Termolecular Recombination Research Articles

Phase-space theory of atomic dissociation and recombination reactions: H + H + H ⇄ H2 + H

The modified phase-space theory of reaction rates was coupled with Monte Carlo trajectory calculations to yield rate constants and energy distributions of reactants and products for the three-atom dissociation and recombination reactions of hydrogen at 4000°K. Sample trajectories selected from those crossing a surface in phase space were calculated in forward and reverse directions to determine the classical rates of formation of bound and quasibound molecules from atoms. The probability of stabilization of quasibound molecules in successive collisions with hydrogen atoms was determined from additional trajectory calculations. The steady state correction factor for recombination, which accounts for dissociation of newly formed bound H2 molecules, was estimated from similar calculations. The computed rate constant for recombination is 3.1×1015 cm6 mole−2 sec−1. For equilibrium between free atoms and quasibound molecules established through tunneling, the over-all rate constant is estimated to be 75% higher. In either case the process of termolecular recombination to produce bound molecules makes a substantial contribution to the over-all rate.

Gas phase recombination of OH with NO and NO2

The termolecular recombination of OH with NO and with NO2 is studied for M=He, Ar, and N2 at pressures from 1–10 torr and temperatures from 230–450°K in a flow tube using resonance fluorescence detection of OH radicals. The reactions are in their low pressure, third-order limit. The rate constants for the NO reaction at 295°K are 3.3, 3.4, and 5.8×10−31 cm6 sec−1 in the above order of M gases. For the NO2 reaction the corresponding values are 1.0, 1.0, and 2.3×10−30, all with σ=±20% including estimates of systematic errors. Both recombinations show the expected negative temperature dependence, the Arrhenius activation energies being −1.7 kcal for NO and −1.8 kcal for NO2. These results are compared with all other published data and with RRKM unimolecular calculations.

Termolecular Recombination Rate Constant and Triple Collision Cross-section

The concept of triple collisions cross-section in termolecular recombination reaction was investigated. The hard-sphere model was tested against experimental data, and it was found to predict, in disagreement with experiments, a positive temperature dependence for the recombination rate constants. Average cross-sections were obtained from experimental rate data. Two empirical functions widely used for summarizing experimental rate data were inverted through an inverse Laplace transform to give the triple collision cross-section.

A spectroscopic study of the hydroxyl radical in an internal-combustion engine

Direct spectroscopic determination was made of hydroxyl radical concentration in the immediate post-combustion gases of a spark-ignition engine operating on isooctane and air. Hydroxyl radical was found to vary by as much as ±50% from cycle to cycle. Measured concentrations exceeded equilibrium calculations by an order of magnitude, but the relative effect of mixture strength was as predicted by equilibrium projection. Operation at a near stoichiometric fuel-air equivalence ratio of 0.98 resulted in a 30%–60% greater concentration of OH radical than that with 25% rich mixture. The experimental results obtained for the high-pressure post-combustion history of the hydroxyl radical agree qualitatively with the trends obtained from low-pressure flame studies by other investigators. The degree of hydroxyl radical hyperequilibrium in the post-combustion process in the engine cylinder increases with increasing mixture richness. OH concentrations approach in absolute magnitude the chemical equilibrium values as the expansion proceeds. Quantitatively, however, excess over equilibrium is considerably less in the engine process than in the falmes. This is probably due to wall reactions and the increased effect of termolecular recombination reactions at the elevated pressures experienced in the engine.

Rate constant for deuterium atom recombination calculated by the orbiting resonance theory

The resonance theory of termolecular recombination kinetics is applied to the reaction D + D + D 2 → 2D 2. The isotope effect, i.e., the rate of deuterium recombination compared to that of hydrogen, is computed over the range 50–300°K. From 100° to room temperature the ratio for D/H is 0.7 1 (±0.02), in agreement with the experimental value of Amdur (1935) and a very recent determination by Kaufman, Ham and Trainar.

