On the interpretation of vibrational relaxation times

1983 ◽  
Vol 61 (6) ◽  
pp. 1253-1266 ◽  
Author(s):  
Heshel Teitelbaum
Keyword(s):  
Shock Tube ◽  
Thermal Effects ◽  
Vibrational Energy ◽  
Chemical Activation ◽  
Relaxation Times ◽  
Boltzmann Distribution ◽  
Vibrational Energy Level ◽  
Rate Laws ◽  
Transfer Processes ◽  
Special Case

Rate laws for the evolution of vibrational energy level populations are derived when the Bethe–Teller law is obeyed. It is assumed that a Boltzmann distribution is maintained via rapid V–V processes. A variety of different rate laws result depending on the size and direction of the perturbation, the extent from equilibrium, and how classical the oscillator is at the initial and final conditions. An earlier analysis by Breshears is shown to be a special case. A prescription is given for procedures to compare relaxation times obtained from shock tube experiments and from laser-induced fluorescence experiments, when T–V energy transfer processes are rate-determining. Corrections for thermal effects are included. Shock tube, fluorescence, and chemical activation experiments are proposed which provide meaningful conditions for testing the Bethe–Teller law and for testing the existence of a Boltzmann distribution.

Solutions of the generalized rate law for vibrational relaxation of a pure diatomic gas

1983 ◽  
Vol 61 (6) ◽  
pp. 1276-1287 ◽  
Author(s):  
Heshel Teitelbaum
Keyword(s):  
Shock Tube ◽  
Time Constant ◽  
Rate Constants ◽  
Vibrational Energy ◽  
Initial Conditions ◽  
Chemical Activation ◽  
Rate Law ◽  
Diatomic Gas ◽  
Energy Formula ◽  
The Mean

The generalized rate law for the relaxation of the vibrational energy of a pure diatomic gas, AB, derived earlier, is solved analytically for a variety of initial conditions corresponding to shock tube, laser-excited fluorescence, and chemical activation experiments. The resulting expressions can be used to easily predict whether a given system will relax according to a V–V or a T–V mechanism or both. The initial conditions and the molecular anharmonicity are shown to be as important, if not more important, for this purpose than the ratio of T–V and V–V rate constants. Behind shock waves the energy relaxes exponentially with a T–V time constant. The initial distribution remains Boltzmann. In laser or chemical activation experiments the energy does not relax exponentially, leading to phenomenological time "constants" [Formula: see text] or [Formula: see text] which are not constant in time and prevent direct comparisons with shock tube data. It is only after an incubation period during which the vibrational energy is redistributed via V–V processes that the energy then exchanges with translational energy and decays. Prescriptions are given to extract T–V and V–V rate constants from such data. The initial degree of laser excitation, a, and the time regime probed, t/τ, must be known for this purpose. However, when direct overtone excitation is used, a careful choice of α can lead to extraction of the T–V constant directly. Even though the vibrational energy itself does not relax exponentially, it is shown that the mean energy, [Formula: see text], and the mean squared energy, [Formula: see text], relax in such a way that the quantity [Formula: see text] does decrease exponentially with a time constant very closely related to the V–V rate constant for 2AB(ν = 1) → AB(ν = 2). A short survey of various laser and chemical excitations in the literature is presented and analyzed in terms of initial conditions. In general, the larger the degree of excitation and the higher the quantum numbers of the excited levels, the more V–V character does the energy relaxation have.

A simple reason for non-linear mixture rules in chemical kinetics. Part 1. Vibrational relaxation of diatomic molecules

1985 ◽  
Vol 63 (2) ◽  
pp. 381-393 ◽  
Author(s):  
Chris Carruthers ◽  
Heshel Teitelbaum
Keyword(s):  
Vibrational Relaxation ◽  
Thermal Effects ◽  
Diatomic Molecules ◽  
Boltzmann Distribution ◽  
Initial Distribution ◽  
Rate Law ◽  
Initial Deviation ◽  
Transfer Processes ◽  
Non Linear ◽  
Morse Oscillators

The generalized rate law for the vibrational relaxation of diatomic molecules is extended to include inert collision partners. V–V energy transfer processes are accounted for explicitly as are thermal effects. The molecules are treated as Morse oscillators as far as energetics are concerned; however, the microscopic rate constants are Landau–Teller type. It is found that the phenomenon of non-linear mixture rules arises when experimental data are forced to fit a first-order rate law. The persistence of V–V processes at times well-advanced into the relaxation zone is responsible for deviations from linearity. The non-linearities are most pronounced at high temperatures, and can be avoided only by using extremely dilute mixtures. Several sources of ambiguity are pointed out. The type of excitation method influences the initial deviation from a Boltzmann distribution and plays a crucial role in determining the importance of V–V processes and hence the degree of non-linearity. Thus, when the initial distribution is Boltzmann as in shock waves, the mixture rule is found to be absolutely linear for the vibrational relaxation of diatomic molecules.Several examples, heretofore not recognized as such, are pointed out in the literature.

