Handbook of Shock Waves, Three Volume Set

CHAPTER 16.1 Chemical and Combustion Kinetics 16.1 Mass Spectrometric Methods for Chemical Kinetics in Shock Tubes RAL...

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CHAPTER

16.1

Chemical and Combustion Kinetics 16.1 Mass Spectrometric Methods for Chemical Kinetics in Shock Tubes RALPH D. KERN, H. J. SINGH AND Q. ZHANG Department of Chemistry, University of New Orleans, New Orleans, Louisiana, 70148, USA

16.1.1 Introduction 16.1.2 Coupling of a Time-of-Flight Mass Spectrometer to a Shock Tube 16.1.3 Chemical Kinetics Results from the TOF-Shock Tube Technique 16.1.4 Summary References

16.1.1

INTRODUCTION

The investigation of the rates and mechanisms by which chemical reactions occur presents a formidable array of obstacles to the experimentalist. The task is rooted in a diversity of experimental techniques and the skills of the workers performing them, although quantum mechanical calculations have established a more complete understanding of the complexities attendant to high-temperature chemical kinetics. The essential observations necessary to formulate a satisfactory mechanism for a particular reaction system involve the identification and measurement of the rates of formation and decay of the various reactants, intermediates, and products as a function of temperature and pressure in a well-defined environment. In the study of gas-phase reactions, it is advantageous to eliminate contributions from the surface of the reactor vessel. In addition, reliable thermodynamic data for the reaction species must be available either from tabulations, from the experiments, or calculated from theory. The proposed mechanism, consisting of forward and/or reverse rate Handbook of Shock Waves, Volume 3 Copyright 9 2001 by Academic Press. All rights of reproduction in any form reserved. ISBN: 0-12-086433-9/$35.00

R. D. Kern, H. J.

Singh and Q. Zhang

constants along with the thermodynamic values for the enthalpies and entropies of pertinent species, is tested by modeling the observed reaction profiles as a function of temperature and pressure. The modeling should extend to data taken outside the range of temperature and pressure and reported by other workers employing different methods. The process is often iterative, and the critical values for the rate constants and thermodynamic quantities are uncovered by sensitivity analysis. The shock tube offers several advantages for the study of chemical kinetic systems: reactions may be investigated over a wide range of known pressures, temperatures, and reaction times in the gas phase in a uniform reaction zone; dynamic reactant, intermediate, and product analysis is possible; only small amounts of reactants dilute in an inert gas environment are required since the experiments demand single-shot analysis; elementary reactions can be observed in some cases (but it is more usual to encounter complex reaction systems); and the variance of the relative amounts of reactants is virtually unlimited. A discussion of each of these advantages follows. Applied to chemical problems the shock tube technique is unmatched for its ability to cover a wide range of temperatures (500-5000 K) and pressures (10-1000atm). These ranges encompass the practical interests of chemical kineticists. Relatively short observation periods ( 10 atm) are used to study combustion reactions related to engine performance and to establish high-pressure limits for dissociation reactions. One of the great advantages offered by the shock tube technique is the avoidance of reactions occurring on the tube walls. The role of surface reactions in conventional static reactors has always been a problem, but the relatively short observation times in shock tube work permit only a small fraction of the heated gas to travel to the walls (which are at room temperature), thereby eliminating surface reactions. The reaction zone is also devoid of sharp temperature gradients as are encountered in flame studies. Analysis of the reaction species by dynamic analytical techniques permits continuous real-time records, which are extremely difficult to achieve by absorption and/or emission spectroscopy. Usually only one or two species may be followed spectroscopically, and information about their respective spectral properties is also necessary. Time-of-flight (TOF) mass spectrometry is capable of identifying numerous species present during the observation period and recording their individual time histories. The TOF technique will be described in sufficient detail later on in this section.

16.1 Mass Spectrometric Methods for Chemical Kinetics in Shock Tubes The advantage of single-shot experiments employing the shock tube technique is that only a small percentage of reactant dilute in inert gas is used as compared to the relatively large amounts of reactants used in steadystate experiments such as flames and flow reactors. This opens the door to investigations of reactants that are either very expensive, difficult to synthesize and/or separate or hazardous and/or toxic and thus not available commercially. Often isotopically labeled compounds can be used to sort out some of the complexities of a reaction system. Some reactants, such as cyclopentadiene and methylcyclopentadiene, are available only in dimeric form from vendors and must undergo separation by distillation. The disadvantage of single-shot analysis is the requirement for fast detectors capable of recording vast amounts of data in often less than i ms observation time. Steady-state experiments enjoy the advantage of signal averaging, thereby reducing the scatter in the experimental data. The high dilution of the inert gas acts as a traditional heat bath, reducing temperature and pressure changes in the reaction zone due to enthalpy and mole changes in the reaction under study. Most chemical mechanisms consist of a sequence of elementary reactions. It is sometimes possible to isolate a particular chemical reaction and measure its rate in a shock tube experiment; several examples are found in the section on atomic resonance absorption spectroscopy. Practical systems of interest--such as flames, internal combustion engines, explosives, incineration, and atmospheric chemistrymrequire hundreds of elementary reactions to describe their behavior. The job of the chemical kineticist is simplify these systems and compile rate constants for as many elementary reactions as possible. For instance, to study the combustion of a complex fuel or fuel mixture, one might start with the studies of the pyrolyses of simpler fuels. Fuels of high molecular complexity often decompose into lower-molecular-weight compounds and/or radicals, and these subspecies then react with molecular or atomic oxygen and oxygen-containing radicals. The study of simpler pyrolyses and oxidations provide the key to building up the library of elementary reactions that may be applied to the modeling of more complex reaction systems. The study of flames to deduce the rates of elementary reactions first requires the flame to be ignited and maintained in some steady state for observation. This state is achieved within a rather narrow range of fuel/oxidizer ratio. Shock tube experiments are totally unaffected by this ratio. In fact, the ratio may be varied from 0 to oo, thus allowing the decomposition kinetics of the oxidizer to be investigated in the absence of the fuel and vice versa. Ignition delay times may also be recorded; these measurements are described in detail in another section. Nearly ideal environments for investigating problems in chemical kinetics can be achieved with the shock tube. The remaining part of the apparatus is the

R. D. Kern, H. J. Singh and Q. Zhang

analytical aspect. Various ingenious techniques have been adopted to monitor the individual rates of species present during the observations. However, the experimental objective is indeed daunting: to record simultaneously concentrations as a function of reaction time of all species from H atoms to highmolecular-weight (several hundred amu) products and intermediates that appear during the observation period. There is simply no one analytical technique that fulfills this objective. Nevertheless, the data from such techniques as TOE laser schlieren densitometry (LS), atomic resonance absorption spectroscopy (ARAS), single-pulse shock tube (SPST) end product analysis, and absorption and emission spectroscopy are complementary in the sense that each is capable of supplying a unique piece(s) of data. When viewed as a whole, these data enable chemical kineticists to assemble a coherent set of reactions that may be used to model some of the complicated features of practical systems. Each of these techniques is discussed in the following sections. The remainder of this section is devoted to the coupling of a TOF to a shock tube to analyze dynamically the chemical species in the reflected shock zone. Four reviews of chemical reactions behind incident and reflected shock waves have appeared in the Annual Review of Physical Chemistry: Bauer 1965; Belford and Strehlow 1969; Tsang and Lifshitz 1990; and Michael and Lim 1993. Another review of interest pertaining to dissociations of diatomic molecules studied by shock tube workers was published in 1976 (Kem 1976). The reader is referred to this and the following sections herein for an update of work in this area.

16.1.2 COUPLING OF A TIME-OF-FLIGHT MASS SPECTROMETER TO A SHOCK TUBE The first description of experimental results obtained from a TOF-shock tube apparatus appeared in 1961 (Bradley and Kistiakowsky 1961). The original version evolved as other workers and laboratories joined in the effort: Dove and Moulton 1965; Moulton and Michael 1965; Glass, Kistiakowsky, Michael, and Niki 1965; Gay, Kern, Kistiakowsky, and Niki 1966; Garnett, Kistiakowsky, and O'Grady 1969; Diesen and Felmlee 1963; Modica 1965; Ryason 1967; Barton and Dove 1969; and Kern and Nika 1971c. The only remaining TOF-shock tube apparatus operating is in the author's laboratory at the University of New Orleans. This apparatus has undergone many modifications since the initial description in 1970; a diagram of the latest version appears in Fig. 16.1.1. The description of the necessary features for successful experiments starts with the driver section, which is short in length relative to the driven section (13 in. vs 10.8 ft) and has an outside diameter of 11.7 in. This allows for the

16.1 MassSpectrometric Methods for Chemical Kinetics in Shock Tubes

FIGURE 16.1.1 Schematicof the TOF-shock tube apparatus.

placement of the spring-driven knife, which cuts the aluminum diaphragm into quadrants and thus preserves the diaphragm material and prevents diaphragm fragments from clogging the entrance to the TOF ion source (Dove and Moulton 1965). If by chance a small fragment from the diaphragm does find its way into the passage leading to the ion source, a lengthy disassembly process must be undertaken to clear the passage. Another essential feature is the placement of a ball valve 6.5 in. downstream of the diaphragm. The internal inside diameter of the ball valve matches that of the shock tube, I in. This allows a high vacuum to be maintained on the TOF side of the shock tube while the other side is raised to atmospheric pressure to change the diaphragm. The one-inch inside diameter of the shock tube is fixed by the TOF manufacturer's design of the entrance sleeve to the ion source. One of the most crucial and controversial aspects of the experiment is the sampling of the reflected shock zone. It was apparent early on that the boundary layer in the reflected shock zone starts to grow shortly after arrival of the shock wave at the end wall. If the hole in the center of the end wall were part of a fiat plate, a significant portion of the gas flowing from the reflected shock zone into the TOF ion source region would consist of the gas in the boundary layer. To minimize sampling from the boundary layer, a reentrant nozzle plate serves as the end wall (Dove and Moulton 1965) with the apex of the conical nozzle facing the reflected shock zone. The hole in the apex is ~0.1 mm in diameter to ensure hydrodynamic flow into the ion source; diffusive flow would favor masses of low amu and would therefore distort the sampling process with regard to chemical kinetics. Since the boundary

R. D. Kern, H. J. Singh and Q. Zhang

layer growth from the end wall to the apex is typically > 1 ms and is greater than the observation time of the experiment, C4H 2 + H reaction is a specific example of this type of experiment (Shin and Michael 1991a).

16.3.3.3 F L A S H A N D / O R LASER P H O T O L Y S I S S H O C K T U B E RESULTS Even though the technique is relatively recent, there have been a large number of FP- or LP-ST investigations to date. In the paragraphs that follow, the results from several laboratories are reviewed. The Stanford University group--Bowman, Hanson, and Davidsonmhave carried out several LP-ST studies following the first LP-ST study by Davidson, Chang, and Hanson (1988). They measured reaction rates for N + NO -+ N 2 + O and N + H 2 --~ NH + H (Davidson, Snell, and Hanson 1990; Davidson and Hanson 1990a). Using a novel pyrolysis-photolysis method, Davidson and Hanson (1990b) studied the reaction of N + CH 3 -+ H2CN-+-H and found rate constants between 1600 and 2000 K. Two FP-ST studies were performed using C-atom ARAS. In the first, Dean,

16.3 AtomicResonance Absorption Spectroscopy with Flash or Laser Photolysis

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Davidson, and Hanson (1991a) measured rate constants for the reactions C 4- H2 --+ CH 4- H and C 4- 02 --~ CO 4- O. Dean, Davidson, and Hanson (1991b) then studied the reactions C 4- NO --+ CN 4- O and C 4- NO CO 4- N. Also, Davidson and Hanson (1990c) have determined rate constants for the O 4- H 2 --+ OH 4- H reaction. After the first FP-ST study using the ARAS technique (Michael, Sutherland, and Klemm 1985), several additional studies have been carried out at Brookhaven National Laboratory. Rate constants for the reaction NH 2 4- H 2 ~ H 4- NH 3 have been reported (Michael, Sutherland, and Klemm 1986) in a study where boundary layer corrections have been applied (Michael and Sutherland 1986). A study followed on the O 4- C H 4 --+ C H 3 4 - O H reaction between 760 and 1760 K (Sutherland, Michael, and Klemm 1986). By observing product H atoms, Sutherland and Michael (1988) measured the rate and equilibrium constants for the NH 3 4- H ~ NH 2 4- H 2 reaction. Rate constants for the O 4- H 2 ~ OH 4- H reaction have also been measured using O-atom ARAS (Sutherland et al. 1986). An H-atom FP-ST investigation on the H 4- H20 --+ H 2 4- OH reaction was done by Michael and Sutherland (1988), and this was followed by a study on the H 4- 02 ~ OH 4- O reaction by Pirraglia, Michael, Sutherland, and Klemm 1989). O-atom ARAS studies on the 0 4 - NH 3 --+ NH 2 4-OH (Sutherland, Patterson, and Klemm 1990a), O 4- C 2 H 4 (Klemm, Sutherland, Wickramaaratchi, and Yarwood 1990), and O 4- H20 ~ OH 4- OH (Sutherland, Patterson, and Klemm 1990b) reactions have been completed using the FP-ST technique. The H 4- C H 4 --+ C H 3 4- H 2 reaction rate constant was measured between 897 and 1728 K using H-atom ARAS (Rabinowitz, Sutherland, Patterson, and Klemm 1991). A direct measurement of rate constants for the O 4- NO 4- Ar ~ NO 2 4- Ar reaction was completed over the temperature range of 300 to 1341 K (Yarwood, Sutherland, Wickramaaratchi, and Klemm 1991). Matsui and coworkers have also carried out several investigations using the LP-ST technique. Koshi et al. (1990) studied the reactions N 4- NO ~ N 2 4- O and N 4- H 2 ~ NH 4- H, using the N-atom ARAS m e t h o d . N(4S) atoms were produced by the photolysis of NO. The reactions C2H 4- C2H 2 --+ C4H 2 4- H and C2H 4- H2(D2) --+ C2H2(HD) + H(D) were then studied by observing product H(D) atoms by Fukada, Koshi, and Matsui (1991) and Koshi, Fukada, Kamiya, and Matsui (1992). These workers then determined rate constants for H 4- H2S--+ H 2 4- SH and attempted to explain the non-Arrhenius behavior with CTST (conventional transition state theory) calculations (Yoshimura et al. 1992). Using both H- and O-atom ARAS, the technique was applied to CH4-O 2 mixtures (Ohmori, Yoshimura, Koshi, and Matsui 1992). LP-ST experiments were then carried out on O(3p) with a series of straightchain hydrocarbons and fluoromethanes using O-atom ARAS (Miyoshi, Ohmori, Tsuchiya, and Matsui 1993). Additional O-atom studies were reported

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on the reactions of O(3p) with a series of alkanes (Miyoshi, Ohmori, and Matsui 1993), on the reaction of O 4- H2S (Tsuchiya et al. 1994; Tsuchiya, Matsui, and Dupre 1995), and on the reactions of O 4-selected alkanes (Miyoshi, Tsuchiya, Yamauchi, and Matsui 1994; Miyoshi, Tsuchiya, Tezaki, and Matsui 1995; Miyoshi, Yamauchi, and Matsui 1996). Miyoshi, Yamauchi, and Matsui (1996) attempted to understand the relative reactivities of primary and secondary hydrogen atoms in alkanes. Rate constants for the reaction of O(3p) with Sill 4 were determined by Iida, Koshi, and Matsui (1996). These workers then turned their attention to the reaction of S(3p) atoms with several molecules in a series of three papers (Tsuchiya, Yamashita, Miyoshi, and Matsui 1996; Miyoshi, Shiina, Tsuchiya, and Matsui 1996; Shiina, Miyoshi, and Matsui 1998). To the credit of this group, many of the results from their numerous studies have been combined with lower-temperature work, and CTST theory, based on ab initio determinations of potential energy surfaces, has been applied. Rate constants have been theoretically calculated from room temperature or below to the high temperatures obtainable with shock tubes, and these constants have been compared to experiment. Michael and coworkers have continued using the FP- or LP-ST techniques for measuring bimolecular rate constants. Rate constants for the O + D 2 (Michael 1989) and O 4-C2H2(C2D2) (Michael and Wagner 1990) reactions were measured. Fisher and Michael (1990) studied the reaction D + D20 ~ D 2 4-OD between 1285 and 2261K. They also studied the fundamental reactions D + H 2 (Michael and Fisher 1990) and H + D 2 (Michael 1990; Michael, Fisher, Bowman, and Sun 1990). Lifshitz and Michael (1990) measured rate constants for the O + H 2 0 ~ O H + O H reaction between 1500 and 2400 K. Using both H- and D-atom ARAS, Shin and Michael (1991b) studied the reactions H + 0 2 and D 4-02 and, within experimental error, an isotope effect was not indicated. Similarly, an isotope effect was not found for the reactions C2H 4- C2H 2 and C2D 4- C2D2, nor was there an appreciable T-dependence (Shin and Michael 1991a). O-atom LP-ST studies on the reactions O 4- CH3C1, O 4- CH2C12 and O 4- CHC13 were completed by Ko, Fontijn, Lim, and Michael (1992) and Su et al. (1994). Michael and Lim (1992) studied the reaction N 4- NO ~ N 2 4- O using the LP-ST technique using N-atom ARAS. Lim and Michael (1993) used the pyrolysis-photolysis method to study the reaction O 4- CH 3 at high temperatures. [Much of this work has already been reviewed and compared to other studies (Michael 1991, 1992a, 1992b, 1992c)]. Kumaran, Lim, and Michael (1994) used Cl-atom ARAS to measure rate constants for C1 4- H 2 and D 2. The LP-ST results were combined with higher-temperature measurements, giving values between 699 and 3000 K. H-atom LP-ST results have been obtained for the H 4- CH 2CO and H 4- NO2 reactions (Hranisavljevic, Kumaran, and Michael 1998; Michael 1996).

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16.3.4 SUMMARY Almost all of the FP- or LP-ST work has been carried out in the four laboratories mentioned above. Most of the work has already been considered in previous reviews, and these can be consulted for details along with the original articles Oust 1981a, 1981b; Tsang and Lifshitz 1990; Michael and Lim 1993). Other methods involving ARAS analysis for measuring rate constants of bimolecular reactions are also continuing unabated, with much of the past work referenced above. Since these methods rely on thermal decompositions to produce the transient atomic species to be observed, it is generally true that unimolecular thermal rate behavior must first be studied before these methods can be used for subsequent monitoring of secondary atomic reactions. Hence, the systems are immediately complex; i.e., they involve two or more concurrent chemical reactions. If only one process depletes the atom, the results can be quite accurate. However, it is sometimes difficult to isolate one reaction, and then it is necessary to chemically model a multistep mechanism. If all rate constants in such a mechanism are known except one, then the fitted value can reflect a relatively accurate determination of the unknown rate constant. In most cases, the additional rate constants are not known with the necessary accuracy. Also, since thermal decomposition is the atomic source, the temperature-range over which experiments are performed can be substantially higher than with the FP- or LP-ST method. In the best work, experiments can be carried out systematically from simple to more complex mechanisms, and relatively good rate constants can be obtained hierarchically. In the case of radical detection (Davidson 2000), this modus operandi is about the only method available since the sensitivity for radical detection is substantially lower than with ARAS. This means that the elimination of secondary reactions, even when photolytic generation is available and used, is difficult if not impossible. Because FP- or LP-ST data are obtained under chemical isolation conditions, it is the view of the authors that these data should almost always be given first priority in mechanism-building efforts. Of course, researchers have been modeling high-temperature kinetics systems for decades using well-documented numerical methods for solving coupled first-order differential equations. Attempts at understanding complex reacting systems has become a separate field with its own history of successes. Therefore, researchers in this field sometimes resist attempts to change rate constants even when better measurements are available. There may be at least two causes for this reluctance. First, a set of particularly important macroscopic observations are adopted as being worthy of explanation. Then mechanisms with rate constants are used in simulations to try to explain the chosen observations. Optimization techniques

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may be used to secure the best possible explanation for the entire set of target observations. The optimized quantities are then taken to be the most correct even if certain of the rate processes and/or constants used in the simulation tum out to be wrong and/or inaccurate. This is the strategy used in GRI-Mech 2.11 (Bowman et al. 1995). The second cause is the continuing move toward commercialization of codes, including chemical mechanisms. If computer routines are purchased by industrial users, commercial owners may be quite reluctant to correct their codes even if additional, more accurate information becomes available. In our view, the possibility for effective chemical isolation of a given reaction is then the most important feature of the FP- or LP-ST method. As mentioned previously, the results can be used by theoreticians to develop and sharpen chemical kinetics theory. In general, the strategy involves first considering the potential energy for interaction of the reacting species using ab initio molecular structure calculations. Then some dynamics theory can be applied to calculate the thermal rate behavior. One such method would be CTST. Theory and experiment can then be compared. Success sometimes requires potential energy scaling of both energies and vibration frequencies. However, once the theory correlates with experiment, theory can then be used with substantial confidence to extrapolate to higher temperatures. Sometimes higher- and lower-temperature data do exist, and these can serve to further secure agreement between theory and experiment. The end result of this process is (a) to establish rate behavior at all temperatures (including high-T) for use in chemical modeling of complex mechanisms, and (b) to give advice to theoreticians on the accuracy and viability of their theoretical formalisms and/or theoretically derived quantities. Even though the FP- or LP-ST results are valuable for two important reasons, the implications to theoretical chemical physics have not been fully appreciated by some shock tube chemists. The same lack of appreciation for theory also exists in the tropospheric and stratospheric chemistry field, and the reasons are clear. Kineticists in these fields are only concemed with the practical implications of their results in chemical modeling. There also seems to be a lack of appreciation for chemistry by shock tube fluid dynamicists and aeronautical engineers. If the past is any measure of the future, these physicists will only become interested if and when they start choking on car exhaust and/or smoke stack emissions.

ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, under Contract No. W-31-109-Eng-38.

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REFERENCES Appel, D. and Appleton, J. P. (1974). Shock tube studies of deuterium dissociation and oxidation by atomic resonance absorption spectrophotometry. Proc. 15th Symp. (Int.) on Combustion, pp. 701-714. The Combustion Institute. Barker, J. R. and Michael, J. V. (1968). Experimental estimate of the oscillator strength of the 2P3/2,1/2 +__2S1/2 transition of the hydrogen atom. J. Opt. Soc. Am. 58:1615-1620. Bethe, H. and Salpeter, E. E. (1977). Quantum mechanics of one- and two-electron atoms, Plenum, New York. Bowman, C. T., Hanson, R. K., Davidson, D. E, Gardiner, Jr., W. C., Lissianski, V., Smith, G. P., Golden, D. M., Frenklach, M., and Goldenberg, M. (1995). GR/MechmAn optimized detailed chemical reaction mechanism for methane combustion. GRI-Mech 2.11. http://www.me.berkeley. edu/gri_mech/. Braun, W., Bass, A. M., and Davis, D. D. (1970). Experimental test of a two-layer model characterizing emission line profiles. J. Opt. Soc. Am. 60:166-170. Braun, W. and Carrington, T. (1969). Line emission sources for concentration measurements and photochemistry. J. Quant. Spectrosc. Radiat. Transfer 9:1133-1143. Braun-Unkhoff, M., Frank, P., and Just, T. (1990). High-temperature reactions of benzyl radicals. Ber. Bunsen-Ges. Phys. Chem. 94:1417-1425. Burns, G. and Homig, D. E (1960). A combined flash photolysis and shock wave method for the study of bromine atom recombination over a wide temperature range. Can. J. Chem. 38:17021713. Carver, J. H. and Mitchell, P. (1964). Ionization chambers for the vacuum ultra-violet. J. Sci. Inst. 41:555-557. Chiang, C.-C., Lifshitz, A., Skinner, G. B., and Wood, D. R. (1979). Resonance absorption measurements of atom concentrations in reacting gas mixtures. II. Calibration of microwave sources over a wide temperature range. J. Chem. Phys. 70:5614-5622. Davidson, D. E (2000). Spectroscopy. In Handbook of Shock Waves, G. Ben-Dor, O. Igra, T. Elperin, eds. Sec. 5.2, Part I. Academic Press, Burlington, MA. Davidson, D. E, Chang, A. Y., and Hanson, R. K. (1988). Laser photolysis shock tube for combustion studies. Proc. 22nd Symp. (Int.) on Combustion, pp. 1877-1885. The Combustion Institute. Davidson, D. E and Hanson, R. K. (1990a). High temperature reaction rate coefficients derived from N-atom ARAS measurements and excimer photolysis of NO. Int. J. Chem. Kinet. 22:843861. Davidson, D. E and Hanson, R. K. (1990b). Shock tube measurements of the rate coefficient for N + CH 3 --+ H 2CN 4- H using N-atom ARAS and excimer photolysis of NO. Proc. 23rd Symp. (Int.) on Combustion, pp. 267-273. The Combustion Institute. Davidson, D. E and Hanson, R. K. (1990c). A direct comparison of shock tube photolysis and pyrolysis methods in the determination of the rate coefficient for 0 4- H 2 --~ OH 4- H. Combust. and Flame 82:445-447. Davidson, D. E and Hanson, R. K. (1991). A shock tube study of reactions of C atoms with H 2 and 02 using excimer photolysis of C30 2 and C atom atomic resonance absorption spectroscopy. J. Phys. Chem. 95:183-191. Davidson, D. E, Snell, D. C., and Hanson, R. K. (1990). Shock-tube excimer photolysis and the measurement of N atom kinetic rates. Proc. 17th Int. Symp. on Shock Waves and Shock Tubes: Current Topics in Shock Waves, AlP Conf. Proc. 208, Y. W. Kim, ed., pp. 525-530. Am. Inst. of Physics. Davis, D. D. and Braun, W. (1968). Intense vacuum ultraviolet atomic line sources. Applied Optics 7:2071-2074.

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Dean, A. J., Davidson, D. E, and Hanson, R. K. (1990). C-atom ARAS diagnostic for shock tube kinetics studies. Proc. 17th Int. Symp. on Shock Waves and Shock Tubes: Current Topics in Shock Waves, AlP Conf. Proc. 208, Y. W Kim, ed., pp. 537-542. Am. Inst. of Physics. Dean, A. J., Davidson, D. E, and Hanson, R. K. (1991a). A shock tube study of reactions of C atoms with H 2 and 02 using excimer photolysis of C302 and C atom atomic resonance absorption spectroscopy. J. Phys. Chem. 95:183-191. Dean, A. J., Davidson, D. E, and Hanson, R. K. (1991b). A shock tube study of reactions of C atoms and CH with NO including product channel measurements. J. Phys. Chem. 95:3180-3189. Ernst, J., Wagner, H. G., and Zellner, R. (1978). A combined flash photolysis/shock wave study of the absolute rate constants for reactions of the hydroxyl radical with methane and trifluoromethane around 1350 K. Ber. Bunsen-Ges. Phys. Chem. 82:409-414. Fisher, J. R. and Michael, J. V. (1990). Rate constants for the reaction, D 4- D20 -+ D2 4- OD, by the flash photolysis-shock tube technique over the temperature range 1285-2261 K: Results for the back-reaction and a comparison to the protonated case. J. Phys. Chem. 94:2465-2471. Fujii, N., Sagawai, S., Sato, T., Nosaka, Y., and Miyama, H. (1989). Study of the thermal dissociation of N20 and CO2 using O(3P) atomic resonance absorption spectroscopy. J. Phys. Chem. 93:5474-5478. Fukuda, K., Koshi, M., and Matsui, H. (1991). Studies on the reactions: C2H 4- C2H2 ~ C4H2 4- H and C2H 4- H 2 ~ C2H2 4- H. Preprints, 202nd ACS Natl. Meet., Symp. Combust. Chem., Div. Fuel Chem. 36:1392-1399. Herzler, J. and Frank, P. (1992). High temperature reactions of phenylacetylene. Ber. Bunsen-Ges. Phys. Chem. 69:1333-1338. Hranisavljevic, J., Carroll, J. J., Su, M.-C., and Michael, J. V. (1998). Thermal decomposition of CF3Br using Br-atom absorption. Int. J. Chem. Kinet. 30:859-867. Hranisavljevic, J., Kumaran, S. S., and Michael, J. V. (1998). H 4- CH2CO --~ CH3 4- CO: A high pressure chemical activation reaction with positive barrier. Proc. 27th Symp. (Int.) on Combustion, pp. 159-166. The Combustion Institute. Iida, D., Koshi, M., and Matsui, H. (1996). Reaction of silane with atomic oxygen at high temperatures. Isr. J. Chem. 36:285-291. Just, T. (1981a). Chemical kinetic studies by vacuum UV spectroscopy in shock tubes. Shock Tubes and Shock Waves, Proc. 13th Int. Symp. on Shock Tubes and Waves: C. E. Treanor and J. G. Hall, eds., pp. 54-68. SUNY Press. Just, T. (1981b). Atomic resonance absorption spectrometry in shock tubes. In Shock Waves in Chemistry, A. Lifshitz, ed., pp. 279-318, Marcel Dekker, New York. Kee, R. J., Rupley, E M., and Miller, J. A. (1989). "Chemkin-II: A fortran chemical kinetics package for the analysis of gas-phase chemical kinetics." Report SAND89-8009; Sandia National Laboratories, Livermore, CA. Klemm, R. B., Sutherland, J. W., Wickramaaratchi, M. S., and Yarwood, G. (1990). Flash photolysisshock tube kinetic study of the reaction of atomic O(3p) with ethylene: 1052 K< T < 2284 K. J. Phys. Chem. 94:3354-3357. Ko, T., Fontijn, A., Lira, K. P., and Michael, J. V. (1992). A kinetics study of the O(3P) 4- CH3C1 reaction over the 556-1485 K range by the HTP and LP-ST techniques. Proc. 24th Symp. (Int.) on Combustion, pp. 735-742. Koshi, M., Fukada, K., Kamiya, K., and Matsui, H. (1992). Temperature dependence of the rate constants for the reactions of C2H with C2H2, H 2, and D2. J. Phys. Chem. 96:9839-9843. Koshi, M., Yoshimura, M., Fukuda, K., Matsui, H., Saito, K., Watanabe, M., Imamura, A., and Chen, C. (1990). Reactions of N(4S) atoms with NO and H 2. J. Chem. Phys. 93:8703-8708. KrUger, B. C. and Wagner, H. G. (1983). Measurement of absolute chlorine atom concentrations behind reflected shock waves. Proc. 14th Int. Symp. on Shock Tubes and Waves, R. E. Archer and B. E. Milton, eds., pp. 738-743. Sydney Shock Tube Symp. Publishers.

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Kumaran, S. S., Lim, K. P., and Michael, J. v. (1994). Thermal rate constants for the C14- H 2 and C1 4- D2 reactions between 296 and 3000 K. J. Chem. Phys. 101: 9487-9498. Kumaran, S. S., Su, M.-C., Lim, K. P., and Michael, J. V. (1995). Thermal decomposition of CF3I using I-atom absorption. Chem. Phys. Lett. 243:59-63. Kumaran, S. S., Su, M.-C., Lim, K. P., and Michael, J. V. (1996). The thermal decomposition of C2HsI. Proc. 26th Syrup. (Int.) on Combustion, pp. 605-611. The Combustion Institute. Ladenburg, R. and Reiche, F (1913). c~ber selektive absorption. Ann. d. Phys. 42:181-209. Lee, J. H., Michael, J. v., Payne, W. A., and Stief, L. J. (1978). Absolute rate of the reaction of N(4S) with NO from 196-400K with the DF-RF and FP-RF techniques. J. Chem. Phys. 69:3069-3076. Lee, P. (1955). Photodissociation and photoionization of oxygen (02) as inferred from measured absorption coefficients. J. Opt. Soc. Am. 45:703-709. Lifshitz, A., Bidani, M., and Carroll, H. E (1981a). The effect of minute quantities of impurities on shock tube kinetics. The reaction H 2 4- D 2 --~ 2HD. Proc. 13th Int. Syrup. on Shock Tubes and Waves: Shock Tubes and Shock Waves, C. E. Treanor and J. Hall, eds., pp. 602-609, SUNY Press. Lifshitz, A., Bidani, M., and Carroll, H. F (1981b). Vacuum uv window system for shock tubes bakeable to high temperature. Rev. Sci. Inst. 52:622-624. Lifshitz, A., Bidani, M., and Carroll, H. F (1983). The reaction H 2 4- D2 ~ 2HD. A long history of erroneous interpretation of shock tube results. J. Chem. Phys. 79:2742-2747. Lifshitz, A. and Michael, J. V. (1990). Rate constants for the reaction, O 4- H2O -~ OH 4- OH, over the temperature range, 1500-2400 K, by the flash photolysis-shock tube technique: Further consideration of the back reaction. Proc. 23rd Syrup. (Int.) on Combustion, pp. 59-67. The Combustion Institute. Lifshitz, A., Skinner, G. B., and Wood, D. R. (1979). Resonance absorption measurements of atom concentrations in reacting gas mixtures. I. Shapes of H and D Lyman-0~ lines from microwave sources J. Chem. Phys. 70:5607-5613. Lim, K. P. and Michael, J. v. (1993). The thermal decomposition of CH3C1 using the Cl-atom absorption method and the bimolecular rate constant for O 4- CH 3 (1609-2002 K) with a pyrolysis photolysis-shock tube technique. J. Chem. Phys. 98:3919-3928. Lim, K. P. and Michael, J. V. (1994). The thermal reactions of CH 3. Proc. 25th Syrup. (Int.) on Combustion, pp. 713-719. The Combustion Institute. Lynch, K. P., Schwab, T. C., and Michael, J. V. (1976). Lyman-~ absorption photometry at high pressure and atom density. Kinetic results for H recombination. Int. J. Chem. Kinet. 8:651-671. Maki, R. G., Michael, J. V., and Sutherland, J. W. (1985). Lyman-~ photometry: Curve of growth determination, comparison to theoretical oscillator strength, and line absorption calculations at high temperature. J. Phys. Chem. 89:4815-4821. Mallard, W. G., Westley, E, Herron, J. T., and Hampson, R. F (1994). "NIST chemical kinetics database--Ver. 6.0." NIST Standard Reference Data, Gaithersburg, MD. Michael, J. V. (1989). Rate constants for the reaction O 4- D 2 --~ OD 4- D by the flash photolysisshock tube technique over the temperature range 825-2487 K: The H 2 to D 2 isotope effect. J. Chem. Phys. 90:189-198. Michael, J. V. (1990). Rate constants for the reaction, H 4- D 2 -~ HD4- D, over the temperature range, 724-2061 K, by the flash photolysis-shock tube technique. J. Chem. Phys. 92:3394-3402. Michael, J. V. (1991). Thermal rate constant measurements by the flash or laser photolysis-shock tube method: Results for the oxidations of H 2 and D2, Preprints, 202nd ACS Natl. Meet., Syrup. Combust. Chem., Div. Fuel Chem. 36:1563-1570. Michael, J. V. (1992a). The measurement of thermal bimolecular rate constants by the flash photolysis-shock tube (FP-ST) technique: Comparison of experiment to theory. In Advances in Chemical Kinetics and Dynamics, vol 1. pp. 47-112. JAI.

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Michael, J. v. (1992b). Isotope effects at high temperatures studied by the flash or laser photolysisshock tube technique. ACS Symp. Ser. 502: Isotope Effects in Gas Phase Chemistry, J. A. Kaye, ed., pp. 80-93. American Chemical Society. Michael, J. v. (1992c). Measurement of thermal rate constants by flash or laser photolysis in shock tubes: oxidations of H 2 and D 2. Prog. Energy Combust. Sci. 18:327-347. Michael, J. V. (1996). Recent advances in the measurement of high temperature bimolecular rate constants. In Gas Phase Chemical Reaction Systems, Experiments and Models 100 Years after Max Bodenstein, Series in Chemical Physics No. 61, J. Wolfrum, H.-R. Volpp, R. Rannacher, and J. Warnatz, eds., pp. 177-189. Springer, New York. Michael, J. V. and Fisher, J. R. (1990). Rate constants for the reaction, D + H 2 ~ HD + H, over the temperature range, 655-1979 K, by the flash photolysis-shock tube technique. J. Phys. Chem. 94:3318-3323. Michael, J. V., Fisher, J. R., Bowman, J. M., and Sun, Q. (1990). Theoretical and experimental rate constants for two isotopic modifications of the reaction H + H 2. Science 249:269-271. Michael, J. V., Kumaran, S. S., and Su, M. C. (1999). Rate constants for CH 3 + 02 ~ CH30 + O at high temperature and evidence for H2CO + 02 ~ HCO + HO 2. J. Phys. Chem. A103:59425948. Michael, J. V. and Lim, K. P. (1992). Rate constants for the N20 reaction system: Thermal decomposition of N20; N + NO ~ N 2 + O; and implications for O + N 2 ~ NO + N.J. Chem. Phys. 97:3228-3234. Michael, J. V. and Lim, K. P. (1993). Shock tube techniques in chemical kinetics. Ann. Rev. Phys. Chem. 44:429-458. Michael, J. V. and Sutherland, J. W. (1986). The thermodynamic state of the hot gas behind reflected shock waves: Implication to chemical kinetics. Int. J. Chem. Kinet. 18:409-436. Michael, J. V. and Sutherland, J. W. (1988). Rate constant for the reaction of H with H20 and OH with H 2 by the flash photolysis-shock tube technique over the temperature range, 12462297 K. J. Phys. Chem. 92:3853-3857. Michael, J. V., Sutherland, J. W., and Klemm, R. B. (1985). The flash photolysis-shock tube technique using atomic resonance absorption for kinetic studies at high temperatures. Int. J. Chem. Kinet. 17:315-326. Michael, J. V., Sutherland, J. W., and Klemm, R. B. (1986). Rate constant for the reaction H + NH 3 over the temperature range 750-1777K. J. Phys. Chem. 90:497-500. Michael, J. V. and Wagner, A. E (1990). Rate constants for the reaction, O + C 2 H 2 and O + C2D 2 ~ products, over the temperature range ~850-1959 K, by the flash photolysisshock tube technique. Determination of the branching ratio and a further theoretical analysis. J. Phys. Chem. 94:2453-2464. Michael, J. V. and Weston, R. E., Jr. (1966). Determination of hydrogen-atom concentration by Lyman-0~ photometry. I. Oscillator strength of the hydrogen-atom 2P3/2,1/2 4--2 S1/2 transition. II. Kinetics of the reaction of hydrogen-atoms with acetylene and ethylene. J. Chem. Phys. 45:3632-3641. Mick, H. J., Matsui, H., and Roth, P. (1993). High-temperature kinetics of Si atom oxidation by NO based on Si, N, and O atom measurements. J. Phys. Chem. 97:6839-6842. Miller, J. C. and Gordon, R. J. (1983). Kinetics of the C1-H2 system. Abstraction vs exchange in D+HC1. J. Chem. Phys. 78:3713-3720. Mitchell, A. C. G. and Zemansky, M. W. (1934). Resonance radiation and excited states. Cambridge. Cambridge University Press, London 1934. Miyoshi, A., Ohmori, K., and Matsui, H. (1993). Reaction rates of atomic oxygen (3p) with a series of alkanes at high temperatures. Proc. 6th Toyota Conf. on Turbulence and Molecular Processes in Combustion, T. Takeno, ed., pp. 85-99, Elsevier.

