Analytic approximation to the solution of vibrational-rotational energy transfer in the dissociation and relaxation of hydrogen, deuterium, and oxygen

Abstract

The analytical solution of the general relaxation problem in a low-pressure system with exponential transition probabilities, as given previously for vibrational energy transfer on collision, is now extended to include rotational energy transfer. The approximation is made that the rotational degrees of freedom are equilibrated and that the barrier to dissociation is linear and asymmetric. The theory is used to calculate the rate constant for dissociation, the number density incubation time, and the vibrational relaxation time in the dissociation of H2, D2, and 02. Agreement with experiment and other more elaborate calculations is very satisfactory.

Analytical solution of vibrational–rotational energy transfer in the dissociation and relaxation of N2, Br2, and CO at high temperature

“…This is approximately true for several diatomics for which potential energy data are available [6], and has the felicitous consequence that it yields a particularly simple solution. Assumptions (1)-( 3) make eq.…”

“…(4) be defined as E * , = E o -k T l n { ( 1 + -"; 3 kT;;r (Eo)] where Nu, (Eo) is the density of vibrational-rotational states near threshold and QUr is the vibrational-rotational partition function. Using the Morse oscillator representation, it can be shown that [6] Qur k T where v is the frequency of the oscillator, and D, = EO + hu/2 is the dissociation energy measured from the potential minimum.…”

“…This destroys the eigenvalue character of the original problem, and consequently only the steady-state rate constant k& can be obtained but no relaxation times. It can then be shown that the harmonic quasidiatomic rate constant is [5,6] we -EoIkT…”

Analytic solution of relaxation and dissociation of ozone and sulphur dioxide at low pressures

“…The general relaxation problem in a gas at low pressure can be solved analytically for the case of exponential transition probabilities, as we have shown in recent publications (1)(2)(3)(4). The calculations were tested, with good results, on the (spinforbidden) dissociation and relaxation of two triatomics, N 2 0 and CO,, both of which are linear.…”

“…[6] is calculated using a 15-point Gauss-Laguerre integration (7), and the densities of states by the method of steepest descents (8) for a collection of (in the present case) three harmonic oscillators and three rigid rotors. Equations [2] and [3] (9)). Owing to the uncertainty in the Lennard-Jones (LJ) well-depth parameter E for 0 3 , it is not useful to calculate collision numbers under LJ potential (ZLJ), which would probably be more appropriate.…”