J. Phys. Chem. 1991,95, 8701-8706 calculation that agreed well with their experimental data. They also employ a "loose" transition state with very little perturbation of the alkane in going from the reactants to the transition state.
Conclusions Rate coefficients for the reaction of C N with methane, ethane, and propane have been studied from 293 to 1500 K by using high-temperature photochemistry. This study represents the widest continuous temperature range over which rate constants for these reactions have been directly measured. In addition, these experiments are also the first to use direct methods to monitor the products of reactions of C N with hydrocarbons. All rate coefficients are independent of pressure and flow velocity. The rate coefficients are large and can be explained by the existence of long-range intermolecular attractive forces. The Arrhenius plots for these reactions are curved. In all cases, H C N is the dominant
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observable room temperature product, even though for ethane and propane lower energy products are possible. Both the curvature and the magnitude of the rate constants can be explained by a long-lived collision complex existing over the entire temperature range. However, the observed lack of any pressure dependence would indicate that the high-pressure limit was reached by 10 Torr of total pressure. In order to unambiguously determine the mechanism of these reactions, further calculations and additional experiments at 800-1 200 K would help by establishing the curvature in this temperature regime. Acknowledgment. One of us (R.J.B.) acknowledges support from the Oak Ridge Associated Universities Postgraduate Research Training program and the U S . Department of Energy. J.S.A. and L.P. thank the Office of Naval Research for financial support through the Naval Research Laboratory.
AIH Gas-Phase Reaction Kinetics Louise Pasternack* and Jane K. Rice Chemistry DivisionlCode 61 I I , Naval Research Laboratory, Washington, D.C. 20375-5000 (Received: February 28, 1991; In Final Form: June 3, 1991)
The reactions of ground-state AIH (lZ+)with 02,H20, H2, D2, C3Hs, C2H2,2-butyne, C2H4 and 2-methyl-2-butene are investigated at 300 K. The AIH is produced by the photodissociation of triethylaluminum at 193 or 248 nm and detected by laser-induced fluorescence of the A III-X IZ+transition. Absolute bimolecular rate constants are obtained from AIH concentration decay profiles as a function of reactant gas concentration. The rate constants for oxygen containing reactants for O2and (3.09 f 0.35) X 1O-" for H20. For H2 and D2, we are reported in units of cm3 s-l are (1.58 0.15) X cm3s-I at 20 Torr of total pressure. unable to observe reactions with AIH at low pressures; we report an upper limit of 1 X The reaction of AIH + D2 is dependent on the total pressure; at 460 Torr we observe AIH depletion with a rate constant cm3 of (1.4 f 0.2) X lo-" cm3 PI. The saturated hydrocarbon reactant, C3H8,also reacts with a rate constant 3 X lo-" cm3 s-I at 300 Torr.21 In contrast to the AI CzH2reaction, ESR results indicate that the AI-C,H4 adduct has a *-coordinated structure with bonding due to the interaction of a partially filled p orbital on AI with an antibonding A* orbital on ethylene.22 A similar structure has been determined from IR spectra taken in a matrix.23 The adduct was observed to be stable in hydrocarbon matrices up to 297 K?4J5 Most recently, evidence for a *-bonded A1-C2H4 adduct in the gas phase has been obtained.28 Ab initio studies support the *-bonded complex as the most stable form of the a d d u ~ t , ~ ~with ' " 'the ~ ~observed ~~ strength of the bond21J5*28 being well represented by the most recent theoretical calculation^?^^^^^ Comparisons to BH and AI reactions with C2H4 suggest that the AIH reaction are expected to proceed via a r-bonded symmetric intermediate followed by stabilization. However, if that is the case, we would expect methyl substitution on the ethylene to enhance the reaction rate, as is observed for the AlH acetylene Our observation reaction and also for BH + C2H4 rea~ti0ns.I~ that the rate is somewhat slower for the 2-methyl-2-butene may indicate that another pathway is present.
+
+
+
+
+
Summary The reaction rates of AIH with nine reactants are reported. Reactions with the oxygen-containing species, O2and H 2 0 are (40) Miralles-Sabater, J.; Merchan, M.; Nebot-Gil, I. Chem. Phys. Lett.
1987, 142, 136.
(41) Schlcyer, P. vR.;Kost, D. J . Am. Chem. Soc. 1988, 110, 2105. (42) Harrison, J. A.; Meads,R. F.; Phillips, L. F. Chem. Phys. Lett. 1988, 150, 299. (43) Tse,J. S.;Morris, H. J . Chem. Soc., Chem. Commun. 1989, 78. (44) Xie, Y.; Yates, B. F.; Yamaguchi, Y.; Schaefer 111, H. F. J . Am. Chem. SOC.1989, 111,6163. (45) Gao, J.; Karplus, M. Chem. Phys. Lett. 1990, 169,410.
