Strong collision behaviour

In fact, it is possible to do better than this, and to derive the whole evolution of the population distribution for all times, as given in equation 17 of [81.V2], but this result is probably of little more than academic interest in view of the unlikelihood of ever finding true strong collision behaviour. 

Also, as is becoming increasingly recognised [80.J2], multichannel thermal reactions possess considerable potential for showing up departure from strong collision behaviour if such departures from strong collision behaviour arise as the result of a randomisation failure, this model quickly yields the relative fall-off behaviour for the various reaction channels, as an extension of equation (7.7). If there are only two interfering channels, m = 1, 2, the result is [81.P2]... 

Fig. 8.1. Comparison of the observed rates of dissociation of nitrous oxide at 2000 K with strict Lindemann and with strong collision behaviour. Notice that the limiting values of and, used in constructing these curves are both about 8-9% higher than the values given by the original Arrhenius expressions in [66,0].

Strong collision behaviour is nothing more than a mathematical convenience which is never attainable in practice there are two precise requirements for such behaviour, that the internal relaxation is pure exponential, equation (2.27), and that the rate of interchange between reactive and unreactive states above threshold is infinite. However, many thermal unimolecular reactions give the appearance of being strong collision processes, a fact which we can rationalise as follows. The internal relaxation is obviously not a pure exponential, but it mimics one moderately closely for this to be so, there would not have to be any bottleneck in the relaxation process, which could happen if the rotational... 

As can be seen, the difference in behaviour of orientational relaxation times Te,2 in models of weak and strong collisions is manifested more strongly than in the case of isotropic scattering. Relation (6.26) is... 

The behaviour of te,2 (tj) is qualitatively different. In the dense media this dependence also satisfies the Hubbard relation (6.64), and in logarithmic coordinates of Fig. 6.6 it is rectilinear. As t increases, it passes through the minimum and becomes linear again when results (6.25) and (6.34) hold, correspondingly, for weak and strong collisions ... 

Notice that the sufficient condition for the occurrence of strict Lindemann behaviour, given a strong collision relaxation matrix, is that the d, are constant alternatively, if there is only one grain having a non-zero value of d, the rate is also strict Lindemann, regardless of the form of the assumed relaxation matrix [81.VI]. In the past, it had often been assumed that strict Lindemann behaviour was a strong collision property only, but we now know that near-Lindemann behaviour can often occur in weak collision systems at high temperature, see Chapter 8. 

It should be understood that there is not necessarily any direct connection between the threshold energy, , for the reaction and any measured Arrhenius temperature coefficient however, as shown here and in the preceding chapter, the assumption of strict Arrhenius behaviour with the threshold taken as , gives an excellent representation of the fall-off shape for strong collision reactions. 

It is quite clear from an inspection of Figures 7.1 and 7.2 that the kind of agreement found between theory and experiment in Chapter 5 could not have occurred unless Pr was effectively infinite in these strong collision systems, because as soon as the randomisation processes become rate determining, there are severe departures from the simple strong collision, i.e. p, = oo, behaviour. We must then ask whether there are any known experimental results from which we can demonstrate a departure from infinitely rapid randomisation, and it appears that the well-studied thermal isomerisation of methyl isocyanide may be just such an example. 

The eigenvalue is easily seen to have the following limiting behaviour as /i,—+00, we recover the standard strong collision formula, equation (5.17) conversely, as the rate. constant becomes strict Lindemann in form. Both limiting forms possess the same high pressure limit = Z,jS,d but the two low pressure limits are vastly different in the one case, the limit is pl-rfr-. because any molecule excited into a reactive grain must eventually react but, in the other, the limit is /iZ n—/rZ,., because only those molecules excited directly into the reactive levels themselves can react. 

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. 

The non-equilibrium energy distribution function of molecules AB depends much more on the activation mechanism than the fall-off curve. The qualitative behaviour of the population ratio X(E)/X (E) for these two cases is shown in Fig. 25. For the strong-collision mechanism the depletion of population is seen to occur only for energy levels above Ea whereas for the stepladder mechanism it is below this level. 

Fig. 6.3. Quasi-static behaviour of relaxation times tgj (upper curves) and r ,i in the case of strong (1,2) and weak (3,4) collisions. The straight lines are the asymptotics of the curves after Q-branch collapse.

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. 

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