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103

Miyoshi, A., Ohmori, K., Tsuchiya, K., and Matsui, H. (1993). Reaction rates of atomic oxygen with straight chain alkanes and fluoromethanes at high temperatures. Chem. Phys. Lett. 204:241247. Miyoshi, A., Shiina, H., Tsuchiya, K., and Matsui, H. (1996). Kinetics and mechanism of the reaction of S(3P) with 02. Proc. 26th Symp. (Int.) on Combustion, pp. 535-541. The Combustion Institute. Miyoshi, A., Tsuchiya, K., Tezaki, A., and Matsui, H. (1995). Studies on the reactions of atomic oxygen (3p) with C2-C 6 alkanes at high temperatures: Examination of the transition state theory. Proc. 19th Int. Symp. on Shock Tubes and Waves, Brun, Raymond, Cumitrescu, and Lucien, eds., pp. 131-136. Springer. Miyoshi, A., Tsuchiya, K., Yamauchi, N., and Matsui, H. (1994). Reactions of atomic oxygen (3p) with selected alkanes. J. Phys. Chem. 98:11451-11458. Miyoshi, A., Yamauchi, N., and Matsui, H. (1996). Site-specific branching fractions for the O(3p) and OH 4-C3H s reactions. J. Phys. Chem. 100:4893-4899. Mozzhukin, E., Burmeister, M., and Roth, P. (1989). High temperature dissociation of CN. Ber. Bunsen-Ges. Phys. Chem. 93:70-75. Myerson, A. L. (1973). Shock-tube atom kinetics of nitric oxide decomposition. Proc. 14th Symp. (Int.) on Combustion, pp. 219-228. The Combustion Institute. Myerson, A. L., Thompson, H. M., and Joseph, P. J. (1965). Resonance absorption spectrophotometry of hydrogen atom behind shock waves. J. Chem. Phys. 42:3331-3332. Myerson, A. L. and Watt, W. S. (1968). Atom formation rates behind shock waves in hydrogen and the effect of added oxygen. J. Chem. Phys. 49:425-433. Niemitz, K. J., Wagner, H. G., and Zellner, R. (1981). A combined flash photolysis/shock wave study on the kinetics of the reaction OH 4-NH 3 --~ NH 2 4- H20 at 1350 K. Z. Phys. Chem. NF124:155-170. Ohmori, K., Yoshimura, M., Koshi, M., and Matsui, H. (1992). A flash photolysis study of CH4 - 02 mixtures behind shock waves: Examination of reaction of CH 3 4- 02. Bull. Chem. Soc. Jpn. 65:1317-1322. Pamidimukkala, K. M., Lifshitz, A., Skinner, G. B., and Wood, D. R. (1981). Resonance absorption measurements of atom concentrations in reacting gas mixtures. VI. Shapes of the vacuum ultraviolet oxygen (3 s - 3p) resonance triplet from microwave sources and empirical calibration in a shock tube. J. Chem. Phys. 75:1116-1122. Pilling, M. J., Turanyi, T., Hughes, K. J., and Clague, A. R. (1996). The Leeds methane oxidation mechanism 1.3. http://www.chem.leeds.ac.uk/Combustion/Combustion.html. Pirraglia, A. N., Michael, J. V., Sutherland, J. W, and Klemm, R. B. (1989). A flash photolysis-shock tube kinetic study of the H atom reaction with 02" H 4- 02 ~ OH 4- H (962 _< T < 1705 K) and H 4- 02 4- Ar --~ HO 2 4- Ar (746 < T < 987 K). J. Phys. Chem. 93:282-291. Rabinowitz, M. J., Sutherland, J. W., Patterson, P. M., and Klemm, R. B. (1991). Direct rate constant measurements for H 4- CH4 ~ CH3 4- H2, 897-1729 K, using the flash photolysis-shock tube technique. J. Phys. Chem. 95:674-681. Radhakrishnan, K. (1994). "LSENS--A general sensitivity and analysis code for homogeneous gasphase reactions." NASA RP 1328, National Aeronautics and Space Administration, Washington, DC. Radhakrishnan, K. and Hindmarsh, A. C. (1993). "Description and use of LSODE, the Livermore solver for ordinary differential equations." NASA RP 1327, National Aeronautics and Space Administration, Washington, DC; Lawrence Livermore National Laboratory Report UCRL-ID113855, Livermore, CA. Rao, V. S. and Skinner, G. B. (1989). Study of the high-temperature pyrolysis of propene by determination of H and D atoms formed from partially deuterated propenes heated behind shock waves. J. Phys. Chem. 93:1869-1876.

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Ross, S. K., Sutherland, J. W., Kuo, S. C., and Klemm, R. B. (1997). Rate constants for the thermal dissociation of N20 and the O(3p) + N20 reaction. J. Phys. Chem. A101:1104-1116. Roth, P. and Just, T. (1975). Atom-Resonanzabsorptionsmessungen beim Thermischen Zerfall von Methan hinter Stosswellen. Ber. Bunsen-Ges. Phys. Chem. 79:682-686. Roth, P. and Just, T. (1977). Atomic absorption measurements on the kinetics of the reaction methane + atomic oxygen---~methyl+hydroxyl in the temperature range 1500 < T < 2250 K. Ber. Bunsen-Ges. Phys. Chem. 81:572-577. Shiina, H., Miyoshi, A., and Matsui, H. (1998). Investigation on the insertion channel in the S(3p) + H 2 reaction. J. Phys. Chem. 102:3556-3559. Shiina, H., Oya, M., Yamashita, K., Miyoshi, A., and Matsui, H. (1996). Kinetic studies on the pyrolysis of H2S. J. Phys. Chem. 100:2136-2140. Shin, K. S. and Michael, J. V. (1991a). Rate constants (296-1700K) for the reactions C2H 4- C2H 2 ~ C4H 2 4- H and C2D + C2D 2 ~ C4D 2 4- D. J. Phys. Chem. 95:5864-5869. Shin, K. S. and Michael, J. V. (1991b). Rate constants for the reactions, H + 0 2 ~ OH + O and D + 0 2 ~ OD 4-O, over the temperature range 1085-2277K by the flash photolysis-shock tube technique. J. Chem. Phys. 95:262-273. Smirnov, V. N., Votintsev, V. N., Zaslonko, I. S., and Moiseev, A. N. (1990). Kinetics of the thermal decomposition of dimethylcadmium. Kinet. Katal. 31:1041-1045. Su, M.-C., Lim, K. P., Michael, J. V., Hranisavljevic, J., Xun, Y. M., and Fontijn, A. (1994). Kinetics studies of the O(3p) 4- CHzC12 and CHC13 reactions over the 468-1355 and 499-1090 K ranges using two techniques. J. Phys. Chem. 98:8411-8418. Sutherland, J. w. and Michael, J. V. (1988). The kinetics and thermodynamics of the reaction H 4- NH 3 ~- NH 2 4- H 2 by the flash photolysis-shock tube technique: Determination of the equilibrium constant, the rate constant for the back reaction, and the enthalpy of formation of the amidogen radical. J. Chem. Phys. 88:830-834. Sutherland, J. W., Michael, J. V., and Klemm, R. B. (1986). Rate constant for the O(3p) 4- CH 4 --~ CH 3 4- OH reaction obtained by the flash photolysis-shock tube technique over the temperature range 760 < T < 1755 K. J. Phys. Chem. 90:5941-5945. Sutherland, J. W., Michael, J. V., Pirraglia, A. N., Nesbitt, E L., and Klemm, R. B. (1986). Rate constant for the reaction of O(3p) with H 2 by the flash photolysis-shock tube and flash photolysis-resonance fluorescence techniques: 504 < T < 2495 K. Proc. 21st Symp. (Int.) on Combustion, pp. 929-941. The Combustion Institute. Sutherland, J. W., Patterson, P. M., and Klemm, R. B. (1990a). Flash photolysis-shock tube kinetic investigation of the reaction of O(3p) atoms with ammonia. J. Phys. Chem. 94:2471-2475. Sutherland, J. W., Patterson, P. M., and Klemm, R. B. (1990b). Rate constants for the reaction system O(3p)4- H20 ~ OH 4- OH over the temperature range 1053 K to 2033 K using two direct techniques. Proc. 23rd Symp. (Int.) on Combustion, pp. 51-57. The Combustion Institute. Takahashi, K., Inoue, A., and Inomata, T. (1996). Direct measurements of rate coefficients for thermal decomposition of methyl halides using shock-tube ARAS technique. Proc. 20th Int. Symp. on Shock Waves, B. Sturtevant, J. E. Shepard, and H. G. Hornung, eds., pp. 959-964. World Scientific. Thielen, K. and Roth, P. (1985). Resonance absorption measurements of N and O atoms in high temperature NO dissociation and formation kinetics. Proc. 20th Symp. (Int.) on Combustion, pp. 685-693. The Combustion Institute. Tsang, W. and Lifshitz, A. (1990). Shock tube techniques in chemical kinetics. Ann. Rev. Phys. Chem. 41:559-599. Tsuchiya, K., Matsui, H., and Dupre, G. (1995). High temperature reaction of O(3p) 4- H2S. Proc. 19th Int. Symp. on Shock Tubes and Waves, Brun, Raymond, Cumitrescu, and Lucien, eds., pp. 71-76. Springer.

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Tsuchiya, K., Yamashita, K., Miyoshi, A., and Matsui, H. (1996). Studies on the reactions of atomic sulfur (3p) with H 2, D 2, CH4, C2H 6, C3H8, n-C4H10, and i-C4H10. J. Phys. Chem. 100:17202-17206. Tsuchiya, K., Yokoyama, K., Matsui, H., Oya, M., and Dupre, G. (1994). Reaction mechanism of atomic oxygen with hydrogen sulfide at high temperature. J. Phys. Chem. 98:8419-8423. Votintsev, V. N., Moiseev, A. N., and Smirnov, V. N. (1989). Decomposition of hydrogen selenide in shock waves. Kinet. Katal. 30:225-226. Watt, W. S. and Myerson, A. L. (1969). Atom formation rates behind shock waves in oxygen. J. Chem. Phys. 51:1638-1643. Weissler, G. L. (1956). Photoionization in gases and photoelectric emission from solids. In Handbuch der Physik, vol. 21, S. Flugge, ed., pp. 304-382. Springer. Woiki, D. and Roth, P. (1992). Shock tube measurements on the thermal decomposition of COS. Ber. Bunsen-Ges. Phys. Chem. 96:1347-1352. Wood, D. R., Skinner, G. B., and Lifshitz, A. (1987). Measurement and modeling of the nitrogen resonance line profiles from an electrodeless discharge lamp. J. Chem. Phys. 87:5092-5096. Yarwood, G., Sutherland, J. W., Wickramaaratchi, M. A., and Klemm, R. B. (1991). Direct rate constant measurements for the reaction O 4- NO 4- Ar --~ NO 2 + Ar at 300-1341 K. J. Phys. Chem. 95:8771-8775. Yoshimura, M., Koshi, M., Matsui, H., Kamiya, K., and Umeyama, H. (1992). Non-Arrhenius temperature dependence of the rate constant for the H + H2S reaction. Chem. Phys. Lett. 189:199-204.

CHAPTER

16.4

Chemical and Combustion Kinetics 16.4

Single-Pulse Shock Tube

WING TSANG National Institute of Standards and Technology, Gaithersburg, MD 20899 ASSA LIFSHITZ Department of Physical Chemistry, Hebrew University of Jerusalem, Jerusalem, 91904, Israel

16.4.1 Introduction 16.4.2 The Single-Pulse Shock Tube 16.4.2.1 Configuration 16.4.2.2 Requirements 16.4.2.3 Limitations 16.4.2.4 Validation 16.4.3 Chemical Kinetics 16.4.3.1 General Considerations 16.4.3.2 Analytical Methods 16.4.3.3 Treatment of Data 16.4.3.4 Experimental Approaches 16.4.4 Complex Reaction Systems 16.4.4.1 Introduction 16.4.4.2 Determination of Reaction Mechanisms 16.4.4.3 Computer Simulation 16.4.5 Single-Reaction Studies 16.4.5.1 Justification 16.4.5.2 Experimental Configurations 16.4.5.3 Internal Standards and the Comparative Rate Technique 16.4.6 Specific Systems and Generalizations 16.4.6.1 Complex Reactions 16.4.6.2 Single-Step Kinetics 16.4.7 Summary and Future Directions References Appendix: Summary of Experimental Results Handbook of Shock Waves, Volume 3 Copyright 9 2001 by Academic Press. All rights of reproduction in any form reserved. ISBN: 0-12-086433-9/$35.00

107

108 16.4.1

w. Tsang and A. Lifshitz INTRODUCTION

The basic characteristic of shock tubes is the pulse nature of the heating phenomenon. Studies on the chemistry of a reacting system obviously require some means of determining the concentration of reactants, products, and intermediates during the course of the reaction. In cases where complicated molecules have many reaction pathways, the analytical capabilities set the constraints on the value of the data obtained. In shock tube research, there have been two approaches to the analysis of the constituents of reacting systems. The first and most obvious is to make concentration measurements as a function of time immediately upon the passage of the shock wave. Since the time scale of shock tube studies are in the microsecond to low millisecond range, this generally means the use of optical techniques with spectroscopic detection of the molecules of interest. This sets limitations on the number of components that can be detected simultaneously (usually one or two) and the concentrations necessary for detection. This opens issues regarding the appropriate reaction pathways. For simple systems such as the decomposition of hydrogen molecules, this is not a problem: Obviously, the only channel for the decomposition of the hydrogen molecule is the formation of atoms. However, even here the assumption is that excited electronic states are not important. As the molecules of interest become more complex, uncertainties increase regarding the true significance of the real-time measurements on the one or two species that can be detected. It is here that single-pulse shock tube studies, with their capability of detecting the whole range of end products, fill a particular niche. Much of this chapter will deal with the use of the single-pulse shock tube to obtain information on the kinetics of decomposition of polyatomic molecules. One of the consequences of generating high temperatures is that polyatomic molecules can be decomposed. In the course of the process new molecules are created and, in the case of oxidation, the latent chemical energy in molecules is released through combustion. An understanding of such processes is an important direction in chemical research. The results are of vital importance for a host of technologies and natural phenomena that are, in general, centered around combustion and related processes. The detailed understanding of the chemistry in combination with modern computational techniques give to technologists a unique tool that can expand and indeed take the place of expensive and frequently uncertain physical testing. The key role of singlepulse shock tube studies is to provide the experimental database for use in simulations and in the testing and validation of predictive theories. A large amount of data have now been accumulated (Tsang 1981; Tsang and Lifshitz 1990) and reviewed. It is clear that for gathering information on the high-

16.4 Single-PulseShock Tube

109

temperature gas-phase behavior of complicated polyatomic molecules, singlepulse shock tube studies are one of the preferred tools. Nevertheless, for the unraveling of the complexities of such phenomena, the ideal situation is to simultaneously detect unstable intermediates and all final products. It is probably only by using all available tools that quantitative chemical kinetic results regarding rates and mechanisms can be unambiguously obtained. For the determination of reaction mechanisms, the important factors are effects on the yields of intermediates and products as a result of variations in the reactants and the physical and chemical environments. Traditionally, this has meant studying reactions in static or flow systems, quenching the reacting mixture and then subjecting it to detailed analysis. Unstable intermediates are not directly detected. Nevertheless, through changes in the reaction conditions much can be inferred. This is a particularly fruitful approach in the context of the tremendous advances in modern analytical capabilities since reaction conditions can be varied over enormous ranges and products at extremely low concentrations can be detected. Single-pulse shock tube experiments represent extensions of the classical static studies with the added feature of short heating time and no possible contributions from surface reactions. This chapter is divided into six main sections. The first deals with operational details and the basic physical phenomena. Evidence is provided to validate the general procedure. The second section contains a detailed discussion of how experiments are carried out and the type of kinetic problems that are accessible through single-pulse shock tube studies. The third section discusses kinetics studies, where the emphasis is on the understanding of the mechanisms and rate constants for the decomposition reactions of a particular molecule. The fourth section covers experiments concentrated on determining the rate expressions for a single reaction. Specific experiments and an outline of what has been learned is covered in the fifth section, followed by a brief summary and a discussion of possible future directions.

1 6 . 4 . 2 THE S I N G L E - P U L S E S H O C K TUBE

16.4.2.1 CONFIGURATION Figure 16.4.1 contains a schematic of the typical configuration of the singlepulse shock tube that is generally used at the present time (Klepeis 1961). Also included is a wave diagram that illustrates the physical phenomena. The various regions of interest are (1) the test gas at its initial configuration, (2) the gas behind the incident shock, (3) the driver gas immediately behind the diaphragm, (4) the initial driver gas, and (5) the test gas behind the reflected

110

w. Tsang and A. Lifshitz

shock. Also included are the particle paths (dotted lines), which are parallel to the driver and driven gas interface. The basic steps are (i)

the breaking of a diaphragm, leading to the formation of a shock wave; its passage through the test gas (region 1), resulting in a temperature and pressure step; (ii) the reflection of the shock wave from the end wall, leading to another temperature and pressure step; and (iii) the interaction of the shock wave with the interface, leading to the formation of an expansion wave cooling the shocked gas. During steps (ii) and (iii) the driver gas is being sucked into the dump tank, which initially was at the same pressure as the test gas. Ultimately the reflected shock is swallowed. The consequence is that the test gas feels a well-defined heating pulse. Due to the exponential dependence of rate constants on temperature, the temperature pulse behind the incident shock wave has no effect. A reproduction of a typical pressure trace is given in Fig. 16.4.2. Note the close correspondence with the idealized sketch in Fig. 16.4.1.

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Pressure Temperature

Schematic of a single-pulse shock tube and associated processes.


111

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time (ms)

FIGURE 16.4.2 Photographof typical pressure trace.

The operation of the single-pulse shock tube is straightforward. It involves preparing the required mixture in a standard vacuum system, filling the dump tank and test section to the desired pressure, pressurizing the driver section, and breaking the diaphragm. Immediately thereafter a sample is removed for analysis. Since the volume of the dump tank is at least 1 order of magnitude larger than the test section, it is usually filled with the pure driven gas (argon, without the test gas). Thus a valve between the two sections is necessary. In recent years, to extend the range of molecules to those with lower vapor pressures, single-pulse shock tubes have been heated. It has been found that a temperature in the 100 to 200~ range is adequate for most purposes. Temperature uniformity is maintained within 1 or 2~ Although this does increase the complexity of the shock tube, no special problems have been encountered. The single-pulse shock tube described here is a variant of the original design described by Glick et al. (1955). The original design involved the dump tank being placed at the high-pressure end of the shock tube and maintained at vacuum. The composition of the driver gas was set so that the shock passed smoothly through the interface. Cooling was effected by the expansion wave generated from the dump tank. Thus it was necessary to properly time the breaking of the two diaphragms and to set a particular composition of the driver gas, a "tailored interface," so that the reflected gas passed smoothly across the interface. These operations are not necessary in the variant used today. Nevertheless, in the original form, the gas dynamics are particularly well described in terms of simple one-dimensional theory. In contrast, the actual behavior of the dump tank at the side of the test section has never been completely characterized. Confidence that this does not introduce significant errors into the data analysis is based on the consistency of the results that has

112


been obtained from such studies. However, this is not completely satisfactory and must be carefully considered, particularly if one is to add real-time detection to single-pulse shock tube studies.

16.4.2.2 R E Q U I R E M E N T S Probably the key physical effect for single-pulse shock tube work is the interaction of the shock wave with the driver-driven gas interface. For the generation of a rarefaction wave, the condition is a3 73- 1

a2 72- 1

where a is the speed of sound and 7 is the specific heat ratio. The subscripts are as given in Fig. 16.4.1. Since the temperature behind the incident shock must be higher than that behind the interface, the condition for quenching can only be achieved with a light driver gas such as hydrogen or helium and heavier driven gases such as argon or krypton. This expansion wave will then cool the heated gas, leading to the single-pulse feature. For hydrogen drivers and argon test mixtures, cooling rates as large as 1 million degrees per second can be achieved. The validity of the general procedure can be readily established by examination of the pressure history from such experiments (see Fig. 16.4.2). The dump tank prevents multiple reflections of the shock. Here again examination of the pressure traces guarantees that the process is operating in the desired manner. Actually, due to the high activation energy of most of the reactions that have been studied, the attenuation of the pulses ensures that none of the secondary pulses are anywhere near the temperature of the initial pulse. The real importance of the dump tank is probably to ensure that mixing between the driver and shocked gas is minimized. This is achieved by moving the driver and test gas interface far away from the sampling port. The authors have found that if the gas analyzer is directly connected to the shock tube and samples are taken within a few seconds after running the shock, losses of samples through mixing do not occur since material balance of better than 95% is easily achieved. However, this must be checked. As will be seen shortly, in cases where this is not achieved corrections must be made. The physical conditions that can be generated in a single-pulse shock tube are determined by the length, pressure, and temperature ratings (if it is heated) of the shock tube, subject only to the constraints of the relation given above. Usually this means a heating time of several hundred microseconds to milliseconds, pressures of a few to hundreds of bars and temperatures as high as 2000 K. This fills a very important niche between real-time shock tube

16.4


113

measurements and the turbulent flow reactors that are now widely used in combustion research (Linteris et al. 1991).

16.4.2.3 LIMITATIONS Due to the necessity of working in the reflected shock region, nonidealities will lead to temperatures considerably different than those determined from shock velocity measurements that assume ideal gas dynamic relations. The general situation has been discussed in detail by Michael and Sutherland (1986) and other authors Belford and Strehlow (1969). The physical situation is the buildup of the boundary layer behind the incident shock and its subsequent interaction with the reflected shock. It is known that these effects are minimized when heavy rare gases are used as the principal component of the test gas. Although it would seem possible to correct for such effects, an important uncertainty is whether the boundary layer is laminar or turbulent. A serious problem is the introduction of temperature gradients into the system, which would make the single-pulse shock tube no longer an isothermal reactor. However, this is probably more serious for real-time measurements than for single-pulse shock tube studies. Indeed, for single-pulse shock tube work this problem is largely eliminated through the use of an "average temperature". All the reactions in the mixture are occurring at this temperature. (We will discuss how this property can be utilized in a subsequent section). Ironically, these problems coupled with the wide range of unexpected phenomena first observed in shock tube experiments Tsang (1981) were in fact detrimental to the acceptance of the shock robe as a kinetics tool. In retrospect, it is apparent that the extension of the temperature range by shock tube experiments has led to a great increase in our understanding of the quantitative details of chemical kinetics. It is now clear that the chemistry can be used to infer properties of the shocked gas and hence to calibrate the reaction conditions. Thus, while it is important to be aware of the problems, there are a variety of essentially chemical means of amelioration. The increasing acceptance of single-pulse shock tube and indeed of all shock tube results has been largely due to the steady accumulation of self-consistent data and greater understanding of the problems intrinsic to high-temperature chemistry. Although the uncertainty in temperature should be borne in mind when considering single-pulse shock tube data, this problem should be kept in perspective. Generally speaking, it is difficult to carry out experiments at high temperatures. The alternative experimental approaches are studies in flow or static reactors. In both cases, heating is by heat transfer from hot walls.

114


Considerable care must be taken to make sure that the actual reaction time is as determined by flow and thermocouple measurements. Past experience has indicated that investigators using classical techniques have usually treated such issues without necessary care and this has led to considerable errors in the literature. This is in contrast to the situation with shock tube studies, where, ironically, awareness of the physical problems has led to an underestimation of the validity of results. In any kinetics experiment, the time required to achieve the desired temperature must be considerably shorter than that of the time-dependent phenomenon of interest. This sets a definite limit on the type of reactions that can be studied using any method. The temperatures that can be interrogated classically are considerably lower than those in shock tube experiments. Thus certain reaction channels are only accessible through the latter. Furthermore, the dependence on heating from hot walls obviously means that the reacting gas must at some time or other make contact with the wall. Thus the possibility of surface reactions must always be considered in classical studies. In contrast, in shock tube studies the heating is the result of the passage of the shock wave and no hot walls are required. Indeed, the walls of the shock tube are cold and hence much less reactive. Furthermore, the short reaction time (in comparison to classical methods) sets definite limits on how many reactive species can move into the main gas stream. Thus surface effects can be eliminated from consideration. All reactions must therefore originate from one or a series of gas phase processes. The determination of such pathways in a quantitative manner is one of the main contributions of single-pulse shock tube studies. The reaction time in single-pulse shock tube experiments is a function of the entire length of the tube and the relative length of the low- and highpressure sections. Since this is not readily changed, measurements in most experiments are all made at one particular time. This can be restrictive since for a given temperature one cannot carry out reactions to any desired extent of reaction by varying the time. As a result, at very low temperatures it is necessary to rely on product formation. The results may therefore be affected by trace impurities. The technique is obviously restricted to the determination of the concentration of all the stable products, and thus all possibilities of determining mechanisms and rate constants on the basis of the temporal behavior of the reactants and products are lost. On the other hand, the prospect of determining a large number of products at a particular time represents a powerful capability. The short residence time means that the operation must be at much higher temperatures. Thus chain lengths are generally shorter than in classical situations. This is not only due to the short reaction time; the higher radical concentrations naturally make the termination reactions more important. Finally, the temperatures used in single-pulse shock tube are very close to those actually found in combustion and pyrolytic processes. Thus extensive extrapolations are no longer needed for practical applications.

16.4

115


16.4.2.4 VALIDATION The ultimate validation of any method is through comparison of the results with those from other techniques. Present-day confidence in the results of the single-pulse shock tube method basically comes from such comparisons as well as from the internal consistency of the data. Generally speaking, it appears that the predictions from fluid dynamics considerations are much more pessimistic than would be warranted by the current results, particularly where some means of internally calibrating the behavior of system is used. Figures 16.4.3a-c contain results from single-pulse shock tube, static, and flow experiments. The reactions selected involve direct formation of stable products and are thus particularly straightforward in the context of single-pulse shock tube studies. The results bear particularly on the issues dealing with nonideal behavior described earlier. Even the most cursory examination of the data will reveal that the single-pulse shock tube studies produce results that are at least

A = diethoxymethane t

".

t

II~

o~

' ~ 9 a=

.~-2

-6

!

i

1.0

1.2

....

~

1.4 1000/T

l

|

1.6

1.8

2.0

al = 1.58x1013e~(-23350/T) (Bigley and Wren, 1972) a2 = 4.05x1013exp(-23752/T) (Bigley and Wren, 1972) a3 = 7.94x1013exp(-23148/T)(Gordon and Norris, 1965) a4 = 1.15x1013exp(-23454/T) (Cross et al, 1976) a5 = 1.07x1013exp(-23300/T) (Herzler et al, 1997) FIGURE 16.4.3a Rate constants for decomposition of diethoxymethane to form ethylene + C2HsOCH2OH. The initial listing refers to static and flow experiments. Those on the bottom are from shock tube studies. The expressions in brackets are shock tube determinations with temperature from shock velocities. Others are from comparative rate studies. The dotted lines are extrapolations from comparative rate studies.

W. Tsang and A. Lifshitz

116

B = t-butylchloride

_

A

-7,=

0-

v

Jr Ol

o

..J

-2-4-

-6

1.0

,

,

I

i

1.2

1.4

1.6

1.8

i"

2.0

2.2

1000/T bl = 7.gx1012exp(-20933/T) (Asahina and Onozuka, 1964) b2 = 5x1013exp(-22594/T) (Maccoll and Wong, 1968) b3 = 5.9x1013exp(-22665/T) (Failes and Stimson,1962) b4 = 8.5x1013exp(-22997/T) (Heydtmann et a1,1975) b5 = 1.9x1014exp(-23148/T) (Brearly et al, 1936) b6 = 2.5x1012exp(-20833/T) (Barton and Onyon, 1949) b7 = 7xl 013exp(_22488/T) (Tsang, 1964b,a) [b8 = 7.9x1013exp(-23248/T) (Tsang, 1964c)] FIGURE 16.4.3b Rateconstants for decomposition of t-butyl chloride to form isobutene 4- HCI. The initial listing to refers to static and flow experiments. Those on the bottom are from shock tube studies. The expressions in brackets are shock tube determinations with temperature from shock velocities. Others are from comparative rate studies. The dotted lines are extrapolations from comparative rate studies. as good as those from more standard techniques and that the classical studies have the problems described earlier. Hence it can be concluded that uncertainties in rate constants arising from fluid dynamic effects are rarely more than a factor of 1.5 and should not be reflected in the activation energies by more than a few percent. Finally, it will be noted that the single-pulse shock tube and classical studies span a total rate constant range of close to 10 orders of magnitude. In the case of the flow experiments, the differences in temperatures are between 100 to 200 ~. Since single-pulse shock tube studies are particularly suitable for studies on the decomposition of larger molecules, an important problem is frequently their low vapor pressure at room temperature. To increase the vapor pressure of the compounds in question and to prevent their adsorption on cold surfaces, the shock tube, the gas-handling manifold, the GC injection unit, and all the

16.4

117


C = cyclohexene

/ QII

0

v

C2 ~

-

r

,6

0.8

i

!

0.9

1.0

. . . . . . . . . . . . . . . . . . . . . . . . i

i

i

1.1

1.2

1.3

i

~1 .

1.4

1.5

IO00/T cl = 1.4x1017exp(-36584/T) (Smith and Gordon, 1961) c2 = 1.2x1012exp(-27727/T) (Kraus et al, 1957) c3 = 8.9 xl012 exp(-28935/T) (Kuchler,1939) c4 = 1.45x1015exp(-33313/T) (Uchiyama et al, 1964) [c5 = 1.45 x1015exp(-32955/T) (Bamard and Parrott,1976)] c6 = 1.8 x 1015exp(-33002/T) (Newman et al, 1980) c7 = 1.4 x1015exp(-33500/T) (Tsang,1973) [c8 = 1.5 xl015 exp(-33666/T) (Hidaka et al, 1984)] [c9 = 2.5x1015exp(-33716/T) (Skinner et al, 1981)] FIGURE 16.4.3c Rate constants for decomposition of cyclohexene to form 1,3-butadiene + ethylene. The initial listing refers to static and flow experiments. Those on the bottom are from shock tube studies. The expressions in brackets are shock tube determinations with temperature from shock velocities. Others are from comparative rate studies. The dotted lines are extrapolations from comparative rate studies.

other parts of the system must be heated. Heating to temperatures of 100 to 200~ depending on the compound to be studied, is in most cases enough. The heating is normally computer controlled and the temperature is kept constant to within +2~

16.4.3 CHEMICAL KINETICS 16.4.3.1 GENERAL CONSIDERATIONS Kinetics studies can be divided into two parts" the determination of a reaction mechanism and the assignment of individual rate constants. If the mechanistic

118


results are ambiguous, one literally does not know what time-dependent phenomena is being measured. For mechanistic determinations, highly accurate time-dependent measurements are not really needed; the key aim is the identification of reaction products under a wide variety of physical and chemical conditions. Due to the wealth of new instrumentation that facilitates quantitative measurements of a few species, this aspect of kinetics is often forgotten. Nevertheless, when one is faced with the issue of the decomposition of a complex molecule, this problem cannot be neglected. In this context, the capability of single-pulse shock tube studies to detect all products formed in the course of particular reaction with well-established analytical methodology represents a powerful mechanistic tool, especially when certain products are not detected. Obviously, if a molecule is a characteristic product of a certain pathway, its absence is the strongest evidence for the unimportance of such a reaction channel. However, such a finding is not completely unambiguous; the molecule could have been destroyed in the course of the work. From a mechanistic point of view, not having to worry about surfacegenerated processes is a tremendous advantage. Surface processes are much less understood than those occurring in the gas phase. If such processes make contributions, it will usually be necessary to consider transport phenomena. Obviously, products from surface reaction must diffuse to the main part of the reacting gas mixture. Single-pulse shock tube studies are completely analogous to static reactor investigations but are mechanistically less complicated. The added advantage, as will be developed below, is the extremely short heating time. The main complication from shock tube experiments is that of deciding whether products are formed through a series of radical-induced decomposition, or directly as a consequence of a single unimolecular or a series of unimolecular processes, or a combination of all the possibilities. Particularly if one wishes to obtain quantitative results, this remains a formidable task. Nevertheless, there are a variety of means m t h r o u g h the addition of inhibitors or initiators or varying reaction conditions over large ranges--for resolving such ambiguities. These techniques are especially pertinent for single-pulse shock tube applications, where concentrations can be easily varied over wide ranges. For example, the addition of sufficiently large quantities of radical inhibitor can often alter the nature of the reaction products or drastically lower rate constants. The invariance of the yields of a particular product in the presence of radical inhibitors gives very satisfactory evidence for the involvement of a direct unimolecular reaction channel. The addition of a source of radicals can indicate what compounds arise from radical-induced decomposition. In making decisions regarding mechanisms, increasing knowledge on the nature of chemical reactivity in the gas phase also plays an important role. It

16.4


119

should be noted that with a complex molecule it is not really feasible to experimentally eliminate all possible reaction channels. Instead, recourse is made to the body of past kinetic and thermodynamic properties that indicate which are the most likely or unlikely pathways. The role of the experiments is then to differentiate between the various possibilities. All of these issues are strongly influenced by the analytical methodology and the treatment of the data.

1 6 . 4 . 3 . 2 ANALYTICAL METHODS 16.4.3.2.1 Gas Chromatography: Determination of Product Concentrations The most commonly used analytical tool in the operation of the single-pulse shock tube is the gas chromatograph, using a variety of detectors such as FID (flame ionization detector), NPD (nitrogen/phosphorus detector), MSD (mass selective detector), TCD (thermal conductivity detector) and others, depending on the compounds to be analyzed. Whereas peaks are normally identified by their retention times on various gas chromatographic columns, the help of an MSD is very often needed for ultimate identification. Gas chromatograms of postshock mixtures contain peaks corresponding to the various products obtained as a result of shock heating and what is left of the reactant. However, to determine extent of reaction, the peak area of the reactant behind the reflected wave prior to shock heating must be known. There are in principle two methods by which this information can be obtained. In one method, the peak area is determined separately in a chromatogram of the unshocked sample and the peak height is then normalized to the pressure at which the postshock sample is introduced into the gas chromatograph. Since, however, there are changes in the sensitivity of the GC detectors from one chromatogram to another and gas originating from the driver section can be mixed with the postshock gas, such a procedure can introduce considerable error and scatter in the data. In the second method, the determination of the product concentrations and the reactant in each experiment is based on a single chromatogram. The peak area of the reactant prior to shock heating is calculated from the sum of the normalized peak areas of the reactant and products. This method is based on the assumption of a complete mass balance. This assumption, which is not always correct, must be verified. In cases where it does not exist, an error may be introduced.

120


The concentrations of the reaction products C5(pri) using the single chromatogram method are calculated from their GC peak areas from the following relations (Lifshitz et al. 1987a): Cs(Pri) = A(Pri)t/S(Pri) x (Cs(reactant)o/A(reactant)o) Cs(reactant)0 = Pl • %(reactant) • (ps/Pl)/lOORT1 A(reactant)0 -- A(reactant)t + 1/n c ~

N(pri) x A(Pri)t/S(pri)

In these relations n c is the number of carbon atoms in the reactant molecule, C5(reactant)0 is the concentration of the reactant behind the reflected shock prior to decomposition, and A(reactant)0 is the calculated GC peak area of the reactant prior to decomposition, where A(pr/) t is the peak area of a product i in the shocked sample, S(pr/) is its sensitivity relative to the reactant, and N(pr/) is the number of its carbon atoms. Ps/PI is the compression behind the reflected shock and T 1 is the temperature of the shock tube. The typical gas chromatograms shown in Fig. 16.4.4 were taken from a study on the decomposition of 4-methyl pyrimidine. The GC analysis was performed on two detectors, an FID (upper trace) for all carbon-containing products and an NPD (lower trace) for compounds containing C - N bonds, for which the latter is much more sensitive (see the caption for peak identification). The chromatograms taken on the two detectors are combined to one chromatogram using the reactant peak or a peak of a high-concentration product as a standard. 16.4.3.2.2 Hidden Peaks: GC-MS There are cases where reaction products cannot be separated on the GC columns and assistance of a gas chromatography-mass spectrometry (GC-MS) becomes necessary. A problem of this nature and its solution can be seen in the study of the thermal decomposition of 2-methylfuran (kifshitz et al. 1997b). In this study the reaction products 1-butyne and 1,2-butadiene could not be separated from the large peak of vinylacetylene (C4H4) and were hidden behind it. These two C4H 6 isomers were discovered in a series of experiments using GC-MS. In Fig. 16.4.5, such chromatogramsmwith m/z 54, 53, 39, and 27, which are characteristic to C4H6 isomers, and m/z 52, characteristic to C4H4m are shown. As can be seen, there are two peaks, slightly separated, of C4H6 hidden behind a large peak of vinylacetylene. These two peaks were identified as 1,2-butadiene and 1-butyne. The identification was based on the relative heights of m/z 39 and 54, which differ considerably in these two isomers (Royal Society of Chemistry 1991; Stein 1998). This method, which uses the SIM (selected-ion monitoring) mode of the GC-MS, has been used successfully in other studies as well (kifshitz et al. 1998, unpublished d).

16.4

121

Single-Pulse Shock Tube /J

140

(s)

-(5)

i

>

E

105

(1)

)

1

~

(201

-

| c: ~

70

i

1 (2)

FID 1

Ii

(2)

35 (!) 13.

1 I

23a4 I

t

I

I

I

b I

1

I

0

I

56

I

t

!

[

I

!

I

1

10

1

|

1

m

I

I

1

I

I

I

1 /J

20

30

/I

I

1 a I

40

I

I

50

I

I

J

60

Retention. time (min) .

250

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

, ;,//it"

(2)

200

(41

.c:

(i)

NPD

1

(4)

100

:40)

jL_ 0

2,,

! 3 4 5,

6 ,

7, ,

10 t

15

20

25

11 !

30

I

,/j,,,,

35

45

12 55

Retention time (min) FIGURE 16.4.4 Gas chromatograms of a postshock mixture of 4-methylpyrimidine taken on FID md NPD detectors. The numbers on the peaks indicate multiplication factors. The reactant was ;ubjected to shock temperature of 1296 K. The list of products is as follows: 1. FID: 1, methane; 2, ethylene; 3, ethane; 4, acetylene; 5, allene; 6, propyne; 7, hydrogen cyanide; 8, cyanoacetylene; 9, acetonitrile; 10, acrylonitrile; 11, propylnitrile; 12, (cis, trans) crotonitrile, vinylacetonitrile; 13, pyrimidine; 14, pyrazine; 15, methylpyrimidine; (a) and (b) are the peaks of the internal standard: (a) 1,1-difluoroethylene, (b) 1,1,1-trifluoroethane 2. NPD: 1, cyanogen; 2, hydrogen cyanide; 3, cyanoacetylene; 4, acetonitrile; 5, acrylonitrile; 6, propylnitrile; 7, cis crotonitrile; 8, vinylacetonitrile; 9, trans-crotonitrile; 10, pyrimidine; 11, pyrazine; 12, methylpyrimidine.


122

120

~100

m r

~

C4H4 (m/z)=52

!!i 'i

'1 ~3IBUtadlene

/A\ /

12 2- Butyne/~

10

80

m

-

i

|

/AI

c m

] t ~ It 1 , 2 - B u t a d i e n e

o 60

[

. . . .

27

i i

,',\1

~ 4O |

line m/z 54 . . . . . 53

/"

/ ~'' ,"" \)!!,:,1 ,Z

/c~,

~

/

~ 1-Butyne

ij}'

?0

'

O. !

17.0

17.5

18.0

18.5

19.0

19.5

Retention time, min FIGURE 16.4.5 GC-MSchromatogram using the selected-ion monitoring mode of the mass selective detector. Peaks of 1,2-butadiene and 1-butyneare hidden behind a large peak of C4H4and can be analyzed only with the assistance of the GC-MS. (See Color Plate 1).

16.4.3.3

T R E A T M E N T OF DATA

16.4.3.3.1 Product Distribution The experimental product distribution in the postshock mixtures is the most important piece of information obtained in the study of any reaction system. This information is essentially the concentration (mole percent) of the products at different temperatures. It is obtained from the experimental gas chromatograms, an example of which was shown in Fig. 16.4.4 for the decomposition of 4-methyl pyrimidine. The method by which the concentration of each product is evaluated from the areas under its corresponding peak in the gas chromatogram was discussed in the preceding section. The product distribution obtained in the study on the decomposition of tetrahydrofuran is shown, as an example, in Fig. 16.4.6 in the form of mole percent vs temperature (Lifshitz et al. 1986a). As will be discussed later, plots of mole percent vs temperature form the basis for computer simulation of the overall decomposition process.

16.4.3.3.2

Arrhenius

Parameters

Another way of presenting the experimental results is an Arrhenius plot of the production rates of the various decomposition products. Figures 16.4.7 and

16.4


123

100 ! . . . . . |

t0

.~\~

~

:

,

,

9

0.25% THF in argon ,0, = ! 00 Torr CO

"~

i

, t~ e-

6O

27 32

40 30

t-

20

tO

o

.>

26

29

25 "11

I,

i

,

I, I,

|

31 |,

[C2HJI[C2DJ=1.65 80-

|

(b)

28

.,..,. t...,=

60-

C2D

C2H4

E

40

C2DH 3

20 0

24

29 |

27 I

26

4

32

1

28

, 30

C2DaH 31 I 32

m/z FIGURE 16.4.11 Isotopic distribution of ethylene in postshock mixture of 50% THF and 50% THF-d8 diluted in argon. The upper diagram (a) shows the original GC-MSspectrum. In the lower diagram (b) only the parent ions are left. The intense peaks of C2H4 and C2D4 verify the assumption that the ethylene molecule retains the skeleton of the original tetrahydrofuran molecule.

