Decay kinetics multi-exponential

Triplet states of xanthone depend upon the composition of the solvent the presence of water enhances the yield of 2 un state Dual phosphorescence from 2-(2 -hydroxyphenyl) benzoxazole is due to keto-enol tautomerism and the kinetics multi-exponential decay is due to differences of environment . Triplet state properties and triplet state-oxygen interactions of the biologically interesting linear and angular furocoumarins are useful in view of possible clinical application . 

The initial steep change in the extinction is ascribed to the temperature equilibration of the sample. Following this, a multi-exponential decay in the extinction is observed, indicating the complex relaxation kinetics of the homogeneous reaction between the various cationic SE s. Finally, the long-term single exponential relaxation... 

In Fig. 10, the transients exhibit quite different behavior from opal A to opal CT. In particular, a bi-exponential decay (Eq. 2) failed to reproduce the kinetics of opal CT. In this material, the emission is red-shifted towards 2.6 eV and the PL is strongly quenched at shorter time delays, with an unusual, non-linear kinetics in semi-log scale, indicating a complex decay channel either involving multi-exponential relaxation or exciton-exciton annihilations. Runge-Kutta integration of Eq. 5 seems to confirm the latter assumption with satisfactory reproduction of the observed decays. The lifetimes and annihilation rates are Tct = 9.3 ns, ta = 13.5 ns, 7ct o = 650 ps-1 and 7 0 = 241 ps-1, for opal CT and opal A, respectively. 

When a fluorophore is encapsulated in heterogeneous media or immobilized on a surface, single exponential emission decays are rarely observed. Multi-exponential kinetics are attributed to the slow reorientation of the molecular environment after photoexcitation, and the heterogeneity of the microenvironment. Different species in the excited ensemble are oriented differently or exist in different microenvironments on the timescale of the emission which influences the excited-state lifetimes of the immobilized species. Studying the number and distribution of decays can provide information on the microenvironment of the immobilized fluorophore. When combined with fluorescence depolarization studies, detailed information on the motion of these species and their interaction with their environment can be obtained. 

A number of experiments measuring the decay of the P state have revealed complicating factors in addition to the multi-exponential decay of the state described above. In measurements monitoring the decay of P using short (SOnlOOfs) laser pulses conducted by Vos and co-workers, oscillations were observed superimposed on the resulting kinetic traces (Vos et al., 1994a,b,c 1993,1991). These oscillations have been attributed to coherent nuclear motion associated with the P state (Vos and Martin, 1999 ... 

In particular, the application of multi-exponential decay kinetics anticipated from models that assume distinct photophysical species within polymer chains may be inappropriate in some cases. The possibility of non-exponential fluorescence decay behaviour arising from energy migration and trapping (11) should also be considered. Additional studies of the mobilities of fluorescent probes incorporated in PMA using time-resolved fluorescence anisotropy measurements provide further support for a "connected cluster" model to describe the conformation of this polyelectrolyte in aqueous solution at low pH. 

The Physical Meaning of the Number of Decay Times and of the Amplitudes in Multi-Exponential Fluorescence Decays. Double-Exponential Decays. When two decay times are contained in the monomer and excimer fluorescence decays, then at least two excited state species are involved in the kinetics. Only when an identical set of two decay times is found, then it can be concluded that two, and only two, excited state species are present, one monomer and one excimer Scheme (I). 

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. 

Many LRe(CO)3(X-phen) complexes, where L is a Lewis base and X-phen is phenanthroline or its derivatives, exhibit overlapping emissions from both MLCT and IL (tt-tt ) excited states at room temperature. By varying L, X-phen, and temperature, the emitting states can be tuned from MLCT to TT-TT in nature. Figure 5 compares the emission spectra of a series of (py)Re(CO)3 (X-phen) complexes at 298 K and 77 K. More structured emissions were observed at 77 K, as well as in complexes with higher MLCT excited states. The excited-state decays are also more complicated at low temperature and feature bi- or multi-exponential kinetics. ... 

It is worth noting that the equations introduced above are based on the assumption that the excited state decays following a first order kinetics. In more complex cases, multi-exponential or non-exponential decays can also be observed such cases are briefly mentioned in Sect. 7.3. Moreover, it must be underlined that lifetime depends on temperature, being a quantity derived from kinetics. Thus, temperature must always be specified together with the lifetime values obtained. 

In order to estimate the stability of triplet carbenes (19) under ambient conditions, laser flash photolysis ( LFP) [26] was carried out on the precursor diazomethanes (18) in solution at room temperature. The transient absorption bands formed upon the flash were recorded by a multi-channel detector. These bands were assigned to the triplet carbenes (19) by comparison with those obtained in matrix at low temperature. The kinetic information was then available by monitoring the decay of the transient absorption with oscillographic tracer. When triplet carbenes decayed unimolecularly, which is often so, lifetime (x) can be determined. However when the decay did not follow a single exponential, which is sometimes the case, x cannot be determined. In this case, a half-life (ti/2) is estimated from the decay curve as a rough measure of the stability. 

Finally we emphasize that other possibilities can not be ruled out. For example, one way to maintain the more conventional view with k2 > k, is to assume that the solution of the above homogeneous kinetic scheme results in a dominant single exponential process but that the observed bi-phasic or multi-phasic decay of P is the result of reaction-center heterogeneity and/or incomplete vibrational relaxation. Such a view would be consistent with past interpretations based on stimulated emission data . ... 

---