OVERVIEWS OF RECENT RESEARCH ON ENERGETIC MATERIALS

Robert W Shaw Thomas B Brill Donald L Thompson Editors .-- — 60 -- faster 40 - Burns slower •*\ \^^ 20 0 5-ATZ ...

Author: Robert W. Shaw; Thomas B Brill; Donald L Thompson

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Robert W Shaw Thomas B Brill Donald L Thompson Editors

.--

—

60 --

faster 40 -

Burns slower

•*\ \^^

20 0 5-ATZ

+

- 60

i

[5-ATZH]CI

» -—80

O

3-

a>

CD

^

100

i

[5-ATZH]l

[5-ATZH]Br

Fig. 9. The percentage of the two main decomposition channels of 5-ATZ and its hydrohalide salts.

in the pyrolysis study. Of course these ratios could also be plotted versus the pK a values of HX. The observation of Sinditskii et al.40 that the burning rates correlate with the pK a of HX is thus placed on the footing of several specific chemical reactions. Reactions shown in Eqs. (6) and (7) may become important under some conditions and are well known to occur during pyrolysis.42

HN 3 + NH2CN

2NH2CN

(NH2)2CNCN

(NH2)2CNCN + NH2CN

(5)

(6)

(7)

NH 2

18

T. B. Brill

An additional feature of Fig. 8 is the different pressure dependencies of the burning rates of the four compounds. The 5-ATZ channel for the salts begins with the dissociative-evaporation as shown in Eq. (8): [5-ATZH]X - • 5-ATZ + HX

(8)

Because the contribution of this step is observed experimentally to decrease in the order 5-ATZ > [5-ATZH]Cl > [5-ATZH]Br > [5-ATZH]I, the relative pressure dependence of the burning rate is expected to decrease in the same order. This result is seen in Fig. 8 and is consistent with the fact that an evaporation-like process is expected to be suppressed as the pressure is increased. The electronic influence of a substituent on the tetrazole ring is reflected in systematic changes in burning rates. 43 Figure 10 shows that the electron density in the tetrazole ring, as mediated by the substituent X on the carbon atom in 5-X-tetrazole compounds, roughly correlates with the burning rate at constant pressure. The highest burning rates occur with the most strongly electron-withdrawing substituents. This series of tetrazoles has not been analyzed by T-jump/FTIR spectroscopy, but the trend in Fig. 10 is

N=NR NN

°2*

• N02

• Tz

• CI • Br

• CN

• H • NHTz

• OH • NH 2 -0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Hammett sigma The burning rates of 5-substituted tetrazoles as a function of the ring electron density (Hammett scale).

Connecting Molecular Properties to Trends

19

consistent with the interpretation given above for the hydrohalide salts of 5-ATZ in that the highest burning rate results when the tetrazole ring has the lowest 7r-electron density. The position of the substituent on the ring has been shown to affect the burning rate of azidonitrobenzene compounds. 44 Substitution in the m and p positions produces the same burning rate, but that is faster than substitution in the o position. The apparent explanation is the formation of the more stable benzofuroxan molecule by loss of N 2 from the o-azidonitrobenzene, shown in Reaction (9). This reaction does not take place when the substituents are in the m and p positions.

N2

N02

Nk

/ N ô

Finally, it has been found that most metal salts of energetic molecules burn faster than the parent molecule despite the dilution of the energy by the mass of the metal ion. 45 The implication is that the metal ion participates as a catalyst in the decomposition/combustion process. The discussion above illustrates that it is possible to learn a great deal about the parent molecular properties and/or chemistry that dominate in determining the burning rate of a material. The examples were, however, carefully chosen to be those in which the process is largely controlled by early-stage, exothermic, condensed-phase chemistry, and the controlling decomposition channels are relatively few in number. Finding controlling factors in HMX and other nitramines requires a somewhat different line of thinking. It appears that the gaseous decomposition products of HMX mainly control the burning rate and surface temperature. HMX decomposes via a complex scheme of reactions that remain to this day a subject of debate. For example, using simultaneous thermal decomposition and molecular beam mass spectrometry, Behrens defined pathways of slow decomposition (see the chapter by Behrens). The role of reversible and recombination reactions in the condensed phase has recently been stressed 46 and is a likely source of many products. This is how the "cage effect" might be manifested in mechanistic data. Some of the pathways in Behrens' findings also appear to occur during fast decomposition and combustion. For example, the formation of the mono nitroso derivative

