Monte Carlo trajectory and master equation simulation of the nonequilibrium dissociation rate coefficient for Ar+H₂→Ar+ 2H at 4500 K

Thermally averaged rate coefficients for state-to-state rovibrational transitions and dissociation from individual states in Ar + para-H₂ collisions at 4500 K are derived from Monte Carlo quasiclassical trajectory calculations. The problem of multidimensional interpolation of state-to-state rate constants is discussed, and the rate matrix is completed by nonlinear least-squares fitting. The relaxation time, the induction time, and the steady dissociation rate are calculated by a matrix eigenvalue solution of the master equation simulating a shock wave experiment on para-H₂ dilute in Ar. Rotational-vibrational nonequilibrium effects are fully included. We have found that multiquantum transitions play a very significant role in determining the observable dissociation rate and that the master equation eigenmodes representing internal energy redistribution are little affected by the reaction process. The final steady dissociation rate is 2.8 times less than at local equilibrium. Various lumping schemes are tested, and we show that the original 162-state system can be well approximated by a 10-state model which predicts a factor of 2.4 for the nonequilibrium effect. However, we are unable to find equally successful models involving smaller numbers of states, and the popular vibrational ladder model and the corresponding rotational ladder model do not reproduce the full results even qualitatively.