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

1976 ◽  
Vol 54 (15) ◽  
pp. 2372-2379 ◽  
Author(s):  
Huw Owen Pritchard
Keyword(s):  
Shock Wave ◽  
Relaxation Time ◽  
Vibrational Relaxation ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Sudden Change ◽  
Heat Bath ◽  
Mode Analysis ◽  
Wave Excitation ◽  
Measured Relaxation

This paper examines, in terms of the normal-mode analysis developed earlier (Part I), the nature of relaxations in which a diatomic gas, highly diluted in a heat bath of inert gas atoms, is subjected to a sudden change as in shock-wave excitation or laser schlieren experiments.It is shown in detail how the observed relaxation time in a shock-wave excitation to a fixed final temperature depends on the initial temperature. At the same time, it is confirmed that the characterisation as 'mainly rotational' of the measured relaxation time in H2 when it is heated from room temperature to 1500 K in a shock wave is perfectly plausible.On the other hand, the calculations show that in laser schlieren experiments in which the v = 1, J = 1 level of H2 is overpopulated, the vibrational relaxation time of H2 at the temperature in question is recovered, although interesting effects should appear if other J levels were populated initially, or if the experiments were carried out at much higher ambient temperatures.The calculations also demonstrate that it is not generally possible to derive relaxation times by following the variation in population of any particular level of the molecule: multiple overshoots sometimes occur, and apparent relaxation times both longer or shorter than the true relaxation times could often result from attempts to follow level populations as a function of time.

scholarly journals On the interpretation of measured rotational and vibrational relaxation times. I. Sound dispersion experiments

1976 ◽  
Vol 54 (2) ◽  
pp. 329-341 ◽  
Author(s):  
Huw O. Pritchard ◽  
Nabil I. Labib
Keyword(s):  
Relaxation Time ◽  
Diatomic Molecule ◽  
Vibrational Relaxation ◽  
Transition Probabilities ◽  
Relaxation Times ◽  
Normal Modes ◽  
Heat Bath ◽  
Inert Gas ◽  
Sound Dispersion ◽  
Approximate Treatment

The simultaneous relaxation to equilibrium of both rotational and vibrational populations is considered for a diatomic molecule immersed in a heat bath of inert-gas atoms. The relaxation is analyzed in terms of normal modes of relaxation, and it is shown that each mode, having its own distinct relaxation time, in general has both rotational and vibrational components. The qualitative form of these modes is very persistent, and survives considerable variations in the assumed temperature and the assumed set of transition probabilities. Using these modes of relaxation, an approximate treatment is given of the contribution made by the diatomic gas to the sound dispersion of the mixture, and conditions under which modes of relaxation may or may not be resolved from each other, or may be characterized as either 'rotational' or 'vibrational' are examined.

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.

Measurement of the Vibrational Relaxation Time of CO behind a Shock Wave by Infrared Emission

1957 ◽  
Vol 27 (1) ◽  
pp. 315-316 ◽  
Author(s):  
M. W. Windsor ◽  
Norman Davidson ◽  
Ray Taylor
Keyword(s):  
Shock Wave ◽  
Relaxation Time ◽  
Vibrational Relaxation ◽  
Infrared Emission

scholarly journals Deciphering the intrinsic dynamics from the beam-induced atomic motions in oxide glasses

2020 ◽  
Vol 27 (5) ◽  
pp. 1247-1252
Author(s):  
Yuriy Chushkin
Keyword(s):  
Relaxation Time ◽  
Structural Relaxation ◽  
Photon Correlation Spectroscopy ◽  
Relaxation Times ◽  
Correlation Spectroscopy ◽  
Oxide Glasses ◽  
Photon Correlation ◽  
X Ray ◽  
Different Temperatures ◽  
Measured Relaxation

Probing the microscopic slow structural relaxation in oxide glasses by X-ray photon correlation spectroscopy (XPCS) revealed faster than expected dynamics induced by the X-ray illumination. The fast beam-induced dynamics mask true slow structural relaxation in glasses and challenges application of XPCS to probe the atomic dynamics in oxide glasses. Here an approach that allows estimation of the true relaxation time of the sample in the presence of beam-induced dynamics is presented. The method requires two measurements either with different X-ray beam intensities or at different temperatures. Using numerical simulations it is shown that the slowest estimated true relaxation time is limited by the accuracy of the measured relaxation times of the sample. By analyzing the reported microscopic dynamics in SiO2, GeO2 and B2O3 glasses, it is concluded that the beam-induced dynamics show rich behavior depending on the sample.

scholarly journals Picosecond-Duration Vibrational Relaxation Kinetics in the Excited S1 State of Perylene and Anthracene Molecules

1983 ◽  
Vol 3 (1-6) ◽  
pp. 249-261 ◽  
Author(s):  
A. Freiberg ◽  
T. Tamm ◽  
K. Timpmann
Keyword(s):  
Steady State ◽  
Luminescence Spectrum ◽  
Vibrational Relaxation ◽  
Vibrational Energy ◽  
Streak Camera ◽  
Relaxation Times ◽  
Temporal Behavior ◽  
Vibrational Energy Relaxation ◽  
The Matrix ◽  
Measured Relaxation

We present and discuss the results of a direct observation of the picosecond range temporal behavior of vibronic lines in the luminescence spectrum of the matrix-isolated perylene and anthracene molecules. A novel subtractive dispersion mount of monochromators in conjunction with the synchroscan streak camera has been used. From spectrochronograms measured at different excitation wavelengths the vibrational energy relaxation times have been obtained. These are in the range of 20–30 ps and are most probably determined by the existence of the phonon bath of the matrix. A comparison of the measured relaxation constants with those estimated from the steady-state hot luminescence spectrum has been made.

