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Generalized rate law for vibrational relaxation of a pure diatomic gas

Teitelbaum, Heshel

Canadian journal of chemistry, 1983-06-01, Vol.61 (6), p.1267-1275 [Periódico revisado por pares]

Ottawa, Canada: NRC Research Press

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  • Título:
    Generalized rate law for vibrational relaxation of a pure diatomic gas
  • Autor: Teitelbaum, Heshel
  • Assuntos: Atomic and molecular collision processes and interactions ; Atomic and molecular physics ; Exact sciences and technology ; Physics ; Scattering of atoms, molecules and ions
  • É parte de: Canadian journal of chemistry, 1983-06-01, Vol.61 (6), p.1267-1275
  • Descrição: The master equation for the vibrational relaxation of a pure gas of diatomic molecules AB is reduced to a simple analytical rate law. Anharmonicity is accounted to first order, and both T-V and near-resonant V-V energy transfer processes are included with the limitation that Δν = ± 1. L and au-Teller type transition probabilities are used to scale the rate constants. The rate law consists of a pair of simultaneous first order non-linear differential equations one for the mean vibrational energy, , and one for the mean squared vibrational energy ; or equivalently a non-linear second order differential equation for , with respect to time, t, plus an algebraic equation for These lead to where χ e is the anharmonicity factor, N the molecular concentration, ν e ,. the spectroscopic vibrational frequency; ν′ = ν e (1 − χ e ); ν″ = ν e . (1 − 3χ e ); ; 1/τ = Nk 1.0 (1 − e −hν″/KT ); k 1.0 the rate constant for the process AB(ν = 1) + AB(ν) → AB(ν = 0) + AB(ν); and the rate constant for the process 2AB(ν = 1) → AB(ν = 0) + AB(ν = 2). It is shown that the Bethe-Teller law, , is valid only in the limit of zero anharmonicity or slow V-V processes, or when the initial population is Boltzmann, such as in shock tube experiments. Furthermore, a population distribution which is initially Boltzmann will remain so; whereas a non-Boltzmann distribution rapidly becomes a Boltzmann distribution on a time scale determined by the sum of T-V and V-V rate constants. The present study allows one to gauge the importance of two common assumptions: the validity of the Bethe-Teller law and the existence of a Boltzmann distribution or vibrational temperature during the relaxation.
  • Editor: Ottawa, Canada: NRC Research Press
  • Idioma: Inglês

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