Pulse single exponential

In principle, pulsed excitation measurements can provide direct observation of time-resolved polarization decays and permit the single-exponential or multiexponential nature of the decay curves to be measured. In practice, however, accurate quantification of a multiexponential curve often requires that the emission decay be measured down to low intensity values, where obtaining a satisfactory signal -to-noise ratio can be a time-consuming process. In addition, the accuracy of rotational rate measurements close to a nanosecond or less are severely limited by tbe pulse width of the flash lamps. As a result, pulsed-excitation polarization measurements are not commonly used for short rotational periods or for careful measurements of rotational anisotropy. 

Figure 5.11 shotvs the temporal profile of the intensity change in the SFG signal at the peak of the Vco mode (2055 cm ) at OmV induced by visible pump pulse irradiation. The solid line is the least-squares fit using a convolution of a Gaussian function for the laser profile (FWFJ M = 20 ps) and a single exponential function for the recovery profile. The SFG signal fell to a minimum within about 100 ps and recovered... 

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... 

For comparatively high repetition-rates (period T < 5t) fluorescence decays could also overlap between adjacent pulses. Thanks to the scale-invariant properties of the exponentials, no error is introduced when the decay is a pure single-exponential. Conversely, the preexponential factors can be altered when multiple lifetime decays... 

The principles of pulse and phase-modulation fluorometries are illustrated in Figures 6.5 and 6.6. The d-pulse response I(t) of the fluorescent sample is, in the simplest case, a single exponential whose time constant is the excited-state lifetime, but more often it is a sum of discrete exponentials, or a more complicated function sometimes the system is characterized by a distribution of decay times. For any excitation function E(t), the response R(t) of the sample is the convolution product of this function by the d-pulse response ... 

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

An efficient way of overcoming this difficulty is to use a reference fluorophore (instead of a scattering solution) (i) whose fluorescence decay is a single exponential, (ii) which is excitable at the same wavelength as the sample, and (iii) which emits fluorescence at the observation wavelength of the sample. In pulse fluorometry, the deconvolution of the fluorescence response can be carried out against that of the reference fluorophore. In phase-modulation fluorometry, the phase shift and the relative modulation can be measured directly against the reference fluorophore. 

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. 

Time-resolved method 1 decay of the donor fluorescence If the fluorescence decay of the donor following pulse excitation is a single exponential, the measurement of the decay time in the presence (td) and absence (t ) of transfer is a straightforward method of determining the transfer rate constant, the transfer efficiency and the donor-acceptor distance, by using the following relations ... 

Th fluorescence lifetime of a sample is the mean duration of time the fluorophore remains in the excited state. Following pulsed excitation, the intensity decays of many fluorophores are single exponential 2 23 ... 

Figure 1. Time dependence of the birefringence signal under the action of a reversing electric pulse of a PVC solution at C = 10 gcm and T = 25°C. The quenching concentration was 0.5 10 g cm". The single exponential curve (dotted line) deduced from the best fit of "Equation 8" to birefringence decay curve is indistinguishable from the experimental curve. Residues (i.e. difference between theoretical and experimental curve) are plotted below the birefringence curve.

When a pulse of light is applied only to the chromium ions, the neodymium decay consists of a single exponential with a time constant of 3.5 msec. From these data one can calculate a chromium-to-neodymium-exchange time of 6.2 msec. As the long decay of the neodymium is a very good... 

A gated deuterium lamp which has a full width at half-maximum (FWHM) ofabout2nsanddecay time of 1 ns has been used. The decay curves are deconvolved by numerical convolution technique with the assumption that the delta-pulse response is a single exponential function. A programme is used that varies the lifetime until the sum oi the squares or tne deviations between the observed and the calculated decay curves is a minimum (Fig. 11.5). If t0 = unquenched fluorescence lifetime and t = lifetime of quenched... 

Fig. 3. (A) Depletion spectra probed at 2 ps and (B) depletion kinetics trace for Ml 1. In graph (A), the ESA spectra with the depletion pulse present (dashed line) and without the depletion pulse (continuous line) are shown. Their difference is represented by the gray area. In graph (B), the curve represents a fit with single exponential rise and decay times, probed at 570 nm. The depletion was at 1000 nm for both graphs.

Various models are used in the literature to account for the kinetics of the excitons involved in optical processes. In the simplest cases, the signal evolution n(t) can be reproduced by considering either a single exponential or multiexponential time dependences. This model is well suited for solutions or solids in which monomolecular mechanisms happen alone. Since in most transient experiments the temporal response is a convolution of a Gaussian-shaped pulse and of the intrinsic kinetics, the rate of change with time of the excited-state population decaying exponentially is given by... 

Figure 7. Time-resolved mass spectrometry. AU-trcms-(2, 4, 6, 8) decatetraene was excited to its 5 2 electronic origin with a femtosecond pulse at A-pump — 287 nm. The excited-state evolution was probed via single-photon ionization using a femtosecond pulse at ApIObe = 235 nm. The time resolution in these experiments was 290 fs (0.3 ps). The parent ion CioH signal rises with the pump laser, but then seems to stay almost constant with time. The modest decay observed can be fit with a single exponential time constant of 1 ps. Note that this result is in apparent disagreement with the same experiment performed at Xprobe — 352 nm, which yields a lifetime of 0.4 ps for the S2 state. The disagreement between these two results can be only reconciled by analyzing the time-resolved photoelectron spectrum.

The protons in acetone, CH3—(C=0)—CH3, are chemically equivalent. As they relax following the pulse, the signal detected is a single, exponentially decaying... 

The v0 is the frequency associated with the u = 0 — 1 or u = 0 — 2 transition and both p and V may be slowly energy-dependent and so vary with v. When T is treated as a constant, the spectral line given by equation (1.2) is a Lorentzian. A well-known consequence is that if the zeroth-order CH state is prepared optically (by a laser pulse broader than the width T), its temporal decay to the states of the rest of the molecule would be a single exponential with a decay constant T. 

The decay of the CO stretch is a single exponential when W(CO)6 has substantial interactions with a solvent. A single exponential (aside from orientational relaxation in liquids) is observed even when very fast pulses are used in the experiments (81). In the gas phase, the transition frequency of the CO stretch evolves over a range of frequencies because of its time-dependent interaction with the low-frequency modes. When a buffer gas or solvent is added, collisions cause the coherent evolution of the slow modes to be interrupted frequently, possibly averaging away the perturbation responsible for the observed fast time dependence. Thus, the fastest and slowest components of the tri-exponential decay are inherently low-pressure, gas phase phenomena. 

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