Multiexponential kinetics

A typical ligand capable of generating a dendritic structure is 1,4,5,8,9,12-hexaazatriphenylene (HAT). Photophysical studies of trinuclear species based on HAT have been reported [14 a, 49]. Representative example of complexes of this type are 26, 27, and 28. For some of these complexes, the luminescence, originating from MLCT levels involving the central HAT ligand, was found to decay with multiexponential kinetics. Furthermore, the vibrational modes responsible for the nonradiative decay of the luminescent MLCT states are different in the polynuclear dendritic edifices with respect to the mononuclear [M(L)2(HAT)]2+ compounds [14a]. 

Overall, a large number of drugs that exhibit apparently multiexponential kinetics obey power-law kinetics. The cogent question is why many of the observed time-concentration profiles exhibit power function properties. Although the origin of the power function remains unclear, some empirical explanations could elucidate its origin ... 

Fig. 1.16 (A) Fluorescence (so/id curve) from a molecule that is excited with sinusoidally modulated light (dotted curve). If the fluorescence decays exponentially with single time constant T, the phase shift (4>) and the relative modulation of the fluorescence amplitude (w) are related to t and the angular frequency of the modulation m) by < = arctan((OT) and w = (1 + o> ) (Appendix A4). The curves shown here are calculated for t = 8 ns, cd = 1.257 x 10 rad/s (20 MHz) and 100% modulation of the excitation light (< = 0.788 rad, i = 0.705). (B) Phase shift (4>, solid curve) and relative modulation (m, dotted curve) of the fluorescence of a molecule that decays with a single exponential time constant, plotted as a functirai of the product on. The relationships among , m, r and m become more complicated if the fluOTescence decays with multiexponential kinetics (Appendix A4)...

From the kinetic point of view SPR experiments have the advantage that both the association and dissociation processes can be measured from the two phases in one sensogram. However, it is possible for artifacts to arise from refractive index mismatch during the buffer change and, for this reason, in general the initial parts of the association and dissociation phases are excluded from the kinetic analysis.73 When multiexponential decays are observed it is important to distinguish between kinetics related to the chemistry and potential artifacts, such as conformational changes of the bound reactant or effects due to mass transport limitations.73,75 The upper limit of detectable association rate constants has been estimated to be on the order of... 

In kinetic analysis of complex reactions, 210, 382 fluorescence decay rate distributions, 210, 357 implementation in Laplace de-convolution noniterative method, 210, 293 in multiexponential decays, 210, 296 partial global analysis by simulated annealing methods, 210, 365 spectral resolution, 210, 299. 

Fig. 4. Kinetics of the SE band probed at 975 nm of peridinin in methanol (triangles), 2-propanol (circles) and tetrahydrofuran (squares). In the main picture the first 8 ps of the traces and in the inset the whole decay traces are shown. The solid lines represent multiexponential fits of the data. The amplitudes of traces are normalized to the maximum of the signal. Excitation at 490 nm.

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... 

Complementary nanosecond experiments ratify the photosensitization of the triplet features in 5 and 6 (Fig. 8.15). In the absence of molecular oxygen multiexponential decay kinetics point to a fairly complex deactivation scheme. 

During the first decades of the development of pharmacokinetic science, a lag time in pharmacological response after intravenous administration was often treated by applying a compartmental approach. If the plasma concentration declined in a biexponential manner, the observed pharmacodynamic effect was fitted to plasma or tissue compartment concentrations. Due to the lag time of effects, a successful fit was sometimes obtained between effect and tissue drug level [414]. However, there is no a priori reason to assume that the time course of a drug concentration at the effect site must be related to the kinetics in tissues that mainly cause the multiexponential behavior of the plasma time-concentration course. A lag time between drug levels and dynamic effects can also occur for drugs described by a one-compartment model. 

Charge injection and charge recombination rate constants for details about light source, light intensity, and excitation wavelength see the reference. The kinetic models used to obtain the rate constants varies first-order, biexponential, multiexponential or second-order kinetic models are used see references for detail. Listed units are not suitable for those who use second-order kinetic models. 

Even in proteins containing a sin e tryptophan residue, multiexponential decay kinetics have been observed suggesting mobility of the protein structure during emission . However, recent time-resolved fluorescence studies of the tryptophan zwitterion and tryptophan peptides indicate that this fluorc hore does not decay... 

For semiconductor clusters with larger Bohr radius, such as CdS and CdSe, the observation of the superradiant effect proves to be more elusive. This is mainly due to the difficulty of preparing high-quality samples of varying sizes of clusters that exhibit exciton luminescence. The spectra and kinetics of the luminescence are usually very complicated, which makes the positive identification of exciton luminescence difficult. For example, sharp band-edge luminescence with well-resolved vibronic structures was observed from 32-A CdSe clusters [60]. The decay kinetics of the luminescence is multiexponential and only the first 100-psec decay is identified with the exciton luminescence. The lifetime of this luminescence, however, is tempera-... 

In a study of the photophysics of 45-A CdS clusters [62] O Neil et al. observed a broad luminescence band from 400nm to over 800 nm. The luminescence decay kinetics is multiexponential at all wavelengths, consisting of two distinct time regimes. The fast decay has a lifetime of 500ps and is weakly temperature dependent. The slower decay has a lifetime, on the order of 20 ns, and is strongly dependent on temperature. The authors invoke the three-level thermal equilibrium model to interpret the results. The electron is assumed to be trapped shallowly at D. Luminescence is assumed to come from recombination between detrapped electrons and trapped holes [62]. The gap between the LUMO and the top of the trap levels is estimated to be 3meV. 

CdS clusters of narrow size distribution were studied by Eychmuller et al. [63], In this case a rather narrow luminescence band can be observed near the absorption band. The decay kinetics of this excitonic luminescence is multiexponential with a typical lifetime on the order of nanoseconds, much longer than the expected exciton lifetime. The temperature dependence of the excitonic luminescence shows complex behavior. Again, the authors use the three-level thermal equilibrium model to explain the data. The excitonic luminescence is identified as delayed luminescence occurring by detrapping of trapped electrons. Furthermore, they invoke the concept... 

The time constant based characterisation of a smell includes an approximation of the response kinetics by multiexponential decay similar to the description (6). A collection of several pairs of the parameters r, a, is usually obtained for each of the sensors in the array from this approximation. The characteristic parameters, namely the time constants r, and the weigh coefficients a, are used for the composition of a graphical representation of the sensor outputs that might be visually inspected. The graphical representation is build up by an original method. 

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