Radiative rate coefficient

The Si excited-state lifetimes of cyclohexane and alkyl cyclohexanes are relatively short, all around 1-2 nsec however, their [Pg.373]

From these equations one also finds the rate coefficient matrix for themial radiative transitions including absorption, induced and spontaneous emission in a themial radiation field following Planck s law [35] ... 

Ion-molecule radiative association reactions have been studied in the laboratory using an assortment of trapping and beam techniques.30,31,90 Many more radiative association rate coefficients have been deduced from studies of three-body association reactions plus estimates of the collisional and radiative stabilization rates.91 Radiative association rates have been studied theoretically via an assortment of statistical methods.31,90,96 Some theoretical approaches use the RRKM method to determine complex lifetimes others are based on microscopic reversibility between formation and destruction of the complex. The latter methods can be subdivided according to how rigorously they conserve angular momentum without such conservation the method reduces to a thermal approximation—with rigorous conservation, the term phase space is utilized. 

In specific applications, it is critically important to know which isomer is produced in a particular situation in order to ascertain its further reactivity. Indeed, further reactivity, in the form of rate coefficients and product ion distributions, both identifies which reactions generate the same isomeric forms and gives information to enable the isomeric forms to be identified (often by determining the energetics and comparing them with theoretical calculations). One such application is to molecular synthesis in interstellar gas clouds. In the synthesis of the >115 molecules (mainly neutral -85%) detected in these clouds,14 a major production route is via the radiatively stabilized analog of the collisional association discussed above,15 viz. ... 

Chemiluminescence is believed to arise from the 2Bj and the 2B2 electronic states, as discussed above for the reaction of NO with ozone [17]. The primary emission is in a continuum in the range =400-1400 nm, with a maximum at =615 nm at 1 torr. This emission is significantly blue-shifted with respect to chemiluminescence in the NO + 03 reaction (Xmax = 1200 nm), as shown in Figure 2, owing to the greater exothermicity available to excite the N02 product [52], At pressures above approximately 1 torr of 02, the chemiluminescence reaction becomes independent of pressure with a second-order rate coefficient of 6.4 X 10 17 cm3 molec-1 s-1. At lower pressures, however, this rate constant decreases and then levels off at a minimum of 4.2 X 1(T18 cm3 molec-1 s-1 near 1 mtorr, and the emission maximum blue shifts to =560 nm [52], These results are consistent with the above mechanism in which the fractional contribution of (N02 ) to the emission spectrum increases as the pressure is decreased, therefore decreasing the rate at which (N02 ) is deactivated to form N02. Additionally, the radiative lifetime and emission spectrum of excited-state N02 vary with pressure, as discussed above for the NO + 03 reaction [19-22],... 

Absorption and extinction coefficients are generally less pH dependent than fluorescence spectra and quantum yields because the radiative rates often compete with intra- and intermolecular relaxation precesses. 

A being the radiative rate (labeled in such a way because it coincides with the Einstein coefficient of spontaneous emission) and Anr being the nonradiative rate, that is, the rate for nonradiative processes. The solution of the differential equation (1.16) gives the density of excited centers at any time r ... 

In the group of nonfluorescing alkanes the lifetimes are very short, x < 0.3 nsec an upper limit of i < 3 x 10 sec is estimated. The absence of fluorescence for these compounds may have two causes the low R, i.e., low rate coefficient of the Si Sq radiative transition and the short lifetime, i.e., the very fast chemical decomposition. In the C5 and C7-C10 cycloalkanes the ring strain, which is mainly caused by the repulsive interaction of their unfavorably displaced H atoms, may enhance the rate coefficient of the chemical decay by C-H decompositions. In the excited sates of the geminally branched... 

Electronically excited ionic states, for which the transitions to the ground state are allowed, normally have very short radiative lifetimes, typically on the order of 10 nsec to 1 jLisec, Yet even these states are quite efficiently collisionally deactivated, particularly on interaction with the corresponding parent gases. Several such systems have been studied in detail, and the Stem-Volmer relation has been employed to determine rate coefficients for collisional deactivation.233-239 Some of these reactions and the pertinent kinetic data are displayed in the reactions that follow. 

The calculated radiative lifetime of benzene vapor based on absorption coefficients111 is in excellent agreement with the mean lifetime measured by Donovan and Duncan112 and is about 5 x 10-7 sec. And yet this agreement must be partly fortuitous, since the emission yield is only about 0.2 and hence there must be processes which compete with radiative emission100 101. It is true that, if twenty per cent of the molecules emit, these competitive processes must have rate coefficients not greatly different from the rate coefficient of the process100... 

In the study of any radiative recombination process, one tries to answer a number of fairly well defined questions, mostly related to potential curves. From what electronic states is emission observed With what atomic states do these molecular states correlate Does the recombination take place on a single potential curve, or is a transition between two curves involved Is a potential curve with a significant maximum involved Is a third body necessary, either to stabilize the atom pair on a single curve, or to induce a transition to another curve In the case of a transition between two electronic states, is there an approximate equilibrium What is the vibrational and rotational distribution of newly formed molecules What is the recombination rate coefficient as a function of temperature or cross section as a function of energy In principle these questions can be answered either theoretically or experimentally. In fact, they have been answered experimentally in most cases, but the answers are seldom as certain or as numerous as one would wish. This becomes clear in the following discussion of particular cases. 

We have seen from the above work that the nonradiative rate constants dominate the luminescence behavior of ruthenium(II) complexes. If one can increase the value of the radiative rate constant, kr, without substantial increases in knr, then emission efficiency can be improved. The radiative rate constant is, in theory at least, related to the molar absorption coefficient, epsilon187. Demas and Crosby188, made a number of assumptions and calculated radiative lifetimes based on observed epsilon values, which were in good agreement with the experimental kr values. Watts and Crosby1895 went on to comment on the possible implications of the epsilon value. 

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