Classical Theory of Rotational Relaxation of Diatomic Molecules

Abstract

The classical equations of motion of colliding diatomic molecules are solved rigorously in two dimensions to obtain the energy transferred to the internal degrees of freedom during collision. The model considers up to four atoms bound by six atom-centered Morse potentials. The effect of varying range parameters is noted. The relaxation of H2 with He and H2 collision partners, D2 with He, and pure N2 and O2 is studied. The vibration—rotation energy exchange is evaluated and accounted for. The resulting relaxation times and average collision numbers agree well with empirical findings. In the temperature range 100°—700°K, except for N2 and O2, a negative temperature dependence was obtained. The contrary is expected at higher temperatures where the relaxation times are functions of the inverse collision frequency only.

Molecular relaxation processes in triatomic molecules. II. The N2–CO2 system

“…The well depths Vijo were selected from heats of vaporization data on Nz, 0 2 , and C O assuming a geometric-mean combining law [23]. The range terms aij were set equal to 2.OA-l based on previous experience in atom-diatomic molecule and diatomic molecule-diatomic molecule energy 'transfer calculations using atom-atom Morse functions as the interaction potential [ 16,17,.…”

“…This was confirmed to be the case by running several sample trajectories with the equilibrium internuclear distances given in Table I angles representing the relative alignment of the molecular axes; and, for V-V studies, the initial vibrational energy E,i in the diatom and 6, the initial phase angle of the vibrating molecule. In V-V calculations, the anharmonic trajectory of the vibrationally excited molecule is described first [23]. The periodic but anharmonic motion of the isolated oscillator is analyzed in the computer to give the distance ~D E as a function of time for each oscillator energy.…”

Rotational Relaxation in Polar Gases. III. Molecular Dynamics

“…A model of this kind has been used to study the relaxation of diatomic molecules in a heat bath by Alterman and Wilson,l1 Raff 12 and Berend and Benson. 13 Alterman and Wilson studied the vibrational relaxation of 50 bromine molecules in a heat bath of xenon atoms. They terminated their calculations after fewer than 250 collinear collisions between the molecules and atoms.…”

“…The calculations which we shall describe in this paper are more akin to those of Alterman and Wilsonl1 than they are to those of Raff 12 and Berend and Benson 13 in the sense that we shall follow the relaxation of a polar gas coupled to a heat bath. However, in contrast to the one-dimensional treatment of Alterman and Wilson we shall carry out a three-dimensional calculation and shall carry out a sufficient number of collisions to assess whether or not there is an exponential approach to equilibrium.…”