Abstract
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.
Highlights
Nitrogen is the most abundant gas in the Earth’s atmosphere
The LT model considered a very simple situation of collinear collision between a structure-less particle and a harmonic oscillator (HO) under the common trajectory (CT) assumptions: (i) the amplitude of vibration is much smaller than the range of inter-molecular potential and (ii) the frequency of vibration is much larger than the inverse of encounter time
The state-to-state transition rates in master equation modeling are calculated by forced HO-free rotating (FHO-FR) theory
Summary
Nitrogen is the most abundant gas in the Earth’s atmosphere. Energy can be stored in degrees of freedom (DOFs) in molecular nitrogen including vibrational, rotational, translational, and electronic levels. The LT model considered a very simple situation of collinear collision between a structure-less particle and a harmonic oscillator (HO) under the common trajectory (CT) assumptions: (i) the amplitude of vibration is much smaller than the range of inter-molecular potential and (ii) the frequency of vibration is much larger than the inverse of encounter time. It successfully gave out the relation between the macroscopic relaxation time and the microscopic transition rates, while the latter obeys the −1/3 power law with the temperature of the heat bath. The study of V–T relaxation with anharmonic effects requires numerical methods
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