Strict Lindemann behaviour

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. 

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 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. 

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].

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