J . Phys. Chem. 1991, 95, 8706-8713
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bimolecular reactions with several possible product channels. A comparison with the rates of the isovalent BH species indicates that the AIH reactions are faster by a factor of 2-3. This may be due to the larger size of AIH and to its larger dipole moment. Since both O2and H 2 0 are present in the MOVPE environment, there may be interest in determining which reaction products may contribute to the contamination of AlGaAs films. The association reaction of AIH with D2 is very slow and occurs at the limits of our detection but offers a rough comparison, when paired with BH D2 results, to the group IVA isovalent reaction pair of C H D2 and SiH D2. In the case of C H and SiH, the reaction rate with D2 decreases by a factor of 5000. We observe the same trend in the group IIIA pair, BH and AIH. Begemann et al.36have SiH(v”=l) data that suggest that the difference in rates between C H and SiH is due to an increased barrier in the
+
+
+
association reaction. It is possible that the same effect occurs in the group IIIA pair. The reactions of AIH with saturated hydrocarbons are slower than our detection limit. In contrast, the reactions with unsaturated hydrocarbons are very rapid. In the case of C2H2,evidence from methyl-substituted analogues indicate that the AIH attacks the a bond. In the case of AIH + C2H4,the rate is slower with methyl substitution, which indicates a mechanism other than a addition may be present. Acknowledgment. We thank the Office of Naval Research for the funding of this research. Registry NO. AIH, 13967-22-1; H2, 1333-74-0 D2,7782-39-0; C3H8, 74-98-6; 02,7782-44-7; H20.7732-I 8-5; C2H2, 74-86-2; C H 3 m C H 3 , 503-1 7-3; CZH4, 74-85-1; (CH,),C=CHCH,, 51 3-35-9.
Canard Explosion and Excitation in a Model of the Belousov-Zhabotinsky Reaction Morten Brans* Mathematical Institute, The Technical University of Denmark, DK-2800 Lyngby, Denmark
and Kedma Bar-Eli Sackler Faculty of Exact Sciences, School of Chemistry, Tel-Aviv University, Ramat Aviv 69978, Israel (Received: February 5, 1991)
The experimental evidence for sudden formation of relaxation oscillations (hard transitions), or the sudden change of amplitude and period of oscillations, is reviewed. It is shown that, in addition to the well-known mechanisms for hard transitions, there is another way in which a very fast transition from small to large oscillations can occur. This mechanism termed canard explosion is analyzed in terms of a well-known chemical model, the two-uariable Oregonator. The theory of the canard explosion, which occurs close to a Hopf bifurcation, is analyzed and compared with computational results. The resulting difficulties of differentiatingexperimentally among the various transition mechanisms are discussed. The well-known phenomenon of excitation, i.e., a large deviation of a system (chemical, neural, or other) after perturbation from a stable steady state, is shown to be. closely related to the canard explosion. The common mathematical properties of the system, on which both phenomena depend, are discussed.
Introduction In many cases, chemical oscillations either start abruptly and go directly to large relaxation oscillations or change suddenly, within very small control parameter range, from small-amplitude oscillations to large ones. A complete citation of all the examples in the literature is impossible, and we shall give a few examples only. Thus in the BZ (Belousov-Zhabotinsky) reaction, using Mn2+ as catalyst and malic acid or a mixture of citric and malonic acids as organic substrates, Maselko’v2 has found, depending on experimental conditions, both small, increasing amplitude, oscillations and direct change of steady state to large relaxation oscillations (with and without hysteresis). Also in the BZ reaction conducted in a CSTR (continuous stirred tank reactor), Schmitz et al.’.‘ have found, as the flow rate changes, transitions from small sinusoidal oscillations to large relaxation ones. Similar results were obtained also by Hudson et al.5 In a system containing chlorite, bromate, and iodide ions in sulfuric acid, Alamgir and Epsteid have found a direct transition from steady state to large relaxation oscillations without hysteresis (1) Maselko, J. Chem. Phys. 1982, 67, 17. (2) Maselko, J. Chem. Phys. 1983, 78, 381.
(3) Schmitz, R.A.; Graziani, K. R.;Hudson, J. L. J . Chem. Phys. 1977, 67, 3040. (4) Graziani, K. R.;Hudson, J. L.;Schmitz, R. A. Chem. Eng. J . 1976, 12, 9. ( 5 ) Hudson, J. L.;Hart, M.; Marinko, D. J . Chem. Phys. 1979, 71, 1601. (6) Alamgir, M.: Epstein, 1. R. J. Am. Chem. SOC.1983, 105, 2500.
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when reversing the system’s constraints. In a similar system, with bromide’ instead of iodide ion, the system remained excitable after the large oscillations disappeared as the flow rate was changed. Similar transitions occur in the permanganate hydrogen peroxide oscillator* and with the bromate sulfite ferrocyanide os~illator.~ In gas-phase reactions such as hydrogen or acetaldehyde oxidations,’*I2 temperature, pressure, and light emission pulses may appear directly and without hysteresis as a system’s constraint, such as ambient temperature, is changed. These phenomena occur also in closed systems in which the constraints are changing slowly in time. Thus Smoes” has found a sudden increase in amplitude and period in BZ reaction as sulfuric acid concentration is changed. Similarly, Burger and KorosI4 have found the BZ relaxation oscillations to appear as soon as bromomalonic acid reaches a critical concentration. (7) Orban, M.; Eptein, I. R. J . Phys. Chem. 1983, 87, 3212. (8) Nagy, A.; Treindl, L. J . Phys. Chem. 1989, 93, 2807. (9) Edblom, E. C.; Yin Luo; Orban, M.; Kustin, K.; Eptein, 1. R.J . Phys. Chem. 1989, 93, 2722. (10) Gray, P.;Scott, S. K. In Oscillations and Traveling Waves in Chem-
ical Systems; Field, R.J., Burger, M., Eds.; John Wiley and Sons: New York, 1985; p 493. ( I 1) Gray, P.; Griffiths, J. F.; Hasko, S. M.; Lignola, P. G . Proc. R. Soc. London, Ser. A 1981, 374, 313. (12) Griffiths, J. F. In Oscillations and Traveling Waves in Chemical Sysfems; Field, R.J., Burger, M., Eds.; John Wiley and Sons: New York, 1985; p 529. ( I 3) Smoes, M. L. J . Phys. Chem. 1979, 71, 4669. (14) Burger, M.; Koros, E. J . Phys. Chem. 1980, 84, 496.
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