The Master Equation for the Dissociation of a Dilute Diatomic Gas IX. Rotation–Vibration Relaxation Times

Abstract

The relationships between individual rotational or vibrational transition probabilities and the eigenvalues of the 172nd order relaxation matrix describing the rotation–vibration–dissociation coupling of ortho-hydrogen are explored numerically. The simple proportionality between certain transition probabilities and certain eigenvalues, which was found previously in the vibration–dissociation coupling case, breaks down. However, it is shown that at 2000°K the second smallest eigenvalue of the relaxation matrix (dn−2), hitherto regarded as determining the "vibrational" relaxation time, is related more to the transition probability assigned to the largest rotational gap which lies in the first (ν = 0 ↔ ν = 1) vibrational gap, i.e. to the transition ν = 0, J = 5 ↔ ν = 0, J = 7, than to anything else; this clearly supports an earlier suggestion that the transient which immediately precedes dissociation in a shock wave has to be regarded as a rotation–vibration relaxation time rather than a vibrational relaxation time. It is suggested that the Lambert–Salter relationships can be rationalized on this assumption.An analysis is then made of the energy uptake associated with each eigenvalue at three temperatures. At 500°K, the greatest energy increment is associated with two eigenvalues (dn−13 and dn−24) and can be characterized as essentially a rotational relaxation: the calculations confirm that the observed rotational relaxation time should first decrease and then increase with increasing temperature, as was recently found to be the case experimentally. At 2000°K, large energy increments are associated with several eigenvalues between dn−2 and dn−14, and at 5000°K, with most of the eigenvalues dn−2 to dn−23; thus, the higher the temperature, the more complex is the (T–VR) rotation–vibration relaxation. Further, relaxation times for the same temperature measured by ultrasonic and shock-wave techniques need not agree.