Competitive partitioning of rotational energy in gas ensemble equilibration

A wide-ranging computational study of equilibration in binary mixtures of diatomic gases reveals the existence of competition between the constituent species for the orbital angular momentum and energy available on collision with the bath gas. The ensembles consist of a bath gas AB(v;j), and a highly excited minor component CD(v';j'), present in the ratio AB:CD = 10:1. Each ensemble contains 8000 molecules. Rotational temperatures (T(r)) are found to differ widely at equilibration with T(r)(AB)/T(r)(CD) varying from 2.74 to 0.92, indicating unequal partitioning of rotational energy and angular momentum between the two species. Unusually, low values of T(r) are found generally to be associated with diatomics of low reduced mass. To test effects of the equi-partition theorem on low T(r) we undertook calculations on HF(6;4) in N(2)(0;10) over the range 100-2000 K. No significant change in T(r)(N2)/T(r)(HF) was found. Two potential sources of rotational inequality are examined in detail. The first is possible asymmetry of -Δj and +Δj probabilities for molecules in mid- to high j states resulting from the quadratic dependence of rotational energy on j. The second is the efficiency of conversion of orbital angular momentum, generated on collision with bath gas molecules, into molecular rotation. Comparison of these two possible effects with computed T(r)(AB)/T(r)(CD) shows the efficiency factor to be an excellent predictor of partitioning between the two species. Our finding that T(r) values for molecules such as HF and OH are considerably lower than other modal temperatures suggests that the determination of gas ensemble temperatures from Boltzmann fits to rotational distributions of diatomics of low reduced mass may require a degree of caution.