Exponential decay kinetics

With some further assumptions, it is possible to use single frequency FLIM data to fit a two-component model, and calculate the relative concentration of each species, in each pixel [16], To simplify the analysis, we will assume that in each pixel of the sample we have a mixture of two components with single exponential decay kinetics. We assume that the unknown fluorescence lifetimes, iq and r2, are invariant in the sample. In each pixel, the relative concentrations of species may be different and are unknown. We first seek to estimate the two spatially invariant lifetimes, iq and t2. We make a transformation of the estimated phase-shifts and demodulations as follows ... 

The apparent lifetimes calculated by these expressions are the true lifetimes only if the fluorophore obeys single exponential decay kinetics. In the case of a single exponential decay, the apparent lifetimes as determined from the two equations should be the same. If the apparent phase and modulation lifetimes are not equal, more than one decay process is indicated. 

The single-exponential decay kinetics, described by the equation... 

In order to arrive at meaningful (exponential) decay rates in such experiments, non-linear triplet quenching by diffusion, has to be avoided. For example, the initial accelerated decay in Fig. 7 is caused by bimolecular triplet-triplet annihilation dominating the decay of the triplets. Similarly, a faster decay is observed at higher temperature, where triplet exciton diffusion to quenching sites is faster than monomolecular decay. Nevertheless, by using low temperatures and low excitation doses exponential decay kinetics are observed yielding radiative decay rates as low as 1 s x, which sets an upper limit for the triplet excited state lifetime [28,34],... 

If the rate of charge-carrier generation at a given point in the bulk is proportional to the light irradiance (/) at that point, and the irradiance obeys exponential decay kinetics, the spatial distribution g(x) of photogeneration of charge carriers is given by... 

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. 

Amiali et al. (2004) showed that Pruit and Kamau s model adequately predicted inactivation of E. coli 0157 117 suspended in dialyzed liquid eggs. The inactivation kinetics followed exponential decay equation with two population sensitivity to PEF treatment. In addition, it was noted that the inactivation rate of E. coli 0157 H7 followed exponential decay kinetic model with some tailing effect due to the resistance of survival fraction to the PEF treatment. They proposed the following model ... 

In these equations and are the excited state populations of the donor and acceptor molecules- and and are the lifetimes of the donor and acceptor molecules in the excited state the notation x° is used to distinguish it from the radiative constant x° (in other words x° = Xg, for the donor) is given by (C3.4.5I and A the corresponding rate constant for the backward energy transfer from acceptors to donors can be foimd by me same means. Finally, and represent external sources of excitation, for example the absorption of laser light by the donor and acceptor molecules. Commonly, for example in the case of 8-pulse excitation (in practice an ultrashort laser pulse), (C3.4.6) yields exponential decay kinetics for p(f) and n t). The opposite case of steady excitation (CW light), yields the equilibrium ratio... 

Breakup and recreation of the associated structure follow exponential decay kinetics. The simplest, single-exponential relation representing the thixotropic behavior is ... 

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%)... 

We see from the dependence of the CD spectra in amide UV region on the TPP/PP molar ratio that the mainly nonregular conformation of free peptide is gradually converted into more regular (X-helical structure in complexes (Fig.l.a). Simultaneously, in the time resolved fluorescence experiment the nonexponential fluorescence decay observed for the free (aggregated) pigment is replaced by the two exponential decay kinetics with components of 24D ps and 2.4 ns. The contribution ot the... 

The dual exponential behavior was apparent at the lowest laser intensity ( 0.5 mJ) and well below the onset threshold at which similar behavior became apparent for 16. Although the probability of depositing 2 photons onto the tetrakisporphyrin ensemble 17 is twice that for the corresponding bisporphyrin 16, the high concentration and low photon density employed should ensure monophotonic excitation of 17. Therefore, the dual exponential decay kinetics observed at low laser intensity are not due to triplet-triplet annihilation but must arise from an additional process. 

This concentration ratio does not follow the simple exponential decay of first-order kinetics and should not be used in fitting the rate constant. If it were used erroneously, the predicted concentration would be 45.6/M ... 

The important phenomenon of exponential decay is the prototype first-order reaction and provides an informative introduction to first-order kinetic principles. Consider an important example from nuclear physics the decay of the radioactive isotope of carbon, carbon-14 (or C). This form of carbon is unstable and decays over time to form nitrogen-14 ( N) plus an electron (e ) the reaction can be written as... 

Comparison of the Experimental and Simulation Results. The preceding discussion has shown that both the experimental anthracene fluorescence profiles and the simulated anthracene concentration profiles decrease in a manner which closely follows an exponential decay. Therefore, the most convenient way to compare the simulation results to the experimental data is to define an effective overall photosensitization rate constant, kx or k2, as described above. Adoption of this lumped-parameter effective kinetic constant allows us to conveniently and efficiently compare the experimental data to the simulation results by contrasting the rate constant obtained from the steady-state fluorescence decay with the value obtained from the simulated decrease in the anthracene concentration. 

Our simplest continuous microheterogeneous model assumes that the luminophore exists in a distribution of spectroscopically different environmental sites. For a tractable, yet plausible, model each site is assumed to be quenched by normal Stem-Volmer quenching kinetics. For luminescence decays each individual component is assumed to give a single exponential decay with the following impulse response ... 

Figure 5.2. Grabowski s model of TICT formation in DMABN the locally excited (LE) state with near-planar conformation is a precursor for the TICT state with near perpendicular geometry. The reaction coordinate involves charge transfer from donor D to acceptor A. intramolecular twisting between these subunits, and solvent relaxation around the newly created strong dipole. Decay kinetics of LE and rise kinetics of the TICT state can be followed separately by observing the two bands of the dual fluorescence. For medium polar solvents, well-behaved first-order kinetics are observed, with the rise-time of the product equal to the decay time of the precursor, but for the more complex alcohol solvents, kinetics can strongly deviate from exponentiality, interpretable by time-dependent rate constants. 52 ...

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