Theory of Spontaneous Decomposition

This rate L(E) will be different for each detailed assignment of the energies E, to the oscillators and is a very complex function of the values E. For sufficiently large molecules with values of E /kT not too small, Slater has estimated that this detailed model behaves like a Kassel model [Eq. (X.5.1)] in which the number of Kassel oscillators n = (s + l)/2. 

On the basis of the RRK model, the over-all rate of unimolecular reaction can be written as 

When P(E) is not perturbed by the reaction, so that the distribution of critically energized molecules is that characteristic of equilibrium, the RRK model leads to a specific first-order rate constant of the form k = A exp —E /RT) where A is the frequency of internal energy transfer between oscillators. The Slater formulation in these circumstances gives k = V exp —E /RT ), both results being similar in form to the Arrhenius equation. The A factor in the RRK model represents the frequency of energy transfer between oscillators, which Jor weakly coupled oscillators would be of the order of their beat frequencies, or about 10 to 10 sec In the Slater model, V represents a weighted rms frequency of the normal frequencies which describe the decomposition [Eq. (X.6.1)] 

In this high-pressure or equilibrium limit these models cannot be distinguished and the justification of a choice between them has to be made on other grounds. They will differ under conditions in which the internal energy distributions P E) and P Eij. . . , E ) are no longer the equilibrium values. But then the differences will be not in form but in the effective number of oscillators assignable to the decomposition. 

The effect of wavelength on the (piantum yield of CO production from the photolysis of CII2CO can be satisfactorily interpreted on the basis of the RE.K model, but unfortunately the lack of data on the precise bond dissociation energy prevents a uiiiciuc assignment of parameters. The wavelength dependence of the fluorescence of photoexcited /3-naphthyl-amine has also been reasonably well interpreted in terms of the rate of spontaneous isomerization to a inetastable state incapable of fluorescence. A model for k E) equivalent to the RRK model was used. 

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