20

T. B. Brill

of RDX (MRDX) is detected in slow decomposition, flash decomposition, and burned propellants that had been rapidly quenched. 47 The amount of MRDX differs, but it is found in every case. Amides are present in both slow and fast heating. Despite these products, the two main global channels that dominate for practical modeling purposes during combustion appear to be the exothermic N2O + C H 2 0 pathway and the endothermic (H)N0 2 + HCN pathway. 32 However, these two pathways occur in parallel and are essentially thermally balanced. Therefore, they are not likely to control the burning rate. Instead, the early strongly exothermic reactions are the most important for this purpose. One of the most important early exothermic processes is the reaction of the fuel (CH2O) from one channel and the oxidizer (NO2) from the other channel as shown in Eq. (10). In fact, a reaction with about the same stoichiometry (in terms of NO, CO, CH2O and N0 2 ) 5CH 2 0 + 7N0 2 -f 7NO + 3CO + 2C0 2 + 5H 2 0

(10)

has been found to occur at the exothermic stage in the flash decomposition of HMX. 32 ' 48 It is also provocative to note that the temperature at which the reactants for this highly exothermic reaction are in their proper stoichiometry for Eq. (10) corresponds to several surface temperature measurements of burning HMX. Could it be that the surface temperature, and correspondingly the burning rate, of HMX settles in at the temperature at which the stoichiometry of this early stage and strongly exothermic reaction is optimized to provide the maximum amount of heat in the reaction zone of the burning surface? Ignition delay in HMX probably results primarily from the need to build the concentrations of NO2 and CH2O before the exothermic Reaction (10) has a major effect. All of the examples above deal with combustion of pure materials. Of course, most energetic materials used in practice are formulated with a binder and other materials to modify the ballistics (e.g. metals, metal oxides) and improve the aging and mechanical properties (e.g. stabilizers and plasticizers). A logical question is whether these additional components can have an overriding influence on the combustion behavior compared to the pure energetic material. Sometimes they do as is evident by the influence of the agent used to cross-link the binder of an AP composite propellant. 49 We have suggested that the influence of the cross-linking agent is related to its volatility from the matrix as the propellant heats toward combustion. 50


21

6. Explosive Behavior and the Parent Material The impact and the shock sensitivity of a material can be experimentally evaluated in several ways, the most common of which are the drop hammer test and the gap test, respectively. In the impact test, a weight having a standard mass and contact area is dropped on the anvil on which a measured amount of sample has been spread. This is done repetitively from different heights and the height at which the sample is judged to have exploded 50% of the time is considered to be the drop height impact sensitivity. It is well known that the drop hammer test is crude and is subject to much uncertainty. The results differ from machine to machine. Shock sensitivity is frequently measured by sending a shock wave through a buffer plate to the explosive of interest. The pressure at which an explosion is initiated 50% of the time for a given density of material is the shock sensitivity. If one assumes a shock velocity of 6000 m/s, then 6 unit cells each having a dimension of 10 A are traversed in I ps. This is space and time enough for reactions to occur assuming that reactions on the ps timescale are important. Owing to the high and changing density and temperature in the shock front, the reactions are very difficult to decipher. Progress has recently been made by simulation of HMX at these conditions, which seems to offer the best opportunity for understanding at this time. 51 Because of the extreme conditions of shock and impact initiation, specifying molecular properties that control explosive behavior has also been a dicey activity attracting considerable thought. An inescapable and widely known fact is that nascent and dynamically-formed defects in a solid energetic material are the sites where the explosive reaction is initiated. Initiation does not originate in the defect-free region. Consequently, the possible relations between impact/shock sensitivity and fundamental molecular, crystal, and bulk properties of an explosive should always be considered in the context of how the behavior of molecules at the defect differ from those in the perfect solid. For example, the orientation of molecules relative to the direction of the shock wave has a significant effect on the shock sensitivity. This has been shown by Dick and co-workers in the case of PETN, 52 ~ 54 where initiation by impact is related to the energy localization and dissipation that takes place during plastic deformation and the shearing along certain axes. Shock sensitivity depends on the crystal orientation; that is, those directions in which shear bands do not easily occur experience the greatest local heating. A fundamental question arises as to how mechanical energy becomes coupled to the molecule in a way that starts a chemical reaction. If thermal

