Three-body reactions

Because these mechanisms did not explain shock tube rate data, Brokaw [8] proposed that the mechanism consists of reaction (3.36) as the initiation step with subsequent large energy release through the three-body reaction (3.42) and... 

One formalism which has been extensively used with classical trajectory methods to study gas-phase reactions has been the London-Eyring-Polanyi-Sato (LEPS) method . This is a semiempirical technique for generating potential energy surfaces which incorporates two-body interactions into a valence bond scheme. The combination of interactions for diatomic molecules in this formalism results in a many-body potential which displays correct asymptotic behavior, and which contains barriers for reaction. For the case of a diatomic molecule reacting with a surface, the surface is treated as one body of a three-body reaction, and so the two-body terms are composed of two atom-surface interactions and a gas-phase atom-atom potential. The LEPS formalism then introduces adjustable potential energy barriers into molecule-surface reactions. 

Alkylperoxy radicals can also react with N02 in a three-body reaction to form a peroxynitrate, R02N02 ... 

The forward reaction is a three-body reaction with values of k ) = 2.2 X 10-3() cm6 molecule-2 s-1 and kx = 1.5 X 10-12 cm3 molecule-1 s-1 at 300 K with Fc = 0.6 (see Chapter 5.A.2 for discussion of this factor) recommended by DeMore et al. (1997). Atkinson et al. (1997b) recommend kf) = 2.8 X 10-3(1 cm6 molecule-2 s-1 and k = 2.0 X 10—12 cm3 molecule-1 s-1 with Fc = 0.45. The recommended value of the equilibrium constant Kt) t) is 2.9 X 10-11 cm3 molecule-1 at 298 K, with an uncertainty of 30% (DeMore et al., 1997). This equilibrium constant has been the subject of numerous experimental studies, which have yielded results that ranged over a factor of two at room temperature. For example, a study by Wangberg et al. (1997) subsequent to the NASA and IUPAC recommendations reports a value of 2.34 X 10" " cm3 molecule-1, about 20% smaller but within the relatively large uncertainty of the recommended value. 

It is often found in combustion reactions that H2O has a greatly enhanced collision efficiency for three body reactions. 

Hydrogen atoms readily diffuse upstream of the flame front into the cooler unbumed region. At temperatures below about 750 K, the production of H02 dominates, but at the higher temperatures in the flame front, the chain-branching dominates. As the temperatures continue to rise, the chain-branching reaction equilibrates and the three-body reaction can... 

Trautz424 argued that there could be no true three-body reactions because of the improbability of a three-body collision, and he considered both (NO)2 and N03 as possible intermediates. Bodenstein at first rejected the idea of intermediates as being artificial, particularly because they required postulating unknown compounds. He argued that if such an intermediate formed it must be so unstable that there would be little difference between it and an NO molecule in a collision of finite duration with oxygen. Later,45 he accepted the idea of (NO)2 as the likely intermediate. In the case of either mechanism... 

The strongest piece of evidence for the NO dimer intermediate is the circumstantial one of the similarity between all the known three-body reactions (excluding recombinations) all consist of two nitric oxide molecules reacting with a third molecule 02, Cl2, Br2, and H2. 

Three-body reactions are rare, but the reaction proceeds through a resonance in 12C at 7.65 MeV corresponding to the second excited state of 12C (Jtt = 0+). This excited state has a more favorable configuration than the 12C ground state for allowing the collision to occur. (In a triumph for nuclear astrophysics, the existence of this state was postulated by astrophysicists to explain nucleosynthetic rates before it was found in the laboratory.)... 

On the assumption that the primary reaction was (45), the following surface or three body reactions were considered to occur ... 

The circumstellar chemistry is often subdivided into three main zones, which are determined by a comparison of the characteristic dynamic flow time, R/vx, with the chemical reaction times (Lafont et al. 1982 Omont 1987 Millar 1988). (i) In the region closest to the star (perhaps R 1014 cm), the density is sufficiently high that three-body chemical reactions occur in a time short compared to the dynamic time. In this regime, we expect the chemical abundances to approach thermodynamic equilibrium, (ii) Somewhat further away from the star (1014 cm < R < 1016 cm), there is a freeze-out of the products of the three-body reactions (McCabe et al. 1979). In this region, two-body reactions dominate the active chemistry, (iii) Finally, far from the star (R > 1016 cm), the density becomes sufficiently low that the only significant chemical processing is the photodestruction that results from absorption of ambient interstellar ultraviolet photons by the resulting molecules that flow from the central star. 

In Table I, the bimolecular rate constants for C2 X3Eg and a3II which we measured are tabulated. The experiments were carried out over a wide range of laser powers, buffer gas pressures, and precursor molecule pressures to assure that the experimental data does not contain artifacts due to three body reactions, vibrational quenching, fragment diffusion, or other fragment reaction. 

Thus, to repeat, when the selected three-body reaction freezes, one can, for impulse purposes, consider the system frozen. Now it is possible to find the point at which the system freezes in the same manner Bray used for the less complicated supersonic tunnel problems. 