Vibrational energy-transfer processes in the system

1997 ◽  
Vol 371 (2-3) ◽  
pp. 213-222 ◽  
Author(s):  
J.C. Cook ◽  
E.M. McCash
Keyword(s):  
Energy Transfer ◽  
Vibrational Energy ◽  
Vibrational Energy Transfer ◽  
Transfer Processes

scholarly journals The calculation of TV, VT, VV, VV' − rate coefficients for the collisions of the main atmospheric components

1998 ◽  
Vol 16 (7) ◽  
pp. 838-846 ◽  
Author(s):  
A. S. Kirillov
Keyword(s):  
Experimental Data ◽  
Energy Transfer ◽  
Vibrational Energy ◽  
Relaxation Times ◽  
Atmospheric Composition ◽  
Rate Coefficients ◽  
Frequency Change ◽  
Vibrational Energy Transfer ◽  
Ion Chemistry ◽  
Vibrationally Excited

Abstract. The first-order perturbation approximation is applied to calculate the rate coefficients of vibrational energy transfer in collisions involving vibrationally excited molecules in the absence of non-adiabatic transitions. The factors of molecular attraction, oscillator frequency change, anharmonicity, 3-dimensionality and quasiclassical motion have been taken into account in the approximation. The analytical expressions presented have been normalized on experimental data of VT-relaxation times in N2 and O2 to obtain the steric factors and the extent of repulsive exchange potentials in collisions N2-N2 and O2-O2. The approach was applied to calculate the rate coefficients of vibrational-vibrational energy transfer in the collisions N2-N2, O2-O2 and N2-O2. It is shown that there is good agreement between our calculations and experimental data for all cases of energy transfer considered.Key words. Ionosphere (Auroral ionosphere; ion chemistry and composition). Atmospheric composition and structure (Aciglow and aurora).

scholarly journals Динамика термолюминесценции при двойном лазерном Vis-IR возбуждении молекул эозина с кислородом и наночастицами серебра в пленке поливинилбутираля

2019 ◽  
Vol 126 (2) ◽  
pp. 126
Author(s):  
Е.И. Константинова ◽  
Б.Ф. Минаев ◽  
А.В. Цибульникова ◽  
Р.Ю. Боркунов ◽  
М.В. Царьков ◽  
...  
Keyword(s):  
Silver Nanoparticles ◽  
Energy Transfer ◽  
Vibrational Energy ◽  
Molecular Complexes ◽  
Polyvinyl Butyral ◽  
Dye Molecules ◽  
Temperature Conductivity ◽  
Transfer Processes ◽  
Vibrational Energy Distribution ◽  
532 Nm

AbstractElectronic and vibrational energy transfer processes taking place in molecular complexes in a polymer are investigated under dual-wavelength (visible at λ = 532 nm and IR at wavelength λ = 10.6 μm) laser photoexcitation of eosin molecules ( С = 4 × 10^–4 М) in air and without it ( р ≈ 10^–4 Torr) in thin polyvinyl butyral (PVB) films containing silver nanoparticles ( R ≈ 36 nm) prepared by laser ablation. Generation of singlet oxygen, singlet–triplet annihilation, and enhancement of plasmon quenching of dye fluorescence are studied. Thermal-energy transfer processes in thin PVB films following pulsed IR excitation are simulated, and the temperature conductivity coefficients of the polymer films in the presence of silver nanoparticles are calculated. Low-temperature processes in PVB films containing dye molecules taking place after IR excitation are investigated, and the mechanism for accelerating intercombination S _1 → Т _1 transitions as a result of thermal heating and intramolecular vibrational-energy distribution is explained.

Modeling of heat transfer processes at catalytic materials in shock tube

10.2514/3.669 ◽  
1995 ◽  
Vol 9 (2) ◽  
pp. 363-365 ◽  
Author(s):  
Vladimir V. Riabov ◽  
Viktor P. Provotorov
Keyword(s):  
Heat Transfer ◽  
Shock Tube ◽  
Catalytic Materials ◽  
Transfer Processes

The Efficiency at Maximum Power Output of a Carnot Engine with Heat Leak

1995 ◽  
Vol 23 (2) ◽  
pp. 157-165 ◽  
Author(s):  
F. Moukalled ◽  
R. Y. Nuwayhid
Keyword(s):  
Heat Transfer ◽  
Power Output ◽  
Maximum Power ◽  
Heat Leak ◽  
Suggested Model ◽  
Maximum Power Output ◽  
Transfer Processes ◽  
Newton’S Law ◽  
New Formulation ◽  
Special Case

Endoreversible thermodynamics are used for studying the performance of Carnot engines with heat leak. This is done by adding a heat leak term into a variation of the model suggested by DeVos [1]. Heat transfer across the engine is assumed to occur via a conduction/convection mechanism and Newton's law of cooling is employed to model the heat transfer processes. The efficiency at maximum power output is found to be deeply affected by the rate of heat leak. Moreover, the Curzon-Ahlborn relation [2] is shown to represent a special case of the new formulation. Since the suggested model allows more flexibility in predicting actual engines' performance, its use is recommended in thermodynamics courses.

scholarly journals A re-examination of the adiabatic correction term for the hydrogen molecule

1976 ◽  
Vol 54 (4) ◽  
pp. 651-656 ◽  
Author(s):  
Huw O. Pritchard ◽  
Lutosław Wolniewicz
Keyword(s):  
Energy Level ◽  
Hydrogen Molecule ◽  
Vibrational Energy ◽  
Correction Term ◽  
Internuclear Separation ◽  
Vibrational Energy Level ◽  
The Difference ◽  
The One

The adiabatic coupling correction term [Formula: see text] has been evaluated by two methods, the one used by Kołos and Wolniewicz in 1964 and the one suggested by Kari, Chan, Hunter, and Pritchard in 1973. The difference between the two procedures for H2 amounts to 0.04 cm−1 and is almost independent of internuclear separation in the range R = 1.0–1.8 a.u. Thus, the method of computing the ΔR-term does not affect the vibrational energy level spacings.

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.

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