22

T. B. Brill

equilibrium is maintained during a mechanical impact, then the sensitivity of a material should directly correlate with its decomposition temperature, which it does not. In fact, direct coupling of mechanical energy into vibrational motions is too slow to cause deviations from thermal equilibrium. 55 A coupling mechanism must exist that allows deviations to occur from thermal equilibrium. A concrete discussion of how shock-generated mechanical energy becomes converted at the molecular level into dissociation reactions has been presented by Dlott and Fayer. 56 They proposed that "up-pumping" of selected vibrational modes occurs to a different degree at the defect site than in the perfect crystal lattice. In particular, hot spots form at the defect sites because the anharmonic coupling between phonons and the low frequency "doorway" modes is greater at defects compared to the ordered crystal sites. Consequently, the molecules at the defect heat faster and to a higher temperature than do the molecules uniformly distributed in the crystal. Following this line of thinking, Fried and Ruggiero 57 considered the coupling between phonons and internal vibrational modes from the point of view of the density of states of the phonon modes. They found that a correlation existed between the rates of energy transfer from the phonon modes to the fundamental modes that probably initiate the reaction. Figure 11

? ! &

-ou

gamma-HMX

*

-50 • RDX

cha

s. c

PETN

• beta-HMX

-40-

>. ?

• TNT

u c 9>

2 -30o

fc c ra

E -20c o E

-10 -

ial

£a.

• NQ • TATB

s c

n0.05

0.1

1

i

1

1

0.15

0.2

0.25

0.3

0.35

1/(N m)

Fig. 11. The energy transfer rate from the phonon density of states compared to the impact sensitivity of primary and secondary explosives.

23


shows this correlation for several important energetic materials that have significantly different impact sensitivity. McNesby and Coffey55 approached impact sensitivity from a similar point of view of rapid deposition of energy from a mechanical event into the phonon modes in such a way that causes non-equilibrium distribution of energy to occur in the internal vibrational modes. Thus impact sensitivity should be determined by how fast energy is transferred from the phonon system to the vibrational modes. As is shown in Fig. 12, they found that the impact sensitivity approximately correlated with the initial change in the phonon manifold of the molecule following shear dislocation. The mechanisms discussed above associate quantum mechanically-based properties of molecules with the macro events of impact and shock sensitivity. I think of these as primary correlations. In addition to these primary correlations, there are a myriad of crystal and molecular properties that sometimes tightly and sometimes loosely intertwine with the phonon and vibrational states of a complex molecule and thereby may also correlate with impact and shock sensitivity. I think of these as secondary correlations. An illustration of the confusion about whether and how various crystal and molecular properties exercise primary or secondary control over the

Pbstyphnate* • gamma-HMX

• RDX • beta-HMX picric acid • styphnic acid

•

• TATB 0

5

10

15

20

25

30

Energy Transfer Rate at 425 cm -1 Fig. 12. The initial energy change in the phonon manifold of several explosives as a function of the impact sensitivity.

24

T. B. Brill

explosive characteristics is illustrated by the aminotrinitrobenzene series, TNB, MATB, DATB, and TATB.

At least seventeen bulk, crystal and molecular properties of these compounds are known to correlate with their impact and shock sensitivity.4 These include the bond distances, charge distribution, degree of hydrogen bonding, electron promotion energy, density, heat of explosion, oxygen balance, melting point, molecular weight, and so on. The existence of so many positive correlations of sometimes unrelated properties cast doubt on whether any (or all) of them contribute fundamentally to the impact and shock sensitivity. For example, the observation that the amount of hydrogen bonding in these compounds is responsible for the trend in sensitivity to shock is frequently heard. The thought is that hydrogen bonds can act as "shock absorbers" to help minimize the concentration of vibrational energy in the molecule. While this may be true because of the influence of hydrogen bonding in the phonon mode structure, the existence of hydrogen bonding alone does not desensitize a material. For example, the extent of hydrogen bonding is very similar in nitroguanidine and trinitroethylnitroguanidine, yet the latter is much more sensitive to impact. 58 The reason is that the added, highly energetic trinitromethyl group sensitizes the molecule regardless of whether hydrogen bonding exists or not. The observation that the oxygen balance of nitroaromatic compounds correlates roughly with their impact sensitivity is evidence that the exothermicity of the secondary reactions following the initial steps is a factor in the operator's interpretation of the response to the hammer. 18 Indeed the types and quantities of products from the aminonitroaromatic series reflect an energy difference that follows the same trend in impact sensitivity.4 As a consequence, oxygen balance, which manifests itself in the impact sensitivity through the degree of exothermicity of the secondary reactions, is as legitimate a parameter as any of the seventeen to correlate with explosive properties of the aminotrinitrobenzene series above (or any other series for that matter). If one dares to make such correlations, then it is wise to


25

choose closely-related compounds. In the case of oxygen balance for example, many explosives are available t h a t do not possess any oxygen yet display the full range of sensitivities. Taken at face value the predictive value of the secondary correlations is doubtful in most cases.

7.

