Towards a quantitative understanding of the role of non-Boltzmann reactant distributions in low temperature oxidation

An essentially universal assumption of chemical kinetics is that bimolecular reactions only occur between reactants of rovibrational energy described by a Boltzmann (thermal) distribution. Given that the O2 mole fraction is roughly 20% under nearly all relevant low-temperature combustion situations, there is significant potential for molecules to undergo reactive collisions with O2 on the same time scale as the energy-transferring collisions necessary to achieving a Boltzmann distribution. Within the context of low-temperature combustion, this phenomenon conceivably gives rise to an entirely non-Boltzmann sequence involving multiple reactions of fuel-derived radicals with O2 to produce multiple OH radicals. Given the complex interplay among simultaneous internal isomerizations, energy-transferring collisions, dissociations and reactive collisions across multiple reaction surfaces, estimating the extent of deviations from conventional thermal assumptions is not straightforward. A novel methodology is presented for coupling multiple master equations and deriving effective phenomenological rate constants for thermal sets of reactants to thermal sets of products in chemically activated sequences that proceed across multiple reaction surfaces. The methodology is used to establish a better understanding of the nature of non-Boltzmann reactant distribution effects and quantify their magnitude. As a case study, we implement the methodology to explore the effect of non-Boltzmann reactants on product branching fractions of the QOOH* + O2 reaction from n-propyl oxidation as well as its associated dependence with O2 mole fraction, temperature, and pressure. While it appears that the effect of non-Boltzmann reaction sequences will be considerably smaller at higher pressures (at least for propane), it appears that consideration of non-Boltzmann reaction sequences is likely required for interpretations of experimental measurements commonly used to investigate the R + O2 and QOOH + O2 reactions central to engine-relevant ignition behavior. With regard to observable signatures of these effects in experiments, the presence of a stronger-than-usual O2 mole fraction dependence may be a likely indicator of non-Boltzmann behavior.