Modeling of nonlinear vibrational relaxation of large molecules in shock waves with a nonlinear, temperature-varying master equation

Abstract

We model recent experiments on the vibrational relaxation of oxirane in a shock tube. A master equation is developed which includes self-collisions of the oxirane, leading to a nonlinear master equation. This master equation is also applied to a more limited study of vibrational relaxation for cyclopropane in a shock tube. The time variation of the temperature dependence of the bath is also included in the calculations. Good agreement between the modeling and experiments are obtained through a fit to the energy transfer parameters. These fits demonstrate that self-collisions are dominant in promoting the relaxation even for mixtures of Kr and oxirane where the oxirane is 2% and 4% dilute. This dominance comes from two sources: (1) much larger energy transfer per collision for oxirane–oxirane collisions and (2) resonant energy transfer effects. For cyclopropane, some of the good fits show smaller energy transfer characteristics for self-collisions than buffer gas collisions. Even in these cases self-collisions are an important part of the energy transfer process through resonant energy transfer effects.