Conclusions

Relating parent molecular properties of an energetic material to decomposition, combustion, and explosion characteristics requires considerable care. There is no question t h a t correlations can be found and t h a t some may be meaningful, but the prima facie existence of a correlation is not necessarily meaningful. Correlations among various molecular properties have the most significance because they may have a q u a n t u m mechanical basis for the connection. Correlations among molecular and crystal properties require greater care to interpret properly, because there may or may not be a chemical or physical basis by which they can be connected. Correlations between molecular properties and macroscale bulk behavior are riskiest of all because the myriad of processes taking place may defeat most of the simple fundamental connections with the parent molecule. This rather pessimistic assessment of molecular correlations with macro events should be taken as a cautionary note as opposed to a call to avoid these types of studies altogether. For example, the connections made between shock and impact initiation and the phonon mode structure appear t o be a step in the right direction. Progress in this area will be an important component for designing b o t h conventional and new generations of energetic materials.

References 1. E. E. Hackman, III and H. C. Beachell, AIAA J. 6, 561 (1968). 2. A. K. Galwey, P. J. Herley and M. A. Mohamed, Thermochim. Acta. 132, 205 (1988). 3. M. L. Batz, P. M. Garland, R. C. Reiter, M. D. Sandborn and C. D. Stevenson, J. Org. Chem. 62, 2045 (1997). 4. T. B. Brill and K. J. James, J. Phys. Chem. 97, 8752 (1993). 5. T. B. Brill, P. J. Brush, K. J. James, J. E. Shepherd and K. J. Pfeiffer, Appl. Spectrosc. 46, 900 (1992). 6. E. S. Kim and S. T. Thynell, CPIA Publ. 685, 145 (1998). 7. J. Wormhoudt, P. L. Kebabian and C. E. Kolb, Combust. Flame 111, 73 (1997). 8. T. R. Botcher and C. A. Wight, J. Phys. Chem. 97, 9149 (1993).

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9. C. J. Tang, Y. J. Lee, G. Kudva and T. A. Litzinger, Combust. Flame 117, 170 (1999). 10. O. P. Korobeinichev, Combust. Explos. Shock Waves 23, 565 (1988). 11. A. C. Aiken, B. A. Jones, C. A. Arrington, Jr., S. J. Buelow and J. E. Anderson, Abstracts of Papers (CHED 904), 223rd ACS National Meeting, Orlando, FL, 7-11 April, 2002. 12. T. B. Brill, Prog. Energy Combust. Sci. 18, 91 (1992). 13. H. Arisawa and T. B. Brill, Combust. Flame 109, 87 (1997). 14. T. B. Brill and B. T. Budenz, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 3. 15. B. D. Roos and T. B. Brill, Appl. Spectrosc. 54, 1019 (2000). 16. G. J. Piermarini, S. Block and P. J. Miller, in Chemistry and Physics of Energetic Materials, ed. S. Bulusu, NATO ASI 309 (Kluwer, Dordrecht, The Netherlands), p. 391. 17. J. Wenograd, Trans. Farad. Soc. 57, 1612 (1961). 18. M. J. Kamlet and H. G. Adolph, Prop. Explos. 4, 30 (1979). 19. G. I. Kanel, Fiz. Goreniya Vzryza 14, 113 (1978). 20. T. B. Brill and K. J. James, J. Phys. Chem. 97, 8759 (1993). 21. T. B. Brill and P. E. Gongwer, Prop. Explos. Pyrotech. 22, 38 (1997). 22. T. B. Brill, K. J. James, R. Chawla, A. Shukla and J. H. Futrell, J. Phys. Org. Chem. 12, 819 (1999). 23. A. A. Zenin, in Nonsteady Burning and Combustion Stability of Solid Propellants, Progress in Astronautics and Aeronautics, Vol. 143, eds. L. DeLuca, E. W. Price and M. Summerfield (AIAA, Reston, VA, 1992), p. 197. 24. A. G. Merzhanov, Combust. Flame 11, 201 (1967). 25. T. B. Brill, H. Arisawa and P. E. Gongwer, in Challenges in Propellants and Combustion, ed. K. K. Kuo (Begell House, Inc. New York, 1997), p. 3. 26. B. F. Henson, B. W. Asay, L. B. Smilowitz and P. M. Dickson, in AIP Conference Proceedings 620, Shock Compression of Condensed Matter, Pt. 2 (2002), p. 1069. 27. T. B. Brill, J. Propuls. Power 11, 740 (1995). 28. T. B. Brill, in Chemistry and Physics of Energetic Materials, ed. S. N. Bulusu, NATO-ASI Vol. 309 (Kluwer Publ. Amsterdam, 1990), p. 277. 29. T. B. Brill and Y. Oyumi, J. Phys. Chem. 90, 2697 (1986). 30. T. B. Brill and Y. Oyumi, J. Phys. Chem. 90, 6848 (1986). 31. B. D. Roos and T. B. Brill, Combust. Flame 128, 181 (2002). 32. T. B. Brill and P. J. Brush, Phil. Trans. Roy. Soc. (London) 339, 377 (1992). 33. H. Arisawa and T. B. Brill, Combust. Flame 112, 533 (1998). 34. T. B. Brill, P. E. Gongwer and G. K. Williams, J. Phys. Chem. 98, 12242 (1994). 35. S. Zeman, Thermochim. Acta. 49, 219 (1981). 36. G. Lengelle, J. Duterque and J. F. Trubert, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 287.