131

16.4 Single-Pulse Shock Tube

and C2H4 + are known, one can remove the daughter ions from the spectrum and leave only the parents. In Fig. 16.4.11b, the spectrum contains only parent ions after removing all the peaks that belong to the daughter ions and peaks at m/z 28 and 32 coming from the air background. Separating N2 and 02 from the spectrum also requires a high-resolution mass spectrometer; however, the mass difference between C2H 4 and N2 and between C2D 4 and O2 is much larger than that of C2D2+ and C2H4. As can be seen, the peak at m/z 30 that is present in Fig. 16.4.11a disappears completely in Fig. 16.4.11b since it corresponds to the species C2D3+ (62% of the parent C2D4+). Some residues of m/z 29 and 31 are still present due to either small isotope exchange or some deviation from the published cracking pattern, which is somewhat instrument dependent. These results clearly show that both ethylenes preserve the original skeleton of the tetrahydrofuran and are thus formed by unimolecular ring cleavage and not by free radical reactions. After establishing the fact that ethylene is formed directly by ring cleavage, it still must be determined from what locations in the ring it is eliminated: It can be formed via elimination from tetrahydrofuran at the 2-3 (or 5-4) positions or from the 3-4 positions.

OH2

)~

OH2 > OHm- CH~ + (CH2-CH2-O)

C . ~ ~

CH=

CH2

> C H2= CH2 + (CH2-O-CH2)

To clarify which channel is operative, a mixture containing 3,3,4,4-tetrahydrofuran-d4 in argon was shock heated. Elimination of ethylene from the 3-4 positions leads to the production of CD2--CD2

OH=

OH=

.~ C D2= CD2 * (CH~,-O-CH2)

whereas elimination from the 2-3 (or 5-4) positions leads to the production of a scrambled ethylene, CD2--CH2.

Cu/~4~-~3~ D2 CH~/,5~ I ' ~ C H ~

> CD2- CH2+ (CD2-CH2-O)

132


loo F

30

(a)

sof E

28

60.

i

e-

40

.E

2(1

e,o (I) >

0

.w,

27

29

26 l,

31

,L

I,

'

[C2D2H2]I[C2D2] ~ 2.2

30

8(1

ID L_

32

-

,

/,

(b)

C2D2H2

617

32

40

20

C2DsH C2D4 27 ,

0 24

'

26

29

|

,

31

II

28

30

32

34

m/z FIGURE 16.4.12 Isotopic distribution of ethylene in postshock mixture of 3,3,4,4-tetrahydrofuran-d4 in argon. The upper diagram (a) shows the original GC-MS spectrum. The lower diagram (b) shows that only the parent ions are left. The intense peaks of C2D4 and C2H2D2 show that ethylene is formed by elimination from both 2-3 (4-5) and 3-4 positions.

The results of these experiments are shown in Fig. 16.4.12. In Fig. 16.4.12a, the original GC-MS spectrum is shown. In Fig. 16.4.12b, the spectrum after removing the air background and the peaks resulting from the cracking pattern of C2D4 + and C2D2H2+ is shown. As can be seen, both molecules are present, which means that both channels take place. The ratio of CD2=CH2 to CD2=CD2 is roughly 2:1, indicating that their rates are practically identical except for a statistical factor of two as there are two ways to produce CH2=CD2 (2-3 and 4-5) and only one way to produce CD2=CD2 (3-4). 16.4.4.2.2 Free Radical Scavengers An additional method to assess the extent of free radical involvement in the production of a specific product is the use of free radical scavengers. The most commonly used scavenger in the single-pulse shock tube research is toluene.

+R" ....

---->

+RH

133


Its function as a free radical scavenger is based on the very high stability of the benzyl radical that is formed by abstraction of a hydrogen atom from its methyl group by an active radical such as H ~ OH ~ CH3 ~ etc. The benzyl radical, which is a very stable and unreactive species, does not react at all in the time frame of the single-pulse shock tube regime. At high temperatures, however, the decomposition of toluene shown here might add free radicals to the system so that there is a temperature limit in the use of this particular scavenger.

OH3

[~~"

Toluene has been used as a scavenger in several single-pulse shock tube studies. Typical examples are the studies of the thermal decomposition of isoxazole (Lifshitz and Wohlfeiler 1992a) and 5-methylisoxazole (Lifshitz and Wohlfeiler 1992b). These molecules are five-membered ring heterocyclic compounds with nitrogen and oxygen as heteroatoms. c.

Their thermal decomposition was studied in the temperature range of 8501100 K, where the decomposition of toluene in the time scale of 1-2 ms is negligible. In both cases the main products in the decomposition are nitriles, acetonitrile (CH3CN) in isoxazole and ethylnitrile (C2HsCN) in 5-methylisoxazole. As major products of the decomposition, it can be assumed that they are formed directly by ring cleavage (either by one or two steps).

HC~c

CH3CN+ CO

C2HsCN+ CO However, to examine the extent of free radical involvement in the formation rate of these two products, mixtures containing a large excess of toluene {[toluene]/[isoxazole] ~ 10 and {[toluene]/[5- methylisoxazole] ,~ 10} were prepared and the results were compared to runs without toluene. As can be

134


I 101

_ 9 - without

toluene w-I

o - with toluene =.--,

x o t~ p..-,

Z

10 ~

0 "i" 0 1 0 -1

900

950

1000

1050

T (K) FIGURE 16.4.13 Ratios of [CH3CN]t/[isoxazole]t at different temperatures with toluene at a ratio of [toluene]0/[isoxazole] 0 = 10 and without toluene. The production rate of CH3CN is independent of the presence of toluene, indicating that it does not involve free radical reactions.

seen in Figs. 16.4.13 and 16.4.14, the data points with and without toluene coincide, showing no effect of the latter on the production rate of acetonitrile from isoxazole and ethylnitrile from 5-methylisoxazole. This is a clear indication that they are formed by unimolecular reactions directly from the reactant molecules.

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135

Reaching a conclusion regarding the mechanism is more complicated for the production of acetylene and hydrogen cyanide from isoxazole. Both can in principle be produced by a direct elimination from the ring, as shown here,

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but both can also be produced by successive free radical reactions. HCN, for example, can be formed by a dissociative attachment of a hydrogen atom to acetonitrile, which, as mentioned earlier, is the main decomposition product of isoxazole: CH3CN + H" ~ HCN + CH3 ~ The effect of toluene on the production rate of C2H2 is shown in Fig. 16.4.15, where the ratio [C2H2]J[isoxazole] t is plotted in arbitrary units on a logarithmic scale against the reflected shock temperatures for tests in mixtures containing 0.1% isoxazole and 1% toluene in argon and 0.1% isoxazole without

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T(K) FIGURE 16.4.15 Ratiosof[C2H2]J[isoxazole]t at different temperatures with toluene at a ratio of [toluene]0/[isoxazole]0- 10 and without toluene. The production rate of C2H2 is strongly dependent on the presence of toluene, indicating that its production mechanism involves free radical reactions.

136


toluene. The figure shows a large effect of toluene on the production rate of acetylene; it is reduced by more than a factor of 3, indicating that free radical reactions are an important factor in its formation. The concentration of HCN (not shown) was found to be affected to a much lesser extent by the presence of toluene. This means that both unimolecular elimination and (probably) the reaction CH 3CN + H ~ -~ HCN + CH3 ~ play a role in its production.

1 6 . 4 . 4 . 3 COMPUTER SIMULATION 16.4.4.3.1 Reaction Schemes and Modeling To model an observed product distribution, one must construct a reaction scheme, which in most cases contains a large number of species and elementary reactions. After the scheme has been constructed, the computer experiments are performed in the following way. The kinetics scheme is numerically integrated under the same initial conditions as those used in the laboratory experiments, to yield concentration time history. The concentration of each product at a time equal to the experimental dwell time is obtained from the calculations, and a product distribution for a given temperature is constructed. The calculations are carried out at different temperatures so that the product distribution as a function of temperature can be obtained. Calculations at different compositions can also be done. There are a number of "experimental conditions" under which a set of coupled differential equations representing an overall kinetics scheme can be numerically integrated: under constant density, under constant pressure, or more precisely coupled to the shock equations. The latter is very cumbersome and requires considerable, and sometimes inaccessible, computer time. However, if the temperature change during the dwell time is small, which is true when small reactant concentrations are being used, the integration of the reaction scheme coupled to the shock equations is unnecessary. The second best choice is the use of a constant density assumption. Here the shock equations are solved without the chemistry to establish the initial conditions behind the reflected shock, and the kinetics scheme is then numerically integrated starting at these conditions. There are several codes available for numerically solving a set of coupled differential equations. All use the Gear integration algorithm. The most commonly used code is Chemkin-II, "A Fortran Chemical Kinetic Package for Analysis of Gas Phase Chemical Kinetics," (Kee et al. 1992), but there are many other codes as well. The ability to perform simulation experiments depends very much on the ability to compose a suitable reaction scheme and on the availability of correct


137

rate parameters. Too many guessed rate constants and the omission of "important" elementary reactions make the simulation a hard task to perform. An example of a scheme describing the thermal decomposition of 2,5dimethylfuran is shown in Table 16.4.2 (Lifshitz et al. 1998). This particular scheme contains 50 species and 181 elementary reactions. The rate constants listed in the table are given as k = A exp(-O/T) in units of cm 3, mo1-1, and s -1. Column 1 lists all the elementary reactions in the scheme, column 2 gives the preexponential factors, and column 3 gives the activation energy (E/R) of each reaction. In some cases, where curvature in the Arrhenius plots exists (normally when the rate constants are given for a wide temperature range), the preexponential factors are expressed as A' x T n. Columns 4 and 5 give the rate constants of the forward and the back reactions calculated at 1250 K, and columns 6 and 7 give the standard enthalpy AH~ and entropy AS~ of the particular elementary reaction at the same temperature. The rate constants of the back reactions are calculated from the rate constants of the forward reactions using the relation kr = kf/Keq, where Keq is the equilibrium constant of the particular elementary reaction. This constant is calculated from the thermodynamic properties of the species that participate in the reaction using the relation Keq- e x p ( A S ~ 1 7 6 (RT) -av, where Av is the change of the number of moles in the reaction. The Arrhenius parameters for unimolecular reactions, such as isomerizations and others, are determined directly from the rate of production of these products. The other reactions in the scheme are either estimated or taken from various literature sources such as the NIST-Kinetic Standard Reference Database 17 (Westley et al. 1998) and other compilations (Warnatz 1984; Atkinson et al. 1999; Baulch et al. 1994; Wang and Frenklach 1994, 1997; Miller and Bowman 1989; Tsang and Hampson 1986). The parameters for the reactions that are taken from the various compilations and from the NIST-Kinetic Database are, in many cases, a best fit to a number of entries. The thermodynamic properties of the species are taken from various literature sources (Stull et al. 1969; Pedley et al. 1986; Melius 1999; Burcat and McBride 1997; Burcat 1999; Stein et al. 1994, 1998; Tsang and Hampson, 1986) or estimated by various methods including the NIST Standard Reference Database 25 (Stein et al. 1994) (Structure and Properties program, SP). In most of the decomposition studies, where very low reactant concentrations are being used, the system is not very sensitive to the precise values of the equilibrium constants. This behavior has been demonstrated in sensitivity studies, as will be discussed later. Figure 16.4.16 shows the overall decomposition of 2,5-dimethylfuran (Lifshitz et al. 1998) expressed as mole percent vs temperature. The data points are the experimental results and the line is the best fit to the calculated points (+) taken at 25-K intervals. Figures 16.4.17-16.4.21 show comparisons

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T (K) FIGURE 16.4.16 Experimental and calculated mole percents of 2,5-dimethylfuran, showing its total decomposition. The symbols are the experimental points and the lines are the best fit through the calculated points shown here as crosses.

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148


between the experimentally measured yields and the calculated yields using the reaction scheme shown in Table 16.4.2. The agreement for most of the reaction products is satisfactory considering the large number of products obtained in this decomposition. 16.4.4.3.2 Sensitivity Analysis To establish a better agreement between the computed and the experimental product distribution by varying estimated rate parameters, a sensitivity analysis of the specific reaction scheme is run. Rate parameters of all the elementary reactions in the scheme are systematically varied by an arbitrary factor, and the effects of such variations on the concentration of the products are examined. The sensitivity factor in this case, Sij, is defined as

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Table 16.4.3 shows that only a relatively small number of elementary steps affect the product distribution in the sense that their elimination from the scheme affects the yield of at least one product. The majority of the elementary reactions that compose the scheme do not affect the distribution at all. They are normally left in the kinetics scheme for completeness and applicability beyond the temperature range of a given series of experiments. It should be mentioned, however, that the sensitivity analysis is performed by removing a single reaction at a time. When a group of reactions is eliminated from the scheme, there can be a strong effect on particular products even though the elimination of only one step, as shown in the table, does not have an effect. Most of the sensitivities that appear in Table 16.4.3 are self-explanatory. They enable one to follow the sequence of steps that lead to a particular product. Cyclopentadiene, for example, is formed by reaction 126 and is turned off completely when this reaction is removed. However, if either the main channel for the formation of CH3(C4H20)CH 2" (reaction 17) or its decomposition to C H 2 = C H - C H - - C H - C H 2 ~ and CO (reaction 40) are removed from the scheme, the yield of cyclopentadiene drops almost to zero. This indicates that the formation sequence of cyclopentadiene is R17--~ R40---~ R126. Many similar examples can be found by examining the sensitivity data shown in the table. In conclusion, the sensitivity analysis of a complex kinetics scheme where there are many parallel routes for product formation and many consecutive steps is a necessary procedure. Without it, it is almost impossible to understand the overall reaction mechanism.

16.4.5

SINGLE-REACTION

STUDIES

16.4.5.1 J U S T I F I C A T I O N We will now describe the determination of rate constants and expressions of single-step thermal reactions with high accuracy. As a preliminary, it is necessary to consider the nature and need for such properties. Single-step thermal reactions are processes involving the interaction of molecules in Boltzmann distributions. The reason for the interest in thermal reactions is that they represent the lowest-level kinetic property related to theory. Thus accurate expressions can form the basis for predictions, extrapolations, and interpolations. Indeed, accurate kinetic data of this type also form the basis for determination of the thermodynamic properties of unstable reaction intermediates. Under certain high-temperature conditions, the distribution functions are perturbed. However, the means to treat such situations are increasingly well established. Practically, this means that it may be necessary

16.4


153

to adjust the thermal rate constants from shock tube studies to reflect the physical environment. The need for such capabilities originate from the well-known fact that the high-temperature behavior of polyatomic molecules under combustion or pyrolytic conditions can be extremely complex in terms of the multiplicity of single-step reactions. The modern tendency is to try to describe the overall reaction or global process using these single-step reactions as the input data for computer programs that increasingly can reproduce the phenomenon of direct interest. The multiple-reaction studies described above are one aspect of such work. The rationale for such an approach, in contrast to the more traditional empirical approach of developing correlations of the observed temporal behavior of reactants and products for the system of interest, arises from the much wider applicability of the more fundamental approach. One cannot yet faithfully describe a complex process purely through computer simulation. Instead computer simulation represents a technique that can aid in the conceptualization or optimization of a process and it is in fact the first step of an iterative procedure where simulations and experiments go hand in hand. The emphasis on theory originates from the fact that for the simulation of any system scores of chemical reactions must be considered. It is patently impossible to determine the mechanisms and rates of reaction of all the processes under the desired conditions. Hence theory is needed to provide large portions of the database. Obviously, for any given overall process all reactions are not equally important. However, as a first cut it is important not to neglect any possible process. Then through the use of sensitivity analysis subroutines in the simulation packages one can describe the overall process in terms of the key reactions. As the physical and chemical environment is changed, the relative importance of particular reactions may also be changed. The thermal rate expressions that are determined can be used directly to extract the properties of the transition state (Benson 1976). Thus from the standard rate expression one finds that

k = kT/h exp(AS+/R) exp(-AE+/RT) where AS+ and AE + are the entropies and energies of activation, respectively. It should be emphasized that high-pressure rate expressions represent the only means of experimentally determining such properties of the transition state. Such expressions are of special importance for developing correlations and as a check of the validity of results of ab initio calculations from programs such as Gaussian. In addition, if the rate expression for the reverse process is known, then it will be possible to determine the thermodynamics of the overall process. Alternatively, if the thermodynamics are known, then kinetics data in one direction leads to the rate expression for the reverse. The breaking of carbon-carbon bonds is the initiating reaction in many combustion and pyrolysis processes. There is also considerable data on the rate

154


expressions for the reverse radical combination process. Combination of the two sets of rate expression leads to the thermodynamic properties of the radicals that are formed during decomposition. Of particular importance are their heats of formatj0n, which are fundamental to any understanding of their reactivity. For malJy years the heats otr formation of organic radicals were thought to be well established (McMillen and Golden 1982). As will be seen below, the results from single-pulse shock tube studies demonstrate that there were in fact serious systematic errors in the generally used heats of formation. This finding led to a variety of new experiments that completely validated the shock tube results and resolved many long-standing problems dealing with the internal consistency of the databases. In the following section, we describe the type of reaction kinetics that the single-pulse shock tube method is uniquely qualified to study. At the fundamental level practically all chemical kinetic processes can be divided into unimolecular and bimolecular processes. In the former category, molecules are excited by collisions until the first or several decomposition channels are accessed. If energy transfer by collisions is sufficiently rapid, then the Boltzmann distribution will be maintained at all times. The decomposition will then be truly unimolecular with the rate constants being pressure independent. If energy transfer effects are present, unimolecular rate constants will be pressure dependent. Since the fundamental quantities are the highpressure rate constants and quantities defining energy transfer, it will be necessary to convert the measured rate constants to these quantities. However, if this is overlaid by other decomposition processes--for example, possible contributions from radical mechanisms--it becomes virtually impossible to make such conversions. The resulting data becomes extremely difficult to extrapolate to different pressures. Thus only if the individual unimolecular reaction can be isolated can one confidently carry out such extrapolations.

1 6 . 4 . 5 . 2 EXPERIMENTAL CONFIGURATIONS The conditions necessa~ for the determination of high-quality kinetics data of the type described above are fairly obvious. One would like a situation where the only process that can occur is the reaction of interest. If this is not achievable, then one should at least understand or have an estimate of the contributions from possible competitive processes. We mentioned earlier the intrinsic advantage of shock tube studies being almost completely independent of surface processes, the lessened importance of radical-induced decomposition, and in any case the possibility of suppressing the latter. We illustrate the latter by the following rough calculations. Consider a typical single-pulse shock tube experiment operating at a temperature of 1100 K, 2 bar pressure of

155


argon and with a heating time of 500 gs. Under such conditions it is easy to calculate that any molecule will suffer approximately 3 million collisions. The consequence is that a compound at the 0.3 ppm level can suffer only 1 collision with a product from its decomposition. This demonstrates the value of the short heating time in the sense of reducing the possibility of long chains. Furthermore, very few chemical reactions proceed on every collision, thus the same effect can be realized at considerably higher concentrations. This inhibiting effect can be further amplified through the addition of a radical scavenger, which was discussed in an earlier section. Here, a more quantitative approach is used. The present aim will be to indicate the concentrations necessary to ensure all radical contributions are suppressed. For many of the studies, methylated benzenes have been used. The reactions they undergo are R ~ + C6HsCH 3 =:} RH + C6HsCH2" =~ CH3 ~ + C6HsR CH3 ~ + C6HsCH 3 =~ CH 4 + C6HsCH2 ~ where C6H5 is a phenyl group, C6HsCH2 ~ is a benzyl radical, and R~ is any reactive radical. For our purposes, the primary concern is the hydrogen atom and methyl radicals. The overall effect is to convert reactive radicals into less reactive benzyl radicals. The lessened reactivity of the benzyl type radical is brought about by its resonance stabilization, which lowers the b e n z y l - H bond energy by nearly 50 kJ/mol. In the short time of a single-pulse shock tube experiment and working with appropriately small concentrations of the target molecule, there is simply no time for resonance-stabilized radicals such as benzyl to attack the molecule being tested. Thus the only reaction a target molecule can undergo is unimolecular decomposition. The benzyl radicals that are formed will largely recombine with themselves or with other radicals that may be present. It should be noted that radical combination reactions are known to be fast and largely unaffected by resonance stabilization. With such a scenario, the benzyl radical is itself a radical scavenger. The amount of scavenger needed to bring about substantial scavenging of the radicals depends on the relative rate constants of radical attack on the benzylated and test molecules. We have found that ratios of 50:1 to 100:1 are sufficient. The actual amount needed can be readily established by carrying out experiments with different ratios and observing the situation when the unimolecular decomposition rate constant becomes invariant. Frequently, the products from a chain reaction may be different than that from the unimolecular decomposition. This makes the appropriate ratio particularly easy to determine.

156


Figures 16.4.22 and 16.4.23 show modeling results on the decomposition of neopentane that illustrate some of the issues discussed here. The rate constants used in the simulation are listed in Table 16.4.4. The results in Fig. 16.4.22 give an indication of the concentrations of various species of concern. Note the relatively larger amounts of the benzyl-type radicals in comparison to the methyl and especially hydrogen atoms. From Fig. 16.4.23 it can be seen, as expected, that progressively larger amounts of the inhibitor leads to decreasing rate constants of neopentane disappearance or isobutene appearance until a

le+1 Mesitylene

le+O le-1

Neopentane

le-2

Isobutene

Methane

Dimesitylene

le-3

m-Xylene

le-4 le-5 r

Mesityl

o '1~

le-6

o :E

le-7

__

t-Butyl Ethyl-dimethylbenzene

le-8 le-9 Methyl

le-10 le-ll

Ethane

le-12 le-13 le-14

.... 100

,

,

200

300

'

,

' ..........

400

, 500

.....

, 600

700

time (l~sec)

FIGURE 16.4.22 Temporalconcentration of reactants, intermediates, and products during the decomposition of 100ppm neopentane in 1% mesitylene at 1250K and 2bar pressure as determined from simulations using data from Table 16.4.4.

16.4

157

Single-Pulse Shock Tube 0.5 w ~ 9 ,,,,=,,

0.4 2

"~ 0.3 c 0

:= 0.2 0.1 ~"

)0

=

i'"

|

|

|

200

300

400

500

600

700

time (psec) FIGURE 16.4.23 Fractional yields (in terms of isobutene formed) during neopentane decomposition as a function of relative quantities of mesitylene/neopentane ratio as determined from simulations using data from Table 16.4.4.

minimum value is reached. Although there may be considerable uncertainties in the rate constants used in these simulations, the results in Figs. 16.4.22 and 16.4.23 are useful in setting guidelines for the relative quanitities of the scavenger and target molecule necessary to achieve accurate results. The general procedure for using radical scavengers to isolate unimolecular reactions was originated by Szwarc (1950). Unfortunately, the rate expressions that he obtained are now known to be in error. This is largely due to the fact that in the flow system used by Szwarc the actual temperatures and heating times were improperly estimated. This led to rate expressions whose rate parameters were much too small. In addition, the ratios of scavengers to test molecules were frequently not large enough, which led to additional errors. An obvious requirement is that the stability of the scavenger be substantially larger than that of the test molecule. Thus there are molecules for which the methylated benzenes are not suitable as scavengers. For such cases we have even adopted methane as the scavenger. Here we make use of the fact that methyl radicals are not particularly reactive in the context of the short heating time of single-pulse shock tube experiments. Thus methane is highly stable and at sufficiently low concentrations of the test molecule it will not be able to abstract a hydrogen (Tsang and Cui 1990). In the case where radicals are formed, it is very important to establish the ultimate fate of the radical since these are not detected from the final product analysis. This can lead to complications in the case where the radical lifetimes are as long as the heating times or longer. A particularly simple situation occurs if t h e lifetimes are much shorter than the heating time where the decomposition products include at least one stable molecule. This is the case for many non-resonance-stabilized organic radicals. For such compounds lifetimes are on the order of a few microseconds under single-pulse shock tube conditions. Thus quantitative conversions can be expected. More thermally stable radicals such methyl or resonance-stabilized species can be expected to appear in the final product analysis as compounds formed from

158

i,,-4

!

,,-i

-.....

o~ ~

09

~

+

a

t

.

~.~

~

+ +

++

~

+

~

~+++

, ~

,'-~

,::,


>

~.~

e~

e~

~ ' ~

+

~

N

~

~

+4-++


159

combination reactions. It should be possible to trap the more reactive radicals with hydrogen donors and use the products as measures of reactions. In fact, this has been done for perfluoromethyl and phenyl radicals with cyclopentane as the hydrogen donor (Tsang 1986; Robaugh and Tsang 1986a). 16.4.5.2.1 Unimolecular Reactions

The comparative rate technique was developed for use in the determination of rate constants for unimolecular decomposition. Most of the experiments have been carried out in this area. In the following, we give a typical example. Figures 16.4.24 to 16.4.26 contain data on the decomposition of 1,7-octadiene (Tsang and Walker 1992). The concentration determinations are summarized in Fig. 16.4.24. The important observation is, except for in allene, the invariance of yields as a function of the inhibitor-to-reactant concentration ratio. The reason for the variation of the allene concentration is that the allyl decomposition reaction is in the kinetic region for the timescale of these experiments. Indeed, the study of the stability of the allyl radical was the main thrust of the work. Note that although there is indeed a small effect on the 1,5hexadiene concentration; most of the allyl radical recombines. Thus the allyl decomposition process is manifested to a much lesser degree in the concentration of this combination product. The general mechanism is summarized in Fig. 16.4.25 and is completely consistent with the nature of the product distribution given in Fig. 16.4.24. For the present, we will concentrate on the initial decomposition process, the results of which are shown in Fig. 16.4.26. It can be seen that the data show a minimal amount of scatter. This is to be expected since all the results are traceable to gas chromatographic measurements. The rate expressions are as follows" k(1,7-octadiene - allyl + 4-pentenyl) - 1.2 4- 0.8 • 1016 exp(-35,700 4- 400/T) s -1 k(1,7-octadiene - propene 4- 1,4-pentadiene) - 3 4- 1.5 x 1012 e x p ( - 27, 900 4- 270) s -1 The uncertainties are the statistical variations and are in the range of factors of 1.5 in the A-factor and 2-4 kJ/mol in the activation energy. Also included in Fig. 16.4.26 are the rate constants for the decomposition of hexene-1 (Tsang 1978c). It can be seen that, except for the reaction pathway degeneracy, the rate constants are very close to each other. This is one of the great advantages of the comparative rate technique. The physical uncertainties cancel out and it is now possible to make intercomparisons between rate constants for different molecules and thus derive correlations that can lead to accurate estimates.

160


E ~

"o

1,7octadiene

A

AA6

0 l9 9 ethylene

2

9 9

Q. X

9

0 0 y--

I

0 ._J

-2 1040

9

~

I

[]

9 O

[]

D" 1,4pentadiene ,-~ o~ O i

o

"o

0

O 9

O

O O

O 9

cyclopentene

e

r

i

1060

1080

.... ~

[

1100

[. . . . .

1120

1140

i

,

1160

1180

1200

Temp(K) e-

2

"a m

1

1,5 hexadiene

V

~:7

V

0 r~.

9 0

O 9

O

9 Q.

9

allene

21

X

0 0

-2

0 _J

-3

y.-

1040

|

1060

~

v

J

i

i

1080 1100 1120 1140 1160 1180 1200 Temp(K)

FIGURE 16.4.24 Fractionalyields of products from 1,7-octadiene decomposition as a function of temperature. Hollow symbolsml00ppm 1,7-octadiene in 1% mesitylene. Solid symbolsm 100ppm 1,7-octadiene in 1% mesitylene. Pressure- 2.5 bar. The comparative rate m e t h o d is of course not a panacea for all m e a s u r e m e n t problems in single-pulse shock tube kinetics. The requirements for isolation of reactions from each other was mentioned earlier. All the requirements for "good practice" must still be observed. For example, the cool b o u n d a r y layer and unreacted gases in the sampling tubes leads to a "dead space." Thus it is probably good practice to carry conversions to no more than 50% to 60%. As noted earlier, since the residence time is not easily changed, there is the temptation to carry out reactions to very high extents of reaction. Failure to

16.4

161

Single-Pulse Shock Tube allene + H

T

allyl + ethylene

allyl + 4-pentenyl

7

\

.i* cyclopentene + H

1,7 octadiene

propene + 1,4 pentadiene allyl + allyl = 1,5 hexadiene FIGURE 16.4.25

Mechanism for the thermal decomposition of 1,7-octadiene.

take this into account can lead to results that show drastic curvatures in the standard Arrhenius plots. This is not to say that Arrhenius plots cannot be curved. Indeed, transition state theory requires a temperature-dependent Afactor and hence curved Arrhenius plots. However, over the limited range of a single set of shock tube experiments curvature is inevitably either an experimental artifact or evidence of multiple-reaction channels.

25 .........,

2.0

I,,,Q

O 1.5-

-....

,

_..J

1.0

-

0.5

i

0.85

i

i

-,...

I

I

0.90

0.95

1.00

1000/T FIGURE 16.4.26 Arrhenius plots for the decomposition of 1,7-octadiene via bond breaking (1,7octadiene ~ allyl 4- pentenyl-4) (square), and retroene reaction (1,7-octadiene ~ propene 4- 1,4pentadiene) (diamond).

162


16.4.5.2.2 H y d r o g e n Atom Attack After determining the mechanism and rate constants for a set of bond-breaking reactions, it is possible to use this as a means of generating radicals to attack other compounds. A key constraint is that the target compound must be much more stable than the radical source. For example, hexamethylethane decomposition has proven to be the most convenient as a source of H atoms. The processes are (t-C4H9) 2 ~ 2t-C4H9 ~ t-C4H9 ~ --+ i-C4H 8 + H ~

(fast)

Thus the isobutene yields provide a means of counting the number of hydrogen atoms released into the system. If the reaction is now carried out in large amounts of another molecule and hydrogen atom reaction leads to a specific product, then the ratio of the concentration of that product to the isobutene yield is a direct measure of the fraction of hydrogen atoms that have reacted with the target compound. Recall that the unimolecular reactions discussed earlier have all been studied in vast amounts of methylated benzenes, thus it is straightforward to study this aspect of the reaction system. A specific example is the reaction of hydrogen atoms with toluene. The reactions of interest are H ~ 4- C6HsCH3 ~ C6H 6 4- CH3 ~ --~ C 6H~ CH2 ~ 4- H2 Thus the yields of benzene are a measure of the importance of the displacement reaction. The difference in the concentration of isobutene and benzene represents the contribution from the abstraction reaction. These results thus establish the branching ratio for hydrogen atom attack on toluene. The results can now be placed on an absolute basis by adding large amounts of methane so as to produce a substantial reduction in the benzene yield. This is due to the removal of hydrogens from the reaction H" + CH 4 -+ CH3 ~ q-H 2 On the basis of the well-established rate expression for this reaction (Tsang and Hampson 1986),

k(H' + CH 4 --+ CH3 ~ +

H 2 ) - 1014 e x p ( - 7 0 0 0 / T ) c m 3 / m o l - 1 / s -1

and making use of the differences of concentrations of benzene formed without methane, the rate constants for the two channels in hydrogen atom attack on toluene can be established. The determined rate expressions for H-atom attack on the methylated benzenes can in turn be used as an intemal standard. This is a particularly useful approach since the demethylated compound is a direct product.

16.4

163


Furthermore, the benzybtype radicals created by abstraction are unreactive and therefore cannot attack the target compound. Some results on the hydrogenatom-induced decomposition on trichloroethylene (Tsang and Walker 1995) can be found in Figs. 16.4.27 to 16.4.29. Note the large number of products in Fig. 16.4.27. Each product represents a particular channel for decomposition. Figure 16.4.28 gives the mechanism for decomposition. The large amounts of hydrogen were added to convert reactive radicals such as C1 to H atoms, thus amplifying the concentrations. The invariance of the results despite the changes in reaction conditions confirms the postulated mechanism and the derived rate constants. Figure 16.4.29 gives rate constant data in terms of the ratio of rate constants for the possible reaction channels with trichloroethylene and that for methyl displacement from mesitylene. The rate expressions are k(H ~ + C2CI3H -- C H 2 C C I 2 + C1 ~

k(H ~ + mesitylene -- m-xylene + H')

= 0.89 -t- 0.2 exp(816 + 122/T)

k(H" + C2C13H - CHC1CHC1 + C1) = 0.55 + 0.1 exp(-691 + 220/T) k(H ~ + mesitylene -- m-xylene + H ~ k(H ~ + C2CI3H -- HCI + ~

= 5.6 4- 1 exp(-3431 + 122/T)

k(H" + mesitylene -- m-xylene + H')

Note again the small statistical uncertainties. As in the case with unimolecular decomposition, also included in Fig. 16.4.29 are comparisons from similar studies. As before, this lays the basis for accurate estimation.

sum

of products

2.0 =,..,-= t-

1,1-dichlorethylene

O3

"o 1.5

2,4 dimethylbenzyl (est)

_

r 0 --t "0

e

meta-xylene

1.0

chloroacetylene

X

trans-dichloroethylene oc~ 0.5

cis-dichlorethylene

._1

dichloroacetylene

0.0

,

I

990

,

,

,

I

1020

,

,

,

,

t

,

,

1050

,

,

I

1080

,

,

,

,

I

......

1110

Temp (K) FIGURE 16.4.27 Product yields normalized to hydrogen atoms, released from the hydrogenatom-induced decomposition of trichloroethylene.

164

w. Tsang and A. Lifshitz CI2C=CH2+ CI displacement, ,

fHCIC=CCIH

+ CI

CI2C=CCIH + H HCI + CI2C=CH* ~ *CIC=CCIH

"~

H2 + CI2C=CCI FIGURE 16.4.28

CICCH abstraction

~- CCICCI

Mechanism for the hydrogen-atom-induced decomposition of trichloroethylene.

The present result represents a graphic demonstration of the capability of single-pulse shock tube studies for uniquely determining the contributions from the various channels of a complex chemical process. Furthermore, through the use of an internal standard, it can be seen that as before it is possible to make quantitative comparisons between different processes. The most serious problem in this type of study is the accounting of all the hydrogen atoms. Some possible reaction channels that may lead to confusion

r

0.4

E d.

_ m:~ o - ~ o - ~

~-z~,-

o ~aAx-- o o ~ - 8x- - - ~

o~---

~

"~

0.0

"IrO c~ - 0 . 4 rO

oao_oo

+

I

_

v

-0.8 o ._1 '"

0.88

'

'

'

'

9

'

i

0.92

.

.

.

.

'

'

!

. . . . .

0.96

,

"

9

''

~

'

'

i

,

,

1.00

1000/T FIGURE 16.4.29 Rate constants for addition and abstraction reactions of hydrogen atoms with trichloroethylene. Circles m mixture containing 200 ppm hexamethylethane, 2% trichloroethylene, and 1% mesitylene. Triangles m mixture containing 100 ppm hexamethylethane, 2% trichloroethylene, 0.5% mesitylene, and 20% hydrogen. Dashed lines--best fits through points. Filled symbols--hydrogen abstraction of chlorine atom. Hollow symbols mdisplacement processes. The higher values are for displacement of the least-substituted chlorine. The lower values are for the more highly chlorine compound and is the sum of cis- and trans-species. Lines A and B are the comparable values times 0.5 for H attack on tetrachlorethylene leading to displacement and times 0.75 for H attack on tetrachlorethylene leading to abstraction.


165

include reaction with the hydrogen atom generator itself (hexamethylethane) or reactions with the radicals that are present in the system. These effects can be minimized by making ratios, of radical source and radical sink as large as possible. By carrying out reactions at a variety of ratios, any such contributions should be discernible. Due to the multichannel nature of these reactions, it has not been possible to make extensive comparisons of results from other type of experiments. However, recently the Stuttgart group (Horn et al. 1998) has made direct studies of hydrogen atom attack on phenol and obtained results that completely reproduce the earlier data from the single-pulse shock tube studies. Besides hydrogen atoms, labile organics can also be used generate radicals. One can then study their stability in the unimolecular sense. For example, the use of 1,7-octadiene as a precusor for allyl radicals was discussed earlier. Similarly, 2,4-dimethypentene-1 (Tsang 1973b) has been used to generate isobutenyl radicals and to determine the rate expression for its decomposition. More recently, n-pentyl iodide has been used as a precursor for n-pentyl radicals (Tsang et al. 1998). In this case, rate constants for decomposition are extremely fast and thus not accessible to single-pulse shock tube experiments. It is however quite straightforward to determine branching ratios for decomposition to form ethylene and propene and the corresponding methyl radicals and hydrogen atoms. The experiments described here, particularly those involving the resonance-stabilized radicals, are essentially inaccessible to classic techniques. On the other hand, the more stable radicals such as benzyl and propargyl need even higher temperatures.

16.4.5.3 INTERNAL STANDARDS AND THE COMPARATIVE RATE T E C H N I Q U E The isolation of unimolecular reactions by the use of scavengers gives one the capability to study several unimolecular reactions simultaneously in the same single-pulse shock tube experiment (Tsang 1964a, 1964b). An obvious prerequisite is that the molecular components of these reactions do not interact with each other. At present this is validated only for systems that produce reactive intermediates of the type that are found in hydrocarbons systems. Other systems, where different types of highly reactive radicals are created, must be treated on an individual basis. A great danger in carrying out this type of experiment is that one always obtains highly precise data that are only directly meaningful if the reactions do not "talk" to each other. The advantage of studying several reactions at once is that one of the reactions can be used as an internal standard. Specifically, if the rate expression of a unimolecular decomposition has been determined by some other means,

166


then that expression can be used as a basis for estimating the reaction temperature. This then removes all the problems originating from the nonideal behavior of real shock tubes. Thus for example, suppose that for a unimolecular reaction with the rate expression k(A = B + C) = A s e x p ( - E ~ / R T ) s -1

one obtains from an particular experiment k(A = B + C) -- -(I/t)ln(Af/Ai) -- - ( l / t ) l n ( [ A i - B(or C)]/Ai)

where t is the heating time and the subscripts f and i refers to the final and initial concentrations, respectively. One can then obtain an average reaction temperature T on the basis of the relation 1 / T = lnA~ - lnk(A = B + C) --- lnA~ - l n ( - 1 / t ) l n ( [ A i - B(or C)]/Ai)

Thus on the basis of a measured heating time and concentrations it is possible to obtain an average reaction temperature. Since the other decomposing species is in the same bath, it must be suffering the exact reaction temperature and the same heating time. This is the basis of the comparative rate measurements that have been used for many years. It is probably the most accurate means of obtaining unimolecular rate constants and expressions. A detailed uncertainty analysis has been published (Tsang 1964b). The increase in precision arises from the sole use of concentration measurements to determined rate expressions. Obviously, if the activation energy for the two processes is the same, there will be no errors in the relative rate constants. Since rate constants are exponentially dependent on the temperature, it is in fact difficult to carry out studies with tremendously different activation energies. Thus the key requirement is easily satisfied. An important input in this procedure is obviously the rate expression for the standard reaction. For this purpose we have chosen decomposition processes that lead directly to the production of stable molecules and for which surface effects have been accounted for. At the present time, the standard to which all the published rate expressions derived from internal standards are related is the reverse-Diels-Alder decyclization of cyclohexene (Tsang 1981), or k(c-C6Hlo -- C2H 4 q- 1,3C4H6) -- 1015"15e x p ( - 3 3 , 5 0 0 / T )

S-1

The estimated uncertainty is probably no more than a factor of 1.5 in the Afactor and 1 - 2 k J/tool in the activation energy. The uncertainty in the rate constants is on the order of a factor of 1.2. Verification of this rate expression can be made through comparison with other well-established rate expressions in the literature. In most applications for which chemical kinetics are important, it is in fact the relative rate constants that are of prime concern. The present type of study represents direct determinations of such quantities.


