Collision frequency hypothesis

We have seen that neither the requirements for activation energy nor the fact that the rates of unimolecular reactions are independent of collision frequency can be explained on the basis of the simple collision hypothesis or the radiation hypothesis. The elaborated collision hypothesis is able to explain them on the assumption of a time-lag in complex molecules between activation and decomposition. In this way a single molecule can collect energy from many successive collisions and store up a sufficient amount for activation. Just because a given hypothesis accounts for the facts, is no reason to consider that the hypothesis has been proved. There may be other hypotheses which will account equally well for the facts. The hypothesis of chain reaction offers a competing hypothesis which up to the present time has been increasing in favor. 

The first attempt to resolve this problem was the radiation hypothesis of Perrin [1], in which the molecule is assumed to be energized by absorbing thermal radiation (in the infra-red) emitted by the walls of the vessel. However it was rapidly realized that the intensity of thermal radiation was quite insufficient to explain the observed rates of reaction [2], although interestingly, under conditions of extremely low collision frequency in interstellar space, Perrin s radiation mechanism is now believed to be significant [3]. 

The capture hypothesis forms the basis for the LGS model for ion-neutral reactions and many exothermic reactions appear to proceed at the collision frequency. Despite the appeal and widespread validity of the LGS model, a number of ion-neutral reactions have rates significantly... 

Lu et al, 2001 Rahaman et al, 2003). Ny is scaled by di ttittyg considering that Ny varies greatly with the Enskog factor. Three surfaces intersect at line 9i = 9j, about which both our results and Rahaman s results are symmetric. That is consistent with theoretical analysis as discussed above, while Huilin s result fails. Furthermore, we can observe that our surfaces are higher than the Huilin s prediction and lower than Rahaman s when 9i<9y This is expected as the Huilin s profile can only be applied in energy equipartition system, which may underestimate the collision frequencies, whereas Rahaman s hypothesis implies aU the collisions happen in a 2D plane, which obviously overestimates the collision frequency. 

Because low amplitude RF burst waveforms do not significantly modify the z-mode amplitudes of ions, the intensities would be expected to reflect the z-mode amplitude distribution just before excitation. This gives us one means of checking the above hypothesis by allowing the z-mode amplitudes to relax via ion-molecule collisions, the relative peak intensities should change. Indeed, at long delay, the high frequency peak increases at the expense of the low frequency peak. 

In order to predict the value of the frequency factor, one may assume that all collisions between reactant molecules with sufficient activation energy result in the instantaneous formation of the reaction products. With this simple hypothesis (collision theory), if the activation energy is known, then the problem of computing the reaction rate reduces to the problem of computing the rate of collision between the appropriate reactant molecules in the ideal gas mixture. This last problem is easily solved by the elementary kinetic theory of gases. 

The hypothesis Chadwick proposed adopting should come as no surprise If we suppose that the radiation is not a [gamma] radiation, but consists of particles of mass very nearly equal to that of the proton, all the difficulties connected with the collisions disappear, both with regard to their frequency and to the energy transfer to different masses. In order to explain the great penetrating power of the radiation we must further assume that the particle has no net charge. We may suppose it [to be] the neutron discussed by Rutherford in his Bakerian Lecture of 1920. ... 

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