Recombination in the hydrogen-oxygen reaction: A shock tube study with nitrogen and water vapour as third bodies

Previous shock tube studies of termolecular recombination in the hydrogen-oxygen reaction have been extended to mixtures containing significant amounts of nitrogen or water vapour. An OH ultra-violet line absorption technique has been used to follow the progress of the overall reaction at temperatures of 1259° to 1912°K and pressures of 1·1 to 3·7 atm. Selective variation of the initial composition, which for the water vapour experiments required the development of a special flow-fill apparatus to introduce up to 7·9 per cent water vapour into the unshocked gas mixtures, has made possible a determination of the effect of both of these species as third bodies on the three important recombination reactions: H + H + M → H 2 + M H + O 2 + M → H O 2 + M H + O H + M → H 2 O + M . Results in mixtures diluted with nitrogen indicate that the rate coefficient of each of these reactions with the third body M = N 2 are approximately 1·5 times the values previously reported for M = Ar. Determination of the water vapour coefficients is complicated by the presence of other important third bodies, i.e. argon and hydrogen or oxygen. However, the results show that water vapour is an efficient catalyst in bringing about recombination. The ratio of rate coefficients for M = H 2O to those with M = Ar for these three reactions is ⩽ 13.25, and 20, respectively.

A study of the chemical kinetics of shock heated H 2/CO/O 2 mixtures

The density field behind a normal shock wave in H 2 −O 2 , H 2 −N 2 −O 2 , and H 2 −CO−O 2 mixtures highly diluted with argon has been measured by optical interferometry. The per cent ratio of H 2 /O 2 has been varied from 8/1 to 1.5/48.5 with 0%–16% N 2 or an equivalent amount of CO present. By shocking mixtures which cover a wide range of fuel-oxidant ratios it has been possible to examine a rather complete reaction scheme for H 2 −O 2 mixtures over the temperature range 1400° to 3000°K. Density profiles based on various sets of kinetics have been generated with the aid of a one-dimensional reactive flow analysis. Good agreement is demonstrated between analytic and experimental density profiles using the recommended set of kinetic coefficients. Kinetic coefficients are presented in units of cm 3 /gmole, sec, and cal/gmole. For Reaction (9), O+H 2 →OH+H, which is influential in very lean H 2 /O 2 mixtures, k 9 is reported to be 6×10 13 exp(−10,000/ RT ). In richer H 2 /O 2 mixtures the density profile is sensitive to Reaction (8), H+O 2 →OH+O; k 8 is deduced to be 2×10 14 exp(−16,700/ RT ). Considerable recombination of hydrogen atoms and hydrogen atoms with hydroxyl radicals occurs in the stronger shocks. For Reactions (11), H+H+Ar→H 2 +Ar, and (12), H+OH+Ar→H 2 O+Ar, a literature value of k 11 of 1.0×10 18 T −1 has been used; k 12 is found to be 1.5×10 17 T −0.5 ; Hydroperoxy radicals are important in the initiation stage and in near-stoichiometric mixtures. The coefficient of the termolecular recombination, Reaction (14), H+O 2 +Ar→HO 2 +Ar, is adequately described as 3.2×10 18 T −1 . In H 2 /CO/O 2 mixtures, additional Reactions of interest are (26), CO+OH→CO 2 +H, and (27), CO+O+Ar→CO 2 +Ar. Values of k 26 , and k 27 of 3.7×10 11 exp(−700/ RT ) and ∼6×10 13 , respectively, fit adequately the experimental density profiles. The technique of matching shock density profiles over a wide range of mixtures and temperatures has proven to be useful in explicating the kinetics of the H 2 /CO/O 2 system. * Re-entry Systems Department, Philadelphia, Pennsylvania. ** Research and Development Center, Schenectady, New York.

Mechanism of Atom Recombination by Consecutive Vibrational Deactivations

The process of atom recombination in the presence of foreign gases, M, not forming complexes with the atoms, is considered in terms of a cascade model in which deactivation occurs by small increments, essentially by one quantum at a time. This leads to an equation for the termolecular recombination rate constant: kr=λZK*G(T), where K* is the equilibrium constant for species X2* in equilibrium with X atoms, Z is the collision frequency of these species with M, and λ, assumed to be unity, is the probability that such species will be de-excited in a collision with M to the top vibrational level of X2, the diatomic molecule. The quantity G(T) is essentially the reciprocal of the number of vibrational states within a range of kT of the dissociation threshold. Methods are given for the calculation of K*, G(T), and Z from physical data for the X2 and M molecules without any undetermined parameters. The use of Morse functions yields values of kr in excellent agreement with available experimental data for H2, N2, O2, Br2, and I2 over the range 300° to 2000°K (6000°K for O2) with argon as M. The temperature dependence of kr is not simple and varies between light and heavy molecules. On the average and almost independently of the potential function used, it is in the range of T—1. It does not appear as though contributions from other electronic states beyond the ground state are significant in the recombination process.