167

Since all properties are determined from Concentration measurements, it is estimated that the relative rate constant should not exceed factors of 1.05. The type of reaction epitomized by cyclohexene decomposition, where stable products are directly formed, represent a category of processes that is particularly easy to study using the single-pulse shock tube technique. This is because no active radicals are formed and one can indeed carry out studies in the absence of a scavenger. On the other hand, it is always wise to study the effect of adding scavengers to ensure that radical-induced decompositions are not making contributions. It should be noted that many such reactions m for example, the dehydrohalogenation of alkyl halidesm are particularly sensitive to surface effects, thus special "seasoning" processes must be undertaken to eliminate such processes in static reactors..These problems do not arise in shock tube experiments. This category of reactions, involving multiple bond breaking and bond formation, is particularly important at the present time because predictive capabilites for the rate constants or expressions for such processes are still uncertain. Many such r e a c t i o n s ~ for example, the decyclization of small ring compounds ~ represent an active research field in physical organic chemistry. The shock tube experiments extend the temperature and pressure ranges where such measurements can be made. In this application, chemical kinetics used to define the properties behind the reflected shock wave. This removes all the uncertainties brought about by the nonideal behavior. This general approach has not been applied by investigators with interest in high-temperature fluid dynamics. Nevertheless, as our understanding of gas-phase chemistry increases, it is clear that there are many interesting possibilities.

16.4.6 SPECIFIC SYSTEMS AND GENERALIZATIONS We will now summarize results from specific systems that have been studied. The data can be found in the appendix. The first section deals with data summarized in Appendix 16.4.9.1.1, which contains information on studies where the process involves a number of elementary reactions. Appendix 16.4.9.1.2 contains information on a number of isomerization processes that occur in parallel with the decomposition reactions listed in Appendix 16.4.9.1.1. The information testifies to the complex rearrangements involving bond breaking and bond formation that even intermediate sized molecules can undergo. The prediction of these pathways is one of the great challenges of theoretical chemistry. The second section deals rwith the rate expressions that have been determined from single-pulse shock wave studies. A number of the

168


generalizations from such results will be discussed. The actual values can be found in Appendix 16.4.9.2.

16.4.6.1

COMPLEX REACTIONS

Appendix 16.4.9.1 provides a list of single-pulse shock tube studies of complex reaction systems. It lists the compounds that were studied, the temperature range, the products obtained under reflected shock heating, and references to the original manuscripts. It also states in what studies computer modeling has been performed. The compounds that will be reviewed are divided into three categories: a. Saturated and unsaturated aliphatic hydrocarbons, with and without functional groups. b. Aromatic hydrocarbons containing one or two rings, with and without functional groups. c. Heterocyclic compounds containing oxygen, nitrogen, and both, as the heteroatoms. We will briefly discuss the main features of the thermal reactions of these compounds. It should be mentioned that many of these reactions have been studied using shock tubes with a variety of diagnostics in addition to the single-pulse shock tube. In particular, one should note the many publications of Hidaka et al., who used diagnostic techniques such as IR emission, UV, and laser absorption for time-resolved information in addition to product identification using the single-pulse shock tube mode. For further details and references to studies using shock tubes and other experimental methods, the reader is referred to the original articles. 16.4.6.1.1 Aliphatic Hydrocarbons A large number of aliphatic hydrocarbons m including those having heteroatoms such as oxygen, nitrogen, and sulfur m h a v e been investigated using sing!e-pulse shock tubes. There are also some data on the decomposition of halocarbons, which involve complex mechanisms. Studies on the decompositions of methane, ethane, acetylene, acetylene in the presence of SO2, propane, propylene, allene and propyne, 2-butene, 1-butyne, 2-butyne, 1,2-butadiene, vinylacetylene, cyclopentadiene, and octane in the presence of hydrogen were reported in the literature. The decomposition of methane was studied by many groups and the mechanism is fairly well understood. The reactions of the methyl radicals produced in the initiation step were studied in detail (Hidaka et al. 1990) to explain the production of ethylene and propyne. Ethane


169

decomposes by cleavage of the C - C bond, and C2H4, C2H2, and CH 4 are identified as the decomposition products (Burcat et al. 1973; Hidaka et al. 1985b). Acetylene decomposition was studied up to a temperature of 2400 K (Colket 1986). Upon decomposition it yields both aliphatic and aromatic products. C4H4, C4H2, and C6H 2 are the aliphatic products, and C6H6 and C8H6 (phenyl acetylene) are the major aromatic products. A mixture of acetylene and sulfur dioxide when elevated to high temperatures yields CO, CS2, C2H4, and CO2 (Fifer et al. 1971). Propane yields upon decomposition CH4, C2H4, C2H6, and C3H 6 (Lifshitz et al. 1973; Lifshitz and Frenklach 1975; Hidaka et al. 1989c). The initiation step is C3H8 --~ C2H5 + CH3, followed by unimolecular split of H atoms from ethyl radicals and free radical attack on propane. Propylene has stronger C - C bonds than propane. To account for the distribution of the reaction products which are C2H4, C2H2, CH4, and allene and propyne (Burcat 1975; Hidaka et al. 1992b), three initiation steps had to be assumed (Hidaka et al. 1992b): C3H 6 -~ CH 3 -b C2H 3, C3H6 -~ H + C3H5, and C3H 6 --~ CH 4 -F C2H 2. The structural isomers allene and propyne have different decomposition channels (Lifshitz et al. 1976; Hidaka et al. 1989b). Propyne gives high yields of methane and acetylene, whereas allene gives a high yield of ethylene (and cumulene), which was shown to be formed by a bimolecular reaction between two allene molecules: CH2--C=CH 2 + CH2---C--CH 2 --+ C2H 4 nt- C H 2 - - C = C - - C H 2. Their major reaction, however, is allene ~ propyne interisomerization, and they equilibrate at a much higher rate then they decompose. Their decomposition channels had to be determined before isomerization takes place, that is, at extremely low extents of reaction. 2-butene, both cis and trans, decomposes to yield methane, propylene, and butadiene, while the cis ~ trans isomerization does not reach an equilibrium (.Jeffers and Bauer 1974). Cyclopentadiene decomposes by H-atom ejection from the CH2 group followed by successive fl-scissions (Burcat and Dvinyaninov 1996). Its main decomposition products are C2H 2 and C2H 4. Both 1butyne (Hidaka et al. 1995b) and 2-butyne (Hidaka et al. 1993a) isomerize to 1,3- butadiene and 1,2-butadiene prior to decomposition. The main decomposition products are CH4, C2H2, C2H 4, C6H6, allene, and propyne. 1,2butadiene (Hidaka et al. 1995a) also isomerizes to other C4H 6 isomers at a faster rate than it decomposes and yields the same products as the other C4H 6 isomers. Vinylacetylene (Colket 1986; Hidaka et al. 1992a) has been assumed to have three initiation reactions: C4H 4 ~ C4H 3 if- H, C4H 4 ~ C2H 2 -+- C2H2, and C4H 4 --+ C4H 2 q - H 2. The major reaction products were C2H2, C4H2, C6H2, and C6H6. The decomposition of octane diluted in argon gives mainly ethylene, methane, propylene, and small yields of ethane. When diluted in a mixture of 50% hydrogen and 50% argon, the yields of methane and ethane increase and the overall decomposition rate of octane increases by 1 order of magnitude (Doolan and Mackie 1983).

170


Among the oxygen-containing species, the decomposition of propanal (Lifshitz et al. 1990), crotonaldehyde (CH3CH--CHCHO) (Lifshitz et al. 1989b), propanoic acid (Doolan et al. 1986), methanol (Hidaka et al. 1989d), and nitromethane (Zhang and Bauer 1997) were investigated using the single-pulse shock tube technique. The oxygen in the aldehydes ends up as carbon monoxide, whereas other oxygen-containing species appear in very low yields or do not appear at all. Propanoic acid yields both carbon monoxide and carbon dioxide. The reaction products in methanol are CO, CH20, CH 4, C2H6, and C2H4. The initiation reaction in nitromethane is cleavage of the relatively weak C - N bond in the molecule, followed by methyl group attack on the reactant. CH4, C2H6, C2H4, and C2H2 appeared as the main carbon-containing reaction products. Oxidative decomposition of methane in the presence of N20 and the decomposition of ethane in the presence of NO have been reported. Methane in the presence of N20 yields mainly C2H4 and C2H6, but at high temperatures carbon monoxide and acetylene perdominate (Mackie and Hart 1990). Ethane in the presence of NO yields a considerable amount of HCN resulting from the attack of CH3 radicals on NO: CH 3 4-NO--~ CH3NO ~ HCN 4- H20 (Lifshitz et al. 1993b). The decomposition of CH3CN (Lifshitz et al. 1987b; Ikeda and Mackie 1996; Lifshitz and Tamburu 1998), CH2=CHCN (Lifshitz et al. 1989a) and butene nitriles (Doughty and Mackie 1992a) were investigated and the product distribution was reported. The major products in the decomposition of CH3CN are CH4, HCN, and C2H2, together with numerous other products. The initiation reaction in this decomposition is an H-atom ejection from the C - H bond in the molecule, followed by dissociative attachment of H atom to CH3CN to produce HCN and methyl radical: CH3CN 4- H'--~ CH3" 4- HCN. The production of HCN and C2H2 from CH2=CHCN is believed to proceed via a four-center transition state. There is not much reported work on single-pulse shock tube decompositions of halocarbons where complex reaction systems are concerned. The overall process is dominated by the direct dehydrohalogenation process. Propargyl chloride (CH2C1C--CH) isomerizes to chloroallene (CHCI=C--CH2) as the main reaction (Kumaran et al. 1996) and equilibrates before considerable decomposition begins. The major decomposition products in addition to isomerization to chloroallene are C2H2, C6H6, C4H2, C6H~C1, and others (Lifshitz and Suslensky unpublished e). 16.4.6.1.2 Aromatic Hydrocarbons Among the aromatic compounds studied with the single-pulse shock tube are benzene, benzonitrile, o-dichlorobenzene, toluene, indene, and phenol. Benzene decomposes by H-atom ejection and opening of the ring in the fl-


171

position to the radical site (Laskin and Lifshitz 1997a). Its main decomposition products are C2H2 and C4H2. However, at the lower-temperature end biphenyl is the major product due to an attack of phenyl radicals on benzene. The thermal reactions of benzonitrile (Lifshitz et al. 1997a) are similar to those of benzene, yielding as major products C2H2, C4H2, C6H6, C H = C - C N , and HCN. O-dichlorobenzene decomposes to yield C2H2, C4H2, C6HsC1, and C6H6 as the major decomposition products (Lifshitz et al. unpublished b). The decomposition of toluene was studied up to a temperature of 1800 K and a large number of products, including conjugated aromatic rings, were obtained (Colket and Seery 1994). The initiation is H-atom ejection from the methyl group at low temperatures and methyl group elimination at the higher end of the temperature range. Indene is cyclopentadiene fused to benzene. The decomposition begins by ejection of H atoms from the CH2 group and further decomposition of the indenyl radical (Laskin and Lifshitz 1999). However, indanyl, which is obtained by H-atom attachment to the cyclopentadiene ring in indene, plays a very important role in the decomposition. This channel is not important in the decomposition of cyclopentadiene itself. Phenol decomposes in a unimolecular reaction to carbon monoxide and cyclopentadiene (Burcat and Olchanski 1999). This is the most important step in the decomposition, although ejection of H atoms from the hydroxyl group takes place as well. The fragmentation of the formed cyclopentadiene is responsible for the production of lower-molecular-weight species. Carbon monoxide, cyclopentadiene, ethylene, acetylene benzene, and methane were identified as the major decomposition products. 16.4.6.1.3 Heterocyclic Compounds With the introduction of a heteroatom to a cyclic hydrocarbon, the symmetry of the molecule decreases and the number of distinguishable reaction channels increases. Three-membered rings, the epoxy family of molecules, where a CH2 group has been replaced by an O atom is a good example. Three molecules in this group have been thoroughly investigated using the single-pulse shock tube (Lifshitz 1995). Oxiran (ethylene oxide) can isomerize only to acetaldehyde (Lifshitz and Ben-Hamou 1983). Propylene oxide (Lifshitz and Tamburu 1994), and 2,3-dimethyloxiran (Lifshitz and Tamburu 1995), yield four isomerization products: aldehyde, alcohol, ether, and ketone. All the three compounds yield decomposition products at relatively low temperatures due to the formation of thermally excited isomers before being de-excited to the ground Boltzmann distribution (Benson 1964). Considerable effort has been devoted to the study of 5-membered heterocyclics containing oxygen (Lifshitz 1988, 1989). The thermal reactions of hydrogenated furans with or without substituents have been investigated.

172

w. Tsang

and A. Lifshitz

Tetrahydrofuran (Lifshitz et al. 1986a) is a kinetically stable heterocyclic compound. It undergoes several unimolecular ring cleavage processes, but no isomerization products were identified in the postshock mixtures. With the introduction of one double bond, the thermal stability decreases. Thus the decomposition of 2,5-dihydrofuran (Lifshitz et al. 1986c) and 2,3-dihydrofuran (Lifshitz and Bidani 1989) occurs at considerably lower temperatures. The main reaction in 2,5-dihydrofuran is H2 elimination from the 2-5 positions forming furan. The extent of fragmentation is by orders of magnitude below the main reaction. There is no H2 elimination from 2,3-dihydrofuran. The major reaction here is isomerization to cyclopropanecarboxaldehyde (C3HsCHO). However, fragmentationmparticularly to CO + C3H6 and the formation of other products mdoes occur at rates comparable to the isomerization. 4,5- dihydro-2-methyl-furan (Lifshitz and Laskin 1994) isomerizes to cyclopropane-methylketone and 3-pentene-2-one with a very low extent of decomposition. With the introduction of an additional double bond, f u r a n ~ t h e most stable p r o d u c t ~ is formed. Furan does not isomerize (Lifshitz et al. 1986b); its main decomposition channel is the formation of carbon monoxide and propyne initiated by H-atom migration from position 5 to position 4 in the ring. Other decomposition channels forming acetylene and other products do exist as well. The thermal reactions of 2-methylfuran (Lifshitz et al. 1997b), 2,5-dimethylfuran (Lifshitz et al. 1998), and 2-furonitrile (Laskin and Lifshitz 1996a) have also been investigated using the single-pulse shock tube technique. Whereas the - C N group in 2-furonitrile does not migrate, migration of a hydrogen atom or a methyl group with the elimination of carbon monoxide in 2-methylfuran and 2,5-dimethylfuran is again the major reaction channel. Four isomers of C4H6 m 1,3-butadiene, 2-butyne, 1-butyne, and 1,2-butadiene~ are formed in the decomposition of 2-methylfuran and the same four isomers of C4H6 and several isomers of C~H8 are formed in the decomposition of 2,5dimethylfuran. Unpublished single-pulse shock tube data are also available on the thermal reactions of 2,3-dihydrobenzofuran (Lifshitz et al. unpublished b) and isodihydrobenzofuran (phtalan) (Lifshitz et al. unpublished a). 2,3-dihydrobenzofuran is 2,3-dihydrofuran fused to benzene in the 4-5 positions of the furan ring. Its thermal stability is higher, and the temperature at which products begin to appear following a dwell time of ~2 ms is approximately 200 K higher. Bond cleavage occurs in the furan ring, whereas the benzene ring stays intact. This results in the formation of several derivatives of benzene, including isomerization products. Dihydrobenzofuran and isodihydrobenzofuran undergo similar isomerization. By cleavage of the 1 - 3 bond in the furan ring and H-atom migration from position 3 to position 1-,2,3-dihydrobenzofuran gives o-hydroxy styrene and phtalan gives o-tolualdehyde.


173

The addition of a nitrogen atom to the furan ring in position 2, adjacent to the oxygen, decreases the symmetry of the molecule. The stability of the molecule is also decreased due to the weak N - O bond (--~315kJ/mol). In view of the weak N - O bond, this compound m isoxazole (Lifshitz and Wohlfeiler 1992a)--and two of its derivativesm 5-methylisoxazole (Lifshitz and Wohlfeller 1992b) and 3,5-dimethylisoxazole (Lifshitz et al. 1995)~have been studied behind reflected shocks at much lower temperatures than used with furan and its derivatives. Migration from position 5 to position 4 in both isoxazole and 5-methylisoxazole and elimination of carbon monoxide is still the major channel of decomposition. H-atom migration in isoxazole yields carbon monoxide and acetonitrile, whereas methyl group migration in 5methylisoxazole yields carbon monoxide and propylnitrile. In 3,5-dimethylisoxazole, the main channel is isomerization to 2-methyl-3-oxo-butyronitrile. Moving the oxygen atom to position 3 in the ring (oxazole) increases the stability of the ring close to that of furan (Lifshitz and Wohlfeiler unpublished), and the decomposition occurs at much higher temperatures than in the isoxazoles. Another group of five-membered heterocyClics is the pyrrole group of molecules. The decompositions of pyrrolidine, pyrrole, N-methylpyrrole, and 2,4-dimethylpyrrole have been studied in the single-pulse shock tube. Pyrrolidine (tetrahydropyrrole), like its isoelectronic tetrahydrofuran, is a kinetically stable molecule and decomposes at temperatures somewhat below those of tetrahydrofuran (Lifshitz et al. 1987a). The main products are ethylene and hydrogen cyanide; only traces of pyrrole are found. No isomerization products were identified in the postshock mixtures. There are no single-pulse shock tube data on the decomposition of the two isomers of dihydropyrrole. Pyrrole is a resonance-stabilized molecule and is kinetically very stable. The temperature range over which it decomposes is similar to that of furan. In contrast to furan, its major reactions are isomerizations to the various isomers of butenenitriles. Its main decomposition products are hydrogen cyanide and acetonitrile (Mackie et al. 1991; Lifshitz et al. 1989c). Pyrrole ring fused to benzene (indole) has also been studied (Laskin and Lifshitz 1997b). It isomerizes to benzyl cyanide, o- and m-tolunitrile and yields also decomposition products resulting from cleavage of the fivemembered ring. N-methylpyrrole fragmentizes to small molecules such as methane and ethane, but also undergoes methyl group migration to other locations in the ring (Lifshitz et al. 1993a; Doughty et al. 1994a). Ejection of a hydrogen atom from the methyl group produces the methylene pyrrole radical, which undergoes ring expansion to yield hydropyridile and finally pyridine (Dubrikova and Lifshitz 2000). 2,4-dimethylpyrrole undergoes ring cleavage to small fragments as well as ring expansion processes to yield 2-picoline, 4picoline, and pyridine (Lifshitz et al. unpublished c).

174


Among the six-membered heterocycles, pyridine (Mackie et al. 1990), 2picoline (methylpyridine) (Terentis et al. 1992; Doughty and Mackie 1992b), 3-picoline (Jones et al. 1996), and pyrimidine (Doughty and Mackie 1994) have been studied, as have quinoline and isoquinoline, which consist of pyridine fused to benzene in two different locations. The initiation of pyridine decomposition is an H-atom ejection from the a-position to the N atom. The pyridile radical, which is resonance stabilized by some 6 kcal/mol, decomposes by successive ]~-scissions. The major decomposition products are C2H2, HCN, CH_=C-CN, and C4H2 . The different isomers of picoline decompose to yield practically the same products, with C2H2, HCN, and CH 4 being the major ones. In pyrimidine, the major products are HCN, CH2=CHCN, and CH_=C-CN. Quinoline and isoquinoline (Laskin and Lifshitz 1998) decompose by breaking the pyridine ring in the a-position to the nitrogen. The two isomers give identical decomposition products and yield the same major products: C2H2, C6H6, C6HsCN, and CH=C-CN. The identical products and yields is explained by assuming that the decomposition routes of the two isomers are coupled by 1-indene-imine radical.

1 6 . 4 . 6 . 2 SINGLE-STEP KINETICS 16.4.6.2.1

Introduction

The results in Appendix 16.4.9.2 deal mostly with unimolecular decompositions and include practically all the known mechanisms for unimolecular decomposition. The total number of items in these tables is close to 200; the review of Benson and O'Neal (1969) covers about 500 items. This is thus a significant contribution to the base of experimental results on unimolecular reactions. Also included are results on hydrogen atom attack on organics, which demonstrate the possibilities derived from the work on unimolecular decompositions. All of these results are indicative of the capabilities of the single-pulse shock tube studies for studying multichannel processes. For all but the simplest molecules, this is probably the rule rather than the exception. The reactions that have been covered are divided into seven different categories. The first, summarized in Appendix 16.4.9.2.1, contains bondbreaking processes. These are conceptually the most straightforward: A chemical bond is broken and two radicals are formed, and the reverse reaction has no barrier. Thus the activation energy can be related to the bond dissociation energy. Since radicals are formed, all the studies have been carried out with inhibitors. Internal standards have also been used in all the studies. The reactions are frequently the initiating processes in chain decompositions.


175

Rate expressions are also important as inputs for the calculation of thermodynamic properties of radicals. More generally, they serve as the experimental basis for testing of theories on the kinetics of bond breaking. Appendix 16.4.9,2.2 contains data on retroene reactions. For unsaturated hydrocarbons, these are processes that often accompany the bond-breaking reactions. When heteroatoms are present, the activation energy is lowered so that they become the predominating process. The reactions proceed through a six-membered transition state. Appendix 16.4.9.2.3 summarizes reactions on molecular elimination. A prerequisite for such a process to be important is the presence of a highly polar group. Thus the general trends upon methyl substitution for the iodides chlorides and bromides track the situation in solution and much lower temperatures. Indeed, it has been found that the activation energy is 28% of the ion dissociation energy (Tsang 1964b). It is unfortunate that the earlier work on the fluorinated compounds were carried out without internal standards; the accuracy of the rate expressions and constants are larger than those using intemal standards so extrapolations to related reactions may be more uncertain. Appendix 16.4.9.2.4 contains results involving decyclization processes. Many of these reactions involve biradical intermediates. These reactions have long been a favorite subject for physical organic chemists. Single-pulse shock tube studies extend the available temperature range and permit the investigation of more stable compounds such as cyclopentane and cyclohexane. These reactions and those involving larger tinged compounds are related to the bondbreaking processes summarized in Appendix 16.4.9.2.1 except that the radicals cannot escape. In these cases, the main products are in fact those arising from internal disproportionation. The results in Appendix 16.4.9.2.5 on cis-trans isomerization and other isomerizations can be considered a subclass of the decyclization processes discussed previously if one considers a double-bonded molecule a two-membered ring. The studies on both class of reactions benefit particularly from the ability of the researchers to synthesize the particular molecules that they wish to study. Appendix 16.4.9.2.6 contains results on a number of organometallic compounds. Much further work is necessary. Intermediates, final products, and patterns of reactivity have very little relationship with the organics discussed earlier. A particular problem is that the unsaturated compounds, unlike the situation for the hydrocarbons, are highly reactive. Thus without appropriate trapping agents they cannot serve as markers for the extent of reactions. Furthermore, the lessened stability puts most of these reactions into the energy transfer region. There remains a need for making appropriate corrections.

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Appendix 16.4.9.2.7 contains data on hydrogen attack on unsaturates. This represents a truly unique set of results in the sense of the absence of comparable results even at lower temperatures. It builds on the data from hydrocarbon decomposition. This general approach has also been used to study the stability of resonance-stabilized radicals (Tsang 1973b; Tsang and Walker 1990) as well as the branching ratio for alkyl radical decomposition (Tsang et al. 1995). A number of the results summarized in Appendix 16.4.9.2.2 are given as a function of pressure. These represent results in the falloff region. An important problem in existing single-pulse shock tube studies is the difficulty in carrying out studies across large pressure ranges. Thus there is always the question as to whether reported results are at the high-pressure limit. In practically all the comparative rate studies, the pressure was varied by a factor of 3 and except for the smallest compounds pressure effects could not be observed. The implication is that the pressure dependence is less than p0.O3. There is an obvious need for more work.

16.4.6.2.2 A-Factors A particularly interesting observation from the results is the relative invariance of the A-factors with respect to reaction type. It would appear that the only important contribution to variations are in the reaction path degeneracy, which is suggestive of transition states that are very localized with respect to structure. This can provide a very simple empirical basis for prediction: It means that a measurement at one temperature can result in accurate rate expressions. Unfortunately, it has not been possible to verify such observations from determinations using other experimental methods. Some of these considerations are illustrated in Fig. 16.4.30, which contains the A-factors for a variety of different reaction types as given in Appendix 16.4.9.2 and restricted to comparative rate studies. This similarity would not be particularly surprising for molecules that decompose through normal or perhaps tight complexes. However, for bondbreaking reactions, there are no reaction barriers for combination. Hence the exact position of the transition state is unclear. It is known that for such reactions the A-factors are large, thus signifying loose transition states. The comparative rate work set definite limits on permissible values. Even more interesting is that such studies can distinguish between cases of reactions where one of the radicals contains structures with resonance energy. From Fig. 16.4.30 it can be seen that these reactions lead to A-factors about half an order of magnitude lower those where simple alkyl radicals are the sole products. This is in accord with the picture of radical combination according


177

FIGURE 16.4.30 A-factors for various types of thermal decomposition processes. (A) retroene reactions, (B) dehydrohalogenation (I, Br, C1), (C) R-X ~ R + X, X ~ Br, (D) ResAlkyl ~ Res + Alkyl, (E) Alkyll-Alkyl2~- Alkyll + Alkyl2. to the Gorin model (Benson 1976). However, note that the A-factors are all much smaller than that derived on the basis of orbiting radicals.

16.4.6.2.3 Bond Energies Probably the most consequential results from single-pulse shock tube work have been the revision of the bond energies of a large number of hydrocarbon compounds or, equivalently, the heats of formation of hydrocarbon radicals (Tsang 1985). Until the advent of the single-pulse shock tube results, these values have been considered to be well established. Since the breaking and formation of chemical bonds is the basis of chemical change, these are the essential factors with regard to chemical reactivity. The single-pulse shock tube studies showed that these established values were too small by 16 to 37 kJ/mol. These studies also imply that the stability or unimolecular lifetimes for branched alkanes at the shock tube temperatures were in error by as much as 3 orders of magnitude. These are enormous errors and their resolution has solved many long-standing problems, including issues dealing with stability of alkyl radicals and the need to postulate barriers for the cyclization of biradicals. With these new values experimental results on radical decomposition and addition to olefins obey detailed balance and cyclization of small biradicals have small or no barriers. A summary of bond energy results derived from single-pulse shock experiments can be found in Table 16.4.5. Also included are the generally accepted results as summarized by McMillen and Golden (1982) and newer results given in a subsequent review by Berkowitz et al. (1995). The

178

w Tsang and A. Lifshitz

TABLE 16.4.5 Summary of Heats of Formation Determined by Shock Tube Studies and Recommendations of McMillen and Golden (1982) and Berkowitz et al. (1995)

Radicals C2H5 n-CBH7 i-CBH7 s-C4H9 i-C4H9 t-C4H9 t- C5Hll C3H5 (allyl) C3H5 (propenyl) C4H7 (isobutenyl) C4H7 (methylallyl) C3H3 (propargyl) C4H5 (methylpropargyl) C6H5 (phenyl) C6HsCH2 (benzyl) C6H50 (phenoxy) CH3CO (acetyl) CH3COCH2 CF3 2-Hydroxyethyl 2-Hydroxypropyl 2-Aminopropyl NH2

Single-pulse shock tube results (ref) (kJ/mol) 117.1 98.4 85.3 63.2 60.2 48 32.2 174 267 138 158 351.4 312.5 341 205 55.3 -13.8 -12.6 -460 -56.9 -91.6 96.3 185.3

Tsang, 1981 Tsang, 1981 Tsang, 1981 Tsang, 1981 Tsang, 1981 Tsang, 1981 Tsang, 1981 Tsang and Walker, 1992 Cui et al., 1988 Tsang, 1981 Tsang, 1981 Tsang, 1981 Tsang, 1981 Robaugh and Tsang, 1996b Walker and Tsang, 1990 Walker and Tsang, 1990 Tsang, 1984a Tsang, 1984a Tsang, 1986 Tsang, 1976 Tsang, 1976 Tsang, 1978e Tsang, 1978e

McMillen and Golden Berkowitz et al. (kJ/mol) (kJ/mol) 108 87.8 76.1 57.7 34.7 163

121 89.9 67 51.4 171

140 338 330 200 -24 -24

203 -10

-63.6 --101 185

degree of agreement between the latter and the earlier shock tube results are extraordinarily good. It should be noted that a great deal of the subsequent work was instigated by the shock tube results.

16.4.6.2.4 Rate Expressions for Bond Cleavage The accurate rate expressions for bond-breaking reactions can also be used to make reliable estimates for the parameters for other bond-breaking processes. Specifically, one can make use of the fact that for many radicals the geometric mean rule is well established. Then for any system where the rate expressions for the decomposition of AA to 2A and BB to 2B has been measured, the rate expression for AB to A and B can be determined using only the thermodynamic properties of the stable compounds. Thus as the database for the decomposition of organic compounds into radicals is built up through experiments, rate

16.4

179


expressions for many others involving the radicals that have been formed can be rigorously calculated. Actually, this has proven to be less useful than once thought due to the empirical observations regarding the similarities in the Afactors for similar types of bond-breaking reactions and the relationship between the experimental activation energy and the bond dissociation energy. Of course, this is applicable only at or near the single-pulse shock tube temperatures. At lower temperatures, as will be discussed below, the Afactors become strongly dependent on molecular structure. Experimental studies of the unimolecular region usually cover a small temperature range. Thus the best fit of experimental results can only be expressed in terms of the standard Arrhenius form. Of course, transition state theory is inconsistent with such a form; hence the frequent use of a temperature-dependent A-factor in rate expressions. There is, however, very little experimental data bearing on this issue. Combination of shock tube results for bond breaking together with rate constants for combination at or near room temperature and the thermodynamic properties of the radicals that are formed permit derivation of rate expressions for decomposition from room temperature to close to 1200 K. These are summarized in Table 16.4.6 for the formation of the three simple alkyl radicals. It can be seen that for these bondbreaking reactions there is a negative curvature of the Arrhenius plot and that the extent of this curvature increases with methyl substitution. The constancy of the A-factors for decomposition of the three prototypical alkanes at the higher temperatures is lost. Indeed, it appears that at room temperature the Afactors are strongly dependent on the size of the alkyl radicals and range from n e a r 1017 s - 1 for ethane to values as large as 1019 to 10 20 s - 1 for hexamethylethane. An interesting issue is whether this decrease in A-factor will continue as one goes to even higher temperatures. In any case, these observations should be a crucial test for any general theory of radical combination. The consequence of the single-pulse shock tube work on unimolecular reactions is that there is now sufficient data for empirical estimation. This is particularly important for bond-breaking processes from a practical point of

TABLE 16.4.6 Rate Expressions for Combination and Decomposition (at the High Pressure Limit) of Some Simple Alkyl Radicals over the Temperature Range 300-1200 K (Tsang and Kiefer, 1995, Tsang, 1978d) Reactions

C2H5-C2H 5 ~ 2-C2H 5 i-C3H7-i-C3H 7 ~ 2-i-C3H 7 t-C4H9-t-C4H 9 ~ 2-t-C4H 9

Rate constants for combination (cm3/mo1-1/s -1)

Rate constants for dissociation (s -1)

1 x 1013 6 x 1012(300/T) 0"7 1.4 x 1012(300/T) 1"5

4.4 x 1025(1/T) 27 exp(-4441/T) 1.6 x 1031(1/T) 4"2 exp(-43,987/T) 5.5 x 1038(1/T) 6"45exp(-41,065/T)

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view since these are the initiation processes in combustion and pyrolytic applications. As noted earlier, with the correct bond energies discrepancies in the measured rate constant for radical decomposition and that derived from the reverse addition and the thermodynamics have also been resolved. Thus the databases including such reactions are consistent with regard to the thermochemistry. 16.4.6.2.5 Hydrogen Atom Attack Appendix 16.4.9.2.7 summarizes the data on the rate constants for hydrogen atom attack on a number of organic compounds. Many of these compounds are complicated unsaturated compounds with abstraction as well as displacement pathways. The latter is actually a composite reaction involving addition, followed by radical decomposition. In all the cases studied, the assumed decomposition process is more favored than the reverse hydrogen emission reaction. Radical lifetimes are extremely short. Hence, physically, the process has the appearance of a displacement process. It can be seen that at the reaction conditions abstraction is slightly favored over displacement. The rate expressions for the former are characterized by larger parameters or looser transition states. Thus, as the temperature is increased abstraction will be increasingly favored. Chlorine for hydrogen substitution in all cases reduces the rate constants. In general, it appears that electronegative group leads to slower rate constants for displacement. Also of interest are the results on the abstraction and displacement of flourine atoms: The rate constants are the smallest of all that have been measured. Here as before the general trends make the results valuable as a basis for estimation.

16.4.7

SUMMARY AND FUTURE

DIRECTIONS

In this review we have summarized the experimental work that has been carried out using the single-pulse shock tube. The large body of information that has now been accumulated can be extremely useful for the detailed understanding of a variety of important practical processes. The accumulated data also represent the basic ingredients for the calibration and validation of theory. There is very little doubt that the single-pulse shock tube represents an extremely powerful tool for the study and quantitative understanding of hightemperature gas-phase processes. This is especially the case for organic processes since it is possible to build on a broad base of earlier knowledge. Of great importance is the fact that shock tube studies cover a range of temperatures that are inaccessible to standard flow and static experiments but are important in many technical processes such as combustion. When coupled


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with some means of determining the actual conditions in the shock tube, such as the internal standard technique or isolation of the reaction to be studied, the results that are produced are probably the most reliable of all methods for determining high-temperature thermal rate constants and expressions. The logical extension of this work is in the studies of highly unsaturated organics and organometallics, more extreme conditions (particularly in terms of pressures), and the use of the single-pulse feature in combination with realtime detection capabilities. It is increasingly clear that the decomposition of the highly unsaturated organics proceeds through a multitude of possible reaction channels. Many of these involve complex rearrangements. There is at present very little predictive capability on these issues. This is fundamentally a very important scientific question as well as an extremely important practical problem since the issue is essentially the quantitative understanding of polynuclear aromatic hydrocarbon and soot formation and all their related problems. The high-quality data for the purely organic compounds described here depended on isolation of the individual reactions for study. There is at present insufficient understanding of the decomposition processes associated with many inorganic compounds, so there are uncertainties regarding how various reactive intermediates can be trapped. The knowledge that has been attained for the organics is applicable to radicals such as H, O, OH, etc. The question regarding the trapping of reactive inorganics associated with the decomposition of the organometalic compounds is still open. In the case of silicon compounds, an important issue is the proper trapping of the silyene radical. Here again interesting science is mixed with important applications, such as the gas-phase contribution to chemical vapor deposition. A particularly interesting extension of the work summarized here will be the carrying out of studies at pressures much higher than those used here (up to approximately 10 bar). As mentioned earlier, as the temperature increases the energy transfer effect becomes more important. The tendency will then be to distort the distribution function, leading to lower rate parameters. We have mentioned our uneasiness with respect to the systems studied here, although the data does not suggest any serious problems. But for three or four carbon systems, distortions arising from this source can be very important. It would also be very important to have, for a number of systems, the unimolecular rate constants over extended pressure ranges. With such data it may finally be possible to test procedures for extrapolation to the true high-pressure limits. Finally, it is clear that much valuable information can be obtained if real-time information can be combined with single-shock tube experiments. There is no question that temporal information combined with final product analysis of all species will permit much more definitive conclusions regarding mechanisms and rate constants.

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Lifshitz, A., Tamburu, C., and Suslensky, A. (1989c). Isomerization and decomposition of pyrrole at elevated temperatures. Studies with a single-pulse shock tube. J. Phys. Chem. 93: 5802-5808. Lifshitz, A., Tamburu, C., and Suslensky, A. (1990). Decomposition of propanal at elevated temperatures. Experimental and modeling study. J. Phys. Chem. 94: 2966-2972. Lifshitz, A., Tamburu, C., and Wohlfeiler, D. (1995). Isomerization and decomposition of 3,5dimethylisoxazole. Studies with a single-pulse shock tube. J. Phys. Chem. 99: 11,436-11,446. Lifshitz, A. and Wohlfeiler, D. (1992a). Thermal decomposition of isoxazole. Experimental and modeling study. J. Phys. Chem. 96: 4505-4515. Lifshitz, A. and Wohlfeiler, D. (1992b). Thermal decomposition of 5-methyl isoxazole. Experimental and modeling study. J. Phys.Chem. 96: 7367-7375. Lifshitz, A. and Wohlfeiler, D. (Unpublished). Thermal reactions of oxazole at elevated temperatures. Single-pulse shock tube investigation. Linteris, G.T., Yetter, R.A., Brezinsky K., and Dryer, E (1991). Hydroxyl radical concentration measurements in moist carbon monoxide oxidation in a chemical kinetic flow reactor. Combustion and Flame 86: 162-170. Maccoll, A. and Wong, S. C. (1968). Gas-phase eliminations. Part VIII. The effect of fl-methylation on the pyrolysis of some t-alkyl chlorides. J. Chem. Soc. B: 1492-1494. Mackie, J.C., Colket, M. B. III, and Nelson, P E (1990). Shock tube pyrolysis of pyridine. J. Phys. Chem. 94: 4099-4106. Mackie, J.C., Colket, M. B. III, Nelson, PE, and Esler, M. (1991). Shock tube pyrolysis of pyrrole and kinetic modeling. Int. J. Chem. Kinet. 23: 733-760. Mackie, J. C. and Hart, M. G. (1990). Partial oxidation of methane by nitrous oxide. Energy and Fuels 4: 285-290. Manion, J. A. and Tsang, W. (1996a). Hydrogen atom attack on fluorotoluenes: Rates of fluorine displacement. Isr. J. Chem. 36: 263-273. Manion, J. A. and Tsang, W. (1996b). Hydrogen atom attack on 1,2-dichlorotetrafluoroethane: Rates of halogen abstraction. J. Phys. Chem. 100: 7060-7065. Marley, S. W. and Jeffers. P M. (1972). Shock tube cis-trans isomerization studies. IV.J. Phys. Chem. 78: 2085-2087. McMillen, D. E. and Golden, D. M. (1982). Hydrocarbon bond dissociation energies. Ann. Rev. Phys. Chem. 33: 493-532. Melius, C. (1999). A Database for 4000 Species Calculated Using the BAC/MP4 and BAC/MP2 Methods at Sandia Natl. Labs. Partially available on the Internet at http://herzberg.ca.sandia. gov/--~ melius/index.html. Michael, J. V. and Suthedand J. W. (1986). The thermodynamic state of the hot gas behind reflected shock waves: Implication to chemical kinetics. Int. J. Chem. Kinet. 18: 409-436. Miller, J. A. and Bowman, C. T. (1989). Mechanism and modeling of nitrogen chemistry in combustion. Prog. Energy Combust. Sci. 15: 287-338. Millward, G.E., Hartig, R., and Tschuikow-Roux, E. (1971). Hydrogen fluoride elimination from shock-heated 1,1,2,2-tetrafluoroethane. Chem. Commun., 465-466. Millward, G. E. and Tschuikow-Roux, E. (1972a). The competitive dehydrohalogenation of 1,1,1,trifluoro-2-chloroethane in reflected shock waves. Int. J. Chem. Kinet. 4: 559-571. MiUward, G. E. and Tschuikow-Roux, E. (1972b). A kinetic analysis of the shock wave decomposition of 1,1,1,2-tetrafluoroethane. J. Phys. Chem. 76: 292-298. Mitchell, T.J. and Benson, S. W. (1993). Modeling of the homogeneously catalyzed and uncatalyzed pyrolysis of neopentane: Thermochemistry of the neopentyl radical. Int. J. Chem. Kinet. 25: 931-955. Muller-Markgraf, W. and Troe, J. (1988). Thermal decomposition of benzyl iodide and of benzyl radicals in shock waves. J. Phys. Chem. 92: 4899-4905.

16.4


189

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1000IT (K FIGURE 16.5.5 Experimental (points) and calculated (lines) ignition delays in two different mixtures of CH3CN+ 02 in argon. From the distance between the two series of experiments, the power dependence with respect to the fuel, ]~(CH3CN),can be determined. A small inhibiting effect of acetonitrile can be seen. (See Color Plate 8).