The only type of chemical reaction we are likely to ever be able to solve rigorously in a quantum mechanical way is a three-body reaction of the type A+BC - AB+C. (See Fig. 5.) The input information to the dynamicist is the potential energy surface computed by the quantum structure chemist. Given this potential surface, we treat the nuclear collision dynamics using Schrodinger s equation to model the chemical reaction process. 

Apart from the very dense inner zone, all reactions in disks are two-body processes. Three-body reactions become competitive only at <10AU, where n > 1010 cm-3 (Aikawa el al. 1999). The processes leading to formation of molecular bonds are radiative association, associative detachment, and surface reactions. Reactions of associative detachment are not efficient despite their high reaction rates (ao 10-9 cm-3 s 1), mainly due to low abundances of negative ions (but see also Herbst 1981 Millar et al. 2000 McCarthy et al. 2006). 

Since the atmosphere obeys the ideal gas law, the magnitude of the variations in density will show a dependence on altitude, latitude, and season similar to that shown by temperature. Unlike temperature, which enters into the rate expression in an exponential and therefore may have a very large effect in a particular production or loss rate, the density enters only as a single product either as the density of a third body or as that of some reactant that is uniformly mixed. In general throughout the troposphere the density is high enough to make three-body reactions—many of which can be treated as effective two-body reactions—very effective. 

Table 2 - Kinetic parameters, k4 = A exp (C/T), describing three-body reaction of O 4- O2 -t- M -> Os 4- M.

The O ( P) atom rapidly reforms ozone by combining with O2 in a three-body reaction ... 

This ultimately leads to the regeneration of ozone by the three-body reaction (R2), resulting in another null cycle. Occasionally, however, 0( D) collides with water to generate two hydroxyl radicals ... 

The dominant reservoir for chlorine in the stratosphere is HQ which diffuses downward to maintain Q atom (bound and free) continuity. Two major temporary reservoirs (those molecules with a lifetime on the order of one diurnal period) are critical to the chlorine system. QJorine nitrate, formed by thie three body reaction... 

Reactions (46) and (47) are not the usual three-body reactions as inefficient. Presumably CI3 and CIO2 intermediates are involved, predicts that for [O2] and [CI2] small, so that reactions (46) and ble compared to (33), then N2 and CO2 are The mechanism (47) are negligi-... 

This mechanism omits the formation of OH bonds in order to accommodate the fact that neither H2O nor B(OH)3 were products. Reaction (7) is endothermic by about 35 kcal.mole" and presumably accounts for the observed activation energy. However, there is still no evidence for oxygen atoms reactions (8) and (9) are unverified. Reaction (11) is too complex to be an elementary step. Reaction (4) must be discarded since three-body reactions cannot be important below the lower explosion limit, and also for theoretical reasons. 

Clerc and Barat " flash-photolyzed CO2 in the vacuum ultraviolet and watched CO formation by kinetic spectroscopy. They found [CO] to increase rapidly to a maximum (at about 25 i sec when [CO2] = 3 torr, [Ar] = 300 torr) and then remain constant. They attributed the observation to the reaction of excess 0( /)) with the CO produced. They calculated a rate coefficient for 0( Z)) + CO recombination of 10 l. mole . sec or 2x 10 l.mole sec depending whether or not the reaction required a third body. They noted that the third-order rate coefficient was too large for a normal three-body reaction, and suggested a long-lived intermediate complex. In two later papers " ° ° they reported the value of the second-order rate coefficient to be first 6x 10 and then 1.2 x 10 ° l.mole" sec As mentioned above, Clerc and Reiffsteck " recently reassessed the relative rates of addition of 0( J9) to CO2 and CO, and found the latter reaction to be approximately 55 times faster than the former. 

The end result of the Chapman mechanism, and of the modified Chapman processes as elucidated by later investigators" "" is that sodium and other metals (if Chapman-like mechanisms hold for the other metals) are abundant in atomic form. The kinetic studies show that molecular compounds are not present in large quantities above 85 km. Further work " showed that following the formation of dense atomic trails during the vaporization process, molecular recombination in the wake occurs to form smoke or dust that can then act as a delayed source of sodium (and other) atoms. It was then suggested that NaO reacts with atmospheric H2O to form gaseous NaOH, with the latter reacting with atmospheric CO2 in a three-body reaction to form NaHCOs" ... 

X lo cm molecule s has been reached where three-body recombination by M and quenching by M is balanced. From the slope of the plot of Icm vs. total pressure a three-body rate constant of 7 x 10 cm molecule s was determined. As a consequence, the air glowreaction proceeds by a two-body as well as by a three-body reaction. When the air glow rate constant is compared with the total recombination rate of NO + O + M, which also was measured in the chamber, it can be concluded that the air glow rate constant represents within the error limits the total recombination rate constant. Further details are given in the publications Becker et al. (1972c) and (1973). 

Radical chain terminations are dominated by H and CH3 recombinations into the void volume these are typical three-body reactions where the third body is generally made up of the close rigid walls of the polymeric material. 

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