Multi-exponential behavior

Drugs and toxicants with multi-exponential behavior depicted in Figure 6.14 require calculation of the various micro constants. An alternative method involves using model-independent pharmacokinetics to arrive at relevant parameters. Very briefly, it involves determination of the area under the curve (AUC) of the concentration-time profiles. The emergence of microcomputers in recent years has greatly facilitated this approach. 

The different behavior in lnZ(t) between the Q—>Q and Na— >Na+ suggests that the multi-exponential behavior is caused not only by the solvent dynamics itself (Fjj (k,t)) but also by the solute-solvent coupling represented by Bjj (k) in Eq. (20). 

Attractive for the use of QDs are their long lifetimes (typically 5 ns to hundreds of nanoseconds), compared to organic dyes, that are typically insensitive to the presence of oxygen. In conjunction with time-gated measurements, this provides the basis for enhanced sensitivity [69]. This property can be also favorable for time-resolved applications of FRET. The complicated size-, surface-, and wavelength-dependent, bi- or multi-exponential QD decay behavior (Fig. 2) can complicate... 

Figure 2a shows a few fluorescence upconversion transients as measured for 1 dissolved in n-heptane, under magic angle conditions. The transients show multi-exponential decay behavior... 

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. 

The emission-lifetime measurements in ns-time region were also carried out for the two emission bands. Multi-exponential decay behavior was observed for both the emission bands. Fast decay component at >.=480 nm less than the order of ns was attributed to the recombination of electrons and holes. Slow decay component at >,=480 nm in the order of a few ns was attributed to thermal detrapping of the electron from the surface states to the conduction band since such thermal activation could enhance the lifetime at the band-edge emission. The emission lifetime at >.=480 nm increased as excess Cshallow trap sites. 

While the exponential stress relaxation predicted by the viscoelastic analog of the Mawell element, ie., a single exponential, is qualitatively similar to the relaxation of polymeric liquids, it does not describe the detailed response of real materials. If, however, it is generalized by assembling a number of Maxwell elements in parallel, it is possible to fit the behavior of real materials to a level of accuracy limited only by the precision and time-range of the experimental data. This leads to the generalized, or multi-mode. Maxwell model for linear viscoelastic behavior, which is represented mathematically by a sum of exponentials as shown by Eq. 4.16. 

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