(The deviation from an exact factor of 2 comes to compensate for the different shock compression in the two mixtures.) The figure shows a strong enhancing effect of the oxygen, and ]~oxygen can be calculated from the distance between the points in the two groups of experiments. The solid lines on the figure are the results of computer modeling, which will be discussed later. A similar plot is shown in Fig. 16.5.5 where mixtures B and D are compared. The figure shows the effect of the fuel concentration on the induction times. The oxygen concentrations and the initial pressures in the two mixtures are the same, but there is a twofold difference in the fuel concentrations. Figure 16.5.5 shows a small inhibiting effect of the fuel; in the mixture with the high fuel concentration, the induction times are somewhat longer. The effect of the inert gas concentration on the induction times can be seen in Fig. 16.5.6, where mixtures A and F are compared. In these two mixtures, the concentrations of both the fuel and the oxygen are the same. The mixture with the low percentage of the components is run at Pl -" 120 Torr, whereas the mixture with the high percentage is run at an initial pressure of P] = 60 Torr. The only difference between the two mixtures is thus the third-body density. A small inhibiting effect of the argon can be seen.

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Figure 16.5.7 shows a final least squares analysis, done to obtain average values of fli and E. Data points from six different experimental conditions are normalized with the parameters obtained by the least squares analysis, and are plotted as 2 vs 1/T. The points scatter along one line, the slope of which gives the average value of E. The parameters obtained are - - tignition /

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1 6 . 5 . 3 . 3 MODELING PROCEDURES One of the main purposes of ignition delay measurements is to provide experimental parameters that can form a basis for computer modeling of the combustion process. As has already been mentioned, a least squares analysis of many tests--run under different experimental conditions such as composition,

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o

~ i

~

° I

I 0 ~ 0 ~ 0 0 0 0 0 0 0 0 0 0 I I

22

~m

~ e ~ .ge .~e e e


,.--i

6

I

I

d

I

o

I

6

I

6

I

o

I

6

I

o

I

o

I

6

I

o

I

o

I

6

I

o

I

o

I

I

~

o

I

]

d

I

I

d

I

I

o

I

I

d

I

I

~

I

I

d

I

d

I

]

;

I

I

d

I

I

d

I

I

d

I

I

I

I

I I

+ o o+ +~o+o o+o+o + + u+u+ 6uuuuuu~uuuuuuu~SCCCCCJJ

=°°°°°

< ~ + + + + + < Z

o

~

I

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

~ I I I I

d

_.L,oL~

-
CO 4- SO unchanged.

16.5 IgnitionDelay Times

229

is slightly inhibited by the methane (Lifshitz et al. 1971; Tsuboi and Wagner 1974). The reaction rate constant of the reaction O ~ + C H 4 is several orders of magnitude higher than the rate constant of the reaction CH] + 02 (Westley et al. 1998). Therefore, the latter determines the rate of the loop and the increase in its rate will shorten the induction period. The reaction O ~ 4-CH 4 has no effect on the induction time (Seery and Bowman 1970 in: Smith et al. 1999, GRI-Mech. 3.0, ig.lb). The strong dependence of the induction time on the oxygen concentration and its very small dependence on the methane concentration is the direct result of the nature of the loop. In the three systems just described, the character of the thermal loop determines to a large extent the behavior of the overall oxidation. Such a behavior is typical to systems where the thermal decomposition prior to oxidation is not significant. In higher hydrocarbonsmpropane, for examplem where there is an early decomposition, the loop loses some of its significance.

16.5.4.3

THERMAL IGNITION WITHOUT

BRANCHING: N20

-+- C O S ,

N20

CHAIN

+ CO

As previously mentioned, chain-branching reactions are the dominant factor responsible for the ignition mode in combustion. However, there are cases where branching reactions cannot take place and the ignition results from heat release during the course of the reaction. If heat is released in a system of chemical reactions under adiabatic conditions, the temperature goes up and the rate increases exponentially, which is a condition for an ignition mode. This behavior can be found in systems where the oxidant is a molecule containing oxygen but it is not a molecular oxygen. Typical examples are the oxidation of carbonyl sulfide and carbon monoxide with nitrous oxide (N20) as an oxidant (Lifshitz and Kahana 1978, Borisov et al. 1978b). A mixture of N20 and COS is a very reactive mixture that readily ignites when raised to high temperatures, although chain branching does not take place (COS + O ~ ~ CO + SO~ The exponential behavior of the rate, which brings about the ignition phenomenon, results from an adiabatic release of energy and temperature rise during the course of the reaction. Since the supply of oxygen atoms comes from the selfdissociation of N20, the induction period is highly dependent on the initiation reaction, also fl(N20) = --1.09. Another test, which may indicate to what extent the temperature increase during the induction time is a dominant factor in ignition process, is a variation in the specific heat of the system. Indeed, when the heat capacity of the COS + N20 + Ar mixture is artificially increased by a factor of 2 in the modelling calculations, the induction times increase by close to 90% (Lifshitz and Kahana 1978). When chain-branching reactions are the

230

A. Lifshitz

dominant factor, the variation in the specific heat has only a minor effect on the ignition delay times.

16.5.4.4

T H E C O N C E P T OF ENERGY

BRANCHING- H 2 q- C12, H 2 q- F 2 The concept of energy branching was raised by Semenov (1962), who suggested the possibility of energy branching in the hydrogen chlorine reaction, where vibrationally excited HC1 formed in the H + C12 --~ HCI* + C1 reaction can transfer its vibrational energy directly to molecular chlorine and enhance its dissociation. To rationalize the fact that multiquantum transitions must occur very efficiently, he suggested a formation of a [HC13] complex, the lifetime of which is sufficiently long to allow a complete equilibration of the vibrational energy among the various degrees of freedom of the complex. This activated complex then dissociates, obeying the theory of unimolecular reactions, with one of the channels being [HC13]*---~ HC1 + C1~ + Cl'. This idea was verified by modeling the results of shock tube measurements of the ignition delay times in mixtures containing C12 and H 2 diluted in argon (Lifshitz and Schechner 1975). A reaction scheme based on a simple exothermal chain propagation, H ~ + C12 --+ HC1 + C1~ C1~ + H 2 @ HC1 + H" could not reproduce the experimental parametric relation. Also, the calculated induction times were longer than the measured ones for the same temperature, pressure and composition by about a factor of 2 and, the calculated Arrhenius temperature dependence was ~40% higher than the measured value. When the energy-branching reactions HCl*(v)i + C12 ~ [HC13]* --+ HCI(v -- 0) + C1 + C1 (i - 0 - 4) were added to the reaction scheme with the right vibrational distribution in HC1 molecules, an excellent agreement with the experimental results was obtained. The preexponential factors in this process were assumed to be independent of v and the activation energies were calculated from the relation Eactivation,v - - EC12 --E v

+

Eo

where Ec12 is the bond dissociation energy of C12, E v is the vibrational energy of the HC1, and E 0 is its ground state energy. Translation --~ vibration deactivation was also taken into account (Lifshitz and Schechner 1975).


231

Energy branching is believed to be a dominant factor in the thermal reactions of C12 and F 2 with hydrogen, where the HX is obtained in vibrationally excited states.

1 6 . 5 . 4 . 5 CORRELATION OF IGNITION DELAY TIMES WITH BOND DISSOCIATION ENERGIES: THE ROLE OF INITIATION VS CHAIN BRANCHING Ignition delay times vary by orders of magnitude from one fuel molecule to another. The temperature must be changed by hundreds of degrees to obtain identical ignition delays in different systems. Ignition delays (300ps, for example) in CH 4 and CH3NO 2 are measured at temperatures that differ by some 700 K (Lifshitz et al. 1990). This is demonstrated in Fig. 16.5.10, which shows plots of log tignition vs 1/T for a series of fuel molecules. As can be seen, there is a large spread in the reactivity of these molecules. The question is what the molecular properties are with which the ignition delays correlate. To answer this question, let us examine Fig. 16.5.11, which correlates the ignition delay times of six different molecules with their lowest bond dissociation energy. The figure shows a plot of 1/T vs Dc_ x, where the temperatures correspond to the same ignition delay time of 316 l~s (log tignition = 2.5) for all the six molecules. The temperatures at which the ignition delays are 316 ~s were calculated from the parametric relations of each system (Table 16.5.2) at

1600 I

3.5

1400 I-

1200 I

I

CH3-CN 0 (t)

1000 I

I

900 I

CH3-Br C H 3-

3.0

7-- 2.5 .9 ._ C O) O

2.0

.p-

CH3-CH 3 NO

o 1.5

2

I 1 I * J I I I I l | I I I * I I I i I ] i i i 1 i i i 0.6

0.8

1.0

|

1.2

1000/T (K -~) FIGURE

energies.

16.5.10 A plot of

log(tignition , ~S)

VS 1/T for fuels with different bond dissociation

232

A. Lifshitz

~ignition = 318 IJs 1.1 1.0

1000

0.9

1100 C H3- N H 2 " ~ I I CH3"C H3

0 X

I---

o.8

1300

C2HsCN9 ~ o.z

1500

CHa"oNto

0.6

CHa-H 0.5

1700

,,,,,,~,,IL,,,i,,J,l~,,,,,,,,

50

7O

9O

110

Dc. x (kcal/mol) FIGURE 16.5.11 A plot of 1/T vs De_ x, which is the weakest bond in the fuel. The temperature on the ordinate at each point corresponds to an ignition delay time of 318 ~s (1ogtignition "- 2.5).

similar fuel, oxygen, and argon concentrations. The bond dissociation energy is a good measure of the initiation rate, so the correlation shown in the figure is essentially the relation between the ignition delay times and the rate of initiation. The stronger the bond dissociation energy (lower initiation rate), the higher the temperature that is required to obtain the same ignition delay time. The question that now arises is, to what extent does this strong dependence of the ignition delay on the rate of initiation express itself in the sensitivity analysis of the kinetics scheme? In many cases it does not. In the system C H 4 + 0 2 , for example, the rate of initiation, C H 4 + M ~ CH~ + H ~ M, does not appear at all in the sensitivity list (Seery and Bowman 1970 in: Smith et al. 1999, GRI-Mech. 3.0, ig.lb). Doubling the initiation rate COS + M ~ CO + S ~ M in the system COS + 02 decreases the ignition delay by only 8% (Lifshitz et al. 1975). At first glance, these two observations might look contradictory. Why is there such a strong dependence of the induction times on the rate of initiation on one hand, and no dependence on this rate in the sensitivity analysis of the kinetics scheme on the other? In shock tube studies, ignition can occur only if the delay time does not exceed a period of 1 to 2 ms, the available reaction times in the shock tube. Moreover, at longer times, heat transfer and diffusion of hydrogen atoms to the walls as well as surface recombinations slow down the process and prevent the


233

ignition from taking place. When the dissociations are too slow, the initial concentrations of free radicals are insufficient for the chain branching to bring them up to a critical value in a matter of a few milliseconds. Ignition will therefore not occur. For ignition to occur, the initial concentrations of free radicals must reach a minimum value, so that branching can increase their number exponentially until the required critical value is achieved. One can therefore state that the temperature range over which ignition will take place is determined almost solely by the initiation rate of one of the reacting partners, as is demonstrated in Fig. 16.5.10. However, once sufficient free radicals are initially formed, the role of initiation in increasing the concentrations of the free radicals becomes negligible compared to the role of the chain branching. Therefore, over the temperature range where ignition can occur, the sensitivity of the system to the initiation reactions is normally small. Both the experimental findings and the explanation hold only when chainbranching reactions are the major factor in the kinetics scheme. In systems where branching does not OccurmCOS + 2N20 ~ SO 2 + 2N 2 + CO (Lifshitz and Kahana 1978) and N20 + CO ~ N 2 + CO2 (Borisov et al. 1978b), for example--and the ignition is the result solely of the temperature increase during the course of the reaction, the findings are completely different. The sensitivity of the ignition delay to the dissociation rate of N20 is high. In the system C O S + N 2 0 , it decreases by 45% for a twofold increase in the dissociation rate constant (Lifshitz and Kahana 1978).

16.5.4.6 T H E D E P E N D E N C E OF THE I G N I T I O N DELAY T I M E ON THE F U E L C O N C E N T R A T I O N 16.5.4.6.1 Inhibiting Effects due to Competition Reactions: Hydrocarbons In addition to the importance of initiation, termination, and chain branching, competition reactions play a very important role in the progress of the ignition process. In fact, as we shall see later, the dominant factor that determines the dependence of the induction times on the fuel concentration is the competition on active free radicals between the fuel and the oxygen. In the hydrocarbon system, methane for example, hydrogen atoms are produced by the initiation reaction CH 4

q- M ~ CH~ + H ~ + M

234

A. Lifshitz

After hydrogen atoms have been produced, a competition between the fuel and the oxygen on the hydrogen atoms takes place: H"/7 +CH4 --+ CH~ + H 2 "N + 0 2 _ + O H ' + O ~ The net rate of these two reactions are roughly the same for the same oxygen and fuel concentration. However, whereas the reaction with oxygen is a chainbranching reaction that is extremely important to the ignition process, the reaction with methane, which competes on the H atoms, is a much less important linear chain and has therefore an inhibiting effect. It not only prevents the chain branching from taking place, it also replaces a reactive hydrogen atom by a considerably less active methyl radical. The positive power dependence, fl(CHO -- +0.33 (Lifshitz et al. 1971; Tsuboi and Wagner 1974), is the direct result of the effect of the reaction of H ~ with C H 4. Indeed, if this step is artificially removed from the reaction scheme, the calculated positive power dependence disappears, and the induction times become independent of the methane concentration. This behavior changes at very low equivalence ratios, 1/10, for example, where flmethane is negative. Under these conditions, the ability of the fuel to compete with the oxygen diminishes drastically and then no longer inhibits the progress of the reaction. Similar behavior is found in higher hydrocarbons, R1-R2, both aliphatic and aromatic, where H atoms are not the main product of the dissociation. Here the competition between the hydrocarbon and the oxygen on R~ is in the following form (Baker and Skinner 1972; Burcat et al. 1972; Hidaka et al, 1981; Burcat et al. 1986b; Hidaka et al. 1983; Burcat and Dvinyaninov 1995; Burcat et al. 1996b; Burcat et al. 1979; Thyagarajan 1990):

RI/7 +R1-R2 '+ R~ + R1H "~ + 0 2 ---> R1O~ + O ~ In the first reaction, a small radical is producing a larger and less-reactive species whereas the second reaction is a chain branching. As can be seen in Table 16.5.2, a positive power dependence on the fuel concentration is common to almost all hydrocarbons and is dictated by this competition reaction. At high temperatures, however, when the dissociation of the higher hydrocarbons becomes quite significant, the dissociation begins to appear among the reactions that shorten the ignition delay. The system COS + 02 is another example of a system with a series of competition reactions of different nature that determine the inhibiting effect (positive 13) of COS (Lifshitz et al. 1975). The process begins with the formation of sulfur atoms by the self-dissociation of COS: COS + M --~ CO + S~ + M

16.5

235


The oxygen molecule and carbonyl sulfide compete on the S atoms in the same manner as in the methane oxygen system: S" 7 + 0 2 ~ S O ' + O" + C O S --+ CO + S2

The reaction with the oxygen is a chain-branching reaction, whereas the reaction with COS is a termination. The latter is in fact the reason for the inhibiting effect of the fuel. There are other competition reactions in this system of a quite different nature, such as the two parallel reactions of oxygen atoms with COS:

c o s + o" "~ c o + so" CO2 + S~ The first reaction is simply a propagation reaction, which important as it may be does not lead to branching. The second reaction produces sulfur atoms that do enter into a branching reaction: S" -~- 0 2 --> SO" -~- O"

The first reaction has an inhibiting effect and the second has an accelerating effect, so they practically cancel one another. The inhibiting effect of the COS fuel comes solely from the reaction S~ + COS --~ CO + $2 which is practically a termination reaction. It prevents the S" atoms from entering into a chain-branching reaction with the oxygen molecule. 16.5.4.6.2 Enhancing Effects due to Thermal Excitation: The Epoxy Group of Molecules In contrast to the ignition characteristics of hydrocarbons where the fuels have positive ]~fuel values, there are fuels in which other factors play a role in the oxidation process and inverse the picture. A very interesting example of such a behavior is the epoxy group of molecules. As can be seen in Table 16.5.3, the common feature in the ignition of this group is the strong enhancing effect of the fuel (a large negative value for/~fuel) and the large inhibiting effect of the diluent. Although the competition reactions discussed earlier play a role in any C - H system, including the epoxy group of molecules, their inhibiting effect is overcompensated in the present line of fuels by two other factors that do not exist in simple hydrocarbons. The three-membered epoxy ring, being an unstable structure, tends to quickly open and isomerize to more stable molecules such as ketones, aldehydes, alcohols, and ethers (Lifshitz and Tamburu 1994, 1995). In view

A. Lifshitz

236 TABLE 16.5.3 Experimental Ignition Parameters for Various Epoxy Fuels: z = 10~exp(E/RT)[Fuel]~[O2]&[M]&

o~

E (kcal/mol)

//1

//2

Ethylene oxide, 02, Ar

- 12.62

29.6

-0.44

-0.72

Ethylene oxide, 02, N2 Propylene oxide, 02, Ar

-12.81 -14.28

30.8 33.6

-0.82 -1.07

-0.91 -0.52

1,2-Epoxybutane, 02, Ar - 14.56

31.5

-0.86

-0.72

2,3-Epoxybutane, 02, Ar -15.73

34.3

-0.92

-0.76

Components

]~3

Reference

0.78 Lifshitzand Suslensky [1995] 1.48 Burcat [1980] 0.78 Lifshitzand Suslensky [1995] 0.92 Lifshitzand Suslensky [1995] 0.89 Lifshitzand Suslensky [1995]

of the large differences in the heats of formation of the epoxy molecules and some of their stable isomers, the more stable molecules are produced with excess thermal energy. This excess energy is equal to Eact + AHr, where Eact is the activation energy of the isomerization process and AH r is its exothermicity. An energy diagram for the isomerization of propylene oxide is shown as an example in Fig. 16.5.12. The thermally excited acetone, and to a lesser extent propanal, can now either lose their energy by collision with the diluent to produce stable isomers, or, as shown in Fig. 16.5.12, can decompose to produce free radicals that support the chain reactions in the process. This feature, which is common to all the epoxy molecules, is responsible for the high production rate of free radicals. Hydrocarbon fuels dissociate from a state of a Boltzmann distribution corresponding to the temperature of the bulk. Since in most cases this is a slow process, the contribution of simple fuel dissociation to free radical production is negligible. Chain branching takes over at the very early stages of the reaction. The competition reaction H ~ 4- RH -~ H 2 4- R ~ which is a fast reaction, is not compensated by any enhancing reactions in which the fuel is involved. In view of the dissociation from a thermally excited state, the dissociation in the epoxy group of molecules is very fast compared to a normal hydrocarbon dissociation. Its contribution to the overall production of free radicals is therefore important during most of the induction time and can compete with the contribution from the chain-branching processes. This contribution overrides the inhibiting effect of the fuel and leaves an overall enhancing effect. It expresses itself experimentally by the high negative power dependence of the induction times on the fuel concentration (Lifshitz and Suslensky 1995).

16.5

237


energy level of the thermally excited isomers C H +CHO

CH2CH=CH2+OH o!

......

/ _ E-59+2 kcal/mol [

....

i

....

" kcal/mol AH=62 kcal/mol [

......

.... I .........

] [

AI4--~ 1 k~al/mol

kcal/mol

[

CH3CH--CH 2 ........ - " " '" """ . . . . . . . . . . . . . I . . . . . . . . . . . . 4 , - 9 . 4 \ / CH2=CH-O-CH ~ [ -'- ~--O -22.7 [ CH2=CHCH2OH I

,-3o.8

CH3COCH 3 FIGURE 16.5.12 Energy diagram for the isomerization of propylene oxide. Acetone and, to some extent, propanal are formed in a thermally excited state with enough energy to dissociate from this state before being de-excited.

When the dissociation from the thermally excited state was introduced into the kinetics scheme, a very good agreement between the experimental and calculated induction times and power dependencies was obtained. When this step was removed from the scheme, the agreement was very poor. An additional factor in the enhancing effect of the fuel is the large amount of heat released in the process of isomerizations. There are several nitrogen- and oxygen-containing fuels that show a negative power dependence on the fuel concentration (see Table 16.5.2). Not all are clear and easily explained unless there are no competition reactions that can cause inhibition. One very important group of fuels is the unstable hydrazines (Abid et al. 1991; Catoire et al. 1994, 1997, 1999). Their enhancing effect results probably from their strong exothermic decomposition during the induction period. Frenklach and coworkers discussed a general relation between exothermicity and induction times (Rabinowitz and Frenklach 1987). Another group of molecules is the organic amines ( - N H 2) (Lifshitz et al. 1991; Lifshitz and Suslensky 1999). It has already been suggested in the study of the ignition of monomethylamine that the normal inhibiting effect of the fuel is compensated by additional reactions that are not effective in the ignition of simple hydrocarbons. These reactions are involved in the produc-

238

A. Lifshitz

tion of H202, which then decomposes quite rapidly to two OH radicals. The sensitivity analysis of the monomethylamine ignition (Lifshitz et al. 1991) shows that the ignition delay times in this system are highly sensitive to the reaction CH3NH 2 + HO~ --~ CH~NH 2 + H202 The ignition schemes do not show sensitivity to the equivalent reactions in simple hydrocarbons.

16.5.4.7

I N H I B I T I N G E F F E C T S OF THE D I L U E N T

As can be seen in Table 16.5.2, in almost all cases where the power dependence of the ignition delay on the diluent concentration//diluent was determined the dependence was positive. Increasing the diluent concentration inhibits the process. In hydrocarbon and many other fuels the diluent (nitrogen if air is being used, or simply argon) plays two different roles during the induction period. One is the role of a third body in dissociation-recombination reactions. Due to chain branching, the concentrations of free radicals in the system overshoot their equilibrium concentrations at the early stages of the reaction. The role of argon or nitrogen as third bodies is thus to enhance recombinations rather than dissociations and to decrease the overall concentration of free radicals. This would manifest itself in a positive, although small, power dependence. The second effect of the diluent is a cooling effect. Since in many systems heat is released as the reaction proceeds, the temperature and the overall rate increase. An increase in heat capacity for the same amount of heat release--by increasing the diluent concentrationmdepresses the temperature elevation and thus inhibits the progress of the reaction. In the epoxy group of molecules, for example, a considerable amount of heat is generated in the process of isomerization so that this effect becomes quite significant. As can be seen in Table 16.5.3,//argon in the epoxy group is high compared to the values that we find for most of the other fuels (Table 16.5.2). There is an additional and more significant inhibiting effect of the diluent in the epoxy group: the quenching of the thermally excited species that are formed in the isomerization (Fig. 16.5.12) (Lifshitz and Tamburu 1994). Since these excited species can lose their excess thermal energy by collisions with argon (or nitrogen), an increase in the diluent concentration will increase the quenching rate and prevent the thermally excited molecules from dissociating to free radicals.

16.5

239


16.5.4.8

E F F E C T OF ADDITIVES

The addition of small amounts of fuels or oxidizers with lower bond dissociation energies shortens the induction times and varies their temperature and concentration dependencies. Borisov et al. (1988) and Zamansky and Borisov (1992) have studied the effects of a large number of additives on hydrocarbon ignition. They examined the effects of additives such as (CH3)2N2, CH3ONO , CH3ONO 2, N2F 2, n-C3H7NO 2, iso-C3H7NO2, and several others. The promoting effects of these additives was attributed to their fast decomposition, which produced a high concentration of free radicals. Propane and/or ethane added to methane (Smith et al. 1999, GRI-Mech. 3.0; Lifshitz et al. 1971; Frenklach and Bornside 1984; Yang et al. 1996), hydrogen to cyanogen (Lifshitz and Bidani 1980, 1986), and nitrogen dioxide to methane (Dorko et al. 1975; Dabora 1975; Burcat 1977) were also examined. In some cases the power dependencies of the ignition delay on the additive concentrations were determined (Spadaccini and Colket 1994; Lifshitz and Bidani 1980, 1986). These dependencies always had, as expected, negative 13 values. Interesting studies on the ignition of methane in the presence CH3-X (where X = C1, Br, or I) were reported by Baug6 et al. (1997) and Burcat et al. (1996c). The presence of these additives, which are known as inhibitors of combustion processes in general as well as flame retardants, cause a decrease in the induction times compared to those in pure methane. These observations imply that the inhibitions in halocarbons caused by the recombinations of Br or C1 with H and by other inhibiting reactions may be very significant, but are not strong enough to override the high decomposition rate due to the weak C-Br and C-C1 bonds.

16.5.5 COMPUTER MODELING

16.5.5.1 REACTION SCHEME The purpose of the computer modeling is to examine the validity of a suggested mechanism in light of the experimental observations. The main issue is to reproduce the induction periods and, perhaps more significantly, the parameters E and ]~i in the parametric relation tignition - 10~ exp[E/RT] I~ C3i i which is obtained by a least squares analysis of all the experimental data. The modeling procedures were discussed in section 16.5.3.3. In Table 16.5.4, the kinetics scheme of the ignition in a mixture of CH3CN and 02

240

uz £ U

o~

~8

iu

~4 J

I

17

I

I

~

I

~

~ = =

,

~

xxxxxx×xxxxxxxxxxxxxxxxxx~xxxxxx

~

~XXXXXXXXXXXXXXXXXXXXX~XX

o~BB

.

7--

~

~

-I,

,

,

,

(a)

t

I

I

1.o

2.0

1.5 ~I,,.~ ,.~

tN) ~1.,,I

1.0

~

0.5

r,~

0.0

__~_~~r~j

(b)

I . . . .

I000

200O

30OO

Time (Its) FIGURE 16.6.2 Transmissionand scattering of light during shock tube pyrolysis of ethylbenzene in argon at 1750K (Graham et al. 1975a)

270

H. Wang 2.0

1.5

- 4

,o ~

•

- 2 1.0

r~

-0

0.5-

0.0I

i

0

500

,,I

1000

Time

I

1

1500

2000

(las)

FIGURE 16.6.3 Soot volume fraction profile from light extinction and pressure record for benzene pyrolysis behind a reflected shock wave. T5 = 1890 K, P5- 50bar, and [C]= 8.3 • 10-e mol/cm3 (Bauerle et al. 1994). The fv data were obtained from light extinction at 632.8 nm, initially derived with the complex refractive index value of Lee and Tien (1981), and were rescaled here using the ffa value of Dalzell and Sarofim (1969). The dashed line is fit to data using the apparent first-order rate equation df~/dt=kf(fv,oo-f~ ) with kf = 2 2 0 0 s -1 and [v,oo = 1.26 x 10 - 6 . The induction time of soot appearance is denoted by z (= 0.124 ms).

diameter (D) (MOller and Wittig 1994), which can be solved with the Mie theory using, for example, the approach of Aden (1951). A log-normal distribution is commonly assumed for the calculation of the right-hand side of Equation (16.6.18), N

n(D) -- x / ~ D In ag

[ ( l n D - l n l D g ) 2] exp 2 In 2 ag

(16.6.19)

where ag is the standard deviation and/Dg is the m e d i u m diameter for which exactly one-half of the particles are smaller and one-half are larger (Seinfeld 1986). In principle, the standard deviation varies as a function of time from the onset of particle nucleation. For a particle growth process dominated by coagulation in the free-molecule regime, however, the PSDF tends to a selfserving distribution (Lai et al. 1972; Graham and Homer 1973a, 1973b; Graham et al. 1975a). In flames, In ag tends to a constant value of 0.34 after a short reaction time. A wide range of In ag values have been reported or used for soot produced from shock robes. Miiller and Wittig (1994) used a In ag value of 0.5 in the evaluation of the dispersion quotient [Equation (16.6.18)], whereas Bauerle

16.6

271

Particulate Formation and Analysis

et al. (1994) and Knorre et al. (1996) reported a geometric standard deviation ln~rg ~ 0.2 for soot produced from shock tube pyrolysis of a variety of hydrocarbon compounds. The dispersion quotient technique may severely overestimate the particle size. Frenklach et al. (1996) showed that irrespective of the assignment of the rh values, the particle sizes determined by the dispersion quotient technique is substantially larger than those determined from transmission electron microscopy. Assuming that the particles are monodispersed results in even larger discrepancies. More sophisticated light extinction and scattering techniques have been developed for studies of particles formation in shock tubes. For example, retrieval of soot aggregate morphology is possible by detection of the scattered light intensities at different scattering angles (di Stasio et al. 1996; di Stasio and Massoli 1997).

1 6 . 6 . 3 . 2 COMPLEX REFRACTIVE INDEX Perhaps the largest uncertainty in the optical measurement of soot volume fraction or yield is the complex refractive index. In earlier studies (Graham et al. 1975a, 1975b; Wang et al. 1981; Frenklach et al. 1983a), soot yields exceeding 100% were observed from light extinction experiments. It is most likely that this overshoot is caused by uncertainties in the complex refractive index. Indeed, a wide range of complex refractive indexes have been reported for carbon particles. The most frequently used values of refractive index are summarized in Table 16.6.4 for soot at 632.8 nm. It is seen that the discrepancy is significant among the published values of refraction index. In particular, the imaginary part of the complex number, (rh 2 - 1)/(~ 2 + 2), varies by as much as a factor of 1.7 when comparing the results of Lee and Tien (1981) and Menna and D'Alessio (1981). In Rayleigh region, the soot yield or soot volume

TABLE 16.6.4 Most Frequently used Values of Complex Refractive Index (rh = n - ik) of Soot Material n 1.57 1.85 1.70

k

Im{(rn2 - 1)/(rn2 + 2)}

I(rn2 - 1)/(rn2 4- 2)1

Reference

0.56 0.48 0.75

0.26 0.18 0.30

0.47 0.51 0.57

Dalzell and Sarofim 1969a Lee and Tien 1981 Menna and D'Alessio 1981

Used in the present compilation of soot yield data

272

H. Wang

fraction evaluated using these index values should different by the same amount. The complex refractive index varies markedly with the wavelength for flame soot. Figure 16.6.4 shows the variation of the index of refraction as a function of the wavelength, from several representative sources. It is known that the refractive index also varies with temperature. However, Lee and Tien (1981) showed that this variation is not significant: changes in n and k did not exceed 30% from 1000 to 1600 K, which are well within the absolute uncertainty of the refractive index itself. For this reason, the temperature dependence of the refractive index is usually ignored above 1000 K. The data shown in Figure 16.6.4 represent an average of the refractive index at these temperatures. Even larger uncertainties exist for silicon particles produced in shock heating of silane and disilane. Frenklach et al. (1996) observed that under the same silicon loading and at a reaction time of I ms, the transmittance at 632.8 and 441.6nm initially increases and reaches a peak at around 11001200 K. The transmittance then decreases up to a temperature of "~ 1300 K, above which it remains unchanged until 1900K. On the basis of kinetic considerations, they concluded that the decrease in transmittance above 11001200 K can only be explained by a change in the complex refractive index of

5i ~176176~176176176176 ~176176176176

~.~

~

-"

"o

tp,,q

1 0.8

.... ..

~...-'" .~"~

0.6

0.4

0.2

......... Dalzell & Sarofim (1969) ~ Lee & Tien (1981) - - -Chang & Charalampopoulos (1990) I

I

I

I,

I

I

I

I

I

,,,

I

1000

I

I

I

I

I,,I

[

100120

Wavelength (nm) FIGURE 16.6.4 Real and imaginary parts of the complex refractive index, ffa = n - ik, of soot material

16.6


273

the silicon particles because of the transition of particles from a solid-phase material to liquid droplets. Using a detailed kinetics model, Frenklach et al. (1996) fitted the transmittance profiles by a unique contour of n versus k for experiments conducted at temperatures above 1286 K. This contour encompasses the complex refractive index of liquid silicon (Jellison and Lowndes 1987), r h - 3 . 5 - 5.2i at 2 = 632.8nm and r h - 2 . 6 - 4 . 8 i at 441.5nm. A further note from that study is that although the melting temperature of bulk silicon is 1683 K, submicron particles can melt at much lower temperatures than that of the bulk material (Buffat and Borel 1976). 16.6.3.3

LIGHT EMISSION

The onset of light emission due to radiation of particles has been used to characterize the induction time of soot formation in shock tubes (Mar'yasin and Nabutovskii 1973; Gosling et al. 1973; Graham et al. 1975a; Graham 1981; Fussey et al. 1978; Tanzawa and Gardiner 1979). The detection of light emission is accomplished simply by a photomultiplier. The peak sensitivity of the photomultiplier should be around the wavelength of maximum radiation intensity of a blackbody, e.g., around 800 nm at 1600 K. A filter must be used to reject light having wavelength below 730 nm, so that the major emission bands from the C 2, CH, and CN radicals can be excluded (Fussey et al. 1978). A typical emission record is shown in Figure 16.6.5, where the onset of emission or soot formation is clearly identifiable. Monochromatic, infrared emission diagnostics was reported by Parker et al. (1990) for soot formation behind reflected shock waves. The emission measurements were made using calibrated, bandpass-filtered radiometers. The emission data are converted to emissivity by taking the ratio of the observed radiance to that of a blackbody. The emissivity e is related to the absorption coefficient KabS by Kabs =

- ln[1 - e(2)] l = O'abs(~)[C]soo t

(16.6.20)

where Crabs(/~) is the effective absorption cross section and [C]soo t is the number density of carbon in soot. The value of the absorption cross section can be evaluated from the index of refraction of the particle material (Parker et al. 1990; Van de Hulst 1981).

1 6 . 6 . 3 . 4 OTHER DETECTION T E C H N I Q U E S Laser Doppler anemometry and particle sizing using laser interferometry (Farmer 1972) has been introduced for particle measurements in shock

274

H. Wang

Induction time

o

al

0

..

~

/

I

I

~

200

~

~

I

400

.

,

,

,

I

600

9

~

,

.

.!.

800

.i..

1000

Time (laS)

~ Onset of emission Shock arrival

t

Contract surface arrival

FIGURE 16.6.5 A typical light emission trace of hydrocarbon pyrolysisin shock tube (Fussey et al. 1978) tubes (Frenklach et al. 1983c). Particle detection methods other than the lightbased measurements have been reported. For example, the material balance of carbon and hydrogen in the products of acetylene pyrolysis in a shock tube was used to quantify the production of soot (Mar'yasin and Nabutovskii 1969, 1970). Vaughn et al. (1981) reported a gravimetric analysis of the solid residue formed from benzene pyrolysis using a removable liner in the end section of the shock tube. Particle samples can be collected on substrates affixed on or near the end wall of a shock tube (Frenklach et al. 1996). The particle sample on the substrate can then be analyzed by transmission electron microscopy (Williams and Carter 1996) to examine the particle size distribution and morphology or by electron diffraction (Cowley 1992) to examine the crystal structure.

16.6.4 SOOT FORMATION 16.6.4.1

INDUCTION TIME

The induction time z can be determined from the intersection of the tangent at the inflection point of a light transmittance or soot volume fraction curve with

16.6

275


the time axis (see, for example, Figure 16.6.3), or by the onset of light emission (see, for example, Figure 16.6.5). Unlike the ignition delay time, the induction time of soot formation is somewhat ambiguous. In the case of ignition delay measurements, the reaction or heat release rate beyond the induction time is so rapid that different methods yield essentially similar quantitative results. This is not the case for soot formation. Fussey et al. (1978) showed that light emission tends to give shorter induction time than light extinction at 632.8nm. Frenklach et al. (1983a) showed that the induction period determined by light extinction in the infrared (3.39 ~tm) are longer than those in the visible (632.8nm). Indeed, an examination of Graham's transmittance traces (Graham et al. 1975a) in Figure 16.6.2 readily points to the difference in the induction time determined at different wavelengths. For this reason and because the induction time correlation does not seem to provide any indication of the nature of a rate-determining step, the real significance of the induction period has been questioned by Haynes and Wagner (1981). Nonetheless, we shall summarize the past experimental results below because these data provide a semiquantitative guidance of sooting tendency. Although ignition delay and induction time of soot formation are completely different physical properties, they share similarity in the methods of correlation. Following the idea of ignition delay correlation (Burcat et al. 1970; Lifshitz et al. 1971), Gosling et al. (1973) correlated the induction time of soot formation with temperature and the initial hydrocarbon concentration in the form of

(E)

zPi_ic -- A exp ~-~

(16.6.21)

where z is the induction time and PHC is the molar density of hydrocarbon. Figure 16.6.6 presents the induction time data of Gosling et al. (1973) and of Fussey et al. (1978) for acetylene, ethylene, and ethane pyrolysis in argon behind incident shock waves. The induction times are plotted in the form of the product of induction time and the C-atom concentration, z[C], which is equivalent to the left-hand side of Equation (16.6.21). Figure 16.6.6 shows that under the same carbon loading, acetylene tends to produce soot earlier than ethylene and ethane. Fussey et al. (1978) found that Equation (16.6.21) does not yield a unique correlation for experiments conducted at different pressures. To account for the pressure effect, they correlated the induction time of soot formation in the form of

(E)

z[C]n -- A exp ~-~

(16.6.22)

H. Wang

276

'~,

A

I0-3

c~i~ C~H~ ,~.~o ~~ 2 ~ 0 c~

~" 10-4 9

A ~"

AA A

A

I

4.5

5.0

,

I,

I

I

I

5.5

6.0

6.5

7.0

104 K / T FIGURE 16.6.6 Inductiontimes of soot formation multiplied by the C-atom concentration as a function of temperature for acetylene, ethylene, and ethane pyrolysis in argon behind incident shock waves. The induction times were determined by the onset of light emission. Solid symbols: data for P2 = 1-2bar from the appendix of Fussey et al. (1978) with initial concentrations [C2H2]0 -" 1.33-2.89 x 10-7 mol/cm3, [C2H4]0 -- 1.79-2.90 x 10-7 mol/cm3, [C2H6]0 = 1.672.63 x 10-7mol/cm3. Open symbols: data for pressures of 0.02-0.04bar from Gosling et al. (1973).

for the pyrolysis of ethane, ethylene, and acetylene in the pressure range of 1-12bar. Figure 16.6.7 presents the selected data and their fits with n - 0.41, E -- 31 kcal/mol for acetylene; n - 0.23, E -- 28 kcal/mol for ethylene; and n - 0 . 4 2 , E -- 36 kcal/mol for ethane (Fussey et al. 1978). Using light extinction at 632.8nm, Yoshizawa et al. (1978) measured the induction time of soot formation from acetylene pyrolysis behind reflected shock waves for pressures between 2.8 and 3.5 atm. They found that the induction time exhibits a first-order dependence on the initial acetylene concentration. Using a similar technique,however, Frenklach et al. (1983b) found that at 632.8 n m and 3.39 ~m the induction time of soot formation from acetylene pyrolysis is not affected notably by the C-atom concentration. Figure 16.6.8 presents the data of Yoshizawa et al. (1978) and Frenklach et al. (1983b). The data at T < 2200 K can be correlated by 1: = 2.9 x 10-3[C]-~

-~

exp(13 , 000/ T)

(~s, m o l / c m 3)

The m a r k e d deviation of the data points from the regression line, however, indicates a certain inadequacy of the empirical correlation. The correlation exhibits only a weak dependence on both the total carbon loading and the argon concentration. The high-pressure data of B6hm et al. (1998) and Knorre

16.6

277


102 g []

C2H4

D

101

C2~

O []

0

9

lOo • t~

lO-I

4.4

)

t

I

I

4.8

5.2

5.6

6.0

.

t

6.4

. 6.8

104 K / T FIGURE 16.6.7 Induction time of soot formation from acetylene, ethylene, and ethane pyrolysis in argon behind incident shock waves (Fussey et al. 1978). The induction times were determined by the onset of light emission. Filled symbols: data for pressures of 1-2 bar and with initial concentrations [C2H2] 0 -- 1 . 3 3 - 2 . 8 9 x 10 -7 mol/cm 3, [C2H6] 0 = 1 . 6 7 - 2 . 6 3 x 10 -7 mol/cm 3. Open symbols: data for pressures of 10-12bar with initial concentrations [C2H2] 0 = 1 . 6 8 - 2 . 1 4 x 10 -6 mol/cm 3, [C2H4] 0 = 1 . 2 9 - 1 . 7 0 x 10-6mol/cm 3, [C2H6] 0 = 1 . 3 1 - 1 . 6 9 x 10 -6 m o l / c m 3. The lines are fits to data: z x [C] n = A e x p ( E / R T ) with n = 0.41, E = 31 kcal/mol ol for acetylene, n = 0.23, E - - 2 8 k c a l / m o l for ethylene, and n = 0.42, E = 36kcal/mol for ethane.

et al. (1996) are also shown in Figure 16.6.8. Knorre et al. (1996) correlated data collected at elevated pressures up to 60 bar and reported the expression z = A e x p ( 2 7 , 4 0 0 / T ) [ C ] -~ The dependence of z on C-atom concentration was found to be similar to that of benzene as well as mixtures of benzene and acetylene under similar pressures. The systematic deviation of the correlations obtained at low and high pressures is obvious. Finally, it is interesting to see the change in the induction time dependence on temperature at around 2300 K (Yoshizawa et al. 1978), which cannot be described by the simple correlation (16.6.22). Such a behavior has not been observed from the pyrolysis of other hydrocarbon compounds. Despite the uncertainty that is likely to exist in the general correlation equation of soot induction time, it is certain that a correlation exists between the induction time and temperature if the C-atom concentration is held fixed. The total pressure affects very little the induction time (Bauerle et al. 1994; Knorre et al. 1996), as evidenced by the weak dependence of z on the argon concentration in induction time correlation reported by Wang et al. (1981) and by Frenklach et al. (1983b). In general, an increase in the C-atom concentra-

278

H. W a n g

10a o 0

~.

