Critical transfer radius

Eq. (8.52) gives a good fit to the data in Fig. 8.20, for values of Rf. of 100-120 A. The fit assumes that there is a single value of the critical transfer radius R, which is a poor approximation because is widely distributed with a corresponding varying value of R. . Nevertheless, the average radiative lifetime of 10 s from Fig. 8.14 and co = 10 s gives... 

The recombination is modified in a multilayer structiu e whose layer spacing is similar to the carrier tunneling distance and is observed in photoluminescence measurements (Tiedje 1985). Fig. 9.22(a) shows that the luminescence intensity of a-Si H/nitride multilayers decreases as the layer thickness drops below about 500 A. The interface states and bulk nitride defect states cause non-radiative recombination because the electron-hole pairs are never far from an interface. The model of non-radiative tunneling developed in Section 8.4.1 can be adapted for recombination in thin layers. When the layer thickness is less than the critical transfer radius, the luminescence efficiency is (see Eq. (8.52)). 

T is the fluorescence lifetime and Rq the critical transfer radius for donor-donor transport (29). For experiments in high viscosity media, the chromophores are essentially static and the appropriate orientation dependent Rq must be used (8.21). N is the number of chromophores in the system. P(r 2) lb] 2 probability that there is a chromophore at a distance r 2 from chromophore 1. The Integral is over the physical space and A is the appropriate normalization factor. Next, it is necessary to average over the possible positions of the initially excited chromophore... 

The pipe in Prob. 2-51 is covered with a layer of asbestos [k = 0.18 W/m °C] while still surrounded by a convection environment with h = 12 W/m2 °C. Calculate the critical insulation radius. Will the heat transfer be increased or decreased by adding an insulation thickness of (a) 0.5 mm, (b) 10 mjn ... 

Critical quenching radius rf) See Forster excitation transfer. 

In the example shown in Figure 5, four BODIPYs were covalently attached to the peiylene diimide core. In accordance with the increase in BODIPY number on the structure, extinction coefficient of the molecule at BODIPY s maximum absorbance wavelength (526 ran) increases dramatically to 250000M cm . Energy transfer efb-ciency was determined to be 99% with a critical Forster radius of 4.7 ran. In the second example shown in Figure 5, enhancement in emission of the core distyryl-BODIPY was observed as the number of terminal BODIPY donors was increased, as expected. ... 

Using the properties of water Li and Cheng (2004) computed from the classical kinetics of nucleation the homogeneous nucleation temperature and the critical nu-cleation radius ra. The values are 7s,b = 303.7 °C and r nt = 3.5 nm. However, the nucleation temperatures of water in heat transfer experiments in micro-channels carried out by Qu and Mudawar (2002), and Hetsroni et al. (2002b, 2003, 2005) were considerably less that the homogeneous nucleation temperature of 7s,b = 303.7 °C. The nucleation temperature of a liquid may be considerably decreased because of the following effects dissolved gas in liquid, existence of corners in a micro-channel, surface roughness. 

The efficiency of resonance transfer is often given in terms of a critical radius R0. If R0 is the distance such that the rate of energy transfer is equal to the sum of all other donor deactivation rates... 

Ro is the Forster critical radius (defined in Section 4.6.3), and rf) is the excited-state lifetime of the donor in the absence of transfer. 

Note that the transfer efficiency is 50% when the donor-acceptor distance is equal to the Forster critical radius. Equation (4.83) shows that the distance between a donor and an acceptor can be determined by measuring the efficiency of transfer, provided that r is not too different from Ro (which is evaluated by means of Eq. 4.80). 

The sixth power dependence explains why resonance energy transfer is most sensitive to the donor-acceptor distance when this distance is comparable to the Forster critical radius. 

Fig. 9.1. Variations in the transfer efficiency as a function of the ratio donor—acceptor distance/Forster critical radius.

The only recent example of Forster transfer of photochemical importance is the demonstration by Saltiel163 that the ability of azulene to increase the photostationary transjcis ratio in direct photoisomerization of the stilbenes is due entirely to radiationless transfer of excitation from traw.y-stilbene singlets to azulene. As expected for Forster transfer, this azulene effect did not depend upon solvent viscosity. The experimental value of R0, the critical radius of transfer in Forster s formula,181 was 18 A, in good agreement with the value calculated from the overlap of stilbene emission and azulene absorption. 

In order to achieve passive safety with reactive material, the radius of the reactor tube is designed to be small to avoid any thermal explosion inside the tube. Using the Frank-Kamenetskii approach (see Chapter 13), the radius remains below the critical radius. Thus, even assuming a purely conductive heat transfer mechanism, corresponding to a worst case, no instable temperature profile can develop inside the reaction mass. The reactor can be shut down and restarted safely. 

The critical heat release rate following the Frank-Kamenetskii theory (see Section 13.4), which describes the passive behavior of the reactor without fluid circulation, when heat transfer occurs by thermal conduction only. The critical heat release rate is the highest power that does not lead to a thermal explosion and varies with the inverse of the squared radius ... 

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