Heshel Teitelbaum

Non-equilibrium thermal dissociation of diatomic molecules. I. Extraction of collision-induced rate constants from experimentally measured reaction rates as a function of temperature for ten diatomic molecules dilute in Ar

Abstract We have solved the master equation for the steady-state low-pressure dissociation of diatomic molecules AB dilute in a bath gas M. Backed by recent a priori calculations we used the truncated harmonic oscillator model with Landau-Teller energy transfer rate constants. No assumptions are made with regards to the values of collision-induced dissociation (CID) rate constants, which we ultimately extract from experimental measurements of non-equilibrium effects available in the literature. An analytical expression for the rate of dissociation takes the form -d[AB]/d t = k d eq [1 + a ( T ) k m* / k 10 ] −1 [AB][M], where a is a simple temperature-dependent function, k m* is the CID rate constant for dissociation from the most-important (last) level m * , and k 10 is the rate constant for collisional de-excitation from ν = 1 to ν = 0. This expression tests well against a numerical solution of the same master equation in the temperature range from 0 to 10θ vib , where θ vib is the characteristic vibrational temperature ( = hv/k ). It also tests well against recent ab initio calculations using rotationally averaged rate constants. It predicts (a) experimental values of activation energies, E a , well for many molecules; and (b) that E a deviates from the bond dissociation energy, D 0 , by an amount varying from - hv e − u /(1 - e − u ) low temperatures to the high-temperature limiting value of ≈ - D 0 /6; and (c) that at high temperatures dissociation rates are determined by energy transfer processes. We deduce the values of CID rate constants for HBr, HCl, HF, H 2 , D 2 , CO, N 2 , NO, O 2 , F 2 (all dilute in Ar). We find the activation energies for the hydrides to be all ≈ 4 hv . We review other analytical expressions obtained over the last 30 years, classifying them according to the approximations made and showing their limitations. We also discuss the relationship between our present quantum result and published classical results in terms of an “average energy transferred per collision”, 〈Δ E 〉.

Vibrational relaxation of N2OAr and CH4Ar mixtures. Shock tube experiments and master equation calculations

Abstract The vibrational relaxation of N2OAr mixtures has been studied by laser schlieren measurements in shock waves and by numerical integration of the master equation for vibration—translation and vibration—vibration energy transfer. The system shows some deviations from the linear mixture rule, particularly at high temperatures and low mole fractions of N2O. The expression log10(pτ/atm μs)N2OAr = −1.317 + 13.655T −1 3 appears to fit our measurements and literature data to within 20% over the range 300–1600 K, but because of mixture rule non-linearity this result should be used with caution, especially at high temperatures. Laser schlieren measurements gave log10(pτ) = −2.680 + 19.235T −1 3 for pure CH4 at 340 to 700 K. Relaxation in mixtures containing from 0.5 to 50% CH4 in Ar was also measured, but here the observed deviations from the linear mixture rule were so great that it was not possible to extrapolate to extrapolate the measurements reliably to obtain a relaxation rate for CH4 at infinite dilution in Ar.

Are vibrational relaxation times really constant? I. The vibrational relaxation of N2O

Abstract Vibrational relaxation times of pure acetylene in the gas phase were measured behind incident shock waves in the temperature range 613–1184 K using a laser-schlieren technique. Overall, the results are in excellent agreement with those of acoustic and laser excitations. However, we find a marked intrinsic time dependence of the phenomenological time, which varies by factors of two to three over a wide dynamic time scale of at least six natural lifetimes. In other words, the Bethe—Teller law fails. This is confirmed by numerical solution of the master equation for a wide choice of intermode collisional coupling parameters. The density of states involved in the energy transfer process determines whether the relaxation time increases or decreases with time, and the effect is amplified by the importance of intermolecular VV processes relative to intramolecular processes.

A rate constant for the VV exhange in hydrogen, 2H2(ν = 1) → H2(ν = 0) + H2(ν = 2)

Abstract An estimate of the rate constant for the vibration-to-vibration energy transfer process 2H 2 (ν = 1)→H 2 (ν = 0) + H 2 (ν = 2) is made by analyzing the dependence of the effective rate of relaxation on the degree of laser excitation. At 82 K it is (6.3 ± 2.1) × 10 −16 cm 3 molecule −1 s −1 .

Failure of the linear mixture rule for the vibrational relaxation of C2H2Ar mixtures

Abstract Measurements of the vibrational relaxation time of mixtures of C 2 H 2 and Ar were made behind shock waves in the temperature range 798–2645 K using a laser-beam deflection technique. The linear mixture rule, 1/ p τ′ = Σ i X i / p τ′ i is found to fail, with deviations being most severe at high temperatures and far from equilbrium. Solution of the associated master equation confirms that this behaviour is theoretically expected.

