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 (d,,-,), hitherto regarded as determining the "vibrational" relaxation time, is related more to the transition probability assigned to the largesf rofafional gap which lies in the first (v = 0 ct u = I) vibrational gap, i.e. to the transition v = 0, J = 5 ct v = 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 OK, the greatest energy increment is associated with two eigenvalues (d,,-l 3 and A_,,) and can be characterized as essetlfinlly 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 OK, large energy increments are associated with several eigenvalues between d,j-2 and d,,-',, and at 5000 "K, with most of the eigenvalues d,,-, to d,,-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. Can. J. Chem., 51. 1923Chem., 51. (1973 In the preceding paper in this ~e r i e s ,~ it was found that the second smallest eigenvalue d,,-, of the relaxation matrix describing the rotational 'Nuffield Foundation Fellow, Physical Chemistry Laboratory, University of Oxford; Visiting Professor, Chemistry Department, U.M.I.S.T., Manchester, 1972Manchester, -1973 2Equations taken from other papers in this series and used in the present paper are prefixed with the part numbers in Roman numerals. and vibrational dissociation of hydrogen in the presence of a large excess of inert gas was changed markedly when only rotational transition probabilities were altered (I), thus implying that the last transient which immediately precedes the dissociation reaction has a lot of rotational character; hitherto, it had always been tacitly assumed that the last transient was a vibrational relaxation (2, 3). At a macroscopic level, there is strong experimental evidence (3) that at low temperaCan. J. Chem. Downloaded from www.nrcresearchpress.com by 54.245.55.244 on 05/10/18For personal use only.

On the interpretation of measured rotational and vibrational relaxation times. II. Sudden change experiments

“…On the other hand, the calculation of these properties for H2 is a challenge in which we can hope to succeed, and in the near future obtain good matching between theoretically calculated and experimentally observed behaviour from a wide range of techniques including sound dispersion, shock-wave, and laser schlieren experiments. Furthermore, the relaxation behaviour of polyatomic molecules having small moments of inertia about one or more axis probably has much in common with the hydrogen molecule; consequently, a good understanding of the 'vibrational' relaxation behaviour of hydrogen and light hydrides should lead to a much better insight into the Lambert-Salter relationships, somewhat along the lines we suggested previously (7).…”