Fall-off regime

Thus, according to this three-step mechanism, a bimolecular recombination reaction is second-order at relatively high concentration (cM), and third-order at low concentration. There is a transition from second- to third-order kinetics as cM decreases, resulting in a fall-off regime for kbi. 

It is also necessary to explain why there are parentheses around the collision partner M in reactions (3.94), (3.95), and (3.99). When RH in reactions (3.94) and (3.95) is ethane and R in reaction (3.99) is the ethyl radical, the reaction order depends on the temperature and pressure range. Reactions (3.94), (3.95), and (3.99) for the ethane system are in the fall-off regime for most typical combustion conditions. Reactions (3.94) and (3.95) for propane may lie in the fall-off regime for some combustion conditions however, around 1 atm, butane and larger molecules pyrolyze near their high-pressure limits [34] and essentially follow first-order kinetics. Furthermore, for the formation of the olefin, an ethyl radical in reaction (3.99) must compete with the abstraction reaction. 

At pressures between these high- and low-pressure limits, the so-called pressure fall-off regime, the rate constant of Eq. 9.105 applies. It is convenient to introduce a dimensionless parameter pr (a reduced pressure ), defined as... 

The experimental investigations by Fagerstrom et al have shown that at a total pressure of 1000 mbar of SF6, the reaction is still in the fall-off regime. The fluorine atoms abstraction reactions, produced by radiolysis of the gas mixture containing SF6 in great excess, can initiate the H-abstraction reactions... 

The ratio kib/(kia+kib) has values of 3.5 xlO", 7.6 x 10" and 1.67 xlO for total N2/O2 diluent pressiues of 20, 50 and 100-700 Torr and 296 K, respectively. The simplest explanation of these observations is that the rate of reaction (lb) is close to its high-pressure limiting value for pressures above 100 Torr but in the fall off regime at pressmes of 50 Torr and below. It is likely that the pressure dependence reported herein for reaetion (lb) can be modelled using more conventional energy transfer parameters as Barker and Golden (2003) suggest. 

The observation of negative apparent activation energy can most simply be interpreted in terms of the competition between the adsorption and desorption of methylacetylene on the surface. This qualitative explanation is illustrated in Figure 3, where the steady-state production of trimethylbenzene is compared with the TPD trace of methylacetylene. The fall off in steady state cyclotrimerization rate matches the tail of the desorption spectrum and illustrates the role of reactant desorption at higher temperatiu-es controlling the availability of alkyne monomers and thus the overall cyclotrimerization rate in this temperatime/pressure regime. 

Figure 2. f inite-time Lyapunov exponents A( t J tor a driven I lulling oscillator with measurement strengths k = 5 x 10-4, 0.01, 10, averaged over 32 trajectories (linear scale in time, top, and logarithmic scale, bottom bands indicate the standard deviation over the 32 trajectories) (S. Habib et.al., 1998).The (analytic) 1/f fall-off at small k values (dashed red line), prior to the asymptotic regime, is evident in the bottom panel. 

At low relative pressures p/p0 or thin adsorbate films, adsorption is expected to be dominated by the van der Waals attraction of the adsorbed molecules by the solid that falls off with the third power of the distance to the surface (FHH-regime, Eq. 3a). At higher relative pressures p/p0 or thick adsorbate films, the adsorbed amount N is expected to be determined by the surface tension y of the adsorbate vapor interface (CC-regime, Eq. 3b), because the corresponding surface potential falls off less rapidly with the first power of the distance to the surface, only. The cross-over length zcrit. between both regimes depends on the number density np of probe molecules in the liquid, the surface tension y, the van der Waals interaction parameter a as well as on the surface fractal dimension ds [100, 101] ... 

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