27

37. R. I. Hiyoshi and T. B. Brill, Prop. Explos. Pyrotech. 27, 23 (2002). 38. A. E. Fogelzang, V. P. Sinditski, V. V. Serushkin, V. Y. Egorshev, Y. K. Shchipin and V. A. Tropynin, in 24th Int. Ann. Conf. ICT, Karlsruhe, Germany, 29 June-3 July 1993, paper 59-1. 39. T. B. Brill and H. Ramanathan, Combust. Flame 122, 165 (2000). 40. V. P. Sinditskii, A. E. Fogelzang, A. E. Levshenkov, A. I. Egorshev, V. Y. Korlesov and V. V. Serushkin, in Proc. 21st Int. Pyrotech. Seminar, Moscow, 1995, p. 162. 41. A. Gao, Y. Oyumi and T. B. Brill, Combust. Flame 83, 345 (1991). 42. C. E. Stoner, Jr. and T. B. Brill, Combust. Flame 83, 301 (1991). 43. V. P. Sinditskii, A. E. Fogelzang, A. I. Egorshev, V. V. Serushkin and V. Y. Kolesov, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 99. 44. A. E. Fogelzang, A. I. Egorshev, V. P. Sinditskii and M. D. Dutov, Bet. Shock Waves 26, 69 (1990). 45. A. E. Fogelzang, V. P. Sinditskii, A. I. Egorshev and V. V. Serushkin, in Decomposition, Combustion and Detonation of Energetic Materials, Proc. Mat. Res. Soc, Vol. 418, eds. T. B. Brill, T. P. Russell, W. C. Tao and R. B. Wardle, 1996, p. 151. 46. C. F. Melius and M. C. Piqueras, in Proc. 29th Int. Symp. Combust. (2002). 47. P. E. Gongwer and T. B. Brill, Combust. Flame 115, 417 (1998). 48. T. B. Brill, P. J. Brush, D. G. Patil and J. K. Chen, in 24th Int. Symp. Combust. (The Combustion Institute, Pittsburgh, PA, 1992), p. 1907. 49. R. R. Miller, R. L. Stacer and B. B. Goshgarian, in 19th JANNAF Combustion Meeting, Vol. II, CPIA Publ. 366 (1982), p. 67. 50. J. K. Chen and T. B. Brill, Combust. Flame 87, 217 (1991). 51. M. R. Manaa, L. F. Fried, C. F. Melius, M. Elstner and T. Frauenheim, J. Phys. Chem. A106, 9024 (2002). 52. J. J. Dick, Appl. Phys. Lett. 44, 859 (1984). 53. C. S. Yoo, N. C. Holmes, P. C. Souers, C. J. Wu, F. H. Ree and J. J. Dick, J. Appl. Phys. 88, 70 (2000). 54. Z. A. Dreger, Y. A. Gruzdkov, Y. M. Gupta and J. J. Dick, J. Phys. Chem. B106, 247 (2002). 55. K. L. McNesby and C. S. Coffey, J. Phys. Chem. B101, 3097 (1997). 56. D. D. Dlott and M. D. Fayer, J. Chem. Phys. 92, 3798 (1990). 57. L. E. Fried and A. J. Ruggiero, J. Phys. Chem. 98, 9786 (1994). 58. Y. Oyumi, A. L. Rheingold and T. B. Brill, Prop. Explos. Pyrotech. 12, 1 (1987).

