Biexponential

This behavior is consistent with experimental data. For high-frequency excitation, no fluorescence rise-time and a biexponential decay is seen. The lack of rise-time corresponds to a very fast internal conversion, which is seen in the trajectory calculation. The biexponential decay indicates two mechanisms, a fast component due to direct crossing (not seen in the trajectory calculation but would be the result for other starting conditions) and a slow component that samples the excited-state minima (as seen in the tiajectory). Long wavelength excitation, in contrast, leads to an observable rise time and monoexponential decay. This corresponds to the dominance of the slow component, and more time spent on the upper surface. 

The bimodal profile observed at low catalyst concentration has been explained by a combination of two light generating reactive intermediates in equihbrium with a third dark reaction intermediate which serves as a way station or delay in the chemiexcitation processes. Possible candidates for the three intermediates include those shown as "pooled intermediates". At high catalyst concentration or in imidazole-buffered aqueous-based solvent, the series of intermediates rapidly attain equihbrium and behave kineticaHy as a single kinetic entity, ie, as pooled intermediates (71). Under these latter conditions, the time—intensity profile (Fig. 2) displays the single maximum as a biexponential rise and fall of the intensity which is readily modeled as a typical irreversible, consecutive, unimolecular process ... 

The buildup of [P] is biexponential. Nonlinear least-squares fitting will provide the best solution for k and k2 (and, if they are unknown, for [A ]o and [A2]o also). Another method is to plot ln([P] - [P],) against time. At long times, the exponent with the higher value of k will have fallen off, such that the slope will approximate the slower one. Calling this ks (it might be either k or k2), we perform a subtraction, emphasizing the data at shorter times ... 

The analysis of biexponential kinetic data obtained instrumentally will now be considered for the case k k2. The instrument reading is... 

It is of course impossible for products to appear faster than the reactants are used up. Let us apply Eq. (4-25) to the situation at 430 nm, where e = 0 and [ = 1.33eP. If kjk] = 1.33, the reaction will follow first-order (not biexponential) kinetics at both wavelengths, the rate constants being ki at 540 nm and (ei/eP) i at 430 nm. Approximate adherence to Eq. (4-25) suffices within the usual error limits, as seems to be the case here. 

This result says that the signal will fit a biexponential equation. The pair of associated rate constants, k] and n, gives rise to the composites shown. 

Biexponential kinetics, 72-76 Biphasic kinetics, 72-76 Bloch equations, 261 Branching reactions, 189 Brpnsted-Bjerrum equation, 204... 

Fortunately, as the reaction is transferred from a purely organic solvent system to mixed organic-aqueous media, which are employed in most RP-HPLC separations, the apparent multiplicity of maxima in the time profile of the intensity dependence seems to be suppressed or to collapse to a reasonably simple biexponential-like dependence. As shown in Figure 11, simply changing the solvent from ethyl acetate to 95% aqueous acetonitrile and the catalyst from triethylamlne to imidazole produces a single maximum profile, one that is more easily modeled mathematically, as defined in Equation 4 ... 

Sheiner LB, Beal SL. Evaluation of methods for estimating population pharmacokinetic parameters. II. Biexponential model and experimental pharmacokinetic data. / Pharmacokinet Biopharm 1981 9 635-51. 

Equation (35) describes the line in Fig. 10, which is a semilog plot of Cp versus time for an orally administered drug absorbed by a first-order process. The plot begins as a rising curve and becomes a straight line with a negative slope after 6 hours. This behavior is the result of the biexponential nature of Eq. (35). Up to 6 hours, both the absorption process [exp(—kat) and the elimination process [exp( keil)] influence the plasma concentration. After 6 hours, only the elimination process influences the plasma concentration. 

In the trajectory study of Cl-—CHjCl complex formation by Cl" + CH3C1 association, the number of complexes with a lifetime t, i.e. N(t), was evaluated for different Cl" + CH3C1 initial conditions.36,37 The resulting plots of N(t) are highly nonexponential and plots of N(t)/N(0) were fit with the biexponential function... 

Ward et al. [130] studied the pharmacokinetics of (+)- and (—)-primaquine in the isolated perfused rat liver preparation. The perfusate plasma concentrations of primaquine in the isolated, perfused rat liver, declined biexponentially following the addition of either (+)- or (—)-primaquine at doses 0.5-2.5 mg in the perfusate reservoir. There were no differences between pharmacokinetic profiles of the two isomers at the 0.5 mg dose. By contrast, the elimination of (—)-primaquine was greater than (+)-primaquine when either was added in a dose of 2.5 mg also, the clearance of the (—)-isomer was greater, the half-life was shorter, and the area under the plasma concentration curve was shorter. The volume of distribution was similar for the two isomers. These results are relevant to both the therapeutic efficacy and toxicity of primaquine. 

