Charles E. Treanor

Vibrational Relaxation of Anharmonic Oscillators with Exchange‐Dominated Collisions

The terms in the master equation for vibrational relaxation of anharmonic oscillators are ordered according to the rates of the relaxation processes (vibrational exchange, vibrational‐energy transfer to translation). The population distributions in the master equation are expanded about their values when the vibration‐vibration mechanism is the only one present. An analytic expression is given for the distribution maintained by the vibration‐vibration mechanism. In the limiting case of the simple harmonic oscillator, this distribution reduces to the usual Boltzmann‐like distribution defined by a single vibrational temperature. The general solution also applies to a mixture of simple‐harmonic‐oscillator gases of different fundamental frequencies. For such a mixture, each gas relaxes in a Boltzmann‐like distribution, but the different gases have different (but related) vibrational temperatures at any given time. The relaxation of the first moment of the distribution function also has been investigated. Anha...

Chemical Relaxation with Preferential Dissociation from Excited Vibrational Levels

The rate of molecular dissociation behind strong shock waves is calculated with the assumption that dissociation can occur preferentially from the higher vibrational levels. An exponential probability of dissociation from the various vibrational levels is employed using an anharmonic oscillator model. Results for the dissociation of oxygen in an argon diluent are presented. Vibrational non‐equilibrium introduces a T−3 temperature dependence into the oxygen dissociation rate constant in the range 4000°–8000°K. A dissociation lag‐time of the order of the extrapolated vibrational relax ation time is predicted immediately behind the shock front. The computed results are shown to be in agreement with available experimental results.

Vibrational energy transfer in high energy collisions

Time‐dependent wavefunctions are used to evaluate the exact transition probabilities for a forced harmonic oscillator. The forcing is represented by a time‐dependent potential, where this potential has a linear dependence on the oscillator coordinate. The results are compared with available numerical solutions for a harmonic oscillator forced with a potential which has an exponential dependence on the oscillator coordinate. The comparison is made for the collision of an N2 molecule with another particle, and it is found that although the results for the two cases are similar, the linear potential gives higher values for the multiquantum transitions. It is then shown that time‐dependent wavefunctions which contain the corresponding classical motion as a parameter provide a good set of functions for a perturbation calculation. The energy transfer to these oscillating wavefunctions is always identical to the energy transfer to the classical oscillator. Thus the perturbation value of the energy transfer repre...

Vibrational energy transfer rates using a forced harmonic oscillator model

This paper addresses the analysis, validation, and application of analytic, nonperturbative, semiclassical vibration-translation (V-T) and vibration-vibration-translation (V-V-T) rate models for atom-diatom and diatom-diatom vibrational molecular energy transfer collisions. These forced harmonic oscillator (FHO) rate models are corrected and validated by comparison with recent experiments, and with three-dimensional semiclassical trajectory calculations for N 2 -N 2 , O 2 -O 2 , and N 2 -O 2 , which are considered to be the most reliable theoretical data available. A remarkably good overall agreement is shown for both the temperature and quantum number dependence of single-quantum and double-quantum V-V-T transitions in the temperature range 200 < T < 8000 K and for vibrational quantum numbers 0 < ν < 40. It is demonstrated that the multiquantum vibrational energy transfer processes occur via a sequential FHO mechanism, as a series of virtual single-quantum steps during one collision. An important exception, asymmetric multiquantum V-V exchange at low temperatures, that occurs via a direct first-order mechanism, is discussed. Analytic thermally averaged FHO V-T and V-V rates are suggested. The FHO model gives new insight into vibrational kinetics and may be easily incorporated into kinetic modeline calculations under conditions when first-order theories are not applicable.

Measured Transition Probabilities for the Schumann‐Runge System of Oxygen

Transition probabilities for the Schumann‐Runge system of O2 have been measured in absorption in the wavelength region 2650–3900 A. Oxygen was heated in a shock tube to temperatures up to 4500°K, thereby populating high vibrational and rotational levels. Absorption spectra were photographed using a high‐speed flash lamp and a large Littrow quartz spectrograph. Transition probabilities for the bands of three sequences, associated with the zero, 1st, and 2nd vibrational levels of the excited electronic state, yield an f value of 0.048±0.008 which, when corrected for wavelength dependence, is about ⅓ that determined in the vacuum ultraviolet. This corresponds to a decrease in transition probability with increasing internuclear separation. Line‐width variations with temperature and density have also been measured. The optical diameter for O2–O2 collisions was determined as 6 A and for O2–O collisions as 10 A.

Kinetics of Nitric Oxide Formation Behind Shock Waves

The infrared radiation of nitric oxide (NO) behind a shock wave in O2-N2 mixtures has been calculated by two different techniques, and compared with recent shock-tube experiments. The first technique (model I) utilizes the Park model. This model incorporates the vibrational relaxation of O2 and N2 and assumes a Boltzmann distribution of vibrational energy during the relaxation process. Model II uses a master equation solution, employing recently published state-to-state vibration-translation and vibration-vibration transition probabilities. Vibration-chemistry coupling is provided through the MacheretFridman-Rich model (MFR). The calculations are compared with experimental results for shock waves in the range of 3-4 km/s. Results of the two model calculations are compared at speeds up to 9 km/s, for both normal shocks and bow shocks. The two models predict nearly the same NO production rates behind all of the normal shocks, and show the prominent effect of N2 vibrational coupling in the reaction N2 + O —> NO + N. For high-altitude bow shocks, where extreme vibrational nonequilibrium is present, there are large differences in the results calculated by the Park and MFR coupling techniques.

An Electrically Excited Gas‐Dynamic Carbon Monoxide Laser

A carbon monoxide laser is reported which utilizes a glow discharge in the plenum of a supersonic nozzle. The discharge selectively excites the CO vibrational mode, while the gas translational temperature remains relatively cold. Continuous output is obtained from optical cavities established transverse to the flow at two nozzle area ratios. Maximum laser power obtained to date is 6.8 W corresponding to an efficiency of 0.6%, based on electrical power input.

Transition Probabilities for the Forced Harmonic Oscillator

Transition probabilities of nitrogen-nitrogen collision obtained with time-dependent wave functions of forced harmonic oscillator and by numerical methods

Nitric Oxide Bands near 1 μ in Shock‐Heated Air

The banded radiation from a strong radiating system has been observed in the near‐infrared spectrum of shock‐heated air. The dependence of the radiant intensity upon species concentration and temperature, as well as an estimate of the oscillator strength, indicate that the radiation results from transitions between excited electronic states of nitric oxide. This system is shown to be a significant contributor to the infrared emission spectrum of high‐temperature air.

Vibrational Relaxation, Nonequilibrium Chemical Reactions, and Kinetics of No Formation behind Strong Shock Waves

The paper addresses development of new theoretical models for the rates of vibrational energy exchange and chemical reactions under conditions of extreme nonequilibrium, and their application to modeling calculations. These models yield analytic expressions for the specific rate constants that can be incorporated into existing high enthalpy flow codes. The models are validated by comparison with the state-of-the-art calculations and available experiments, including recent shock tube study of NO production kinetics behind shock waves. The models are also applied to simulation of NO formation behind strong bow shocks.