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CHAPTER 2 T H E R M A L D E C O M P O S I T I O N PROCESSES OF E N E R G E T I C MATERIALS IN T H E C O N D E N S E D P H A S E AT LOW A N D M O D E R A T E T E M P E R A T U R E S Richard Behrens Sandia National Laboratories Combustion Research Facility Livermore, CA 94551-0969, USA

Contents 1. Introduction 1.1. Scientific Issue: Understanding Processes Far from Equilibrium 2. Reactive Processes: Experimental Methods 2.1. Experimental Challenges 2.2. Experimental Requirements 2.2.1. Experimental Design Principles 2.2.2. Analysis of Data from High-Level Information Content Experiments 2.3. New Mass Spectrometry-Based Experimental Protocol 2.3.1. Qualitative Models Require Both Chemical and Spatial Information 2.3.2. Development of Mathematical Models 2.4. Comparison of Conventional Thermal Decomposition Experiments 2.4.1. Global Measurements 2.4.2. Product Identification Measurements 3. Condensed-Phase Reactive Processes 3.1. Evidence for Complex Processes 3.2. HMX Decomposition Processes 3.2.1. General Nature of Condensed-Phase Reactions in Energetic Materials 3.2.2. Decomposition of Composite Materials 3.3. Characterization of Decomposition Processes: RDX and HMX Case 3.3.1. Development of a Conceptual Framework to Represent and Analyze Decomposition Processes 29

30 31 35 35 36 36 37 38 38 42 43 44 44 46 46 48 50 53 53 53

30

R.

Behrens

3.3.2.

Reaction Pathways: Solid-Phase Reactions, Nonlinear Processes, Feedback Loops and Autocatalysis 3.3.3. Emergent Phenomena 3.4. Effects of Experimental Conditions on Observed Decomposition Processes 3.4.1. Reaction-Coordinate Vectors 3.4.2. Environmental Conditions Determine Location of Reaction-Coordinate Vector 3.4.3. Conditions Probed by Various Experiments 4. Reaction Kinetics 4.1. Extracting Reaction Kinetics from Condensed-Phase Experiments 4.1.1. Simple Kinetics — Direct Inversion from Experiment 4.1.2. Kinetics of Complex Reaction Networks 5. Conclusions and Future Research Acknowledgments References

54 59 60 60 60 62 64 65 65 65 67 70 70

1. I n t r o d u c t i o n T h e processes t h a t control the thermal decomposition of energetic materials in the condensed phase at low and moderate temperatures present a challenge to the chemical kineticist in the 21st century. Meeting this challenge will provide new means t o develop improved propellants and explosives and to assess the safety and aging characteristics of existing ones. Currently, there is great interest in developing less sensitive munitions and extending the shelf life of existing ones. T h e development of new insensitive munitions will require understanding how reactive processes t h a t occur at t e m p e r a t u r e s associated with fires or other abnormal environments will alter the characteristics of the energetic ingredients and lead to violent reactions. 1 ' 2 A more fundamental understanding of the underlying reactive processes, which occur in these environments, can guide the development of new compounds, or the development of new formulations, t h a t will mitigate t h e violence of t h e reactions and lead t o less sensitive munitions. T h e underlying reactive processes are also related to safety, aging, and performance in propulsion and explosive applications. Slow reactions related to aging behavior clearly involve spatiotemporal controlled reactions. They are also influenced by interfacial reactions with other ingredients. Safety issues related t o slow and fast cook-off behavior are influenced by changes in the chemical, physical and morphological properties of the material. Finally, performance issues related to the combustion process t h a t occurs on the surface of a burning propellant are dependent on condensedphase reactive processes. To develop the understanding required to address

Thermal Decomposition

Processes of Energetic

Materials

31

these issues demands a more fundamental understanding of the processes that occur in the condensed phase, at low and moderate temperatures, than is currently available.

1.1. Scientific Issue: Understanding from Equilibrium

Processes

Far

As the temperature at which reactions occur in energetic materials are lowered from those that are associated with combustion (600-3000° C), new types of processes start to play a more dominant role in controlling their decomposition. As the temperature decreases, the rates of reaction of individual molecules decrease and transport processes become more important. In the temperature range from room temperature up to approximately 400° C, most energetic materials are present as solids or liquids so that reactions in the liquid and solid phases can play the major role in the decomposition processes. This transition in the types of physical and chemical processes that control the decomposition of energetic materials creates reaction systems that are difficult to characterize. At lower temperatures the focus for examining the reactions shifts from the molecular spatial scale to larger spatial scales associated with thermal and mass transport processes that give rise to nonhomogeneities in the system. In the liquid phase, localized reactions may form in the vicinity of bubbles and gaseous products may diffuse into the surrounding liquid, creating gradients of the gaseous products in the liquid phase. In the solid phase, reactions may occur preferentially on the surface of particles or complex processes may occur within the solid phase via nucleation and growth processes. In addition, lower temperatures allow reactions to occur that create compounds that may have higher molecular weights and be more complex than the energetic materials themselves. Growth of these more complex compounds in the reaction environment opens new "catalytic-like" reaction pathways, where the secondary and tertiary structure of the complex compounds may play a role in controlling the reactive process. This type of process is analogous to the catalytic behavior of enzymes in living systems. Each new type of process that may occur during the decomposition of energetic materials in the condensed phase at low and moderate temperatures is irreversible and may occur far from equilibrium conditions. Thus, to understand the decomposition of energetic materials under these lower temperature conditions, one must work within the framework of the physics

32

R.