101

x

t

xx

+ X X r n O +4~ X .4 ^ , , . ~ +4.+. + X~D 0 ~ n ~ "~ v O4- +.+, 9 ++ + O0 ~ +

10o

< r~ •

~ ~'O+ " +

+

OtJ

J

-I

%

~#+

v , - + ~++Jrr

lO-1

I

I

3.5

4.0

.....

I

I

4.5

5.0 10 4

......IJ

5.5

I

6.0

6.5

K/T

FIGURE 16.6.8 Induction time of soot formation from acetylene pyrolysis in argon behind reflected shock waves. The induction times were determined by laser light extinction at 632.8 nm. Triangles (Frenklach et al. 1983b): 1.09%C2H2 in argon, [C] = 3.34-3.42 x 10 -7 mol/cm 3. Open diamonds (Frenklach et al. 1983b): 4.65% C2H2 in argon, [C] = 3.22-3.44 x 10 -7 mol/cm 3. Circles (Frenklach et al. 1983b): 4.65% C2H2 in argon, [C] = 8.08-8.56 x 10 -7 mol/cm 3. Squares (Frenklach et al. 1983b): 20% C2H2 in argon, [ C ] - 7.78-9.12 x 10 -7 mol/cm 3. x (Yoshizawa et al. 1978): 2.5% C2H2 in argon, P5 = 2.8-3.5atm. Crosses (Yoshizawa et al. 1978): 5% C2H2 in argon, Ps =2.8-3.5atm. Filled diamonds (BOhm et al. 1998): [C]=3.8 x 10-6 mol/cm 3, p5 = 56bar. Solid line: fit to the low-pressure data of Yoshizawa et al. (1978) and Frenklach et al. (1983b) z - 2.9 x 10-3[C]-~ -2"95 exp(13, O00/T) (its, m o l / c m 3) for T < 2200 K. Dashed line (Knorre et al. 1996): from the fit of data at 60bar in the form of z x [C]~ - A exp(O/T).

tion r e d u c e s the i n d u c t i o n time. T h e e x t e n t of this i n f l u e n c e varies a m o n g different h y d r o c a r b o n s . F i g u r e 16.6.9 p r e s e n t s the i n d u c t i o n t i m e data of e t h y l e n e pyrolysis in reflected s h o c k w a v e s at 5 0 b a r a n d the C - a t o m c o n c e n t r a t i o n e q u a l to 4.26 x 10 -6 m o l / c m 3 (Bauerle et al. 1994). T h e c o r r e l a t i o n yields z(].ts) = 2.6 • 10 -4 e x p ( 2 6 , 0 0 0 / T ) . Bauerle et al. (1994) n o t e d t h a t o n l y a s m a l l c h a n g e in the i n d u c t i o n t i m e was o b s e r v e d w h e n the C - a t o m c o n c e n t r a t i o n was varied f r o m 3 x 10 -6 to 1.6 • 1 0 - S m o l / c m 3. F i g u r e 16.6.10 s h o w s the i n d u c t i o n times of allene a n d 1 , 3 - b u t a d i e n e pyrolysis at a C - a t o m c o n c e n t r a t i o n of ~ 3 . 3 x 10 -7 m o l / c m 3 ( F r e n k l a c h et al. 1983b). It is s e e n t h a t i n d u c t i o n t i m e of allene is s h o r t e r t h a n t h a t of 1 , 3 - b u t a d i e n e by a b o u t a factor of 3. U n d e r the c o m p a r a b l e c o n d i t i o n , the i n d u c t i o n time for allene is j u s t slightly l o n g e r t h a n that for t o l u e n e . T h e i n d u c t i o n t i m e of 1 , 3 - b u t a d i e n e , o n the o t h e r h a n d , is close to that of a c e t y l e n e u n d e r c o m p a r a b l e c o n d i t i o n s .

16.6

279

Particulate Formation and Analysis 104

103

3J f

102

101

Z 4.4

46

7

jo

4.8

50

5.2

5.4

5.6

5.8

6.0

10 4 K / T FIGURE 16.6.9 Induction time of soot formation from ethylene pyrolysis in argon behind reflected shock waves (Bauerle et al. 1994). The induction times were determined by laser light extinction at 632.8nm. Ps = 50bar; [C]= 4.25 x 10 -6 mol/cm 3.

10"

103

102

10 ~ z,.0

i

i

i

i

i

4.5

5.0

5.5

6.0

6.5

7.0

10 4 K / T FIGURE 16.6.10 Induction time of soot formation from allene (0.726% in argon) and 1,3butadiene (0.54% in argon) pyrolysis behind reflected shock waves (Frenklach et al. 1983b). In both experiments, [C]= "~3.3 • 10 -7 mol/cm 3. The induction times were determined by laser light extinction at 632.8 nm. The data can be correlated by z(~ts)= 1.33 x 10 -2 exp(18, 200/T) for allene and z(~s)= 7.54 x 10 -2 exp(17, 100/T) for 1,3-butadiene.

280

H. Wang

Figure 16.6.11 presents the induction time data of soot formation from benzene pyrolysis in argon behind reflected shock waves (Bauerle et al. 1994; Knorre et al. 1996; B6hm et al. 1998). All of the data were collected at the elevated pressures of 50 to 60bar. Bauerle et al. (1994) noted a strong dependence of ~ on the C-atom concentration and reported an empirical correlation equation, z = 3.1 x 10 -10 exp(31,300/T)[C] -~ (Its, mol/cm3). This correlation was obtained by varying the C-atom concentration from 3.3 x 10 -7 to 4.2 x 10 -5 mol/cm 3. Under comparable conditions, the onset of sooting in benzene pyrolysis is 1 order of magnitude faster than that of ethylene and n-hexane. Figure 16.6.12 shows the induction time data for n-hexane pyrolysis behind reflected shock waves (Hwang et al. 1991; Bauerle et al. 1994). Again all data reported in the literature are obtained at elevated pressures, ranging from 20 to 100 bar. Very little pressure dependence was observed for hexane, and the data show an activation energy of about 51 kcal/mol (Bauerle et al. 1994). For a variation of the C-atom concentration between 5 x 10 -6 to 4 x 10 -5 mol/cm 3, hardly any dependence of ~ on [C] was found. Figure 16.6.13 presents the induction time data for toluene pyrolysis behind reflected shock waves (Wang et al. 1981; Frenklach et al. 1983a; Parker et al. 1990). Although Wang et al. (1981) did not report actual data, they

lO'

lo3 o 102

101

J 1

o

04.0

.

I

i

i

4.5

5.0

5.5

,,.

i

i

6.0

6.5

7.0

104 K / T FIGURE 16.6.11 Induction time of soot formation from benzene pyrolysis in argon behind reflected shock waves. The induction times were determined by laser light extinction at 632.8 nm. Circles (Bauerle et al. 1994): P5 = 50bar, [C]= 4.2 • 10 -6 mol/cm 3. Diamonds (B6hm et al. 1998): P5 -- 60bar, [C]-- 4.2 x 10 -6 mol/cm 3. Line (Knorre et al. 1996): from the fit at 60bar in the form of ~ x [C]~ - - A e x p ( O / T ) .

281

16.6 Particulate Formation and Analysis 10 4

oo

10 3

*9 ,~,,,'%~ a

oo % a ~ * O o

;

102

#4 ~ 9

T

l

lOa

4.5

5.0

9

. . . . . .

1.

.

5.5

.

.

.

.

6.0

104 K / T FIGURE 16.6.12 Induction time of soot formation from n-hexane pyrolysis in argon behind reflected shock waves. The induction times were determined by laser light extinction at 632.8 nm. Circles (Hwang et al. 1991): P5 -- 20bar, [C]= 4.3-5.7 x 10-6 mol/cm 3. Squares (Hwang et al. 1991): p~ = 63bar, [C]-- 6.1-6.8 x 10-6 mol/cm 3. Triangles (Hwang et al. 1991): P5 = 100bar, [C]= 4.6-6.2 x 10-6 mol/cm 3. Diamonds (Bauerle et al. 1994): P5 = 20-100bar, [C]= 5.3 x 10-6 mol/cm 3. Line: from Geck (1975).

p r e s e n t e d an empirical correlation in the form of z = 5.4 x 10 -9 exp(17,900/T)[C]-~ -~ (ITS, m o l / c m 3 ) , w h i c h fits very well the data collected at later times. The e x p o n e n t for the C-atom c o n c e n t r a t i o n is closed to - 1 w h i c h points to a strong d e p e n d e n c e of i n d u c t i o n time on the C-atom concentration. The total pressure does n o t seem to affect the i n d u c t i o n time, as indicated by the small e x p o n e n t of the argon concentration. This observation is consistent with the data of Parker et al. (1990), w h o s h o w e d hardly any d e p e n d e n c e of z w h e n the pressure is varied from 10 to 3 0 a t m . The i n d u c t i o n time of soot formation has also been studied in fuel-rich h y d r o c a r b o n oxidation (Wang et al. 1981; Wittig et al. 1990; MMler and Wittig 1994; Kellerer et al. 1996). Similar to the correlation of ignition delay times (Burcat et al. 1970; Lifshitz et al. 1971), an empirical equation in the form of z -- A exp(E/RT)[C]~[O2]fl[Ar] ~

(16.6.23)

has been used to correlate the i n d u c t i o n time of soot formation. Figure 16.6.14 shows such a correlation for toluene oxidation b e h i n d reflected s h o c k waves, as reported by W a n g et al. (1981). The correlation yields Z-

5.8 • 10 -15 exp(32,200/T)[C]-191[O2] 0 "78 [Ar]- 0 36

(its, m o l / c m 3)

282

H. W a n g

1 0 -2

O

t~

~.

10 "3

A

l0 4

rj 10-s :~ 3.5

I

I

!

1

4.0

4.5

5.0

5.5

,

_1,

I

I

6.0

6.5

7.0

7.5

10 4 K / T FIGURE 16.6.13 Induction time of soot formation from toluene pyrolysis in argon behind reflected shock waves. The induction times were determined by laser light extinction at 632.8 nm. Circles (Frenklach et al. 1983a): 0.311% toluene in argon, [C]= 3.32 x 10 - 7 mol/cm 3. Squares (Frenklach et al. 1983a): 1.75% toluene in argon, [C]- 2.69-3.32 x 10 - 7 mol/cm3. Triangles (Parker et al. 1990): p = 10-30 bar, 0.021-0.064% toluene in argon (specific conditions under which the induction times were measured were not given. Here it is assumed that the mixture contains 0.03% toluene and P5 = 20bar); line: empirical correlation reported by Wang et al. (1981), ~ = 5.4 x 10-9 exp(17, 900/T)[C]-~ -~ (~ts, mol/cm3).

C o m p a r e d to toluene pyrolysis, the d e p e n d e n c e on the C-atom c o n c e n t r a t i o n increases w h e n o x y g e n is present. An increase in C-atom c o n c e n t r a t i o n decreases the i n d u c t i o n time, whereas an increase in the oxygen c o n c e n t r a t i o n increases the i n d u c t i o n time. W i t h the presence of oxygen, the influence of pressure is s o m e w h a t larger than that of toluene pyrolysis. Mflller and Wittig (1994) s h o w e d that the i n d u c t i o n time of soot formation from m e t h a n e oxidation can be well correlated with the partial pressure of the fuel.

16.6.4.2 SOOT YIELD Soot yield is defined as the fraction of carbon atoms a c c u m u l a t e d in soot, and it characterizes the conversion efficiency of a h y d r o c a r b o n to soot (Frenklach et al. 1988). In almost all studies, the soot yield is d e t e r m i n e d by the laser light extinction technique. Figure 16.6.15 shows typical soot yield traces as a function of time, observed d u r i n g the pyrolysis of a t o l u e n e - a r g o n m i x t u r e b e h i n d reflected shock waves (Frenklach et al. 1983a). Similar traces have been

16.6

283


0

10"4

0 E

:::t.

10 ~

,~o

~D el.

~o ooodP 0 o

u.____l

A

~~

1 0 "~

,(.).

10 -8

9

I

5.0

0

,.

I

I

5.5

6.0

. . . . . . .

I

6.5

,

I

7.0

7.5

104 K / T FIGURE 16.6.14 Induction time of soot formation from toluene-oxygen-argon mixtures behind reflected shock waves (Wang et al. 1981). The induction times were determined by laser light extinction at 632.8nm. Circles: 0.15% C7H8-0.0875% O2-argon, [ C ] - - 7 . 5 • 10 -7 mol/cm 3. Squares: 0.6% C7H8-0.35% O2-argon, [C]= 7.5 • 10 -7 mol/cm 3. Open triangles: 0.2% CFH 80.35% O2-argon, [C]= 2.5 • 10 -7 mol/cm 3. Diamonds: 0.3% C7H8-0.875% O2-argon, [C]-- 7.5 x 10 -7 mol/cm 3. Filled triangles: 0.3%C7Hs-0.21%O2-argon [C]-- 7.5 x 10 -7 mol/cm 3. Line: correlation given by z - 5.8 x 10 -15 exp(32, 200/T)[C]-l'91[O2]~ -0"36 (Its, mol/cm3).

reported by Knorre et al. (1996) for a benzene-acetylene mixture. It is seen that the dependence of these time traces on temperature is quite complex. At a temperature of 1495 K, little soot is observed. As temperature increases, carbon is converted to soot in larger rates and greater amounts. A further increase in temperature beyond 1729 K, however, brings the soot yield down at long reaction times, even though the rate of soot conversion may still be larger at small reaction times. Graham et al. (1975b) noted that at a fixed reaction time, the soot yield from the pyrolysis of various aromatics and related compounds exhibits a pronounced bell-shaped dependence on temperature. This dependence is illustrated in Figure 16.6.16 for data collected at a reaction time of 2.5 ms. The maximum yield is attained at a temperature around 1750 K with nearly 100% conversion of carbon to soot. Graham and coworkers suggested that the observed behavior is caused by the competition between the fragmentation rate of the parent hydrocarbon and the rate of molecular growth process, both of which increase as the temperature is elevated. More detailed shock tube analyses of soot yield followed. However, before the results of these analyses can be presented and systematically compared, we

284

H. W a n g

100 ~1729 K 1799 K

80 1672 K

"c3

60

e~

o o r,r

40 2059 K .. 1587 K

20

0

I

0

I, ~,

,

I

1

223 Ii

2

1495

1"

3

Time (ms) F I G U R E 16.6.15

T h e time trace of soot yield from the pyrolysis of 0.311% t o l u e n e in argon

([C]= 3.3 • 10-7 mol/cm3) behind reflected shock waves (Frenklach et al. 1983a). The traces are smoothed from the experimental profiles obtained from light extinction at 632.8nm, using the complex refractive index fit = 1.56-0.56i (Dalzell and Sarofim 1969).

shall discuss several issues related to soot yield measurements. It is important to note that the term soot is rather ambiguous because the lower bound of the particle sizes cannot be unambiguously determined. In practice, the term soot means an ensemble of particles that attenuate a laser beam. Because of different sensitivities of laser attenuation by particles at different wavelengths (Figure 16.6.2), soot yields at lower conversions may differ significantly when different wavelengths are used. Frenklach et al. (1983a) showed that at 0.5ms the temperatures of maximum soot yield differ quite significantly during the pyrolysis of toluene, as seen in Figure 16.6.17. In particular, for temperatures between 1600 and 1800 K, the result at 632.8 nm shows about 7% of conversion, whereas at 3.32~tm no soot particles are observed. The observed difference is consistent with the possibility of marked light attenuation by pre-particles at 632.8nm, whereas these particles do not attenuate light at 3.32 ~tm, as discussed previously. For this reason, it is important to report soot yield data along with the wavelength used in the measurement. A second ambiguity in the soot yield measurement arises from the uncertainty in the complex refractive index (Table 16.6.4). Figure 16.6.17

16.6

285


80 r9

[] 4+ n

0 []

0

benzene

9

ethylbenzene

•

toluene

[]

indene

9 9 + 9 A

cyclohexatriene 1,4-cyclohexadiene cyclopentadiene acetylene pyridine

.+

[]

20

0

I

,

+

"

A

i...... I 1600

,

, 1800

2000

2200

I .... 9 2400

Temperature (K) FIGURE 16.6.16 Yields of soot at a reaction time of 2.5 ms from the pyrolysis of various hydrocarbons in argon in incident shock waves, aU with [C] = 3.3 • 10 -7 mol/cm 3 (Graham et al. 1975b). The data were collected from light extinction measurements at 4 4 8 n m with Im{(fla2 - 1)/(fla2 + 2)} -- 0.254 (Graham et al. 1975a). Lines are fits to data.

120 t

o 9 O

9 O/~'-"~

100

0.5 ms, 632.9 nm 0.5 ms, 3.32 larn 2 ms, 632.9 nm .

"d "~.,

0 1400

1600

1800

2000

2200

2400

Temperature (K) FIGURE 16.6.17 Effect of laser wavelength on the measured yields of soot at two reaction times, for the pyrolysis of 0.311% toluene in argon ([C] - 3.3 x 10 -7 mol/cm 3) behind reflected shock waves (Frenklach et al. 1983a). The complex refractive indexes used for the calculation of soot yields are fla - 1.56-0.56i at 632.8 nm and fla - 2.28-1.39i at 3.39 ~tm from Dalzell and Sarofim (1969). Yields over 100% are obtained at 3.39 ~tm, indicating the uncertainty in fla. Lines are fits to data.

286

H. Wang

shows that at the reaction time of 2 ms, the maximum soot yields at 632.8 nm and 3.32 ~tm differ markedly. Moreover, the yield at 3.32 ~tm exceeds 100%, indicating the uncertainty of the complex refractive index. This problem was noted by Graham (1975a) and further discussed in the work of Frenklach et al. (1983a, 1983b). The data in Figure 16.6.17 were converted from transmittance using r h - 1 . 5 6 - 0.56i at 632.8nm and r h - 2 . 2 8 - 1.39i at 3.39 ~tm from Dalzell and Sarofim (1969). The use of refractive index reported by Lee and Tien (1981) does not resolve the problem. To emphasize this ambiguity, Frenklach et al. (1983a, 1983b) reported their results in the form of soot yield multiplied by Im{(ffi 2 - 1)/(ffl 2 + 2)}. Here we shall uniformly use the data collected at 632nm and the refractive index of Dalzell and Sarofim (1969) to facilitate data comparison, although the absolute soot yield is questionable. Figure 16.6.18 shows the variation of soot yield as a function of temperature at the reaction times of 0.5, 1.0, 1.5, and 2.0 ms for acetylene pyrolysis behind reflected shock waves (Frenklach et al. 1983b). It is seen that soot yield exhibits a pronounced bell-shaped dependence on temperature, as noted by Graham et al. (1975b). The position of maximum soot yield is not universal under a given shock condition, but it is dependent on reaction time. The Catom concentration was also found to affect the shape of the soot yield curve, as seen in Figure 16.6.19. A larger C-atom concentration generally leads to a higher conversion to soot.

15 +j~,

--e-

/+ \ y

~,

10

Q O ~

5

/

T~-r

0.5 ms

o \

1.0m

t ~12:50m:

-

+

\ 0

1600

, ~

~ ' ~ ' r ~ - ' - - ' L ' ~) n ' T ~ " , - -

1800

2000

I

2200

J

I

2400

,

I

2600

)

I

2800

~

I

3000

J

3200

Temperature (K) FIGURE 16.6.18 Yields of soot at the reaction times of 0.5, 1.0, 1.5, and 2.0ms from the pyrolysis of a 1.09% acetylene-argon mixture ([C] = 8 . 1 - 8 . 6 x 10 -7 mol/cm 3, P5 - 1.27-2.33 bar) behind reflected shock waves (Frenklach et al. 1983b). Lines are fits to data.

16.6

287


10

%C2H2 [C]•

_

r x oo of O~

_

"O -g

o

4.65

?

o o

0 1600

.~-.,-...~

.~...er~

1800

iZXl

2000

Ps

(raot/ern3) (bar) 1.09 3.3 2.14-3.87 zx 4.65 3.3 0.52-0.91 8.3

1.27-2.33

Oo/j/oO ,

I

2200

,

I

2400

~

I

~

2600

I

2800

,

I

3000

,

I

3200

Temperature (K) FIGURE 16.6.19 Yields of soot at a reaction time of 1.5 ms from the pyrolysis of acetylene-argon mixtures behind reflected shock waves (Frenklach et al. 1983b). The data were obtained from light extinction at 632.8 nm. Lines are fits to data.

Under the same C-atom concentration, the pyrolysis of benzene leads to the largest conversion to soot, as seen in Figure 16.6.20, when compared to acetylene, allene, vinylacetylene, and 1,3-butadiene (Frenklach et al. 1988, 1990). At temperatures below 2100 K, acetylene leads to the lowest amount of conversion to soot. Below the same temperature, vinylacetylene and 1,3butadiene have approximately the same sooting tendency. Soot formation from allene is much faster and in much larger quantities than from vinylacetylene and butadiene. Frenklach et al. (1983b) noted that the characteristics of soot formation from allene are similar to those of aromatics. In addition, the maximum soot yields for benzene and allene are achieved at lower temperatures than those for acetylene and 1,3-butadiene. At elevated pressures, the dependence of soot yield on temperature is still a bell-shaped curve, as seen in Figure 16.6.21 (Bauerle et al. 1994). Comparing between aromatic and nonaromatic hydrocarbons, the absolute difference in the maximum soot yield at elevated pressures is not as large as that at low pressures (cf. Figure 16.6.20). Benzene still has a higher propensity to soot than nonaromatic hydrocarbons (ethylene and n-hexane). Figure 16.6.22 presents the soot yields obtained in argon-diluted hydrocarbon mixtures: (a) allene-acetylene, (b) 1,3-butadiene-acetylene, and (c) benzene-acetylene (Frenklach et al. 1986a, 1988). The yields from each single component are also shown in the same figure. It is seen that the interaction of

H. Wang

288

9 * +

2f,

~

_

o

1.09%C2H 2 + At' 0.726% C3H4 + Ar 0.54% C4H4 + Ar 0.54% C4H6 + Ar

1-

~

o or ~

:lZ/ 7 o o ,I

!

~

1600

,I

~

1800

I

,

2000

I

~,

2200

Temperature

I

2400

~

,,,t

2600

(K)

FIGURE 16.6.20 Yields of soot at a reaction time of i ms from the pyrolysis of acetylene-, allene-, vinylacetylene-, butadiene-, and benzene-argon mixtures ([C] = 3.3 x 10 -7 mol/cm 3) behind reflected shock waves (Frenklach et al. 1988, 1990). The data were obtained from light extinction at 632.8nm, initially reported for the complex refractive index value of Menna and D'Alessio (1981). The data shown here are recalculated using the complex refractive index value of Dalzell and Sarofim (1969).

~'

80 / / /

--6mol/cm3, P5 = 50 bar

O

C6H6-Ar, [C] = 4.2•

9

C2H4-AI',[C] = 4.2x 10-~ mol/cm3, P5 = 50 bar

+

n-C~Hl4-Ar, [C] = 5.3•

-~ mol/cm3, P5 = 20-100 bar

6~I 40 8

200

1500

2000

2500

Temperature (K) FIGURE 16.6.21 Maximum yields of soot from the pyrolysis of benzene-, ethylene-, and nhexane-argon mixtures behind reflected shock waves (Bauerle et al. 1994). The data were obtained from light extinction at 632.8 nm, initially using the value of the complex refractive index of Lee and "lien (1981). The data presented in the plot are rescaled by using the ffa value of Dalzell and Sarofim (1969). Lines are fits to data.

16.6

Particulate Formation and Analysis 25

+ o a

,-, 20 ~.

289

(a)

0.726% C3H4 + 1.09% C2H2 + Ar 0.726% C3H4 + At" 1.09% C2H 2 + AT

"1::1 15-

+'

~

o o

105n_

0

.,4-

-~h

+'

~

.....

)

8 ~

+ o a

76x:l

5-

9,..4

4

o o

(b)

0.54% C4H6 + 1.09% C2H2 + Ar 0.54% C4I-I~ + Ar 1.09% C2H2 + Ar + +

.%

3

+

~+

+

2

+

1

0 70

(c)

+ 0.311% C6I-I~ + 1.09% C2I-I2 + Ar o 0.311% C6I-I~ + Ar &" 50 .......... 1.09% C2H2 + Ar 6O

_

,--, 40 0 ,., o o

30 20 10 0

.m. O+

1600

-r'-,.

1800

2000 2200 Temperature (K)

....

t ......

2400

~,

I

2600

FIGURE 16.6.22 Yields of soot at a reaction time of i ms from the pyrolysis of single-component and binary mixtures behind reflected shock waves (Frenklach et al. 1988). The data were obtained from light extinction at 632.9nm, initially reported for the complex refractive index value of Menna and D'Alessio (1981). The data shown here are recalculated using the complex refractive index value of Dalzell and Sarofim (1969). For single-component mixtures, [C]-3.3 x 10 -7 mol/cm3; for binary mixtures, [C] = ~ 6 . 7 x 10 -7 mol/cm 3. Lines are fits to data.

the binary components

is r a t h e r c o m p l e x .

like a l l e n e a n d b e n z e n e ,

t h e a d d i t i o n o f a c e t y l e n e l e a d s to l i t t l e c h a n g e i n t h e

soot yield, while

for a weakly

sooting

In strongly sooting hydrocarbons

hydrocarbon

like 1,3-butadiene,

the

a d d i t i o n o f a c e t y l e n e s e e m s to s h o w s o m e s y n e r g i s t i c e f f e c t w i t h r e s p e c t to s o o t formation.

290

H. Wang

Addition of hydrogen strongly suppresses soot formation from acetylene (Wang et al. 1981; Frenklach et al. 1988), as seen in Figure 16.6.23. This effect is evident at both near-atmospheric pressure (Figure 16.6.23a) and at elevated pressures (Figure 16.6.23b). A similar effect of soot suppression was observed in the shock tube pyrolysis of toluene (Wang et al. 1981). This effect was

5

-

+

4.65% C.2H 2 + Ar, Ps = 1.27-2.33 bar

o

4.65% C z H 2 + 4.65% H 2 + At', P5 - 1.3-1.8 bar

44-

++

@ O

/+

+

~

(a) 0

'

t

.

t

v

,,

v

I

,

I

,

I

,

8070-

60" 0 9 t,...t

0 o

oO.,

.... ..C2H2 "- o. o~

:

50-

/

40-

O

C2H2/I'I2-1/1, [C] -- 2x10 -6 m o l / c m 3 Ps = 60 bar

,.

6"..

...

C2H2/H2=l/1, [C] = 4x10 -6 mol/cm 3

"'"% . . "

:

9

3020-

/

10 0 1400

I

"

,

I

1800

,

I

,'"'"

I

2200

,

{

~

I

2600

~,,

i

,

I

,

3000

Temperature (K) FIGURE 16.6.23 Effect of hydrogen addition on the yield of soot from the pyrolysis of acetylene behind reflected shock waves. (a) Data at a reaction time of i ms for pressures at 1.27-2.33 bar from Frenklach et al. (1988); (b) maximum soot yields at the pressure at 60bar (Knorre et al. 1996). Both data sets were obtained from light extinction at 632.8 nm. The data in panel (a) were initially reported for the complex refractive index value of Menna and D'Alessio (1981). The data shown here are recalculated using the complex refractive index value of Dalzell and Sarofim (1969). In panel (b), the dotted lines are for the pyrolysis of pure acetylene or ethylene with total C atom concentration [C] - 4 x 10 -6 mol/cm 3. Lines are fits to data.

16.6

291


attributed to a reduction of aromatic radical concentrations by H 2 via the back reaction of the H abstraction of the growing aromatic molecules (Frenklach 1984b, 1988). The complex bahavior exhibited for the dependence of soot yield on temperature extends to chlorinated hydrocarbons. Frenklach et al. (1986b) examined soot formation from the pyrolysis of chlorinated hydrocarbons behind reflected shock waves. Figure 16.6.24 shows the soot yields at 0.5 ms of pyrolysis time, comparing chloromethane-, dichloromethane-, trichloromethane-, tetrachloromethane-, methane-, and acetylene, all with the same Catom concentration of ~8.3 • 10 -7 mol/cm 3 and under similar pressure. Marked differences in the sooting characteristics were observed for these compounds. Upon shock heating, chlorinated compounds generally produce soot much faster and in larger quantities than do methane and acetylene. There are notable differences in the dependence of the soot yield on temperature. Dichloromethane exhibits a bell-shaped dependence at temperatures below 2400 K and appears to have the largest sooting propensity of all the chloromethane compounds. The maximum soot yield from the pyrolysis of trichloromethane is larger than that of dichloromethane, but this maximum is obtained at some 700 to 800 K higher than that for dichloromethane. For tetrachloromethane, the soot yield profile shifts to even higher temperatures. Chloromethane, on the other hand, has sooting propensity not so different from that of acetylene. 6O

~

40

~ 9

30

9.3% CHCI 3

"

9.3% CC14

9

rm

20 H2

10

1500

2000

2500

3000

Temperature (K) FIGURE 16.6.24 Yields of soot at a reaction time of 0.5 ms from the pyrolysis of chloromethane-, dichloromethane-, trichloromethane-, tetrachloromethane-, methane-, and acetylene-argon mixtures ([C] = ~ 8 . 3 • 10 -7 mol/cm 3) behind reflected shock waves (Frenklach et al. 1986b). The data were obtained from light extinction at 632.9 nm.

292

H. W a n g

50 4.65% CH2CI 2 + Ar [C] = 1.7x10 -7 mol/cm 3

40

Reoflected shock -~ o ~

3O

20 r~

lO d]~ 0

'

9~1 1600

Incident shock ,

i ....

2000

,

i

1

2400

2800

I 3200

Temperature (K) FIGURE 16.6.25 Yields of soot at a reaction time of i ms from the pyrolysis of dichloromethane behind incident and reflected shock waves (Frenklach et al. 1986b). The data were obtained from light extinction at 632.8 nm. Lines are fits to data.

An interesting yet unsettling observation by Frenklach et al. (1986b) was that soot yields determined behind incident and reflected shock waves may be qualitatively similar but quantitatively different. Figure 16.6.25 shows soot yields at a reaction time of i ms from the pyrolysis of dichloromethane, comparing the results obtained behind incident and reflected shock waves. It is seen that the soot yield determined behind reflected shock waves are larger than those from incident shock waves, by as much as a factor of 2. This difference was attributed to the possibility of additional hydrogen atoms formed from impurities behind reflected shock waves (Lifshitz and Frenklach 1977; Lifshitz et al. 1983), which promote soot formation by providing additional H abstraction from aromatic molecules and thereby increase the rate of aromatic growth reactions (Frenklach et al. 1984b). In general, an increase in pressure promotes soot formation from the pyrolysis of hydrocarbon, although the actual response of soot yield varies among different hydrocarbons. In some cases, an increase in pressure increases the soot yield over an entire temperature range. Figure 16.6.26 shows that for ethylene pyrolysis at a constant C-atom concentration behind reflected shock waves, a higher pressure leads to a larger soot yield at a given temperature (Bauerle et al. 1994). In other cases, an increase in pressure first shifts the soot bell curve to lower temperatures (Frenklach et al. 1983a, 1983b), as seen in Figure 16.6.27. A further increase in pressure does not shift the soot bell to even lower temperatures, nor does it increase the soot yield. This can be seen

16.6

293


100

Ethylene-argonmixture [C] = 4.2x10 -6 mol/cm 3

80

i ......

[] +

I00 bar 50 bar

ix

25 bar

20 0

1700

1800

1900

2000

21oo

2200

Temperature (K) FIGURE 16.6.26 Maximum yields of soot from the pyrolysis of ethylene in argon behind reflected shock waves at three different pressures (Ps) for a constant C-atom concentration (Bauerle et al. 1994). The data were initially obtained from light extinction at 632.8nm. The reported data were derived from the complex refractive index value of Lee and Tien (1981) and were rescaled here using the rh value of Dalzell and Sarofim (1969). Lines are fits to data.

in Figure 16.6.27 by comparing the data of Frenklach et al. (1983a), determined at 1.83-3.06bar, to the data of Parker et al. (1990), determined at a much higher pressure (30 bar). Note that the C-atom concentrations in the experiments shown in Figure 16.6.27 are about equal, thus any difference observed for soot yield is presumably due to the influence of pressure. Hwang et al. (1991) and Bauerle et al. (1994) showed that for pressures between 20 and 100 bar, the soot yield remains the same for n-hexane pyrolysis behind reflected shock waves. This pressure insensitivity is similar to the behavior just discussed of toluene at elevated pressures. In general, the addition of oxygen causes the soot bell curve to shift to lower temperatures (Frenklach et al. 1984a, 1990). Figure 16.6.28 demonstrates the influence of oxygen when it is added to acetylene, allene, vinylacetylene, 1,3butadiene, and toluene. The most drastic effect is seen in the case of acetylene, where the addition of oxygen shifts the bell curve to a temperature as much as 500 K lower than in the case of acetylene pyrolysis, without significantly affecting the maximum soot yield. The enhanced soot production at low temperatures was attributed to the fact that the addition of oxygen results in the formation of reactive species, which promote the pyrolysis reactions (Frenklach et al. 1984a). The addition of oxygen to toluene at subatmospheric pressure of no. 4 bar (Figure 16.6.28e), on the other hand, has little effect on

294

H. Wang

o 80

1.75%C.TH8 + Ar, [C] = 3.3• -7 mol/cm3 (P5 - 0.31--0.53 bar)

+

0.311%CTH8 + At, [C] = 3.3• -7 tool/era3 (P5 = 1.83-3.06 bar)

ix

CTH s + At, [C] = 3•

60

-7 mol/cm 3, P5 = 30 bar []

~

9.,

O o r~

40

20-

0 + 1500

i

D

I

2000

2500

,,

i

3000

Temperature (K) FIGURE 16.6.27 Yields of soot at a reaction time of i ms from the pyrolysis of toluene-argon mixtures behind reflected shock waves. The low-pressure data (Frenklach 1983a, 1984a) were measured with light extinction at 632.8 nm and the data at 3 0 a t m (Parker et al. 1990) from light extinction at 389 and 633 nm or from emission measurements. Lines are fits to data.

soot formation at temperatures below 2150 K, but it decreases soot production at higher temperatures. Under a higher-pressure condition (1.87-3.08 bar), the addition of oxygen to toluene simply reduces the soot yield over the entire temperature range without significantly affecting the shape of the soot bell curve, as seen in Figure 16.6.29. The effect of oxygen on soot formation from allene, vinylacetylene, and 1,3-butadiene is somewhat intermediate between the effects observed for acetylene and toluene. The promotion effect of oxygen at low temperatures is obvious for vinylacetylene and 1,3-butadiene, yet such an effect is hardly seen for allene. Wang et al. (1981) showed that an increase in the amount of oxygen addition reduces the yield of soot from the pyrolysis of toluene, but such an effect is more drastic at the higher-temperature end of the bell curve. Figure 16.6.30 shows that an increase in the oxygen addition suppresses soot formation, notably toward high temperatures. Lowering both the initial toluene and oxygen concentrations does not affect the soot yield at the lowtemperature side of the bell curve, but it increases soot yield at higher temperatures. These results again illustrate the competition between the soot-suppression effect of oxygen by oxidizing the precursor to soot and the soot-promotion effect by increasing the concentrations of reactive species.

16.6

295

Particulate F o r m a t i o n and A n a l y s i s 5 "

" A +

4.65% C.2H2 + Ar 4.65% C 2 H 2 + 1.5%

(a) O=+

ha"

[C]= 8.3x+I0-7mol/cmS ~

2O A +

(b)

0.726% CsH, + Ar 0.726% C 3 H 4 + 0.726% 02 + Ar [C] = 3.3x 10-I tool/all3

..i o o

I. zx +

4

!

(c)

0.54% C i H 4 + Ar 0.54% C4H, + 0.54% Oa + At" [C] = 3.3x 10-v mol/cm 3

3 4-

2-

A

1

0 4

o ....4

(d)

Ar

0.54% C,Hs + 3

+

0.54% C4H s + 0.54% 02 + Ar [C] = 3.3x 10 -7 moI/cm3 ,~

A

1.75% C.~Hs + Ar 1.75% C~H s + 1.75% 02 + Ar

2

1

0 7O

60

+

50 ....,

[(3] = 3.3x10-~ mol/arn3

./ +

4O

(e) ......_& a

a~

3O a +~

2O

~

AaA

l0 1

200

1

!

1400

1600

.

.

.

1800

.

2000

.

2200

2400

I

2600

i

2800

I

Temperature (K) FIGURE 16.6.28 Yields of soot at a reaction time of i ms from the pyrolysis of (a) acetylene, (b) allene, (c) vinylacetylene, (d) 1.3-butadiene, and (e) toluene in argon behind reflected shock waves, with or without oxygen addition (Frenklach et al. 1984a, 1990). All data were obtained from light extinction at 632 nm, initially reported for the complex refractive index value of Menna and D'Alessio (1981). The data shown here are recalculated using the complex refractive index value of Dalzell and Sarofim (1969). Lines are fits to data.

296

H. Wang

60-

zx o

0.311% C_,TH8 + Ar 0.311% C,TH8 + 0.311% 02 + Ar

50-

40

-

"d 30 o r~

20

-

10 -

0

1400

~

m~ _

1600

1800

2000

2200

o

q

,

2400

Temperature (K) FIGURE 16.6.29 Yields of soot at 1ms from the pyrolysis of toluene in argon ([C] = 3.3 x 10 -7 mol/cm 3, P5 = 1.87-3.08 bar) behind reflected shock waves, with or without oxygen addition (Frenklach et al. 1984a). The data were obtained from light extinction at 632.9nm, initially reported for the complex refractive index value of Menna and D'Alessio (1981). The data shown here are recalculated using the complex refractive index value of Dalzell and Sarofim (1969). Lines are fits to data.

120 100 -

o o ~ ~ t ~ 6

o

0.3% C7H$ + 0.21% 02 +Ar

o zx

0.3% C7H$ + 0.875% 02 + Ar 0.15% CTH,+ 0.0875% 02 +Ar

80 9,-, o

r~

60

40

20 0 1400

1600

1800

2000

2200

2400

2600

Temperature (K) FIGURE 16.6.30 Yields of soot at a reaction time of 2.5 ms for toluene-oxygen-argon mixtures ([C]-- 7.5 • 10 -7 mol/cm 3) behind reflected shock waves (Wang et al. 1981). The data were obtained from light extinction at 632.8nm and initially reported for I m { ( r h 2 - 1 ) / (rh 2 + 2)} --0.292. Here the data are shown for the complex refractive index value of Dalzell and Sarofim (1969). Lines are fits to data.

