Tri-exponential decay

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. 

The fluorescence decay of BCECF observed in Hb. salinarum is also shown in Figure 31.5. It was necessary to assume a tri-exponential decay to reproduce the decay observed in vivo. The pH dependence of the fluorescence lifetime in Hb. salinarum could be measured using monensin, which is a kind of Na + /H + ionophore and forms an equilibrium between intracellular and extracellular pH [18, 19]. Thus the cell suspension was mixed with 2.5 mm3 of DMSO solution of monensin at 1.0 x 10-2moldm-3. After 10 min, the pH of the suspension was adjusted to give different values of the pH, at each of which the fluorescence decay was measured. 

We model the four PS II fluorescence components (three experimentally resolved ones and a potential 10 ns component with an amplitude of 0.1% relative to the total fluorescence). The kinetic model we apply, given in Fig. 2, is an extension of our previously proposed model (3) by taking into account a reversible relaxation of the primary radical pair (PRP) state to a RRP. This is in contrast to the proposal by Schlodder and Brettel (1) who ignored the possible reversible character of such a relaxation process. The kinetic equations have been solved (9) and predict tri-exponential decay kinetics for the Chi states (state B, Fig. 2). All four possible tri-exponential combinations of the four PS II components were tested, i.e., cases I-IV Case I 380 ps (16%), 1.34 ns (84%), 10 ns (0.18%)... 

The decay kinetics of excited electron donor molecules (the intensity of fluorescence is proportional to the concentration of excited molecules at any given time) can be interpreted in two ways. First, one may try to approximate it with the sum of two exponents, one of which refers to the decay of the fluorescence of free donor molecules and the other to that of the complex between the donor and the acceptor. This interpretation is similar to the description of the two-exponential decay of the fluorescence observed in the presence of two compounds containing heavy atoms [40]... 

Gas phase experiments utilized the same laser system but employed a different sample cell, a 1.5 cm long stainless steel cell with CaF2 windows. A turbomolecular pump was used to evacuate the cell down to the vapor pressure of the W(CO)6. The cell was heated slightly to 326 K to increase the vapor pressure and produce an optical density of 1.0. The gas phase decays are not single exponentials, but rather tri-exponentials. This triexponential character will be discussed in the results section. 

K (80 °C), the decay becomes faster. A tri-exponential fitting is performed at different temperatures. The first component (-430 fs) does not show temperature dependence, but the second component shows dependence which gives an activation energy of 1.0 kcal/mol. 

The time-resolved method was applied to another photodissociation reaction [124], Upon the photoexcitation of diazo compounds (Fig. 16), nitrogen is dissociated to yield the singlet carbenes. In alcoholic solvents such as methanol, the O—H bond is inserted into the carbene part quickly (within 40 ps for diphenylcarbene), and an ether is formed. The AH and AV values for the ether formation from DPDM in methanol were measured by the time-resolved method. A similar TG signal to the DPCP case was observed after the excitation of DPDM in methanol. The signal rises within 50 ns after the excitation and decays monotonously. The time profile of the signal was found to be expressed well with a tri-exponential function... 

Tj and Tg are usually different in solids, although this can happen quite often in liquids as well. (This should be considered as a blessing rather than a nuisance since nature is trying to give us additional information. ) In IV. A. 2. we say that solids usually have a lineshape close to a Gaussian while most liquids have Lorentzian lineshapes. Since we have so far treated T as a time constant for an exponential decay, there is an inconsistency here. How should we define a T2 for a Gaussian or some other non-Lorentzian line ... 

A second pertinent feature of the decay kinetics of complexes that display charge-transfer luminescence is the exponentiality of the observed transients at all temperatures reached — 1.5 K). This behavior is in stark contrast to that exhibited by organic systems at low temperatures. For the latter, single exponential decays are maintained to 10°K, but they are replaced by complicated kinetics at lower temperatures (2). Nonexponential decays have also been observed at low temperature for tris complexes of rhodium (III) that exhibit states lowest (14),... 

Under stoichiometric conditions, fluorexon and its derivatives form 1 1 complexes with Ln ions. However when the ratio Ln Fx is increased, complexes with other stoichiometries are observed, the exact nature of which has not been determined. On the other hand, luminescence data of solutions with a ratio Yb Fx < 1 clearly indicate the presence of only one luminescent species, the 1 1 complex. Monoexponential luminescence decays are observed corresponding to a lifetime of 1.9 ps, whereas multi-exponential decays are measured when the Yb Fx ratio is increased. Further proof of the existence of 1 1 complexes has been brought by mass spectrometry. Competitive titration with edta has been followed by monitoring the Yb luminescence, since the edta complex is non-luminescent, contrary to the chelate formed with Fx. After addition of 5 equivalents of edta to a solution of [Yb(fx)] in Tris-HCl buffer, the Yb luminescence intensity decreases to 12% of its initial value. The thermodynamic stability of the fluorexon chelate is, therefore, comparable to [Yb(edta)] . In addition, the luminescence decay after addition of edta aliquots is relatively slow, the estimated rate constant being 7.1 x 10" s indicating a reasonably high kinetic stability of the fluorexon chelate. 

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