Vibrational–translational relaxation in nitrogen discharge plasmas: Master equation modeling and Landau–Teller model revisited
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Vibrational–translational (V–T) relaxation is quite common in molecular nitrogen discharge non-equilibrium plasmas. In this paper, the energy relaxation in V–T transition is investigated by master equation modeling on all vibrational levels below the dissociation limit. The state-to-state transition rates are calculated by a forced harmonic oscillator (HO)-free rotating model. Meanwhile, the classic Landau–Teller model based on the HO of vibrational levels is revisited. First, the V–T relaxation in a heat bath is compared between the HO model, Morse’s anharmonic oscillator (AHO) model, and realistic vibrational levels by a direct-potential-fit analysis of spectroscopic data. The relaxation of average vibrational energy using the AHO model is faster than that using the HO model. Then, the influence of more frequent vibrational–vibrational (V–V) collision on the V–T transition in the heat bath is investigated by using different numbers of vibrational levels. The anharmonic effect is significant with more vibrational levels. Finally, the V–T energy transfer is modeled by a coupled solution to master equations and gas heating. The stronger the non-equilibrium between vibrational and translational temperature in the beginning, the larger the difference that can be obtained between the HO model (Landau–Teller theory) and realistic vibrational levels.Keywords:
Vibrational energy relaxation
Vibrational partition function
Morse potential
Vibrational energy relaxation
Vibrational temperature
Vibrational energy
Vibrational partition function
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Vibrational energy relaxation
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Vibrational partition function
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Chemical reactions occur due to energy accumulation in specific vibrational intramolecular degrees of freedom (dofs). Thus, vibrational energy redistribution among different dofs inside a molecule as well as intermolecular vibrational energy transfer to external dofs is of particular importance for chemical reactions. In many cases these processes take place on a picosecond time scale such that short pulse lasers may be used to excite vibrations and analyze microscopic vibrational processes in a media. The process of photodissociation of organic peroxides carbon dioxide is formed with a broad vibrational energy distribution disposed mainly in the bend and symmetric stretch vibrational degrees of freedom. The highest frequency asymmetric stretch mode seems to remain unexcited because in all the solvents its vibrational relaxation is very slow. Comparatively fast vibrational cooling of CO/sub 2/ is insured by the Fermi resonance between the bend and symmetric stretch vibrations and proceeds through V-V near resonant energy transfer to solvent molecules.
Vibrational energy relaxation
Vibrational partition function
Fermi resonance
Picosecond
Vibrational energy
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Nonequilibrium molecular dynamics (MD) simulations and instantaneous normal mode (INMs) analyses are used to study the vibrational relaxation of the C−H stretching modes (νs(CH3)) of deuterated N-methylacetamide (NMAD) in aqueous (D2O) solution. The INMs are identified unequivocally in terms of the equilibrium normal modes (ENMs), or groups of them, using a restricted version of the recently proposed Min-Cost assignment method. After excitation of the parent νs(CH3) modes with one vibrational quantum, the vibrational energy is shown to dissipate through both intramolecular vibrational redistribution (IVR) and intermolecular vibrational energy transfer (VET). The decay of the vibrational energy of the νs(CH3) modes is well fitted to a triple exponential function, with each characterizing a well-defined stage of the entire relaxation process. The first, and major, relaxation stage corresponds to a coherent ultrashort (τrel = 0.07 ps) energy transfer from the parent νs(CH3) modes to the methyl bending modes δ(CH3), so that the initially excited state rapidly evolves into a mixed stretch−bend state. In the second stage, characterized by a time of 0.92 ps, the vibrational energy flows through IVR to a number of mid-range-energy vibrations of the solute. In the third stage, the vibrational energy accumulated in the excited modes dissipates into the bath through an indirect VET process mediated by lower-energy modes, on a time scale of 10.6 ps. All the specific relaxation channels participating in the whole relaxation process are properly identified. The results from the simulations are finally compared with the recent experimental measurements of the νs(CH3) vibrational energy relaxation in NMAD/D2O(l) reported by Dlott et al. (J. Phys. Chem. A 2009, 113, 75.) using ultrafast infrared-Raman spectroscopy.
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The effect of various vibrational transitions on the formation of non-equilibrium distributions, rates of vibrational relaxation and chemical reactions, and fluid dynamics in CO2 flows is discussed. Several state-resolved models are applied: the most detailed model taking into account all kinds of vibrational energy exchanges and coupling of CO2 vibrational modes as well as reduced models with limited number of vibrational states and kinetic processes. It is shown that vibrational transitions between different CO2 modes and between CO2 asymmetric mode and CO molecules may significantly affect the rate of vibrational relaxation and dissociation. Whereas vibrational distributions strongly depend on the processes included to the kinetic scheme, the heat flux is practically insensitive to the vibrational kinetics and can be evaluated using simplified models.