297

16.6 Particulate Formation and Analysis

8070~',

60-

,~

50-

0.35%C6H 6 + 0.875% 02 + Ar o 0.30%C7Hs + 0.875% 02 + At ~x 0.157%C7H8 + 0.5% C2H2 + 0.875% 02 + Ar

[]

~ .p,,

;~

~_.-~

o~

40-

O c

3020100

1300

1400

1500

1600

1700

1800

1900

T e m p e r a t u r e (K) FIGURE 16.6.31 Yields of soot at a reaction time of 2.5 ms for benzene-, toluene-, toluene + acetylene-oxygen-argon mixtures ([C] = 7.5 x 10 - 7 mol/cm3) behind reflected shock waves (Wang et al. 1981). The data were obtained from light extinction at 632.8 nm and initially reported for I m { ( t n 2 - 1)/(tn 2 q- 2)} = 0.292. Here the data are shown for the complex refractive index value of Dalzell and Sarofim (1969). Lines are fits to data.

For the same C-atom concentration and with the same a m o u n t of oxygen addition, the soot yield from the pyrolysis of b e n z e n e is higher than that of toluene. Figure 16.6.31 shows that the n u m b e r of aromatic rings in the reactant influences the a m o u n t of soot p r o d u c t i o n (Wang et al. 1981). This observation is further s u p p o r t e d by the evidence that for the same C-atom concentration, the toluene-acetylene m i x t u r e produces less soot than toluene alone. In mixtures of h y d r o c a r b o n - o x y g e n - i n e r t with similar total C-atom concentrations, the soot yields at elevated pressure, say, at 40 bar, are similar a m o n g various alkane c o m p o u n d s , including m e t h a n e , propane, and nheptane at a given temperature (Kellerer et al. 1996), as d e m o n s t r a t e d in Figure 16.6.32. The d e p e n d e n c e of soot yield on temperature remains to be that of a bell-shaped curve with m a x i m u m a r o u n d 1800 K. Pressure is seen to have a drastic effect on soot yield in an oxidizing e n v i r o n m e n t (Kellerer et al. 1996). Figure 16.6.33 shows that for the reaction of an n - h e p t a n e - o x y g e n argon m i x t u r e at the equivalence ratio of 5, the soot yield increases by about a factor of 2 w h e n the pressure is increased from 30 to 50 bar. The notable effect of pressure in an oxygen-containing m i x t u r e is s o m e w h a t different from that in the pyrolysis of n-hexane, where it is observed that pressure has little effect on soot yield (Hwang et al. 1991; Bauerle et al. 1994).

298

H. Wang

30-

a

C3Hs.Oz_Ar' [C]_-.6.0x10..6 moi/r 3

P5 = 40 bar

x

n_CTHl6_O2_Ar' [C]=5.9x10-6 mol/cm 3

0=5

zx

CH4-O2-Ar,[C]=7.6x10-~ mol/crn3 •

ID ~

20-

g r~ 10-

0 1600

I

i

t

1700

I

J

1800

I

I

,,

1900

,

,

2000

,

,,

2100

2200

Temperature (K) FIGURE 16.6.32 Yields of soot for the reaction of propane-, n-heptane, and methane-oxygenargon mixtures with similar C-atom concentrations, behind reflected shock waves (Kellerer et al. 1996). The data were obtained from light extinction at 632.8nm and initially reported for the complex refractive index value of Lee and Tien (1981). Here the data are shown for the complex refractive index value of Dalzell and Sarofim (1969). Line is fit to data.

n-CTHl6 + 02 + 99%Ar, (r = 5) 30-

"m

[]

30 bar

0

40 bar

zx

50 bar

20 z )

o o r~

zx

10

0

1600

,

I

1700

,

I

1800

,

I

1900

,

i

2000

,

2100

Temperature (K) FIGURE 16.6.33 Yields of soot for the reaction of n-heptane-oxygen-argon mixtures at three different pressures, behind reflected shock waves (Kellerer et al. 1996). The data were obtained from light extinction at 632.8nm and initially reported for the complex refractive index value of Lee and Tien (1981). Here the data are shown for the complex refractive index value of Dalzell and Sarofim (1969). Lines are fits to data.

299

16.6 Particulate Formation and Analysis

16.6.4.3

SOOT GROWTH RATE

It has been shown (Bauerle et al. 1994) that the time trace of soot volume fraction profile can be empirically fitted by the first-order rate equation (Haynes and Wagner 1981),

df. dt = - h f ( f v

- fv, oo)

(16.6.24)

where the rate constant kf is used as a measure for the rate of soot formation, and fv, oo is the final soot volume fraction. Indeed, the soot volume fraction profile beyond the induction time can be well fitted into Equation (16.6.24), as demonstrated in Figure 16.6.3. Obviously, to determine kf the reaction time must be long enough so that the soot volume fraction approaches its final value, fv,~. This requirement could pose some problems as the soot volume fraction may continue to rise before the contact surface arrives. For shock tube experiments at sufficiently high pressures and high temperatures, this is usually not a problem because the rate of soot formation is large enough so that the soot volume fraction should reach a plateau within, say, 2ms of reaction time. Bauerle et al. (1994) and Knorre et al. (1996) showed that the rate constants kf can be well represented in an Arrhenius plot when they are normalized by the total C-atom concentration. No influence of pressure was observed for kf/[C] for acetylene, ethylene, benzene, n-hexane, and mixtures of acetylene and benzene over a wide range of pressure (20-100 bar) and temperature (1600-2500 K). For acetylene, ethylene, n-hexane, and mixtures of acetylene and benzene, kf/[C] approaches a maximum at a temperature of about 2000 K, whereas no maximum was observed for benzene. For a given C-atom concentration, the rate constant for benzene is at least 1 order of magnitude larger than those for ethylene and n-hexane. The apparent activation energy for ethylene and n-hexane in the temperature range from 1600 to 2000 K, and benzene and mixtures of benzene and acetylene in the temperature range from 1600 to 2500 K is about 48 kcal/mol. For benzene, the pre-exponential factor was reported to be 1.2 x 1015/s-1 (Knorre et al. 1996). Tanke et al. (1998) showed that the apparent rate constant can be significantly affected by additives, such as iron pentacarbonyl.

16.6.4.4

REM AND TEM STUDIES

Soot particles can be collected on carbon-film-coated copper grids mounted near the end wall of a shock tube. These particles have been analyzed by transmission electron microscopy (TEM) and raster electron microscopy

300

H. Wang

(REM). Under a variety of shock tube conditions, the morphology of soot was found to be similar to that in hydrocarbon flames. These particles are aggregates of many individually spherical particles (Bauerle et al. 1994; Knorre et al. 1996), known as the primary particles. The average diameter of the primary particles is usually around 10nm. The particle size can be described by a log-normal distribution (Equation 16.6.19) with a geometric standard deviation In crg-~ ~0.2. The particle size does not seem to change markedly over a wide range of temperature, pressure, and C-atom concentration (Bauerle et al. 1994).

16.6.5

NANO-PARTICLE

SYNTHESIS

Despite the fact that the shock tube technique is ideal for kinetics studies of particulate formation at high temperatures, as demonstrated by the work reported for soot formation, the use of the shock tube for particle or nanopowder synthesis has been limited. Steinwandel and coworkers (1981a, 1985) generated silicon clusters or particles from the pyrolysis of silane behind incident and reflected shock waves. The light extinction technique at two wavelengths [e.g., 248 and 366nm, Steinwandel and Hoeschele (1985)] was used to detect and quantify the particles. A comprehensive shock tube study of silicon particle formation from the pyrolysis of silane and disilane diluted in argon and hydrogen was reported by Frenklach and coworkers (Frenklach et al. 1996). The experiments were conducted behind incident shock waves, at temperatures from 900 to 2000 K and pressures from 0.2 to 0.7 atm. The formation of particles was monitored by light extinction at two wavelengths. The fractional yield, particle size, and number density were simultaneously determined. Within the available reaction time, particles begin to form at temperatures around 1000 K for silane and around 900 K for disilane. The transmittance reaches a maximum at around 1100 to 1200 K, although it is most likely that the observation is caused by a change in the index of refraction, as discussed previously. Silicon particles were collected on a substrate mounted on the end wall of the shock tube. The particles were analyzed with electron diffraction, TEM, and secondary ion mass spectrometry. It was found that loosely aggregated particles are formed, consisting of nearly spherical primary particles that ranged from 10 to 40 nm in diameter and contained ~ 15% hydrogen on an atomic basis. The formation of binary-component particles has also been examined in shock tubes. Carmer and Frenklach (1989) studied the formation of silicon carbide (SIC) particles in a silane-methane-argon mixture behind incident and reflected shock waves at temperatures between 800 and 3650 K and pressures of 0.46 to 4.16 atm. The progress of particle formation was monitored by light

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extinction at 632.8 nm, and the formed particles were analyzed by TEM and electron diffraction. It was found that (a) no particles were formed at temperatures below 900K; (b) particles formed between 900 and 1400K contained silicon only, having diameters ranging from 10 to 50nm; and (c) above 1400 K, particles contained both silicon and carbon. The ratio of t-SiC to Si increases steadily from 1400 to 1700 K, and remains constant above 1700 K. At very high temperatures, T~ > 2800 K, particles having diameters of 500 nm were observed. These particles consisted of//-SIC and were in the form of thin single-crystal platelets. A growth rate on the order of 106 lam/h was measured, which is unseen for silicon carbide formed by any other technique. The experimental observations led the authors to postulate a two-stage process of SiC particle formation, involving the homogeneous nucleation of SiC particles, along with Si particles, which are etched by hydrocarbon intermediates. The resulting products can add to the growing SiC particles by coelescence and reaction with the particles. Herzler et al. (1998) studied the formation of titanium nitride (TIN) particles from mixtures of TiC14-NH3-H 2 behind reflected shock waves at temperatures between 1400 and 2500 K and pressures of 1 to 2.3 bar. The formation of particles was monitored by light extinction, and the TiN molecules detected by laser absorption spectroscopy (A21-I ~-- X2X]). In most experiments, an induction time of particle formation was observed, which was found to be dependent only on temperature. The dependence of induction time on temperature was found to be similar to that in soot formation from hydrocarbon pyrolysis. The TiN molecule profile also shows an induction time, after which the TiN concentration increases steadily, reaches a maximum, and then decreases, presumably due to consumption by particle nucleation and growth.

16.6.6 HOMOGENEOUS METAL PARTICLES

NUCLEATION

OF

In a series of papers, Bauer and coworkers examined the homogeneous nucleation of metal particles by shock heating volatile metal-bearing compounds diluted in argon (Freund and Bauer 1977; Frurip and Bauer 1977a, 1977b, 1977c; Stephens and Bauer 1981). In these experiments, supersaturated metal vapor at controlled densities and temperatures were generated following the fast decomposition of the organometallics within the shock front. Thus, unlike soot formation from shock heating hydrocarbon compounds, the production of particles is not influenced by the pyrolysis kinetics of the reactant. For this reason, the shock tube technique is ideally

302

H. Wang

suited for the examination of homogeneous nucleation theory, as was done in the work of Bauer and coworkers. The homogeneous nucleation of metal particles was followed by light extinction, scattering, and/or density gradients behind the shock front. The heat of condensation was measured for iron clusters as a function of particle size (Freund and Bauer 1977). The critical supersaturation ratio for the onset of rapid condensation from the vapors was determined for iron, lead, and bismuth as a function of temperature (Frurip and Bauer, 1977a, 1977b). The cluster growth rates were measured with light scattering (Frurip and Bauer 1977c). In all studies, Bauer and coworkers illustrated the difficulties in predicting the nucleation phenomenon by thermodynamic equilibrium or by the classical nucleation theory. Based on these studies, a self-consistent model had emerged (Bauer and Frurip 1977), featuring the kinetic phenomenon in the nucleation process and a kinetic criterion for the onset of condensation. Bauer's work was further extended to metal oxides by shock heating mixtures of Fe(CO)5 with N20 and Sill 4 with N20 (Stevens and Bauer 1981). Similar metal-vapor condensation experiments were reported by Steinwandel and coworkers (Steinwandel et al. 1981a, 1981b; Steinwandel and Hoeschele 1985, 1986). In these experiments, the nucleation of particles was detected by time-resolved integral atomic absorption spectroscopy for metal vapors and by light extinction for the metal particles. Again, large discrepancies were found to exist between the experimental data and the classical nucleation theory. The necessity of considering the nonequilibrium behavior is again emphasized (Steinwandel and Hoeschele 1986).

16.6.7

SUMMARY

In this chapter we discussed the methods and results of particulate formation in shock tubes. We have seen that the shock tube technique is ideally suited for the study of soot formation from gases at high temperatures. Induction time and soot conversion data have provided the much-needed information regarding the mechanism of soot formation and the influence of various parameters and fuel structures on soot formation (Haynes and Wagner 1981; Frenklach et al. 1984b, 1986a; Frenklach 1988; Wagner 1994). The use of shock tubes for the study of particulate formation relevant to material synthesis is limited. However, past studies in this area have opened a venue for approaching a basic understanding of the intricate kinetics of particle formation in chemical vapor deposition. In addition to the obvious advantage of well-defined conditions in which spatial transport of gas and particles is entirely eliminated, the relative ease of laser diagnostic techniques make the shock tube technique an ideal tool for this purpose. It is reasonable to

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a n t i c i p a t e t h a t this t e c h n i q u e will c o n t i n u e to b e w i d e l y u s e d in r e s e a r c h areas i n v o l v i n g t h e f o r m a t i o n of c o n d e n s e d - p h a s e m a t e r i a l s f r o m gases a n d in n a n o science and technology.

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Park, C. and Appleton, J. P. (1973b). Shock tube measurements of soot oxidation rates at combustion temperatures and pressures. Proc. 9th Shock Tube Symp.: Recent Developments in Shock Tube Research, pp. 793-803. Stanford University Press, Stanford. Parker, T. E., Foutter, R. R., and Rawlins, W. T. (1990). Soot initiation and particle growth in the pyrolysis of toluene at high inert gas pressures. Proc. 17th Int. Symp. on Shock Waves and Shock Tubes: Current Topics in Shock Waves, pp. 481-486. American Institute of Physics, New York. Penndorf, R. B. (1962). Scattering and extinction coefficients for small absorbing and nonabsorbing aerosols. J. Opt. Soc. Am. 52:896-904. Rawlins, W. T., Cowles, L. M., and Krech, R. H. (1983b). Optical signatures of soot formation in the pyrolysis of toluene near 2000 K. Paper presented at the Fall Technical Meeting of the Eastern States Section of the Combustion Institute, Providence, RI. Rawlins, W. T., Tanzawa, T., Schertzer, S. P., and Krech, R. H. (1983a). "Synthetic fuel combustion: Pollutant formation. Soot initiation mechanisms in burning aromatics." Physical Sciences Report TR-361. Roberts, T. A., Burton, R. L., and Krier, H. (1993). Ignition and combustion of aluminum/ magnesium alloy particles in 0 2 at high pressures. Combustion and Flame 92:125-143. Roth, P. and Brandt, O. (1990). Shock tube measurements of soot oxidation rates by using a rapid tuning IR-laser. Proc. 17th Int. Symp. on Shock Waves and Shock Tubes: Current Topics in Shock Waves, pp. 506-511. American Institute of Physics, New York. Roth, P., Brandt, O., and yon Gersum, S. (1990). High temperature oxidation of suspended soot particles verified by CO and CO 2 measurements. Proc. 23rd Symp. (Int.) on Combustion, pp. 1485-1491. The Combustion Institute. Seeker, W. R., Wegener, D. C., Lester, T. W., and Merklin, J. E (1978). Single pulse shock tube studies of pulverized coal ignition. Proc. 17th Symp. (Int.) on Combustion, pp. 155-166. The Combustion Institute. Seinfeld, J. H. (1986). Air pollution. Wiley, New York. Steinwandel, J., Dietz, T., Joos, V., and Hauser, M. (1981a). Condensation kinetics of iron and silicon in the vapor phase. Proc. 13th Int. Symp. on Shock Tubes and Waves: Shock Tubes and Waves, pp. 700-706. State of University of New York Press, Albany. Steinwandel, J., Dietz, T., Joos, V., and Hauser, M. (1981b). Homogene kondensation von tibers/~ttigtem eisendampf. Kinetische untersuchungen mit einem stogwellenrohr. Ber. Bunsenges. Phys. Chem. 85:683-686. Steinwandel, J. and Hoeschele, J. (1985). Spectroscopic detection of particles from shock-waveinduced decomposition of Sill4. Chem. Phys. Lett. 116:25-29. Steinwandel, J. and Hoeschele, J. (1986). Spectroscopic investigation of the homogeneous nucleation of nickel induced by shock pyrolysis of Ni(CO) 4. J. Chem. Phys. 85:6765-6772. Stephens, J. R. and Bauer, S. H. (1981). Investigation of homogeneous nucleation of Fe, Si, Fe/Si, FeO x, and SiOx vapors and their subsequent condensation. Proc. 13th Int. Symp. on Shock Tubes and Waves: Shock Tubes and Waves, pp. 691-699. State of University of New York Press, Albany. Szydlowski, S. L., Wegener, D. C., Merklin, J. E, and Lester, T. W. (1981). Short residence-time pyrolysis and oxidative pyrolysis of bituminous coals. Proc. 13th Int. Symp. on Shock Tubes and Waves: Shock Tubes and Waves, pp. 800-808. State of University of New York Press, Albany. Tanke, D. (1995). "Rugbildung in der kohlenwasserstoffpyrolyse hinter stogwellen." Ph.D. Dissertation, Universit/it G6ttingen, G6ttingen. Tanke, D., Wagner, H. Gg. and Zaslonko, I. S. (1998). Mechanism of the action of iron-bearing additives on soot formation behind shock waves. Proc. 27th Symp. (Int.) on Combustion, pp. 1597-1604. The Combustion Institute. Tanzawa, T. and Gardiner, Jr. W. C. (1979). Thermal decomposition of acetylene. Proc. 17th Symp. (Int.) on Combustion, pp. 563-573. The Combustion Institute.

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Ural, E. A., Sichel, M., and Kauffman, C. W. (1981). Shock wave ignition of pulverized coal. Proc. 13th Int. Symp. on Shock Tubes and Waves: Shock Tubes and Waves, pp. 809-817. State of University of New York Press, Albany. Van de Hulst, H. C. (1981). Light scattering by small particles. Dover, New York. Vaughn, S. N., Lester, T. W., and Merklin, J. E (1981). A single pulse shock tube study of soot formation from benzene pyrolysis. Proc. 13th Int. Symp. on Shock Tubes and Waves: Shock Tubes and Waves, pp. 860-868. State of University of New York Press, Albany. Wagner, H. Gg. (1994). The influence of operating conditions on the formation of soot and hydrocarbons in flames. Hazardous Waste Hazardous Mater. 11:5-29. Wang, T. S., Matula, R. A., and Farmer, R. C. (1981). Combustion kinetics of soot formation from toluene. Proc. 18th Symp. (Int.) on Combustion, pp. 1149-1158. The Combustion Institute. Williams, D. B. and Carter, C. B. (1996). Transmission electron microscopy: A textbook for materials science. Plenum, New York. Wittig, S., M~ller, A., and Lester, T. W. (1990). Time-resolved soot particle growth in shock induced high pressure methane combustion. Proc. 17th Int. Symp. on Shock Waves and Shock Tubes: Current Topics in Shock Waves, pp. 468-474. American Institute of Physics, New York. Yoshizawa, Y., Kawada, H., and Kurokawa, M. (1978). A shock-tube study on the process of soot formation from acetylene pyrolysis. Proc. 17th Symp. (Int.) on Combustion, pp. 1375-1381. The Combustion Institute.

CHAPTER

17

Detonation Waves in

Gaseous Explosives JOHN H. S. LEE Professor of Mechanical Engineering, McGill University, Montreal, Quebec, Canada

17.1 17.2 17.3 17.4 17.5 17.6

17.1

Introduction The Structure of Nonideal Detonations Initiation of Detonation Waves Detonation Limits Theory of Nonideal Detonations Concluding Remarks

INTRODUCTION

A gaseous explosive mixture can sustain two modes of combustion distinguished by their propagation mechanism. A deflagration wave propagates via molecular (or turbulent) transport of heat and chemical species from the reaction zone to the unburned mixture ahead of it to effect ignition. According to classical theory, a detonation wave propagates via autoignition induced by the adiabatic compression of the gas by the leading shock front ahead of the reaction zone. A deflagration wave is essentially a diffusion front and propagates at low subsonic speeds with a pressure drop across the wave. A detonation wave is a compression shock wave and must necessarily propagate at supersonic speeds. In smooth tubes, experiments indicate that a unique detonation velocity is obtained for a given explosive mixture at a given initial state. This unique detonation velocity is only weakly dependent on boundary conditions (i.e., tube diameter) in general. Typical propagation velocity of detonations in stoichiometric fuel-air mixtures at standard initial conditions is on the order of 1800 m/s. The corresponding detonation pressure is typically about 20 bar. Shortly after the detonation phenomenon had been identified by Mallard and LeChatelier 1 and Berthelot and Vielle 2 in the late 1800s, Chapman 3 proposed a theory whereby the detonation velocity could be computed.

Handbook of Shock Waves, Volume 3 Copyright 9 2001 by Academic Press. All rights of reproduction in any form reserved. ISBN: 0-12-086433-9/$35.00

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Chapman noted that a unique solution to the one-dimensional conservation equations across the detonation wave corresponds to the minimum velocity solution where the Rayleigh line is tangent to the equilibrium Hugoniot curve. Using this as a criterion, the detonation velocity can be determined from the conservation laws and thermodynamic data for the product species (i.e., heat of formation, heat capacity, equilibrium constant). The computed detonation velocity from Chapman's theory agrees quite well with experimental observations in general. Jouguet 4 in the early 1900s independently demonstrated that the minimum velocity solution also corresponds to the condition of sonic flow (relative to the shock) at the end of the reaction zone. Thus, the sonic condition can also serve as an independent criterion for determining a unique solution from the conservation laws. Jouguet's criterion (i.e., sonic flow) and Chapman's criterion (i.e., minimum velocity or tangency solution) are in fact identical and differ only in the iteration method used in obtaining the solution from the conservation equations. Chapman's criterion is simply a postulate, but Jouguet's criterion can provide some physical explanation as to why the tangency solution should be chosen. If the flow is sonic behind the detonation, expansion waves associated with the relaxation of the highpressure detonation products cannot travel upstream to the reaction zone and quench the reactions. Thus, the steady detonation can be isolated from the nonsteady flow downstream. The same physical argument also applies when the flow is supersonic at the end of the reaction zone, corresponding to the lower intersection point of the Rayleigh line and the equilibrium Hugoniot. However, the arguments used to eliminate this supersonic or weak detonation solution become more complicated. Chapman and Jouguet's criteria provide the necessary condition to close the set of conservation equations and permit a unique detonation solution to be obtained. In general, the Chapman-Jouguet (C-J) solution is found to agree quite well with experimental measurements, especially for conditions well within the detonation limits in large-diameter, smooth tubes. Thus, very early in the study of the detonation phenomenon, a successful theory had been formulated for the prediction of the detonation state in a given explosive. It is interesting to note that the very reason for the success of the C-J theory (i.e., determination of the detonation solution without the need to consider the nonequilibrium structure of the wave and the propagation mechanisms) is also the cause of its limitations. For example, the C-J theory cannot provide any information on the detonation initiation requirements, the effect of boundaries and confinement that leads to failure (i.e., detonability limits), or the critical conditions that permit the transition from deflagration to detonation. The preceding questions can only be resolved by considering the detailed physical and chemical processes inside the nonequilibrium reaction zone itself and the influence of external conditions on these processes. To determine the non-

Detonation Waves in Gaseous Explosives

311

equilibrium, rate-dependent parameters (i.e., initiation energy, limits, etc.), a model for the detonation structure is required. The next major development in detonation theory occurred in the early 1940s when Zeldovich, 5 von Neumann, 6 and DOring 7 independently proposed a model for the structure of detonation waves. The ZND model for detonation structure assumed a leading shock front, which compresses the explosive mixture to a sufficiently high temperature to initiate rapid chemical reactions in its wake. The subsequent expansion of the high-pressure reacting gases provides the momentum change to sustain the propagation of the leading shock front. Thus, the detonation is sustained by the chemical energy release via the work done in the expansion behind the shock front. The ChapmanJouguet theory involves only the conservation laws across the entire detonation complex (shock-reaction zone) and hence does not contain any information on the propagation mechanism. However, the ZND model provides the propagation mechanism, i.e., autoiginition via adiabatic shock heating and expansion work from the high-pressure reacting gases to maintain the shock. If the reaction rates are known, then the ZND model permits the details of the detonation structure to be computed. The effect of initial and boundary conditions on the propagation of the detonation wave can also be determined based on the ZND model for the structure. Therefore, in principle, velocity deficit, initiation energy, detonation limits, etc., can all be predicted based on the ZND model. However, early attempts to develop quantitative theories to predict these so-called dynamic parameters (i.e., critical energy, velocity deficit, detonation limits, critical diameter) using the ZND model failed to produce results in accord with experiments. For example, critical energies for direct initiation of spherical detonations are found to be three orders of magnitude less than experimental values, s The reason for this discrepancy is that the ZND structure does not correspond to reality. The structure of real detonations is three-dimensional and transient even though the average overall velocity is constant and close to the theoretical C-J value. The next major advances in detonation research occurred in the late 1950s and early 1960s when the three-dimensional, unstable structure that characterizes all real detonation fronts was conclusively demonstrated both theoretically and experimentally. Using high-speed photographic observations (schlieren and interferometry), fast-response pressure and temperature gauges, and recordings on smoked foils inscribed by the passing detonation front, it was shown that all self-sustained detonations have a three-dimensional cellular structure formed by an ensemble of interacting transverse shock waves sweeping laterally across the leading shock front of the detonation wave. The boundaries of the shock intersections define the observed cellular pattern when the detonation is observed "head-on." The trajectories of the triple shock intersections of the front forms the characteristic "fish scale" pattern on a

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carbon-soot coated foil placed in the path of the cellular detonation. Theoretical stability analyses (e.g., Erpenbeck 9 and Zaidel lO) also confirmed that the ZND structure is unstable to small perturbations. In spite of all the conclusive evidence that real detonations are unstable, the ability of the C-J theory to predict remarkably well the detonation velocity caused a great deal of reluctance to relinquish the C-J theory and seek alternate models. Detonation research appears to focus on different aspects at various times over the four decades. However, the main objective has always been to u n d e r s t a n d the complex, three-dimensional structure and to reconcile this complexity within the simple, one-dimensional C h a p m a n - J o u g u e t theory that has always been the "Rock of Gibraltar" on the subject. The central t h e m e of detonation research had been repeatedly stated by the p r o m i n e n t workers in the field from the early 1960s to the present. At the 4th AGARD C o l l o q u i u m in Milan in 1960, O p p e n h e i m 11 ended his review on the d e v e l o p m e n t and structure of plane detonation waves with the following remarks: Although according to classical observations the detonation appears as an extremely steady process, on closer inspection, it seems that it is neither uniform in time nor in space. Consequently the detonation may form an essentially nonsteady, non-uniform regime so that in order to explain its precise nature, multidimensional effects in space as well as its irregular behavior in time have to be taken into account. In fact, in view of this evidence one should express amazement that the one dimensional steady flow theory was so successful in rationalizing so many experimental observations. O p p e n h e i m thus recognized the importance of integrating the three-dimensional, n o n s t e a d y effects of the structure into the one-dimensional steady C-J theory. In a later review article by Fay 12 in 1962 on the structure of gaseous d e t o n a t i o n waves, he remarked: The peculiar disadvantage of detonation research is that it was too successful at too early a date. The quantitative explanation of the velocity of such waves given over fifty years ago by Chapman and Jouguet has not been improved upon and has perhaps intimated further inquiry. Thus, Fay also emphasized the need to improve u p o n the C-J theory to account for the effects due to the three-dimensional transient structure. The same views on the future direction of detonation research were again echoed by Davis 13 in an article in Scientific American on the detonation of explosives: It had been thought that even if turbulence or other similar small scale perturbations arose from the mechanical flow of material in the reaction zone, the effects of such perturbations on the chemical reactions would be small enough not to warrant any qualitative change in the detonation models. Most workers now believe that the effects are not negligible and that detonation theory must be extended to take into account the effects of turbulence and of curved detonation waves, both of which are influenced by the type of inert material that surrounds the explosive.


313

The preceding remarks made by these three prominent detonation researchers spanning the past four decades form the basis of this article, the aim of which is to elaborate on what they said and to demonstrate that these threedimensional fluctuations in the reaction zone are indeed essential for the propagation of the detonation. Furthermore, this article also points the way to the modification of the classical Chapman-Jouguet criterion and the ZND theory to take these "turbulence" effects into consideration for the description of real detonations. We shall define all real detonations as nonideal detonations, in contrast to the classical theories of Chapman-Jouget, Zeldovich, von Neumann, and D6ring that address ideal and one-dimensional laminar detonations. Classical detonation theories of ideal detonations have been discussed in most textbooks and are not covered in this article, even though the importance of their thorough understanding cannot be overemphasized. A good summary of recent development in detonations (experimental, numerical, and various analytical studies of detonation stability) can also be found in numerous review articles in the past two decades. Of particular interest are the books by Strehlow, 14 Fickett and Davis, is and Glassman 16 that provide a more complete discussion of classical theory as well as some of the essential results for real detonations. For completeness, the present article summarizes key results obtained in the past four decades and puts them into proper perspective for interpretation. An attempt is made to provide a general framework for the development of a theoretical description of real detonations where all the nonideal effects are accounted for as source terms in the quasi-one-dimensional conservation equations for the detonation structure. The future challenge lies in the formulation of appropriate models to describe the nonideal effects (i.e., curvature, turbulence, etc.). The subject of detonation encompasses many specialized areas in physics, chemistry, applied mathematics, and computational physics, as well as engineering. As such, the researchers in the field come from a variety of disciplines. Thus, any general discussion of detonation phenomena is bound to be biased toward the authors' personal interpretation. This article is no exception. It is more of a view than a review article.

17.2

THE STRUCTURE

OF NONIDEAL

DETONATIONS The ideal one-dimensional ZND model for the detonation structure is not realized experimentally. Toward the late 1950s and early 1960s, experimental evidence of the universal three-dimensional "turbulent" structure of real detonations began to appear. The random density distribution within the

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J . H . S . Lee

reaction zone of gaseous detonations is best illustrated by the interferograms of D. R. White. 1 Figure 17.1 shows a typical example of interferograms of detonations in hydrogen-oxygen mixtures at different initial pressures. The random, turbulence-like density variations within the reaction zone are quite evident. At lower initial pressure, the fluctuations take on a more regular periodic pattern of a larger scale. In the late 1950s, an alternative method was used by Soviet researchers for observing the detonation structure. Denisov and Troshin 2 and Schelkhin and Troshin 3 applied the smoked-foil technique (first

FIGURE 17.1 Interferograms of gaseous detonations in hydrogen-oxygen mixture diluted by xenon at various initial pressures. Reprinted with permission from White, D.R., Turbulent structure of gaseous detonations, Phys. Fluids 4, 465-480, 9 American Institute of Physics (1961).


315

used by Mach to record the triple point trajectory of a three-shock "Mach interaction") to investigate the structure of real detonations. A characteristic "fish scale" pattern is left on the s m o k e d foil u p o n the passage of a d e t o n a t i o n wave. A typical laser schlieren cinematography of a propagating d e t o n a t i o n in low pressure H2-O2 mixtures with the "fish-scale" pattern i m p r i n t e d on the soot-coated w i n d o w of the detonation channel is illustrated in Fig. 17.2. This

FIGURE 17.2 Stroboscopic laser schlieren photographs of a detonation wave in H 2 - O 2 mixture propagating in a two-dimensional channel with one of the windows coated with soot. Reprinted from Lee, J.H.S., Soloukhin, R.I. and Oppenheim, A., Current views on gaseous detonation, Astronautica Acta 14, 565-584 (1969), with permission of Elsevier Science.

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J.H.S. Lee

conclusively demonstrated that the "writing on the wall" is due to the shock interactions occurring at the detonation front itself. The "end-on" normal reflection of a detonation wave on a smoked foil produces a characteristic cellular pattern, quite similar to the morphology of a turbulent flame front (Fig. 17.3). The cell boundaries in Fig. 17.3 are formed by the intersections of transverse shock waves with the leading normal shock front of the detonation. Thus, a real or nonideal detonation front consists of an ensemble of transverse shock waves sweeping across the leading normal shock front. The cell boundaries correspond to triple shock Mach intersections where the temperature, and hence the chemical reaction rate, is most intense. Self-luminous

FIGURE 17.3 Smoked-foilrecord of the end of reflection of a detonation wave in C2H 2 Jr-0 2 mixture propagating in a 25-mm diameter tube. Reprinted with permission, from the Annual Review of Fluid Mechanics, Volume 16, 9 1984, by Annual Reviews www.AnnualReviews.org.


317

"head-on" photography of a detonation also revealed the similar cellular pattern shown in the smoked record of Fig. 17.3. From experiments and numerical simulations, we can reconstruct an idealized picture of the cellular detonation front showing the leading shock, transverse waves, and reaction zones at different times. Figure 17.4 is a schematic diagram illustrating the details of the structure of a cellular detonation front at different times as it propagates from left to right. The trajectories of the triple shock intersections result in the characteristic "fish-scale" pattern are illustrated in Fig. 17.2. Although the entire cellular detonation front propagates at a constant average velocity quite close to the Chapman-Jouget value, large velocity fluctuations occur locally. The local velocity can fluctuate between the limits of about 1.5 to 0.5 times the average C-J velocity depending on the mixture and its composition. Thus, the detonation locally propagates in a pulsating cyclic manner. Starting at the beginning of the cycle at point A when a pair of transverse waves has just collided, the detonation is highly overdriven (~1.5 Vc_J) locally. The overdriven detonation then decays with progressive decoupling of the reaction front from the leading shock. Toward the end of a cycle at point D, the shock velocity can be as low as 50% of the C-J velocity before a pair of transverse

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318

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waves collide again and start the next pulsating cycle. The decay of the overdriven detonation in a pulsating cycle is not continuous in general. An initial rapid decay to about 0.5 Vc_J first occurs when the detonation has propagated about half the cycle length (i.e., "BC"). A "quasi-steady" regime where the shock velocity remains practically constant then occupies the second half of the pulsating cycle. For the first half of the cycle from "•' to "BC," the strong leading shock front serves as the Mach stem to the incident shocks of the adjacent weaker part of the leading shock. For the second half of the cycle, i.e., "BC" to "D," the weak leading shock then becomes the incident shock to the adjacent Mach stems. Thus, the leading shock locally alternates between incident shock and Mach stems of a triple shock Mach interaction as the transverse shocks collide and reflect in a cyclic manner. At the beginning of a pulsating cycle, the leading shock (Mach stem) is sufficiently strong that the reaction zone is intimately coupled to it. For the second half of the cycle where the leading front has decayed and becomes the incident shock, the reaction front is decoupled from it and the mixture is now burned behind the transverse waves. Experimental studies of the detailed structure of a cellular detonation front were carried out in the late 1950s and early 1960s by various researchers; most notable among them were Voitsekhovskii and co-workers, 4 Schott, s Edwards, 6 Strehlow, Z Takai et al., s and Van Tiggelen and co-workers. 9 Because of the three-dimensional transient nature of the cellular detonation front, it is extremely difficult to obtain detailed information on the detonation structure experimentally. However, numerical simulation of the cellular detonation structure has been proven to be extremely useful in providing detailed information on the complex wave interaction processes and the corresponding transient flow field. Numerical simulation of one-dimensional, unstable, pulsating detonation using the method of characteristics was first carried out by Fickett and Wood 1~ as early as 1966. Since then, more thorough studies on one-dimensional pulsating detonations have been carried out by Abouseif and Toong 11 and Moen et al. 12 In a one-dimensional simulation, the detonation instability is manifested by the periodic longitudinal pulsation of the detonation front with the velocity fluctuating typically between the limits of 1.5 to 0.5 Vc_J. This velocity fluctuation is similar to the local velocity fluctuation in a three-dimensional cellular detonation front. The stability limit is governed by the activation energy of the one-step Arrhenius rate law usually assumed in theoretical and numerical studies. The cyclic pulsations change from harmonic oscillations to nonlinear and eventually to chaotic as the value of the activation energy is increased from its value at the stability limit. Similar behavior is also obtained when the degree of overdrive is reduced (for a given unstable value of the activation energy). Figure 17.5 illustrates the behavior of a one-dimensional pulsating detonation as the activation energy is increased beyond the stable value (Fig. 17.5a to 17.5c), and when the degree of overdrive is reduced

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(for a fixed unstable value of the activation energy (Fig. 17.5d to 17.5f). The numerical result is in accord with the stability analyses of Erpenbeck ~3 or Lee and Stewart. ~4 The numerical simulations provide details of the nonsteady flow field behind the unstable detonation and elucidate the important cyclic amplification process leading to the overdriven phase at the beginning of each pulsating cycle. Simulation of two-dimensional cellular detonations began in the late 1970s with the pioneering works of Taki and Fujiwara, ~50ran and co-workers at NRL, 16 and Markov. 17 Since then, rapid advances in computational power and numerical algorithms have brought these simulations to a very high degree of accuracy. The majority of these simulations are for two-dimensional detonations using a single-step Arrhenius reaction rate model. However, simulations of three-dimensional detonations or two-dimensional detonations using more complex reaction models have also been carried out. Most of the early twodimensional simulations essentially demonstrate the ability to reproduce qualitatively the experimentally observed features of the cellular structure. Simulations of three-dimensional cellular detonation have proven to be of rather limited value thus far because of the difficulty in displaying the complex three-dimensional structure and in the reduction of the vast amount of numerical information obtained in a comprehensible manner. Most of the simulations also suffer from a dependency on the resolution of the numerical computation. However, the recent investigations by Gamezo et al. 18'19 were carried out much more carefully and thus can elucidate a number of physical issues and enhanced our current understanding of unstable detonations. In Gamezo's simulations, great attention was exercised to ensure that the results obtained are independent on the resolution of the numerical computations. It is of interest to review Gamezo's results in order to present a more complete picture of our current understanding of the cellular detonation structure. Since the transient development of the cellular structure depends on the initial conditions, it is worthwhile to first briefly describe the computational procedures in Gamezo's numerical investigations. The two-dimensional reactive Euler equations are solved using the FCT technique 2~ for a two-dimensional domain bounded by free slip solid walls at the top and bottom. The reactants enter at the right boundary at specified initial conditions and exit at the left boundary of the computational domain. The domain is defined by a uniform Eulerian grid with a resolution chosen so that the detonation cell size and regularity of the structure are independent of the grid size used. The height of the computational domain is also chosen to be sufficiently large to accommodate at least two to three detonation cells. Thus, the structure is not influenced by the dimension of the channel. A single-step Arrhenius rate law of the form

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322

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with 0~ being the reaction progress variable, and A, E a and R represent the preexponential factor, activation energy, and the gas constant, respectively. The parameters and initial conditions were chosen to represent approximately stoichiometric 2H 2 + 0 2 mixtures at P0 = i bar and TO = 293 K. The numerical computation is initiated by imposing a planar shock with a square wave profile and a pressure of 2pcJ near the left boundary. This strong initial shock wave induces chemical reactions that produce an overdriven detonation advancing toward the right of the domain and decays asymptotically to a steady C-J detonation. With a proper choice of the frame of reference, the detonation can be made to eventually stabilize near the right boundary of the domain. The preexponential scale factor A is also chosen to ensure that the length of the computation domain always contains several detonation cells. Thus, even though this initial condition does not correspond to a real experimental initiation process, the transient development of the instability leading to the eventual steady cellular C-J detonation from an initial overdriven wave is described in the numerical simulation. The time-integrated maximum pressure contour from the numerical simulation is found to correspond to the trajectories of the triple point of Mach interactions, which have been demonstrated to be similar to the writing on the smoked-foil records. The numerical results therefore indicate that the peak pressure in a cellular detonation is also localized at the triple shock intersections. A typical "numerical smoked foil" corresponding to a value of the activation energy Ea/RT* = 2.1 (where T* -- 1709 is the shocked temperature) is shown in Fig. 17.6. We note that in the initial overdriven state, the detonation is stable and the pressure is uniform across the planar front. Instability develops and cell formation appears only later on as the overdriven detonation decays to near its final C-J velocity. In the final frame, one can see that the cell pattem is also quite regular for this particular value of the activation energy. For a regular cell pattern, the transverse waves are weak and correspond to acoustic perturbations sweeping across the leading shock front. Weak transverse waves are analogous to Mach waves in a supersonic flow and they play a minor role in the propagation mechanism of the detonation wave. For higher values of the activation energy, i.e. E ~ / R T * = 4.9 and 7.4, the corresponding development of the cellular pattern from the initial overdriven state is illustrated in Figs. 17.7 and 17.8. For higher activation energies, the strength of the transverse waves are much stronger and the cell pattem also becomes more irregular with increasing activation energy. These numerical results are in qualitative agreement with experimental observations and stability theory. The growth of initially weak transverse perturbations to form the final cellular detonation as the overdriven wave decays to its final C-J value is similar to the experimental observation of Strehlow et al. 21 for reflected shock initiation of detonation. The dependence of the regularity of

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132 or h > 102), then reinitiation would be able to occur near the tube axis even though all the transverse waves are eliminated at the boundary defined by the tube wall. The necessity for the shock wave interactions in the reaction zone is to attain sufficiently high reaction rates to sustain the propagation of the detonation wave. This is associated with the shock wave enhancement of the turbulent mixing rate in the reaction zone. In D. R. White's original description of the unstable detonation structure as being "turbulent," he may not have considered that shock wave interactions can be considered as part of the turbulence mechanisms. Conventional notions of turbulence are derived essentially from studies of low-speed, incompressible flows where shear and vorticity interactions constitute the principal energy dissipation mechanism. In high-speed, compressible turbulent flows, the intense pressure fluctuations generate an ensemble of shock waves. The presence of shock waves brings in


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FIGURE 17.13 Decay of a cellular detonation to a deflagration wave due to the damping of the transverse shock waves by an acoustic attenuating wall.

