Overall radiative rate constant

Regarding the two latter non-radiative pathways of de-excitation from Si, it is convenient to introduce the overall non-radiative rate constant kfu such that... 

The rates of radiationless transitions between electronic states of porphyrins and their derivatives play a dominant role in their photochemistry because they are the major decay channels of the electronically excited states. Radiative channels, such as fluorescence, rarely exceed 10% of the overall decay rate constant at room temperature. The lifetimes of the lowest electronic states of free-base porph3nins and closed-shell metalloporphyrins vary by more than 10 orders of magnitude with the nature of the substituents. The understanding of such variations is essential to design and control the photochemistry of porphyrins and justifies an incursion on the fundamentals of radiationless transitions. 

By taking into account the radiative and nonradiative decay processes described above, Eq. 8 gives the overall decay rate constant of the emitting state of the metal. In this equation, kt is the radiative rate constant and knr and knr(T) are the nonradiative temperature independent and temperature dependent decay rate constants, respectively. 

In the case of lanthanides, foUowing direct excitation of the metal ion, the efficiency of emission is called the intrinsic emission efficiency which is directly related to the overall rate at which the emissive state is depopulated through radiative/ and non-radiative NR pathways, and the radiative rate constant, k/, or their corresponding... 

Figure 3 Recombination of oppositely charged, statistically independent carriers (e, h) can lead to the creation of an emitting excited state through a Coulombically correlated charge pair (e—h). The charge pair formation time (diffusion motion time) and its capture time are indicated in the figure as im and tc, respectively. The excited states decay radiatively (hi/) with the rate constant k and non-radiatively with an overall rate constant kn. After Ref. 21a.

In the electron-transfer process generalized in Eq. 1, one of the components of the reactant state may be fluorescent. This spin-allowed radiative process will thus be in competition with the nonradiative electron-transfer reaction and the two processes will contribute to the overall decay of the reactant state. The intrinsic lifetimes of fluorescent molecular states range typically from 10 to longer than 10 s. The occurrence of electron transfer involving the fluorescent state will shorten its lifetime and measurement of this quantity will therefore allow computation of the rate constant for electron transfer. 

Ln-L distance, energy transfer occurs as long as the higher vibrational levels of the triplet state are populated, that is the transfer stops when the lowest vibrational level is reached and triplet state phosphorescence takes over. On the other hand, if the Ln-L expansion is small, transfer is feasible as long as the triplet state is populated. If the rate constant of the transfer is large with respect to both radiative and nonradiative deactivation of T, the transfer then becomes very efficient ( jsens 1, eqs. (11)). In order to compare the efficiency of chromophores to sensitize Ln - luminescence, both the overall and intrinsic quantum yields have to be determined experimentally. If general procedures are well known for both solutions (Chauvin et al., 2004) and solid state samples (de Mello et al., 1997), measurement of Q is not always easy in view of the very small absorption coefficients of the f-f transitions. This quantity can in principle be estimated differently, from eq. (7), if the radiative lifetime is known. The latter is related to Einstein s expression for the rate of spontaneous emission A from an initial state I J) characterized by a / quantum number to a final state J ) ... 

The three components in the middle term represent (1) the efficiency r p pWith which the feeding level ( T, ILCT, LMCT, MLCT, possibly a 4f5d state) is populated by the initially excited state (the corresponding rate constant is if S is excited and T is the donor level, see Fig. 7), (2) the efficiency of the energy transfer (r et) from the donor state to the accepting Ln ion, and (3) the intrinsic quantum yield. The overall sensitization efficiency, rj ens can be accessed experimentally if both the overall and intrinsic quantum yields are known or, alternatively, the overall quantum yield and the observed and radiative lifetimes ... 

The regenerators were included in the model to account for potential changes in air preheat temperature. The checkers were modelled as a porous media subject to radiative and convective heat transfer. A baseline case with a stoichiometric ratio of 1.12 (12% excess air) was compared to an OENR case with a primary SR reduced to 1.06 and an overall SR kept at 1.12. For both case, the glass throat temperature was controlled and kept constant to 1400 C by a PID controller which adjusted the air and fuel flow rates, so that the reduction in fuel consumption can be estimated. The oxygen injections for the OENR case are located on the opposite side of the flame near the exhaust port. 

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