Revisiting falloff curves of thermal unimolecular reactions

Abstract

Master equations for thermal unimolecular reactions and the reverse thermal recombination reactions are solved for a series of model reaction systems and evaluated with respect to broadening factors. It is shown that weak collision center broadening factors F(cent) (wc) can approximately be related to the collision efficiencies β(c) through a relation F(cent) (wc) ≈ max {β(c) (0.14), 0.64(±0.03)}. In addition, it is investigated to what extent weak collision falloff curves in general can be expressed by the limiting low and high pressure rate coefficients together with central broadening factors F(cent) only. It is shown that there cannot be one "best" analytical expression for broadening factors F(x) as a function of the reduced pressure scale x = k(0)∕k(∞). Instead, modelled falloff curves of various reaction systems, for given k(0), k(∞), and F(cent), fall into a band of about 10% width in F(x). A series of analytical expressions for F(x), from simple symmetric to more elaborate asymmetric broadening factors, are compared and shown to reproduce the band of modelled broadening factors with satisfactory accuracy.

Representation of “Broad” Falloff Curves for Dissociation and Recombination Reactions

“…A number of expressions have been proposed, see e.g. [10][11][12][13][14][15][16]. As there is no unique form of the broadening factors ( ), one cannot claim that the one expression is better than the other in all generality.…”

“…For systems with the same cent , nevertheless, ( ) does not deviate too much from an average general form [10]. Although Equations (1)- (4) have found wide application and are useful in many situations, their evident problems have stimulated search for better approximations, either for the broadening factors ( ) or, abandoning the separation in Equation (2), of / ∞ as a more general function of 0 / ∞ .…”

“…[5] and expressions of the type of Equations (2)- (4) were developed. It was, however, shown [10] that there cannot be a unique form of ( ) which is adequate for all reactions.…”

Barrierless association of CF 2 and dissociation of C 2 F 4 by variational transition-state theory and system-specific quantum Rice–Ramsperger–Kassel theory

“…In this work, the necessary physical parameters for treating the pressure dependence of collisional activation (43)(44)(45)(46)(47)(48)(49)(50) are directly taken from the literature; in the high-pressure limit, no empirical parameters are adjusted to the experimental data, and our calculations are from first principles. At finite pressure, the rate constant depends on the average energy transferred per collision <ΔE> all , which has been fitted to experiments in refs.…”

“…6. A simplified version of Troe's (46) master equation-based treatment of collision effects is used for computing the collisional efficiency β c (44), and the unimolecular F E factor is computed using the Whitten-Rabinovitch method (49,50,65). For these calculations, Lennard-Jones parameters σ and «/k B for C 2 F 4 are 4.68 Å and 235.9 K (66), respectively, and for Ar are 3.4 Å and 120 K, respectively (67).…”