Classical Model for Vibrational and Rotational Excitation of Diatomic Molecules by Collision. I. Hard-Sphere Collision

Abstract

The details of inelastic energy transfer between a diatomic, classical, harmonic oscillator, A—B, and a hard‐sphere atom C are explored for the simple case of colinear collisions. The influence of the masses M_A, M_B, and M_C on the efficiency of energy transfer is examined in detail. The case of equally matched masses (M_B = M_C) does not necessarily correspond to high efficiency. It is shown that for colinear collisions not all phase angles of the oscillator can occur at the instant of collision, but that instead certain phase angles are excluded. In the case of a highly excited oscillator in a ``cold'' gas, these excluded phase angles are just those that restrict the energy transfer from the oscillator to small amounts of energy. For a harmonic oscillator, near the dissociation threshold, this implies a small, stepwise deactivation process. It is also shown that even for the hard‐sphere case, 100% efficiency of energy transfer is not possible, i.e., there is an activation energy in excess of the energy transferred. This is required as an ``escape energy'' in order to avoid a double collision whose effect would be to reduce the energy transferred. This escape phenomenon is also shown kinetically to favor stepwise energy transfer for quantized oscillators. Some simple cases of rotational‐energy transfer are examined.