The Master Equation for the Dissociation of a Dilute Diatomic Gas. XI. Vibrational Freezing in a Nozzle Flow

1974 ◽  
Vol 52 (6) ◽  
pp. 939-941 ◽  
Author(s):  
Nabil I. Labib ◽  
Huw O. Pritchard
Keyword(s):  
Relaxation Time ◽  
Energy Level ◽  
Master Equation ◽  
Rate Constant ◽  
Ground State ◽  
Vibrational Relaxation ◽  
Vibrational Energy ◽  
Nozzle Flow ◽  
Vibrational Energy Level ◽  
Diatomic Gas

A previously reported calculation on a model expansion in a nozzle flow is extended to the point where the whole vibrational energy "freezes" and the behavior of the vibrational relaxation time is examined. Starting with the high levels, each individual vibrational energy level becomes decoupled from the ground state in sequence, down to and including υ = 1; under these conditions, all measures of the vibrational relaxation time fail, but perhaps surprisingly the rate constant for recombination remains well defined.

The Master Equation for the Dissociation of a Dilute Diatomic Gas. VI. Solution of Coupled Sets of Master Equations

1972 ◽  
Vol 50 (6) ◽  
pp. 897-906 ◽  
Author(s):  
D. L. S. McElwain ◽  
H. O. Pritchard
Keyword(s):  
Relaxation Time ◽  
Differential Equations ◽  
Master Equation ◽  
Normal Mode ◽  
Rate Constants ◽  
Vibrational Relaxation ◽  
Master Equations ◽  
Diatomic Gas ◽  
Full Solution ◽  
Mode Technique

Three coupled sets of master equations, representing the equilibration of [Formula: see text] via atoms only, have been solved by the normal-mode technique; the set of 57 simultaneous differential equations describing the H2/D2/2HD system was considered as a suitable trial model. It was found that at times (t) in excess of the longest vibrational relaxation time, even though some of the populations in the system appeared highly non-Boltzmann, all the phenomenological rate constants were well-behaved: they were either constant and obeyed the rate–quotient law, or they were dependent on t2.The paper concludes with a discussion of the information required before a full solution of the [Formula: see text] reaction could be contemplated, and suggests methods by which an approximation to such a solution could be obtained.

scholarly journals A re-examination of the adiabatic correction term for the hydrogen molecule

1976 ◽  
Vol 54 (4) ◽  
pp. 651-656 ◽  
Author(s):  
Huw O. Pritchard ◽  
Lutosław Wolniewicz
Keyword(s):  
Energy Level ◽  
Hydrogen Molecule ◽  
Vibrational Energy ◽  
Correction Term ◽  
Internuclear Separation ◽  
Vibrational Energy Level ◽  
The Difference ◽  
The One

The adiabatic coupling correction term [Formula: see text] has been evaluated by two methods, the one used by Kołos and Wolniewicz in 1964 and the one suggested by Kari, Chan, Hunter, and Pritchard in 1973. The difference between the two procedures for H2 amounts to 0.04 cm−1 and is almost independent of internuclear separation in the range R = 1.0–1.8 a.u. Thus, the method of computing the ΔR-term does not affect the vibrational energy level spacings.

Generalized rate law for vibrational relaxation of a pure diatomic gas

1983 ◽  
Vol 61 (6) ◽  
pp. 1267-1275 ◽  
Author(s):  
Heshel Teitelbaum
Keyword(s):  
Rate Constant ◽  
Rate Constants ◽  
Vibrational Relaxation ◽  
Vibrational Energy ◽  
Boltzmann Distribution ◽  
Rate Law ◽  
First Order ◽  
Non Linear ◽  
Energy Formula ◽  
The Mean

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, [Formula: see text], and one for the mean squared vibrational energy [Formula: see text]; or equivalently a non-linear second order differential equation for [Formula: see text], with respect to time, t, plus an algebraic equation for [Formula: see text] These lead to[Formula: see text]where χe is the anharmonicity factor, N the molecular concentration, νe,. the spectroscopic vibrational frequency; ν′ = νe (1 − χe); ν″ = νe. (1 − 3χe); [Formula: see text]; 1/τ = Nk1.0(1 − e−hν″/KT); k1.0 the rate constant for the process AB(ν = 1) + AB(ν) → AB(ν = 0) + AB(ν); and [Formula: see text] the rate constant for the process 2AB(ν = 1) → AB(ν = 0) + AB(ν = 2). It is shown that the Bethe–Teller law, [Formula: see text], 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.

scholarly journals Modeling the Vibrational Relaxation of Polyatomic Molecules. The Methylfluoride Case Study

1990 ◽  
Vol 10 (3) ◽  
pp. 147-158
Author(s):  
V. Tosa ◽  
R. Bruzzese ◽  
C. de Lisio ◽  
S. Solimeno
Keyword(s):  
Relaxation Time ◽  
Relaxation Process ◽  
Vibrational Relaxation ◽  
Vibrational Energy ◽  
Polyatomic Molecules ◽  
Rate Equations ◽  
Strongly Nonlinear ◽  
Nonlinear Character ◽  
Intermediate Size

We present in this paper a theoretical analysis of the vibrational translational (V-T) relaxation process in CH3F, carried out by using a numerical model based on rate equations. In particular, we have analysed the dependence of the V-T relaxation time on the average vibrational energy absorbed per molecule. We have also investigated the influence of the dependence of the rate constants used in the model, on the gas translational temperature. The results of the model clearly outline the strongly nonlinear character of the V-T relaxation process in CH3F, a situation commonly observed in other important polyatomic molecules of intermediate size each as SF6, freons, and related methylhalides.

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