Vibrational rate enhancement

In this section we introduce collision theory and derive expressions for simple cross-section models allowing for variation of reactivity with relative translational energy. We then introduce quantum-state-selected reactivity and discuss the influence of vibrational rate enhancement on the thermal rate coefficient. As an alternative approach we then turn to transition state theory and consider the evaluation of rate coefficients from molecular properties. 

Non-Arrhenius behavior as a result of vibrational rate enhancement In the... 

State-specific and thermal rate coefficients for this reaction are shown in Fig. 7. Substantial Arrhenius curvature is predicted above 1500 K, although the curvature predicted on the basis of the vibrational rate enhancement is insufficient to account for all of the experimentally observed behavior (see also Section 4). 

We have demonstrated that vibrational rate enhancement can cause positive departures from a simple Arrhenius relation. We now investigate how this is modified under nonequilibrium conditions. To do this we again use OH + H2 (i = 0, 1) H2O + H as a reference reaction and consider first a situation in which the reactants are highly diluted in an inert gas such as Ar. 

A summary of the symmetry analysis for the various isotopomers is presented in Table 5 where, in keeping with the conclusions of the general analysis, only ground vibrational states of the reactants are considered. Inspection of Table 5 indicates that isotopic substitution that preserves the CO2 centrosymmetry lifts the restriction based on I while preserving the restriction based on the e parity label state. Because C substitution will always preserve molecular centrosymmetry, the symmetry analysis predicts that ( 02)2 clusters containing a C isotope could show at most a formation-rate enhancement of a factor of two above that of (002)2- Also, because this symmetry restriction is independent of the detailed nature of the quantum states of the COj ions, the C SIKIE is predicted to be independent of the way in which the ion is prepared (i.e., E. Conversely, Table 5 indicates that when the COj centrosymmetry is removed, there are no symmetry restrictions to cluster formation. The extent to which the formation of (002)2 containing a ion will be enhanced above that of ( 62)2 depends on the e/f parity label state distribution of the CO2 ions, which, as was demonstrated in the O2/O2 study,can depend on E. ... 

The shorter shaft and disc assembly in the horizontal mill is capable of higher speed without destructive vibration (3400 ft,/min or 17 meters/sec,). The high shear rates enhance media action for particle size reduction (impact action) and agglomerate separation (shear action). 

The fact that enzymes employ dynamics, should in no way be surprising -evolution knows nothing of quantum mechanics, classical mechanics, or vibration-ally enhanced tunneling. Rates of reaction are optimized for living systems using all physical and chemical mechanisms available. It is also important to point out that such protein dynamics are far from the only contributor to the catalytic effect. In fact in an enzyme such as alcohol dehydrogenase, transfer of a proton from the alcohol to the coordinated zinc atom is critical to the possibility of the reaction. The specific modulation of the chemical barrier to reaction via backbone protein dynamics is now seen to be part of the chemical armamentarium employed by enzymes to catalyze reactions. 

The reactions of excited hydrogen halides are convenient to study because of the availability of hydrogen halide chemical lasers for excitation. The correlation between ground-state heats of reaction and vibration-ally induced reaction rate enhancement is striking for these processes (Table I). As expected, reaction enhancement is observed for all reactions except for those that are exothermic. In the case of reaction (2) the reaction rate is... 

Sims et al have carried out tr ectory calculations on the endothermic reactions (-55a) and ( -55b), and on the analogous reaction with X = I. These also cast some doubt on the interpretation of Stedman s experiments, since they indicate a rate enhancement for H2(v = 1) five times less than that deduced from the earlier experiments. In addition to their calculations, Sims and his colleagues performed experiments similar to those of Stedman et al but with X == Br and the temperature of the reactor raised to 712 K. They found that the presence of vibrationally excited enhanced the rate of HBr production, and attributed this to an increase in rate of reaction ( -55b) of ca. 7 x 10 as H2 is raised from v =0 to v = 1. 

Gomaa and Rao [83] studied filtration performance enhancement of submerged flat sheet membranes by the vertical vibration. Their experiments showed that the vibration could enhance the flux up to threefold with the flux increasing with the shear rate in a power around 0.22. The model developed based on a modified film theory predicted that an effective filtration performance enhancement of the flat sheet membrane can be achieved by vibration at frequencies <25 Hz and amplitude <15 mm [83]. 

Experiments using vibrationally excited hydroxyl radicals do indicate that OH (v=l) is quenched by CO at least as rapidly as it reacts with it A rate enhancement of less than a factor of two was measured at room temperature [35]. Vibrational excitation of the CO molecule should provide another clue to the microscopic mechanism of this reaction. The energy of the vibrational quanta in CO... 

As reviewed elsewhere in this volume (l,2) considerable recent progress has been achieved with respect to our understanding of the dynamics of atomic fluorine reactions. A central objective of chemical dynamics research involves the elucidation of coupling mechanisms by Ich various forms of energy affect reaction rates ( ). Vibrational excitation has been shown to promote certain blmolecular processes (] ) In cases that Involve mode selective reeigent excitation, the rate enhancement may be siifficient to provide a basis for isotope separation ( ). Reactivity and energy transfer characteristics of novel electronically excited species have also been investigated (6-8). 

A recent trajectory study of the O3 + NO NO2 + O2 reaction also found elements of both nonspecific and specific mode related effects.The reaction rate enhancements, for example, did not show specificity with respect to O3 or NO vibrational excitation, but excess NO vibrational excitation was specifically distributed to certain vibrational modes in the product NO2- These results for O3 + NO and OH -i- H2 suggest that there is much yet to be learned about the reaction dynamics of polyatomic molecules. 

For reasons given in Section 1.2.2, there have been few direct experiments on bimolecular reactions involving molecules with more than one quantum of vibrational excitation. However, the energies associated with single quanta are comparable with the activation energies of many elementary atom-transfer reactions, so the resultant rate enhancement can be considerable and revealing. In this section, data on the reactions (and parallel relaxations) of diatomic hydrides such as Hg, HX (X = F, Cl, Br, I), and OH, are reviewed first, and then some examples are provided of measurements on reagents excited by CO2 laser photons. 

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