Studies in Nonequilibrium Rate Processes. IV. The Rotational and Vibrational Relaxation of a System of Rotating Oscillators

Abstract

In continuation of previous papers in this series a theoretical study has been made of the rotational and vibrational relaxation of a system of rotating oscillators, represented by a rigid rotator-harmonic oscillator model, in their interaction with a constant temperature heat bath. The relevant relaxation equations for this system have been derived and both numerical solutions, computed with an IBM 704 electronic computer, and approximate analytical solutions have been obtained for the mode and rate of change of the rotational-vibrational level population with time. The results show that, owing to the large order of magnitude difference in the efficiency of translational-rotational and translational-vibrational energy transfer, there is very little coupling between the vibrational and rotational relaxation and the system of rotating oscillators relaxes essentially as if composed of two independent and noninteracting systems of harmonic oscillators and rigid rotators. A calculation of the rotational relaxation time, t(relax), using the adiabatic transition probabilities given by Brout and by Takayanagi and the concomitant selection rules ΔJ=±1 (for heteronuclear molecules) gives values for t(relax) which are greater by a factor of several orders of magnitude (∼102) than the experimental relaxation times found from shock wave studies. This indicates clearly that rotational relaxation does not take place via a stepwise ``ladder process'' involving only transitions between neighboring rotational levels.