Activation strong-collision

Kolomoitsev D. V., Nikitin S. Yu. Analysis of experimental data on nonstationary active spectroscopy of molecular nitrogen in the strong-collision approximation, Opt. Spectr. 66, 165-8 (1989) [Optika i Spectr. 66, 286-93 (1989)]. 

The collisional stabilization (de-activation) efficiency is assumed to be unity, which is consistent with the strong collision assumption. Thus the stabilization rate constant ks is equal to the hard-sphere rate constant kHS, and Eq. 10.120 becomes... 

The most satisfactory explanation is that the rate is increased beyond the maximum rate of activation by collision through the operation of a chain mechanism. The observations of Sprenger on the peculiar behaviour of nitrogen pentoxide at low pressures suggest strongly that chains are propagated. Moreover, if the rate of the azoisopropane reaction at the lowest pressures should prove to be greater than can be accounted for on the basis of the simple collision mechanism, a chain mechanism can be assumed without difficulty since the reaction is quite markedly exothermic. 

If the rate of the reaction step depends on energy it is necessary to consider the model of activation in more detail. The simplest possibility is to follow the strong collision idea of Hinshelwood, that the energy of the molecule is completely randomized according to a Boltzmann distribution at every collision. The rate of activation into the energy interval from E to E + 5E is therefore... 

The low pressure limit (activation) rate coefficient is given in the strong collision approximation by... 

In reality, more complicated expressions apply because of the multi-step character of the reaction ki and k i depend on the energy E and the angular momentum (quantum number J), and the colhsional energy transfer is a multi-step process with activations and deactivations, to be characterized by a master equation. It has become customary to consider "strong collisions" first and to introduce "weak collision effects" afterwards. For strong collisions, equation (6) takes the form... 

Hassoon, S., Oref, I. and Steel, C. (1988) Collisional activation of quadticyclane by azulene an example of very strong collisions, J. Chem. Phys. 89, 1743-1744. 

An assumption made in all of the theories discussed is that activation and deactivation occur as single steps as opposed to processes in which energy is gained or lost in a series of steps. The assumption that large amounts of energy are transferred in molecular collisions is called the strong collision hypothesis. In essence, it means that consideration of the detailed collision dynamics is not necessary. The energy transfer process can be studied by... 

On the other hand, the strong collision treatment is quite poor in describing the shapes of the fall-off in rate with pressure for the reactions of many simpler molecules, as is shown for the case of the thermal dissociation of nitrous oxide in Figure 8.1 here, the experimental measurements [66.0] lie rather close to a strict Lindemann curve, whereas the strong collision shape exhibits a much more gradual decline. This approach to strict Lindemann behaviour is easily understood in terms of a sequential activation process as the pressure declines and we enter the fall-off region, the states just above threshold decay so quickly... 

The only time when the calculated rate constants show any marked sensitivity to the variation of the elements of the relaxation rate matrix is when those elements happen to lie in the region of a bottleneck in the activation process [71.K1]. Thus, we might suppose, conjecturally, that marked deviations from strong collision fall-off behaviour will only occur when severe bottleneck effects are present in the activation processes. 

Until now, it is virtually impossible to evaluate the function k(E, E ) for polyatomic molecules. For this reason, the theory of collisional activation and deactivation is to a considerable extent based on hypotheses concerning the general properties of the function k(E, E ). The two alternative hypotheses substantially simplifying the microscopic kinetic equations are the strong-collision hypothesis and that of stepladder activation and deactivation [336, 339, 486]. 

According to the strong-collision mechanism each collision AB + M leads to deactivation of the active molecule whereas activation is the result of transitions E E for which the initial state is specified by the equilibrium distribution function. In other words, the mean square of the transfer energy ((AE) ) is assumed to be large compared to (kT). In this case, relaxation is described by a simple kinetic equation of the explicit form [Eq. (17.4)]. 

In terms of the strong-collision mechanism, the integral in Eq. (17.8) may be interpreted as the rate of appearance of the active molecules in all states with E > E. ... 

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