Raluca Niesner, B. P., Schliische, P. and Gericke, K. H. (2004). Noniterative Biexponential fluorescence lifetime imaging in the investigation of cellular metabolism by means of NAD(P)H autofluorescence. Chem. Phys. Chem. J, 1141-9. 

Alternatively, arene displacement can also be photo- rather than thermally-induced. In this respect, we studied the photoactivation of the dinuclear ruthenium-arene complex [ RuCl (rj6-indane) 2(p-2,3-dpp)]2+ (2,3-dpp, 2,3-bis(2-pyridyl)pyrazine) (21). The thermal reactivity of this compound is limited to the stepwise double aquation (which shows biexponential kinetics), but irradiation of the sample results in photoinduced loss of the arene. This photoactivation pathway produces ruthenium species that are more active than their ruthenium-arene precursors (Fig. 18). At the same time, free indane fluoresces 40 times more strongly than bound indane, opening up possibilities to use the arene as a fluorescent marker for imaging purposes. The photoactivation pathway is different from those previously discussed for photoactivated Pt(IV) diazido complexes, as it involves photosubstitution rather than photoreduction. Importantly, the photoactivation mechanism is independent of oxygen (see Section II on photoactivatable platinum drugs) (83). 

In the case the kr and kET are of the same order of magnitude, the intensity time curve can be represented as a biexponential function. 

For vacuum sublimed thin films, Grabuzov et al. [138] reported a photoluminescence quantum efficiency of 32 2%. In the same paper, data on the absorption coefficient at the maximum, a = (4.4 0.1) x 104 cm 1, and the refractive index at 633 nm (n = 1.73 0.05) can be found. Other reported values for the photoluminescence quantum efficiency that can be found in the literature are 30 5% [124] and 25 5% [139]. Naito et al. [109] reported a quantum yield of 5% in the amorphous film compared to 35% in the crystalline state. The fluorescence lifetime is reported to be biexponential with x = 3.4 and 8.4 ns, which is much shorter than in the crystal (17.0 ns). In the amorphous state, the larger free volume allows more vibrations and rotations to take place, which favors nonradiative decay. 

Nafion is thought to form dimers giving rise to a biexponential decay. 44,46) Using diode laser excitation at 670 nm, the fluorescence of oxazine in Nafion and its quenching by copper ions has been shown to give rise to a complex fluorescence decay.(47) Despite such complications there is still room for optimism. For example, Zen and Patonay(48) have demonstrated a pH sensor based on cyanine dye fluorescence intensity in Nafion excited with 30 mW diode laser excitation at 780 nm. 

Becker.(49) The lifetimes were all reported as being single-exponential. Rousslang and his collaborators have recently reexamined a number of these compounds at pH 3 and 5.(50) In general, the phosphorescence decays are biexponential, but are dominated by a longer lived component of about 3 s which comprises 98 % or more of the decay. 

With the development of multifrequency phase-modulation technology, Lakowicz and co-workers(171) were able to examine the time dependence of the anisotropy decay of BPTI. They noted that the intensity decay of the fluorescence is best fit by a biexponential decay law and that the anisotropy decay is also complex. At 25 °C and pH 6.5, correlation times of 39 ps and 2.25 ns were recovered from analysis of data obtained over the range 20 MHz to 2 GHz. The longer correlation time is close to that predicted for the overall rotational motion of a molecule of the size of BPTI. They indicated, however, that additional experiments need to be done to resolve whether the 39-ps... 

Proteins having one chromophore per molecule are the simplest and most convenient in studies of fluorescence decay kinetics as well as in other spectroscopic studies of proteins. These were historically the first proteins for which the tryptophan fluorescence decay was analyzed. It was natural to expect that, for these proteins at least, the decay curves would be singleexponential. However, a more complex time dependence of the emission was observed. To describe the experimental data for almost all of the proteins studied, it was necessary to use a set of two or more exponents.(2) The decay is single-exponential only in the case of apoazurin.(41) Several authors(41,42) explained the biexponentiality of the decay by the existence of two protein conformers in equilibrium. Such an explanation is difficult to accept without additional analysis, since there are many other mechanisms leading to nonexponential decay and in view of the fact that deconvolution into exponential components is no more than a formal procedure for treatment of nonexponential curves. 

Fig. 7 Left Arrhenius plot of the approximate folding and unfolding rates of 15. Right At low temperatures, the relaxation is better fitted by a stretched exponential or biexponential the stretching exponent is shown here as a convenient measure of the deviation from single exponentiality...

To finalize this section, we will comment on the isoindoline-derived spiro-oxazine NOSI5. This compound also photo-converts efficiently and very rapidly into their open merocyanine. In this case, the reaction is over within 30 psec and has a biexponetial rise with 2- and 15-psec lifetimes. The merocyanine spectrum does not evolve in time after this time. A broad absorption occurs around time zero, which is either the excited singlet state or the often hypothesized transient X. The data for NOSI5 are shown in Fig. 6 The biexponential absorption rise... 

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