General rotational relaxation matrix: Its properties, M dependence, and relation to experiment

1974 ◽  
Vol 61 (5) ◽  
pp. 1923-1933 ◽  
Author(s):  
Herbert M. Pickett
Keyword(s):  
Rotational Relaxation ◽  
Relaxation Matrix

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

1973 ◽  
Vol 51 (12) ◽  
pp. 1923-1932 ◽  
Author(s):  
E. Kamaratos ◽  
H. O. Pritchard
Keyword(s):  
Shock Wave ◽  
Relaxation Time ◽  
Vibrational Relaxation ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Relaxation Times ◽  
Rotational Relaxation ◽  
Relaxation Matrix ◽  
Coupling Case ◽  
Increasing Temperature

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.

Modelling of the rotational relaxation matrix in line-mixing effect calculations

2004 ◽  
Vol 102 (16-17) ◽  
pp. 1843-1850 ◽  
Author(s):  
A. V. Domanskaya ◽  
N. N. Filippov ◽  
N. M. Grigorovich ◽  
M. V. Tonkov *
Keyword(s):  
Rotational Relaxation ◽  
Mixing Effect ◽  
Relaxation Matrix ◽  
Line Mixing

Two-Dimensional Infrared Spectroscopy From the Gas to Liquid Phase: Density Dependent J-Scrambling, Vibrational Relaxation, and the Onset of Liquid Character

2019 ◽  
Author(s):  
Greg Ng Pack ◽  
Matthew Rotondaro ◽  
Parth Shah ◽  
Aritra Mandal ◽  
Shyamsunder Erramilli ◽  
...  
Keyword(s):  
Vibrational Energy ◽  
Rotational Relaxation ◽  
Vibrational Energy Relaxation ◽  
Pump Probe ◽  
Solution Dynamics ◽  
Supercritical Phase ◽  
Supercritical Solution ◽  
Asymmetric Stretch ◽  
Two Dimensional Infrared Spectroscopy ◽  
Vibrational Equilibrium

Ultrafast 2DIR spectra and pump-probe responses of the N2O n 3 asymmetric stretch in SF6 as a function of density from the gas to supercritical phase and liquid are reported. 2DIR spectra unequivocally reveal free rotor character at all densities studied in the gas and supercritical region. Analysis of the 2DIR spectra determines that J-scrambling or rotational relaxation in N2O is highly efficient, occurring in ~1.5 to ~2 collisions with SF6 at all non-liquid densities. In contrast, N2O n 3 vibrational energy relaxation requires ~15 collisions, and complete vibrational equilibrium occurs on the ~ns scale at all densities. An independent binary collision model is sufficient to describe these supercritical state point dynamics. The N2O n 3 in liquid SF6 2DIR spectrum shows no evidence of free rotor character or spectral diffusion. Using these 2DIR results, hindered rotor or liquid-like character is found in gas and all supercritical solutions for SF6 densities ³ r * = 0.3, and increases with SF6 density. 2DIR spectral analysis offers direct time domain evidence of critical slowing for SF6 solutions closest to the critical point density. Applications of 2DIR to other high density and supercritical solution dynamics and descriptions are discussed. <br>

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