Behrens

of nonequilibrium processes, which uses concepts such as self-organization and dissipative structures. Reactive systems that evolve under conditions far from equilibrium are characterized by processes that become unstable at some distance from equilibrium and bifurcate along multiple reaction pathways. When systems pass this bifurcation point, a set of new phenomena arises in which nonequilibrium spatial structures, chemical waves, or oscillating chemical reactions are observed. These spatiotemporal organizations are known as dissipative structures. The conditions that are usually necessary for this type of behavior and the creation of dissipative structures are: (1) reactions that occur far from equilibrium, and (2) catalytic-like reactions. Many experiments that have examined the decomposition of energetic materials in the condensed phase involve reactive processes that meet the criteria required for the creation of dissipative structures. In some cases, direct visual evidence of the evolution of the spatial structures is observed as will be described below. The complex nature of the reactive processes that control the thermal decomposition of energetic materials in the condensed phase at low and moderate temperatures present a great challenge to the chemical kineticist. The conventional methods available to the kineticist focus on characterizing reactions at the molecular level. While this is an important component of understanding the thermal decomposition process in the condensed phase, it does not address many of the issues associated with the irreversible processes that control their decomposition behavior. Given the complex nature of these reactive processes, how can a better understanding and characterization of these processes be achieved? This is the main question addressed in this chapter. To address this question, an analogy to the development and use of elementary reactions for characterizing gas-phase reactions may be posed, and then the ability to develop a similar understanding for condensedphase reactions examined. Elementary reactions 3 are fundamental to our ability to characterize and predict the behavior of complex physicochemical processes, such as gas-phase combustion. Can the concept of elementary reactions also be applied to the characterization of complex processes in the condensed phase? If so, how? A range of different types of reactions can control the decomposition process in the condensed phase. What are the reactions? How do the types of reactions change with increasing temperature and pressure ? At low temperatures, reactions may occur at interfacial boundaries, reaction rates may be



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33

limited by transport processes, nucleation and growth processes may play a role, or enzymatic reactions may be involved.4 For reactions at higher temperatures, the materials are heated more rapidly, thus, transport processes and the development of spatiotemporal features are less important, and reactions at the molecular level become dominant. In this realm, unimolecular decomposition and elementary bimolecular reactions control the reactive processes. Roles of different types of physical and chemical processes will change with experimental conditions (temperature and pressure). How does the transition from low-temperature spatiotemporal controlled reactions to hightemperature molecularly focused reactions occur? How rapid and how distinct is the transition? Reactions that are initiated by thermal heating, and occur in the solid and liquid phase, are likely to be controlled by more complex spatiotemporal processes. For this reason, compounds with lower rates of vaporization are more likely to remain in the condensed phase and react. Thus, condensed-phase processes may be relevant up to ~100°C above the melting point of a material, which would correspond to a temperature range from 200 to 400°C for energetic materials. There is a wide range of different types of processes that must be considered in condensed-phase reactions. The processes include the following: (1) (2) (3) (4) (5)

phase transitions: solid-solid, solid-liquid; reactions on the surface of particles; nucleation and growth of reaction regions (bubbles) within the solid; creation of other condensed-phase products within the sample; reactions between the reactant and its gas and condensed-phase reaction products; (6) creation of new morphological structures within the sample that can form new reaction zones with localized temperature and pressure environments; (7) reactions at surfaces and interfacial boundaries. The challenge is to unravel and understand these underlying processes. The scientific community has generally avoided this challenging problem. The main difficulty stems from the inability to divide the system (i.e., decomposition of the material in the condensed phase) into its individual components for independent examination. This standard "divide and examine" methodology has been used extensively to understand reactions in the gas phase, but it is difficult, perhaps impossible, to apply to organic materials in the condensed phase. For