Vibrational energy relaxation
Rotational–vibrational coupling
Vibrational temperature
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Vibrational energy
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The overall rate of vibrational relaxation of symmetric stretch-excited carbon dioxide, CO2 (1000), was measured in a new laboratory experiment. A perturbation–relaxation approach was used where the (1000) vibrational state of CO2 was populated via a temperature jump, and the rate of collisional energy exchange was monitored using transient diode laser absorption spectroscopy. The rate coefficient for the overall de-excitation of this state through collisions with carbon dioxide, which includes both vibrational–vibrational and vibrational–translational pathways, was determined to be (2.9 ± 0.3) × 10–11 cm3 s–1. This work provides new information about the efficiency of the vibrational–vibrational collisional energy exchange processes involving the (1000) state, which are expected to be significantly faster than the vibrational–translational process. These results should be useful for improving non-local thermodynamic equilibrium models for CO2-rich planetary atmospheres.
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Anharmonicity in the crystal potential leads to phonon interactions which result in vibrational relaxation and dephasing. For many crystal systems a satisfactory description of vibrational relaxation is obtained by considering the first anharmonic correction to the crystal potential, namely a cubic interaction. However, recent results on vibrationally sparse systems have shown that the next higher order anharmonic relaxation term (i.e quartic) is necessary to account for the observed thermally induced dephasing [1-3]. In this work we focus on the importance of anharmonic relaxation mechanisms by creating a large vibrational energy gap. One expects the mode immediately above the gap to have an increased lifetime relative to other vibrational modes of the molecule due to the absence of any cubic decay channels.
Dephasing
Vibrational energy relaxation
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We consider an approach for describing vibrational energy relaxation processes in liquids for solutes excited to states which are dominated by single-mode excitations. The method utilizes the fact that adding a suitable linear term to the solute intramolecular potential, creates excitations in the first excited state of a chosen vibrational mode. The fully quantum energy decay rate of the vibrational excitation can then be derived using quadratic response theory, which expresses the decay rate as the decay of a second-order Kubo transformed correlation function. This correlation function can be exactly related to a path integral centroid second-order correlation function, which can be evaluated approximately by centroid molecular dynamics. The abilities and limitations of the approach are discussed. It is shown that the method should work best when only a single vibrational state is occupied prior to excitation. Practical matters require also that the relaxation is in the pico-second regime or shorter. In contrast to the usual golden rule approach, the present method incorporates quantum effects and does not require explicit evaluation of vibrational coupling elements or Fourier transforms. It also incorporates the intramolecular vibrational coupling, whereby intramolecular relaxation can be monitored explicitly. The approach is tested on asymmetric stretch excited OClO(aq), using a classical bath, and gives results which are in good accord with earlier findings. The theory also points in the direction of how to improve the so-called classical approach to vibrational energy relaxation, where energy is put directly into the mode subsequently undergoing relaxation.
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The pathway for vibrational-energy flow following the excitation of the first excited state of the acetylenic C−H stretch is investigated for a series of 10 terminal acetylenes in room-temperature gases and dilute solutions using transient absorption picosecond infrared spectroscopy. The transient absorption infrared spectra are obtained at three different probe frequencies. These experiments separately detect the population of the excited C−H stretch state, the population of vibrational states with 2 quanta of acetylenic C−H bend excitation, and the population of all other vibrational states with C−H stretch absorption frequencies within the laser bandwidth (25 cm-1) of the C−H stretch fundamental frequency. These measurements show that the initial redistribution event for the isolated molecule involves population transfer to vibrational states with bend overtone excitation. The secondary intramolecular vibrational-energy redistribution (IVR) process, which involves population transfer to the remaining near-resonant vibrational states, occurs on a time scale that is about 5 times slower than the initial redistribution event. The same relaxation pathway is observed in dilute solution. The total relaxation rate in solution for the slower process can be quantitatively described using a simple model where IVR and solvent-induced vibrational-energy relaxation (VER) proceed independently. The main effects of the solvent are to increase the extent of population relaxation for the first stage of IVR and to cool vibrational excitation rapidly in the low-frequency acetylene wag normal-mode vibrations produced by the IVR dynamics.
Vibrational energy relaxation
Overtone
Vibrational partition function
Picosecond
Overtone band
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Vibrational energy relaxation
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