Master Equation Study of Vibrational and Rotational Relaxations of Oxygen

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Master Equation Study of Vibrational and Rotational Relaxations of Oxygen

Andrienko, Daniil A. / Boyd, Iain D.

Transition rates in $O_{2} - O$ collisions for each vibrational and rovibrational state are generated by means of the quasi-classical trajectory method using potential energy surfaces of different fidelities. The first potential energy surface, obtained via the double many-body expansion method, is adopted to obtain vibrational transition rates assuming transrotational equilibrium. The trajectory simulation on a simpler potential surface, based on the two-body pairwise interaction, generates a complete set of rates for each internal state. Vibrational and rotational relaxations of oxygen in a heat bath of parent atoms are modeled by a system of master equations at translational temperatures between 1000 and 20,000 K. It is shown that the vibrational relaxation becomes less efficient at high temperatures, in contrast with the conventional equation for relaxation time proposed by Millikan and White (“Systematics of Vibrational Relaxation,” Journal of Chemical Physics, Vol. null, No. null, 1963, Paper 3209). Rotational and vibrational relaxation times are the same order of magnitude in the range of temperatures observed in hypersonic flows. The excitation of the vibrational mode in $O_{2} - O$ collisions under typical postshock conditions occurs earlier than in other molecular systems. The exchange channel plays an important role in the internal energy randomization.