title: When Rate Constants Are Not Enough.
abstract: Real-world chemical systems consisting of multiple isomers and multiple reaction channels often react significantly prior to attaining a steady state energy distribution (SED). Detailed elementary reaction models, which implicitly require SED conditions, may be invalid when non-steady-state energy distributions (NSED) exist. NSED conditions may result in reaction rates and product yields that are different from those expected for SED conditions, although this problem is to some extent reduced by using phenomenological models and rate constants. The present study defines pragmatic diagnostics useful for identifying NSED conditions in stochastic master equation simulations. A representative example is presented for each of four classes of common combustion species: RO2 radicals, aliphatic hydrocarbons, alkyl radicals, and polyaromatic radicals. An example selected from the seminal work of Tsang et al. demonstrates that stochastic simulations and eigenvalue methods for solving the master equation predict the same NSED effects. NSED effects are common under relatively moderate combustion conditions, and accurate simulations may require a master equation analysis.
authors: †Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, Michigan 48109-2143, United States.
authors: John R
authors: JR
authors: Barker
authors: ‡Department of Mechanical Engineering, University of California-Berkeley, Berkeley, California 94720-1740, United States.
authors: Michael
authors: M
authors: Frenklach
authors: §Department of Mechanical Engineering, Stanford University, Stanford, California 94305-3032, United States.
authors: David M
authors: DM
authors: Golden