The linear mixture rule in chemical kinetics. II. Thermal dissociation of diatomic molecules

Abstract The master equation for the steady non-equilibrium thermal dissociation of diatomic molecules, AB, in mixtures with inert species, M, is solved analytically. A simple expression for the rate coefficient, k d , takes the form k d = k d eq ( X M + φ d X AB )/[1+δ( X M + φ d X AB )/( X M + φ r X AB )], where k d eq is the “equilibrium” rate constant, X M and X AB are the mole fractions of M and AB respectively, φ d is the relative AB:M efficiency for collision-induced dissociation (CID), φ r is a measure of the relative AB:M efficiency for energy transfer (ET), and δ is a constant involving CID, ET rate constants as well as molecular properties. The result predicts a breakdown of the linear mixture rule (LMR) is chemical kinetics: Contributions to the rate of reaction by each component in the gas mixture are not linearly additive. Deviations are most severe when φ d and φ r differ most and at high temperatures. The most precise published experimental data for the dissociation of H 2 in Ar mixtures and of O 2 in Kr mixtures are re-examined using the new expression, and found to be direct evidence for the breakdown of the LMR. Our method provides superior estimates of the rate coefficients for pure H 2 and O 2 as well as for H 2 and O 2 infinitely dilute in Ar or Kr. In addition, the corresponding equilibrium rate constants are estimated for high temperatures. The implications are far-reaching for our knowledge of the behaviour of diatomic dissociation.

Non-equlibrium kinetics of bimolecular reactions. IV. Experimental prediction of the breakdown of the kinetic mass-action law

Abstract The relative steady-state concentrations of the diotomic molecules HCl and OH in specific vibrational levels were determined using an analytical solution of the master equation describing the elementary bimolecular reaction, O+HCl→OH+Cl and its reverse reaction Cl+OH→O+HCl over the temperature range 300–800 K. Reaction from v =0–4 and vibrational energy transfer among these levels were included. In analogy to the experimental procedure each reaction was considered in isolation from the other. The forward thermal phenomenological rate coefficient, k f , and the reverse thermal phenomenological rate coefficient, k r , were calculated. It was demonstrated that the ratio, k f / k r , does not equal the equilibrium constant, K eq , when the reactions proceed far from equilibrium.

Kinetics of the Decay of CH3 Radicals in Shock Waves

Mixtures containing up to 13% CH3 radicals diluted in Ar and N2 were produced by the near-instantaneous decomposition of azomethane behind incident shock waves at 1360 to 4070 K and at concentrations of 1.0 to 1.5 x 10-6 mol cm-3. The laser-Schlieren technique was used to monitor the rate of heat evolution and to determine precisely the rate coefficients for 2CH3→C2H6 and for 2CH3→C2H4+H2.

Non-equilibrium kinetics of bimolecular reactions. Part 7: The puzzle of the H+O2 reaction

The steady state master equation is solved to determine the population distribution of vibrationally excited O2 while reacting with H atoms at temperatures ranging from 300 K to 8000 K. State-selected reactive rate constants are used which are consistent with the known theoretical and experimental rates of the H+O2 reaction at all levels of detail. Known V–T energy transfer rate constants are also used. Calculations are performed for a variety of H, O2 and Ar compositions, revealing the conditions where non-equilibrium effects can play a role. The results of the calculation show that the thermal rate coefficient at 2000 K is less than the value expected, by as much as 25%. This is due to a much distorted vibrational population distribution caused by the reaction itself. Although the predicted behaviour of the rate coefficient qualitatively mimics the experimental one, it does not quantitatively explain the observed experimental discrepancies, which have puzzled kineticists and dynamicists for the past 20 years.

Non-equilibrium kinetics of bimolecular reactions. Effect of anharmonicity on the rate law

Abstract The master equation is solved numerically for the thermal reaction H+H 2 →H 2 +H over the temperature range 300–8000 K using as input data the rate constants for state-selected reaction and relaxation of vibrationally excited H 2 as determined by ab initio quasiclassical trajectory calculations in the literature. The thermal rate coefficient is found to be depressed from its equilibrium value by less than 20%, and is most severe around 7000 K. There is practically no difference between a calculation which treats H 2 as an anharmonic oscillator and one which treats H 2 as a simple harmonic oscillator. The reasons are discussed. The result permits one to use an improved non-equilibrium rate law (developed for the case of harmonic oscillators) in analytical work.