Obtaining effective rate coefficients to describe the decomposition kinetics of the corannulene oxyradical at high temperatures

Abstract

Unimolecular reactions play an important role in combustion kinetics. An important task of reaction kinetic analysis is to obtain the phenomenological rate coefficients for unimolecular reactions based on the master equation approach. In most cases, the eigenvalues of the transition matrix describing collisional internal energy relaxation are of much larger magnitude than and well separated from the chemically significant eigenvalues, so that phenomenological rate coefficients may be unequivocally derived for incorporation in combustion mechanisms. However, when dealing with unimolecular reactions for a large molecule, especially at high temperatures, the large densities of states of the reactant cause the majority of the population distribution to lie at very high energy levels where the microcanonical reaction rate constants are large and the relaxation and chemical eigenvalues overlap, so that well-defined phenomenological rate coefficients cannot be determined. This work attempts to analyze the effect of overlapping eigenvalues on the high-temperature kinetics of a large oxyradical, based on microcanonical reaction rates and population distributions as well as the eigenvalue spectrum of the transition matrix from the master equation. The aim is to provide a pragmatic method for obtaining the most effective rate coefficients for competing elimination, dissociation, and bimolecular reactions for incorporation in combustion mechanisms. Our approach is demonstrated with a representative example, thermal decomposition and H addition reactions of the corannulene oxyradical.

Energy transfer in intermolecular collisions of polycyclic aromatic hydrocarbons with bath gases He and Ar

“…In addition, our previous studies 7,8 on the reaction kinetics of PAH oxyradicals at high bath gas temperatures (above 1500 K) showed that the radical loss was highly nonexponential. Several eigenvalues contributed to the decay because of the overlapping of chemically significant eigenvalues (CSEs) and internal energy relaxation eigenvalues (IEREs) for these large reactants on the time scales at which the reactant was consumed.…”

“…The supplementary material shows the results of these calculations. Generally, microcanonical sampling of vibrational energy has been employed in trajectory calculations, with energies typically similar to reaction thresholds (∼100 kcal/mol), because reactions of interest in combustion, such as H-atom elimination and carbon-carbon bond dissociation reactions of hydrocarbons [9][10][11] as well as those of PAHs, 8,[18][19][20][21][22] have threshold energies in this region. However, for large PAHs at high bath gas temperatures (>1500 K), because of their very high densities of states, the majority population of the Boltzmann distribution lies at very high energies (∼200-450 kcal/mol), well above the reaction threshold.…”

“…However, for large PAHs at high bath gas temperatures (>1500 K), because of their very high densities of states, the majority population of the Boltzmann distribution lies at very high energies (∼200-450 kcal/mol), well above the reaction threshold. 8 This suggests that choosing the reaction threshold as E vib might be inappropriate at high bath gas temperatures; the canonical sampling method is therefore investigated in this work, and its influence on ⟨∆E down ⟩ is also discussed. The canonical sampling better represents the situation that is encountered in experiments where contact with a thermostat is maintained and where reactants will in general have a range of internal energies, rather than having the same uniform energy which is what is implied by fixing the internal energy of a single molecule, a situation more likely to be found in molecular beam experiments.…”

“…For such molecules, because of the high number of vibrational modes and consequently high densities of states, the thermal vibrational distribution peaks at energies well above typical reaction threshold energies, and so a different approach is needed. 8 For aromatics, there are a few experimental studies [13][14][15][16][17] on the collisional deactivation of highly vibrationally excited benzene or toluene, which were prepared by internal conversion and detected by IRF or UVA. However, for larger PAHs, both experimental and theoretical data are scarce.…”

“…These values were suggested by Jasper et al 11 who used the classical trajectory method to investigate hydrocarbons as large as C 8 H 18 interacting with several different bath gases. However, Frenklach et al [18][19][20][21][22] and You et al 7,8 used a constant ⟨∆E down ⟩ of 260 cm −1 when solving the ME for PAH reaction systems with Ar as a collision partner; this value was based on an analysis of phenoxy decomposition rates, 22 as the rate coefficients calculated with ⟨∆E down ⟩ = 260 cm −1 agreed well with experimental results for bath gas temperatures of 1000-1500 K. Carstensen and Dean 23 used a lower ⟨∆E down ⟩ value of 200 cm −1 in their work on phenoxy decomposition. The significant discrepancies in ⟨∆E down ⟩ values among these previous studies suggest that a systematic analysis of intermolecular energy transfer for PAHs is essential.…”