336

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FIGURE 17.13

(continued)


337

an array of additional mechanisms of vorticity generation and dissipation. For example, the baroclinic mechanism of vorticity production due to the interaction between pressure and density gradient fields becomes important for high-speed compressible flows. Nonlinear shock-shock interactions (e.g., Mach interactions) produce vorticity even in the absence of boundaries to create the velocity gradient fields. Shock-vortex interactions also lead to breakdown of the large-scale mean flow to increase kinetic energy dissipation rates. With the presence of strong density interfaces associated with the chemical reactions, increased turbulence production also arises from the various interface instability mechanisms (e.g., Richtmyer-Meshkov, TaylorMarkstein) due to shock wave-density interface interactions. The effects of shock waves cannot be excluded from the consideration of high-speed compressible turbulence. As early as 1955, Lighthil141 had already recognized the inherent role of shock waves in compressible turbulence. Because of its clarity, it is of interest to quote directly from Lighthill's eloquent statement of compressible turbulence: Extending the picture to three dimensions, one may imagine the turbulence to consist not only of the usual vortex motions, but also of a three-dimensional statistical assemblage of N-Waves, that is, of shock waves of all shapes rushing about in all directions with regions of more gradual expansion between them and with continual interactions taking place between pairs of shock waves (including unions, regular intersections and Mach intersections) and, to a lesser extent, between them and the longitudinal expansion waves and shear turbulence. The interactions between shock waves actually create additional vorticity; also a single shock wave along which entropy increase is non-uniform creates vorticity in proportion to the gradient of that increase. Thus, to some extent, the shock wave system can generate new turbulence. Whether as a result of all this, any kind of equipartition between the energy of longitudinal and shearing motion is likely to be set up can only be a matter of opinion. The Author feels rather that the system has become one in which the division of the motion of turbulence on the one hand and sound (or shock waves) on the other is ahnost without significance.

Thus, if we broaden the conventional definition of turbulence to include the role played by shock waves, then detonations can simply be regarded as an extension of turbulent deflagrations to the high-speed compressible regime. Returning to the original question as to why Nature requires real detonations to have such a complex cellular structure, the response is simply that the additional, powerful dissipative mechanisms associated with shock wave interactions have to be recruited to produce the required reaction rates to cope with the high propagation speed of the detonation wave. In a largediameter, smooth tube, or in a spherical wave, the ensemble of interacting shock waves have to be produced via hydrodynamic instability, that is, growth of small perturbations. Thus, the onset of detonations is abrupt when the propagation mechanism changes from the diffusional transport of the deflagra-

338

J . H . S . Lee

FIGURE 17.14 Flame acceleration due to turbulent mixing enhancement by transverse shock waves generated by wall obstacles.

339


tion regime to autoignition via shock heating and turbulent mixing of the detonation regime. In a very rough tube, experiments have indicated that the acceleration to detonation is relatively smooth, without the usual abrupt jump to an overdriven detonation that subsequently decays to a C-J wave. 42 This is due to the dominant role now played by the rough wall in generating the vorticity and pressure waves necessary for the detonation regime. There is no longer the need to rely on instability to form the transverse waves. Figure 17.14 illustrates a sequence of framing schlieren photographs of the flame acceleration process in a very rough-walled tube. The train of transverse waves (shock waves generated by the roughness on the walls of the channel) is clearly demonstrated. The mixing enhancement due to the interaction of these transverse waves with the turbulent reaction zone leads to a continuous increase of the burning rate and acceleration of the deflagration until it reaches a final steady-state velocity. With the rough wall controlling the production of transverse waves, the final steady-state velocity can span the entire spectrum of supersonic speeds (up to the C-J velocity) depending on the tube diameter, the dimension of the wall roughness, and the natural cell size of the mixture. The existence of a continuous spectrum of high-speed deflagrations (or quasidetonations) implies that the combustion mechanism is also continuous, with transverse shock waves entering and enhancing the turbulent burning rate as the deflagration accelerates. Without the rough wall, the transverse shocks can only be formed from the growth of small perturbations from instability. Thus, the flame has to accelerate to a sufficiently high speed to generate the critical conditions for this to occur. With a rough-walled tube, the transverse pressure waves can now be generated continuously by the wall protrusions. Without a distinct difference between either the propagation mechanism or the propagation speed, a unique separation between the two phenomena of high-speed, turbulent deflagration and detonation can no longer be made. Only in situations where the influence of boundary conditions is small and the detonation has to rely on self-generation of transverse waves from instability can detonation phenomena be uniquely defined. However, in terms of the mechanism of combustion, detonations and high-speed, turbulent deflagrations can be considered to be similar if shock wave interaction is considered as an inherent part of high-speed compressible turbulence. Hence, it is the nature of how the transverse waves are being generated that separates the detonation from deflagration phenomena.

17.3

INITIATION

OF DETONATION

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In general, a detonation wave can be obtained via the process of a transition from a deflagration wave (DDT, i.e., deflagration to detonation transition) or

340

J.H.S. Lee

from the decay of a strong blast wave generated by a powerful ignition source (i.e., direct initiation). Direct initiation is a relatively well-defined phenomenon characterized by a critical energy required for the initiation of a detonation wave. DDT, however, is an ill-defined phenomenon that includes a spectrum of different processes leading to the formation of the detonation wave. In the classical experiments of Mallard and LeChatelier 1 and Berthelot and Vielle 2 where a long, smooth combustion tube is used, the DDT process is characterized by a continuous acceleration of the deflagration followed by an abrupt transition to a detonation. Figure 17.15 shows a typical streak photograph of DDT in a smooth tube. Ignition is effected by a hot jet of combustion products from a small orifice from the reflection of a detonation wave on the left side of the orifice plate. Subsequent to ignition, the deflagration wave accelerates continuously until an abrupt transition to detonation occurs. The flame acceleration is mainly due to the effect of turbulence and hence includes all processes that can lead to an increase in the flame area and transport rates across the flame surface. Thus, the intrinsic instability of the flame, the various interface instability mechanisms associated with the acceleration, and acoustic and shock wave interactions with the flame, as well as the velocity gradient and turbulence induced in the displacement flow of the unburned gases ahead of the propagating flame, are all responsible for increasing the burning rates. A detailed discussion of all the various flame acceleration mechanisms can be found in the review articles by Lee and Moen 3 and Shepherd and Lee. 4 The different flame acceleration mechanisms are very sensitive to initial and boundary conditions (e.g., type and strength of the igniter, its location, tube geometry and size, wall roughness, closed or opened ends of the tube). Hence, the relative roles played by each of the different mechanisms in the DDT process differ under different conditions. As a result, the transition distance (i.e., the distance the flame travels from ignition to the location of the onset of detonation) can be orders of magnitude different for the same explosive mixture under different conditions. The transition distance is not a unique parameter that can characterize the DDT phenomenon. Note that the transition distance is also referred to as the "run-up distance" and in some of the older literature, it is referred to as the "induction distance. ''5 The transition distance is typically 50-100 tube diameters in smooth circular tubes with a weak spark ignition at a closed end. Attempts have been made in the early studies of DDT to correlate the "induction distance" to the properties of the mixture (at least for one geometry of smooth circular tubes); however, these correlations lack generality and are of limited value in terms of promoting fundamental understanding of the DDT phenomenon. The termination of the flame acceleration phase of DDT is the abrupt onset of detonation. Early views of the DDT process were that the flame must accelerate to a sufficiently high velocity so that the precursor shock in front of


341

FIGURE 17.15 Streak photograph of DDT in C2H 2 - O 2 mixtures in a smooth tube. Ignition is by a hot gas jet from the reflection of a detonation wave off an orifice plate. Reprinted, with permission, from the Annual Review of Physical Chemistr3; Volume 28, i{~, 1977, by Annual Reviews www.AnnualReviews, org.

342

J . H . S . Lee

it can result in autoignition of the mixture. 6'7 However, later investigations indicated that the onset of detonation can correspond to a variety of different conditions. Perhaps the best illustration of the different modes of DDT is given by Urtiew and Oppenheim. s From their excellent stroboscopic laser schlieren photographs, they demonstrated that the onset of detonation can originate from a "hot spot" in the turbulent flame zone, in the precursor shock-boundary layer interaction region and at the interface formed from the coalescence of two shock waves. The "hot spot" is a rather arbitrary definition of the location of the origin of the incipient detonation kernel and may not actually represent a local high-temperature region. The origin of the hot spot has not been clearly established. In the article by Meyer, Urtiew and Oppenheim, 9 they demonstrated that the origin of the hot spot cannot be due to the adiabatic compression of the mixture from the precursor shock waves. They carefully followed the thermodynamic history of the particle due to the various wave compression processes and found that only about 4% of the induction process occurred when the onset of detonation happened. Hence, they concluded: Gasdynamic processes of compression ahead of the accelerating front are entirely insufficient to bring about the transition to detonation. The occurrence of this event must be due, therefore, to other phenomena of which the most influential should be those associated with heat and mass transfer from the flame.

Thus, Oppenheim and co-workers implicitly credited turbulent mixing as the dominant mechanism that brings about autoignition for the onset of detonation. The typical process of the onset of detonation from a hot spot in the turbulent mixing zone is illustrated in Fig. 17.16. The incipient detonation kernel grows to catch up with the precursor shock front to form an overdriven detonation. The detonation kernel becomes a shock wave when it propagates back into the combustion products where there is no unbumed mixture. This shock is known as the retonation wave. When the spherical detonation kemel grows and reflects from the tube walls, a transverse shock wave is formed that reverberates between the walls and attenuates slowly as the detonation and the retonation waves move apart. All of these features are also illustrated in the streak photograph of the transition processes shown in Fig. 17.15. The autoignition process required for the onset of detonation can be brought about by free radicals obtained via thermal dissociation at high temperatures and also by other means. For example, direct initiation of detonation in hydrogen-chlorine mixtures at room temperature by photodissociation of chlorine had been demonstrated by Lee et al. 1~ Furthermore, Knystautas et al. 11 have also showed that by rapid, turbulent mixing of combustion products with the unbumed mixture in a turbulent jet, direct initiation of detonation can also be achieved. In this case, the free radicals to


343

FIGURE 17.16 Stroboscopic laser schlieren photograph of the onset of detonation in H202 mixtures. Detonation kernel originates at bottom wall in the turbulent flame brush. (Courtesy of A. K. Oppenheim.)

344

j.H.S. Lee

induce autoignition are present in the hot combustion products originally. These experiments showed conclusively that autoignition is a necessary condition for the onset of detonation and can be achieved by means other than by shock heating. Thus, the DDT phenomenon encompasses all the different processes that can bring about the onset of detonation from an initial deflagration wave. However, it is now generally acknowledged that rapid turbulent mixing leading to autoignition constitutes the key mechanism of DDT. Considerable attention has been devoted to the onset of detonation resulting from shock-flame interaction. 12-17 Enhancement of turbulent mixing due to shock-flame interaction has proven to be a very efficient means of generating the necessary conditions for the onset of detonation. Shock-flame interaction also provides a well-defined initial condition for numerical simulation as well as in actual experiments. In addition to the crucial role played by shock waves in the propagation mechanism of self-sustained detonation waves as discussed in the previous section, we now see that shock wave enhancement of turbulent mixing also provides an effective mechanism for generating the critical conditions for the onset of detonation in the DDT process. Although autoignition at a local region (hot spot) of the turbulent mixing zone represents the start of the detonation formation process, the shock or compression wave from the energy released at the hot spot must also be capable of amplifying rapidly to form the detonation wave. Even for an instantaneous constant volume explosion of the hot spot, the shock generated is only of the order of M ~ 2.5. Experiments indicate that the incipient detonation kernel is formed within a very short distance of the shock propagation from a local hot spot. Thus, a further requirement for the onset of detonation is the condition necessary for the rapid amplification of the shock wave formed from the explosion of the hot spot. From a study of the photochemical initiation of detonation, Lee et al. 1~ had proposed the shock wave amplification by coherent energy release (SWACER) mechanism as being responsible for the onset of detonation. In the photochemical initiation process, a gradient of chlorine atoms is generated in the direction of the irradiation. Thus, a gradient in the induction time is also generated, resulting in the sequential autoignition of the mixture along the induction time gradient. A progressive reaction front is thus obtained, although the propagation speed of this reaction wave is a phase velocity predetermined by the initial induction time gradient and not by any physical or transport process. The termination of the induction period is followed by the recombination or a rapid energy release process that then generates a shock or compression wave. If the gradient field is such that the reaction wave path is coincident with the shock wave trajectory, then the chemical energy released is in phase with the shock propagation, resulting in a very rapid amplification of the shock wave. This amplification process is similar to the laser concept and led Lee to adopt a


345

similar acronym (i.e., SWACER). In an earlier investigation, Zeldovich et al. i s had also considered an induction time gradient resulting from a temperature gradient. It was shown that shock amplification also requires the coincidence of the path of the shock with that of the reaction wave. Figure 17.17 illustrates results of the numerical simulation of the SWACER mechanism in an induction time gradient field in an H2-C12 mixture from the photodissociation of C122~ Figure 17.17a illustrates the supercritical regime where the irradiation intensity I0 = 2 k W / c m 2 is above the critical level to produce an optimum induction time gradient for the onset of detonation due to the SWACER mechanism. The critical regime shown in Fig. 17.17b (I0 = 1 k W / c m 2) indicates that the initial gradient field did not lead to the formation of a detonation wave immediately, but created the conditions corresponding to the quasi-steady regime similar to blast initiation (at around profile 5). A second longitudinal acceleration process occurs between profiles 5 and 7, resulting in the onset of an overdriven detonation. In Fig. 17.17c, the intensity is much higher (I0 = 15 k W / c m 2) than the critical and thus gives a much smaller induction time gradient. The SWACER mechanism is suppressed and a progressing volumetric explosion front results. In the limit of even higher irradiation, the entire mixture undergoes a constant volume explosion. It is interesting to note that the three regimes of direct initiation do not correspond to the irradiation energy but on achieving of an appropriate induction time gradient. Thus, we see that successful initiation of detonation requires a combination of induction gradient and heat release profiles as well as a critical length of the gradient field itself. Because of the nonlinear effect of the shock wave on the initial induction time gradient profile as the shock amplifies, it is difficult to derive an analytical criterion for the SWACER mechanism. Numerical simulations had first been carried out by Yoshikawa 19'2~ on the H2-C12 system, because the detailed kinetics are well established. Since then numerous studies on the SWACER mechanism have been carried OUt 19-26 with the gradient field formed via turbulent mixing. A detailed, recent review of this mechanism is given by Bartenev and Gelfand 27 in which a complete bibliography on the subject can be found. It is also of great practical importance to know if DDT can occur in a given explosive mixture under given initial and boundary conditions. The criterion for the possibility of DDT is closely related to that for the detonability limits. It is clear that if the conditions are outside the detonability limits, then DDT cannot occur. However, the reverse is not true, that is, DDT may not be possible even though the conditions are well within the detonability limits. A typical example is the case for spherical detonations. In purely unconfined geometry, almost all the flame acceleration mechanisms are ineffective, and it is extremely difficult for a spherical deflagration to accelerate and transit to a spherical detonation. However, if a powerful ignition source is used for direct

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347

initiation, the spherical detonation can readily sustain itself once initiated. Since DDT depends on the effectiveness of the various flame acceleration mechanisms, it is no longer possible to establish a general criterion for the occurrence of DDT. The onset of detonation, that is, growth of the incipient detonation kernel from a local hotspot, appears to be sufficiently general in all DDT processes. Hence, it is possible to establish a criterion for the successful growth of the detonation kernel subsequent to its formation from a hotspot. In an extensive experimental study by Peraldi et al. 2s on the transition in circular tubes of three different tube diameters (i.e., 5, 15, and 30 cm) in a variety of fuel-air mixtures (hydrogen, acetylene, ethylene, propane, and methane) at standard conditions, it was initially found that DDT requires that the tube diameter D be at least equal to a detonation cell size 2, i.e. D / 2 > 1. In a rough tube with periodically spaced orifice plates of orifice diameter d, it was found that DDT also requires that the minimum transverse dimension to be of the order of a cell size, i.e., d / 2 > 1. Although this is a necessary condition, it is not sufficient by itself, since DDT also requires sufficiently rapid turbulent mixing to achieve autoignition and the subsequent amplification of the shock wave from the explosion of the "hotspots" (i.e., the SWACER mechanism). Thus, we see that DDT is a more demanding phenomenon requiring a set of critical conditions that have to be met simultaneously before it can occur. Direct initiation is a relatively simpler phenomenon than DDT, requiring only a powerful ignition source to generate a strong blast wave of sufficient duration. The strong blast wave then decays asymptotically to a C-J detonation as it propagates away from the ignition source. For direct initiation, the initial strength of the shock wave required is typically above the C-J detonation velocity, and the duration (i.e., the period of time in which the shock is above some critical value) should be long enough to permit a sufficient amount of energy release by the chemical reactions to sustain the shock and prevent its further decay. The strength and duration of the initiating shock wave depend on the energy-time characteristics of the ignition source. However, in the limit of an instantaneous point, line, or planar energy source, an ideal blast wave is obtained and the direct initiation process can then be characterized by a single parameter, i.e., the ignition source energy. It has been well established that condensed explosives approach the ideal point source since the energy density is extremely high (i.e., dimension of the explosive charge is small compared to the explosion length R o -- (Eo/Po)l/3). Extensive studies have been carried out in the 1960s and 1970s on direct initiation using electric sparks in an attempt to correlate the critical energy with the energy time profile and the power density of the source. These studies have been summarized in the review article by Lee. 29 With the interest in less sensitive fuel-air explosives, the critical energies required for direct initiation are met using condensed explosive charges in practice. The characteristics of the initiating blast wave are therefore

348

J.H.S. Lee

closely approximated by the ideal point blast in the direct initiation of fuel-air mixtures with condensed explosive charges. The direct initiation phenomenon by an ideal point blast wave is determined by a single parameter of the source energy only. For a given explosive mixture at a given initial thermodynamic state, it is found that there exists a critical minimum value of the blast energy below which a detonation is not obtained. The reaction zone is found to separate from the decaying blast wave as it propagates away from the source and the shock eventually decays to an acoustic wave while the decoupled reaction front propagates subsequently as a spherical deflagration wave. For ignition energies below the minimum critical value, the phenomenon is generally referred to as the subcritical regime (Fig. 17.18a). For initiation energy above the critical value, the blast wave decays asymptotically to a C-J detonation wave. The reaction zone is always coupled to the shock, and the onset of cellular instability is observed as the blast decays near the C-J velocity of the mixture. This is referred to as the supercritical regime (Fig. 17.18b). There exists a narrow range of initiation energy around the critical value in which the phenomenon is more complex. It is found that the blast at first decays below the C-J velocity with a distinct separation of the reaction zone from the shock front. This is followed by a quasi-steady period in which the shock propagates at a relatively constant velocity with the reaction front trailing behind at approximately the same velocity (i.e., the separation distance is constant). At the termination of the quasi-steady period, hot spots began to appear near the reaction front surface from which detonation wavelets or kernels develop. These detonation wavelets then grow rapidly to engulf the entire shock surface, forming an asymmetrical detonation that eventually becomes more spherically symmetric as it expands. At around the minimum initiation energy, the velocity of the shock wave in the quasi-steady regime is typically of the order of half the C-J velocity. The initiation processes near the minimum initiation energy is referred to as the critical regime (Fig. 17.18c). The formation of hot spots and the subsequent growth of the detonation kernels to eventually form the cellular C-J detonation wave in the critical regime are similar to the onset of detonation in DDT. The quasi-steady regime is also analogous to the final stage of DDT at the onset of detonation. Thus, DDT and direct initiation differ only in the initial processes involved in the creation of the critical condition required for the onset of detonation. In the critical regime of direct initiation, the formation of hot spots is due to the instability and hydrodynamic fluctuations in the reaction front during the quasi-steady period. The critical energy for direct initiation can readily be measured experimentally and can serve as a quantitative measure of the sensitivity of a gaseous explosive. Matsui and Lee3~ had suggested the use of the critical energy for the assessment of the detonation hazard of explosive gases. Extensive measure-


FIGURE 17.18

349

(a) Subcritical regime of blast initiation of C2H2-O 2 mixture by laser spark.

ment of the critical initiation energy for fuel-air were carried out by Bull and co-workers at Shell's Thornton Research Centre in the 1970s. 31-33 The dependence of the critical energy on the equivalence ratio for various fuelair mixtures is illustrated in Fig. 17.19. These typical U-shaped curves are qualitatively similar to those for the dependence of the detonation cell size 2 on the equivalence ratio. In the pioneering study of direct initiation of spherical detonations by Zeldovich et al., 34 a dependence of the critical energy on the cube of the induction zone length of the detonation was proposed. This cubic dependence can be shown from dimensional considerations since the blast wave is characterized by the explosion length R o --(E/po) 1/3, while the detonation wave is represented by its chemical length scale s (the induction distance); thus, the critical energy E "~ s Since the cell size 2 is proportional to the ZND induction length s the critical energy is E ~ 23 also. Following Zeldovich's pioneering work on direct initiation, numerous attempts have been made to develop a quantitative theory from Zeldovich's criterion. All these attempts evolved around the choice for an appropriate critical shock strength and its duration. Zeldovich's original criterion states that direct initiation requires that the distance traveled by the decaying blast must

350

J.H.S. Lee

FIGURE 17.18 (b) Supercritical regime of blast initiation in H2-C12 mixture by an electrical spark discharge. be at least equal to the induction zone length by the time the shock strength has decayed to the C-J value of the mixture. Using the similarity solution of ideal point blast of Taylor,35 Lee et al. 36 showed that Zeldovich's theory underestimated the critical energy by about three orders of magnitude. If a more representative reaction zone length such as the "hydrodynamic thickness" were used, a more reasonable agreement with the experiment can be achieved. In the detonation kemel theory of Lee and Ramamurthi, 37 the shock strength corresponding to the quasi-steady regime was used instead of the C-J velocity. This value of the shock strength is quite close to the autoignition limit for the mixture. The critical distance (or the detonation kernel size) was determined from a balance between the blast decay rate and the chemical energy release rate. It was argued that a balance between these two competing rates led to the quasi-steady condition of the critical regime. Reasonably good agreement between experimental results for acetylene-oxygen and hydrogenoxygen mixtures and the prediction using the detonation kernel theory was obtained. In a later study, Lee et al. 38 proposed an alternate kernel size based on the equivalence of the surface area of the kernel (i.e., 4~R .2) and the critical tube diameter of the mixture (i.e., d c = 132). The kernel size is thus


351

FIGURE 17.18 (c) Critical regime of blast initiation in C2H4-O 2 mixture with a laser spark ignition. Reprinted, with permission, from the Annual Review of Physical Chemistry, Volume 28, 9 1977, by Annual Reviews www.Annual Reviews.org.

R* = 3.252, and using a value for the quasi-steady shock strength of Mcj/2 in the strong blast theory, the following expression for the critical energy was obtained: E = 14.5rtTp0M~j23.

(17.1)

From independent measurements of the detonation cell size 2, the above expression predicts reasonably well the critical energy for fuel-air mixtures when compared with experiments (see Fig. 17.19). Note that the cubic dependence on 2 renders the critical energy extremely sensitive to the accuracy in the measurement of the cell size itself. Since the uncertainty in measurement of the cell size from smoked foils can be quite large, the semi-empirical expression obtained is probably as good as can be expected if it is based on the cell size 2. Since the similarity solution for strong blast decay can readily be applied to geometries other than spherical, similar expressions for the critical initiation

352

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energies for cylindrical and planar detonations can readily be derived. The experimental realization of an instantaneous planar energy source is very difficult. However, using the hypersonic blast wave analogy, 39 the critical energy for the direct initiation of cylindrical detonation can be obtained indirectly via the direct initiation by a hypervelocity projectile 4~ Similar to a hypervelocity projectile, a condensed phase detonation in a detonating cord 41 can also be used to obtain cylindrical initiation. Figure 17.20 illustrates


353

different regimes of direct initiation using a PETN detonating cord in ethyleneair mixtures. In the supercritical regime shown in Fig. 17.20a, a conical detonation is established with the energy source traveling along the cord at a velocity VDc of about 6.3 km/sec. The cone angle of the detonation is - - sin -1 V c j / V D c , where Vc_J is the detonation velocity of the ethylene-air mixture at 1.8 km/sec. The cone angle obtained is approximately 16 ~ in good agreement with experimental observation. Note that according to the hypersonic blast analogy, the conical detonation is equivalent to a cylindrical detonation under the transformation z = Vc)ct where z is the distance along the axis from the apex of the cone, and Vt)c is the velocity of the condensedphase detonation along the cord. Thus, the instantaneous photograph of the conical detonation can be interpreted as a streak photograph of an expanding cylindrical detonation. For the critical regime shown in Figs. 17.20b and 17.20c, we see that the conical detonation is formed from the growth of discrete detonation kernels originating from hot spots distributed on the conical blast wave surface. For the subcritical case in Fig. 17.20d, the weak conical deflagration can be seen just ahead of the condensed-phase detonation products. The decoupled blast wave in air cannot be seen in the self-luminous photographs. The initiation phenomena illustrated in Fig. 17.20 for cylindrical detonations are identical to those for spherical detonations shown in Fig. 17.18.

FIGURE 17.20 Regimesof cylindrical blast initiation in C2H4-air mixture by a PETN detonation zord: (a) supercritical, (b, c) critical, (d) subcritical. (CourtesyofM. Radulescu). (See Color Plate 12).

354

j.H.S. Lee

The analogous expression for the critical energy (per unit length) for the direct initiation of cylindrical detonation can readily be obtained as E-

10.12p0M2122.

(17.2)

According to the hypersonic blast wave analogy, the work done (per unit length) by the drag force on a hypervelocity projectile is equivalent to the cylindrical blast wave energy. Equating the work done to the blast energy results in the following expression relating to the critical diameter of the hypervelocity projectile d and its velocity Mo~ to the C-J velocity Mc_J and the cell size of the mixture:

M~

2

~ = 5.3Mcj d" A comparision of the critical diameter of the projectile, predicted by the preceding expression, to the experimental results obtained by Higgins 4~ is shown in Fig. 17.21. The agreement is reasonably good in spite of the fact that the velocity of the projectile in Higgins' experiment is only slightly higher than the C-J velocity of the detonating gas. Hence, we would not expect the hypersonic blast analogy to be valid under this circumstance. In the more recent study using a detonating cord, 41 the velocity of the condensed phase denotation along the PETN cord is of the order 6-8 km/sec. This is 3 to 4 times the C-J velocity of the mixture, and thus the hypersonic blast analogy should be more applicable in this case. The experimental results obtained using the PETN cord are also found to be in good agreement with the prediction of Eq. (17.2). Since the behavior of an ideal blast wave is characterized by a single length scale, that is, the explosion length R0 (E/po)l/j+l; where j = 2, 1, 0 for the spherical, cylindrical and planar geometries, respectively, and the detonation sensitivity is represented also by a chemical length scale (e.g., the cell size 2), dimensional considerations indicate that the ratio R0/2 should be invariant. In other words, for the same explosive mixture, hence 2, the critical explosion length R0 should be the same. This explosion length invariance was first suggested by Lee 29 to permit the critical energy for any geometry to be estimated if it is known for one particular geometry. This explosion length invariance was recently verified experimentally by Radulescu et al. 42 where the critical energy of ethylene-air mixtures was determined for both spherical and cylindrical geometries. The explosion length determined from the critical energy obtained was found to be identical for the two geometries. The ratio of the critical explosion length to the detonation cell size was also found to be invariant (i.e., R~/2 ~, 32 for the case of ethylene-air mixtures) in accordance -

-

355

Detonation Waves in Gaseous Explosives 2.00

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Experiment with Spheres Cylindrical Initiation (Theory)

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i 2.6

Sphere Diameter (cm) FIGURE 17.21 Critical initial pressure of mixture for direct initiation by a hypervelocity projectile as a function of the sphere diameter. (Courtesy of A. Higgins)

with ideal blast wave theory. Thus, ideal blast initiation is a fairly wellestablished phenomenon. The ideal blast initiation problem is also amenable to numerical simulation. The one-dimensional reactive Euler equations with simplified kinetic rate laws can be integrated with a high degree of accuracy with current numerical algorithms. Thus, the detailed flow field of the transient development of the detonation wave can be determined numerically much more readily than experimentally. Although the structure of self-sustained detonations is invariably three-dimensional, the growth of cellular instability appears to take place only during the final phase of the initiation process as the overdriven detonation decays to its C-J state. Thus, it appears that the entire blast initiation process can perhaps be described by just one-dimensional simulations. Although the development of local hot spots at the termination of the quasi-steady regime appears to give the impression that the onset of detonation is a three-dimensional phenomenon, the formation of hot spots is due to small fluctuations that greatly amplify because of the strong exponential temperature dependence of the induction time. This results in a temporal and spatial variation of hot spots on the surface of the reaction front. However, the essential physics of the onset of detonation, that is, the SWACER process, is

356

j.H.S. Lee

not influenced by the spatial distribution of hot spots. The important threedimensional event of cellular instability comes later when the overdriven detonation decays to a self-sustained C-J detonation. Using a single-step Arrhenius reaction rate law, the three regimes of direct initiation (i.e., supercritical, critical, and subcritical) for the planar geometry are shown in Fig. 17.22, where the shock pressure is plotted against the distance (normalized with respect to the half ZND reaction length) from the ignition source. 43 The numerical results are in good agreement with experiments and reproduce the same qualitative behavior of the three regimes. At the critical regime, we note that the blast pressure decays to about one-half of the C-J value, as observed experimentally, before reaccelerating to an overdriven detonation at the termination of the quasi-steady period. The advantage of numerical simulation is that the detailed transient flow field of the initiation process can be obtained readily. Figure 17.23 illustrates the temperature profiles behind the blast wave for the subcritical and the 120

100

8O

t/

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t-

~. 60

.

Critical initiation

4O Pv.n. 2O

0 0

50

100

150

200

250

300

Xsh

FIGURE 17.22 Numerical simulation of planar blast initiation showing the three regimes. Reprinted from Higgins, A. and Lee,J.H., Comments on criteria for direct initiation of detonation, Phil. Trans. R. Soc., Lond. A 357 3503-3521 (1999).


357

supercritical regimes. In Fig. 17.23a, for the subcritical regime, the progressive decoupling of the reaction front from the shock front as it decays can be observed. In the supercritical regime (Fig. 17.23b), decoupling does not occur as the blast decays asymptotically to a C-J detonation. Note that for a sufficiently high value of the activation energy, the C-J detonation is unstable. However, in a one-dimensional simulation, the instability is manifested by a longitudinal pulsating detonation. Thus, for a high (unstable) value of this activation energy, the initiating blast decays to a pulsating detonation oscillating about the C-J state of the mixture. 12 a) 10

E

,

0

.

,

~

~

~

,

|

,

9

~

I

,

,

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100

120

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12 (b) 10 86421

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100

'

120

,

,

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FIGURE 17.23 Temperatureprofiles behind blast wave for (a) subcritical and (b) supercritical regimes. Reprinted from Higgins, A. and Lee, J.H., Comments on criteria for direct initiation of detonation, Phil. Trans. R. Soc., Lond. A 357 3503-3521 (1999).

358

J.H.S. Lee

In the critical regime shown in Fig. 17.24, we can see that the reaction zone decouples from the decaying blast initially. During the quasi-steady regime, the shock amplitude as well as the temperature profile behind the shock appears to be stationary (e.g., 81 _< x rc -- 3.14), the detonation is very unstable and exhibits large velocity fluctuations (Figs. 17.26a and 26b). For rigid circular tubes, the velocity deficit near the limits seldom exceed 10% in general. In fact, Manson et al. 16 have used the velocity fluctuation to define the wave stability and limits. Fig. 17.27 shows the extensive experimental results of Dupre et al. 13 for the velocity deficit of H2-air mixtures in tube diameters ranging from 38 to 152 mm. Most of the data fall in the region bounded by D / 2 - - 1 / r e and A V / V c j - 0 . 1 . This indicates that the onset of single-headed spin as given by D / 2 - 1/re defines quite well the detonation limits and that the velocity deficit seldom exceeds 10% at the limits for smooth tubes. As the detonation limits are approached, the detonation velocity exhibits very large fluctuations. Using a microwave doppler interferometer to obtain a continuous monitoring of the detonation velocity, Lee et al. lz have studied the unstable, near-limit propagation of the detonation wave. Six different types of unstable, near-limit behavior were identified and shown in Table 17.1. The velocity-time histories as well as the velocity histograms for the six modes of propagation are illustrated in Fig. 17.28. In the stable mode (Fig. 17.28a), the detonation propagates at a constant velocity very close to its theoretical C-J value. The stability of this mode is indicated by the very narrow band in the velocity histogram. The mean value is only slightly below the theoretical C-J value. For the rapid fluctuation mode shown in Fig. 17.28b, the velocity spectrum is wider and the deficit of the mean velocity is also larger and of the order of A V / V c j "" 0.2 or V ~ 0.8 Vc3. For the stuttering mode (Fig. 17.28c), the velocity alternates between Vc_J and 0.6 Vc_J for long periods of

366

J. H. S. Lee

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FIGURE 17.26 (a) Velocity fluctuation near the concentration limit for H2-air mixtures in a 49mm diameter tube. The vertical bars represent the velocity fluctuation for different shots for the same concentration. (b) Velocity fluctuation near the lean concentration limit of H2-air mixtures in a 38-mm diameter tube. Vertical bars denote shot to shot variation for the same concentration. 9 1986 AIAA, reprinted with permission.

367


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FIGURE 17.27 Velocity deficit as a function of 2/d near the limits of H2-air mixtures for various tube diameters. 9 1986 AIAA, reprinted with permission.

TABLE 17.1 Mode 1 2 3 4 5 6

Types of Unstable, Near-Limit Behavior Name

Brief description

Stable Rapid fluctuation Stuttering Galloping waves Low velocity stable Failure

Vc_J with 3% ~ 0.7 Vc_J to ~ 0.9 Vc_J ~ 0.6 Vc_J to ~ Vc_J ~ 0.5 Vc_J to ~ 1.5 Vc_J ~ 0.5 Vc_J with 5% "-~ 0.5 Vc_J and no reinitiation

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the wave propagation (e.g., about a period of 1 ms or about 26 tube diameters of wave propagation). The velocity histogram also clearly demonstrates the two dominant velocities of this "stuttering mode." Further away from the limits, we have the so-called "galloping detonation" mode shown in Fig. 17.28d where the velocity fluctuates between 0.5 Vc_J and 1.5 Vc_J. For most of the duration of a galloping cycle, the detonation remains at the low velocity phase of about 0.5 Vc_J. Rapid acceleration to an overdriven detonation of about 1.5 Vr occurs at the end of the galloping cycle. The overdriven detonation then decays to the C-J where it will remain for a short duration before the wave fails and decays to a low velocity of ~0.5 Vc_J again. The period of the galloping cycle is of the order of 100 tube diameters and the phenomenon is reminiscent of the transition from deflagration to detonation. For the so-called "low velocity stable" mode (Fig. 17.28e), the detonation decays to about 0.5V c_J and remains at this velocity for over 65 tube diameters with little variation. The detonation of this metastable low-velocity regime is dependent on the tube diameter, and small perturbations can cause it to accelerate as in the galloping or fail. Still further away from the limits, the initial C-J detonation fails and the velocity drops again to a metastable state at about 0.5 Vc_J and remains at this low velocity for long distances of travel. However, the low velocity regime is much less stable and velocity perturbations can lead to failure, that is, the detonation fails. Since the detonation fails (Fig. 17.28f) easily under perturbations and does not reinitiate again. This mode is referred to as the failure mode. Note that all these unstable regimes are dependent on the tube diameters. If a larger tube is used, some of these unstable regimes may not be observed. For the rapidly fluctuating mode (Fig. 17.28b), the value of D / 2 ~ 0.3 corresponds to the onset of single-headed spin detonation. The other unstable modes are all "outside" the limits as defined by the D / 2 ~- rc criterion. Thus, even in smooth tubes, what constitutes the detonation limits is difficult to define since there exists a spectrum of unstable phenomena beyond the stable single-headed spin detonation that is the lowest detonation mode according to the acoustic theory of Manson 9 and Fay. 1~ Hence, the specification of the detonation limit depends on what is considered as a "bona fide" detonation wave. Stability (i.e., narrow velocity fluctuation about the C-J value) and a maximum deviation of the mean velocity from the C-J velocity (e.g., velocity deficit A V / V c j < 0.1) could be used as a limit criterion. From Fig. 17.28b, we see that the criterion defined by D / 2 ~ rc also provides a fairly reasonable criterion for the detonation limits in circular, smooth tubes in terms of the stability of the detonation wave. Of particular interest is the mechanism in which the detonation re-accelerates from about 0.5 Vc_J to an overdriven detonation in the galloping mode. Moen et al. 12 have measured the pressure-time history of a galloping detonation that illustrates the reacceleration mechanism (Fig. 17.29). In the top trace

372

J . H . S . Lee

FIGURE 17.29 Pressure records of onset of detonation resulting from the amplification of transverse pressure waves in the reaction zone. (a) Amplification of transverse pressure waves. (b) Formation of overdriven detonation and subsequent decay to a C-J wave. Moen, I.O., Donato, M., Knystautas, R., and Lee, J.H., Proc. Combust. Inst., 18:1615-1622 (1981).

of Fig. 17.29a, one can observe the normal shock preceding the reaction zone where intense transverse pressure fluctuations occur. The transverse pressure fluctuations amplified and also longitudinal compression waves are being sent forward toward the shock front resulting in a pressure rise ahead of the reaction zone. In the first pressure trace of Fig. 17.29b, we can see that the longitudinal compression waves steepen to form a shock, and this shock also catches up with the leading shock front. When it catches up with the leading shock, an overdriven detonation is formed (third trace of Fig. 17.29b). This overdriven detonation then decays subsequently to a C-J detonation (third and fourth traces of Fig. 17.29b). These pressure histories illustrate that the


373

mechanism for the reacceleration of the decoupled shock reaction zone complex is due to the amplification of the transverse pressure fluctuation in the turbulent reaction zone behind the leading shock front. This mode of transition is different from the one due to hot spots in the turbulent flame brush as illustrated in the studies by Urtiew and Oppenheim. 18 For the propagation of detonations in rough or obstacle-filled tubes, the limits are difficult to define because of the existence of multiple quasi-steady propagation regimes in which the combustion wave is supersonic. For a given tube and obstacle geometry (i.e., blockage ratio and obstacle spacing), it was found that as the sensitivity of the mixture is varied (e.g., equivalence ratio ~b or the initial pressure), there corresponds a so-called quasi-detonation regime (1000m/s_< V < 2 0 0 0 m / s for fuel-air mixtures) and the choking regime ( 8 0 0 m / s < V

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