Molecular Dynamics Simulations and Instantaneous Normal-Mode Analysis of the Vibrational Relaxation of the C−H Stretching Modes ofN-methylacetamide-din Liquid Deuterated Water

2010 ◽  
Vol 114 (43) ◽  
pp. 11450-11461 ◽  
Author(s):  
Adolfo Bastida ◽  
Miguel A. Soler ◽  
José Zúñiga ◽  
Alberto Requena ◽  
Adrián Kalstein ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Normal Mode ◽  
Vibrational Relaxation ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Deuterated Water ◽  
Instantaneous Normal Mode ◽  
Dynamics Simulations

Mode-Wise Phonon Properties of Bismuth Telluride

2012 ◽  
Author(s):  
Yaguo Wang ◽  
Xianfan Xu
Keyword(s):  
Bismuth Telluride ◽  
Thermal Transport ◽  
Phonon Dispersion ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Mode Analysis ◽  
Phonon Modes ◽  
Time Resolved ◽  
Transport Control ◽  
Phonon Properties

Thermal transport properties and thermal transport control are important for many materials, for example, low thermal conductivity is desirable for thermoelectric materials. Knowledge of mode-wise phonon properties is crucial to identify dominant phonon modes for thermal transport and design effective phonon barriers for thermal transport control. In this paper, we adopt the normal mode analysis to investigate spectral phonon properties, and to calculate phonon dispersion relations and phonon relaxation times in bismuth telluride. Our results agree with previously reported data for long-wavelength longitudinal acoustic phonon and A1g optical phonon obtained from ultrafast time-resolved measurements. By combing the frequency dependent anharmonic phonon group velocities and lifetime, mode-wise thermal conductivities are predicted to reveal the contributions of heat carriers with different polarizations and wavelength.

Effect of Rotation to a Half-Sapce in Magneto-Thermoelasticity with Thermal Relaxations

2007 ◽  
Vol 353-358 ◽  
pp. 3018-3021
Author(s):  
Ying Pan ◽  
Zi Hou Zhang ◽  
Li Hou Liu
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Induced Magnetic Field ◽  
Coupled Problem ◽  
Analytical Expressions

Based on Green and Lindsay’s generalized thermoelasticity theory with two relaxation times, a two-dimensional coupled problem in electromagneto-thermoelasticity for a rotating half-space solid whose surface is subjected to a heat is studied in this paper. The normal mode analysis is used to obtain the analytical expressions for the considered variables. It can be found electromagneto-thermoelastic coupled effect in the medium, and it also can be found that rotation acts to significantly decrease the magnitude of the real part of displacement and stress and insignificantly affect the magnitude of temperature and induced magnetic field.

Perturbed normal-mode analysis of induction times, relaxation times, and reaction rates in unimolecular reactions

1979 ◽  
Vol 57 (13) ◽  
pp. 1723-1730 ◽  
Author(s):  
Andrew W. Yau ◽  
Huw O. Pritchard
Keyword(s):  
Normal Mode ◽  
Transition Probabilities ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Normal Modes ◽  
Reaction Rates ◽  
Mode Analysis ◽  
Decomposition Reactions ◽  
Induction Times ◽  
Network Relationship

A perturbed normal-mode analysis is presented of the induction (or incubation) time, the relaxation rate, and the reaction rate of a diluted unimolecular system. At high temperature, the unimolecular rate approaches the Lindemann behaviour and the low-pressure rate is related to the normal modes of relaxation of the reactive states in a simple manner. In a step-ladder model system, the network relationship between the normal modes and the microscopic transition probabilities leads to explicit theoretical correlations between the respective experimental quantities. Illustrative calculations of such correlations are presented for the decomposition reactions of N2O and CO2 diluted in Ar at shock wave temperatures, and are compared with experiment.

Effect of rotation and gravity on generalized thermo-viscoelastic medium with voids

2018 ◽  
Vol 14 (2) ◽  
pp. 322-338 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Montaser Fekry
Keyword(s):  
Viscoelastic Material ◽  
Viscoelastic Medium ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Mode Analysis ◽  
Content Type ◽  
Analysis Technique ◽  
Effects Of Rotation ◽  
Physical Quantities ◽  
Coupled Theory

PurposeThe purpose of this paper is to study the effect of rotation and gravity on a homogeneous, isotropic, and generalized thermo-viscoelastic material with voids. The problem is studied in the context of the coupled theory, Lord-Shulman theory with one relaxation time, and Green-Lindsay theory with two relaxation times.Design/methodology/approachThe analytical method used was the normal mode analysis technique.FindingsNumerical results for the physical quantities were analyzed and presented graphically. The graphical results indicated that the effects of rotation and gravity were observable physical effects on the thermo-viscoelastic material with voids. Comparisons were made between the results obtained in the absence and presence of rotation and gravity.Originality/valueIn the present work, the authors investigated the effect of rotation and gravity on thermo-viscoelastic medium with voids. Comparisons were also made between the three theories in the absence and the presence of rotation and gravity. Such problems are very important in many dynamical systems.

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