recovery is also temperature dependent and may be expressed, in a number of cases, by a simple empirical equation of the form... 

Thus, for the temperature-dependent electron tunneling reactions, the mismatch of the decay curves for the samples kept at different temperatures all the time can be observed only with large observation time intervals. In contrast to this, the presence or absence of the acceleration of the reaction with the rapid increase in temperature at a certain instant t0 can be easily noticed even with a very short observation time interval. Consequently, the method based on registering the change in kinetics with a jumpwise variation in temperature, is a more sensitive test for the presence or absence of the activation energy for the electron tunneling reaction than the method based on comparing the isothermic kinetic curves. 

The experimental points for the samples stored at 4.2 K and transferred for a short time to the EPR cavity where a temperature of 77 K was maintained are located quite close to the et decay curve at 77 K (Fig. 11). The decay curve at 120 K is virtually identical with that at 77 K. The coincidence of the kinetic curves for samples irradiated at the same temperature (77 K) but later stored at significantly different temperatures (4.2 and 77 K) indicates that, at T 77 K, reaction (4) has a zero activation energy (see Chap. 5, Sect. 2.3) and, hence, cannot be controlled by the thermal diffusion of the reacting particles. 

Figure 2. Attenuation curve measured for 0+ in argon. Curves A, B, and C are for ionizing electron energies of 20 eV, 50 eV, and 100 eV, respectively. Curve D represents decay of only excited 0+ ions that are present in ion beam for 100-eV electron-energy case. Curve D is obtained by subtracting from low-pressure data points of C, the linear extrapolation of high-pressure portion of C.4 ...

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