Decay integral definition

For the experimental determination of the 0, it is necessary to quantify the light output of the direct chemiluminescent process. The experimental definition of the direct chemiluminescence quantum yield is given in Eq. 36, that is, the initial rate of photon production (/q ) per initial rate of dioxetane decomposition k )[D]o). Alternatively, the total or integrated light intensity per total dioxetane decomposed can be used. The /t )[Z)]o term is readily assessed by following the kinetics of the chemiluminescence decay, which is usually first order. Thus, from a semilogarithmic plot of the emission intensity vs. time, the dioxetane decomposition rate constant kjj is obtained and the initial dioxetane concentration [Z)]o is known,especially if the dioxetanes have been isolated and purified. In those cases in which the dioxetanes are too labile for isolation and purification, [/)]o is determined by quantitative spectroscopic measurements or iodometric titration. 

The use of the analogy between (42) and Boltzmann statistical mechanics leads to a simple semi-quantitative description of radiationless processes in aromatic hydrocarbons, but a more accurate approach to the calculation of nonradiative decay rates has also been investigated in other contexts. For the case in which the vibrational modes are harmonic, but need not be parallel or have the same frequencies in the two electronic manifolds s and l, Eq. (40) is mathematically similar to expressions considered by Kubo and Toyazawa in discussions of optical line shapes in solids s°). In particular, they showed how the double summation in (40) can be expressed as a single definite (Fourier) integral of the form... 

Besides various detection mechanisms (e.g. stimulated emission or ionization), there exist moreover numerous possible detection schemes. For example, we may either directly detect the emitted polarization (oc PP, so-called homodyne detection), thus measuring the decay of the electronic coherence via the photon-echo effect, or we may employ a heterodyne detection scheme (oc EP ), thus monitoring the time evolution of the electronic populations In the ground and excited electronic states via resonance Raman and stimulated emission processes. Furthermore, one may use polarization-sensitive detection techniques (transient birefringence and dichroism spectroscopy ), employ frequency-integrated (see, e.g. Ref. 53) or dispersed (see, e.g. Ref. 54) detection of the emission, and use laser fields with definite phase relation. On top of that, there are modern coherent multi-pulse techniques, which combine several of the above mentioned options. For example, phase-locked heterodyne-detected four-pulse photon-echo experiments make it possible to monitor all three time evolutions inherent to the third-order polarization, namely, the electronic coherence decay induced by the pump field, the djmamics of the system occurring after the preparation by the pump, and the electronic coherence decay induced by the probe field. For a theoretical survey of the various spectroscopic detection schemes, see Ref. 10. 

The correlation functions relevant for spectroscopic observables have been computed, and compared with correlation functions for the decay of trans and gauche populations of specific bonds, whose time integrals lead quite naturally to the definition of effective kinetic rates. 

Such a definition of chargeability has an infinite number of possibilities to define the time t. Modem IP methods are directed on a study of the decay curve shape. One way is to integrate under a portiOTi of the decay curve between the decay time and <2 and define chargeability as ... 

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