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example, one could consider examining the decomposition of an energetic compound, say RDX, in the gas phase. 5 Done properly, this provides basic information on the elementary unimolecular decomposition of RDX. Unfortunately, this provides only one of several possible rate-limiting reaction pathways that may occur in the condensed phase. For example, a more rapid reaction may involve the interaction between RDX and one or more of its gas-phase or condensed-phase reaction products. Thus, the RDX unimolecular decomposition kinetics, while a useful piece of basic information, may not play a significant role in the rate-limiting processes that control its decomposition in the condensed phase. Therefore, we are left with the problem of how to extract information from a set of different processes that occur simultaneously during the course of an experiment. Given the complex and irreversible nature of reactions that occur in energetic materials in the condensed phase, and the limited experimental methods available to probe these reactions, a new conceptual framework is required to understand and communicate the ideas that are needed to address these issues. This framework must provide the basis for examining and understanding reactive processes in the condensed phase, in a way that is similar to the framework used to examine complex reaction processes in the gas phase. It must incorporate features that (1) allow discovery of underlying reactive processes, (2) relate underlying features to material properties, (3) assess the competition between underlying processes as a function of experimental conditions, and (4) provide a basis for mathematical characterization of the underlying processes. With these features, the conceptual framework will provide a basis for creating new knowledge of the underlying processes that occur in energetic materials in the condensed phase and building a roadmap, based upon this knowledge, that can be used to examine each of these underlying processes in more detail. This chapter focuses on the development and application of an experimental protocol to understand and characterize the reactive processes that occur in the condensed phase of energetic materials and how this work has lead to the development of a new conceptual framework to examine and communicate the details of these processes. It presents an outline of the type of information that is required, a discussion of experimental methods for obtaining the information, an overview of new numerical simulation methods for extracting reaction mechanisms and chemical kinetics from the data, an illustration of these methods with recent results on the



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decomposition of RDX and HMX, and a discussion of future directions for research on the thermal decomposition of energetic materials in the condensed phase. 2. Reactive Processes: Experimental Methods To obtain a better understanding of the reactive processes of energetic materials in the condensed phase, we have developed a new experimental protocol. This section describes the development of the experimental protocol and compares it with more standard measurement methods, which have been used in the past to examine the decomposition of energetic materials. First the experimental challenges are described. Next the experimental requirements needed to address these challenges are outlined. This is followed by a brief description of the experimental protocol. Finally, the protocol is compared to other methods. 2.1. Experimental

Challenges

Four general features of thermal decomposition reactions of energetic materials in the condensed phase pose significant experimental challenges: (1) A wide range of reactive processes controls the thermal decomposition of energetic materials. (2) Chemical, physical and morphological (spatial) features can play significant roles in controlling the decomposition process. The experimental method must be capable of capturing the nature and roles of these spatiotemporal processes. (3) The different reactive processes are often nonlinearly coupled. The experimental methods must enable us to characterize these nonlinearities. (4) The state of the sample is a function of the extent of decomposition. Consequently, the state of the reaction conditions changes continuously during the course of an experiment making steady-state experiments infeasible. This behavior makes it difficult, if not impossible, to isolate specific individual reactions to study in an independent manner. Hence, traditional chemical kinetics methods, which isolate and control the concentration of specific reactants and measure their rates of reaction, have limited applicability. These four general features of condensed-phase energetic material reactions are characteristic of nonequilibrium processes, which involve

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self-organization and the development of dissipative structures, 6 and require new methods to understand and characterize the underlying reactions. 2.2. Experimental

Requirements

Given the general features of the thermal decomposition process, guidelines for developing the experimental methods can be denned as follows: (1) Assume it is not feasible to isolate reactive processes to study them individually. Furthermore, assume that the development of dissipative structures are important and develop as a result of interactions between reactive components of the entire system. (2) Focus on identifying and characterizing underlying physicochemical processes. Experiments must identify and characterize the underlying physicochemical processes that control the decomposition. (3) Develop experiments that provide a high level of information content. The overall approach must use experiments that provide a high level of information on the underlying reactive processes over a wide range of controllable conditions. 2.2.1. Experimental Design Principles Several general principles are used to guide the development of new instrumental methods that will provide the high information content needed to study the reactions of energetic materials in the condensed phase. These principles may be summarized as follows: (1) Maximize simultaneous measurements. Design new experimental methods using the general principle that the greatest amount of information will be obtained by measuring as many different properties of a sample as possible, with the widest range of measurement methods, at the same time. This allows direct comparison of different types of information. Otherwise the data represents reactions collected under different reaction conditions and makes interpretation of the results more difficult. (2) Collect chemical information as a function of spatial location. Chemical reactions in the solid or liquid phase can occur in localized regions or at interfacial boundaries associated with the development of dissipative structures. Thus, their reaction rates are often controlled by both the rate of chemical reaction and the transport of reactants and products in the localized region. Development of instruments to provide detailed molecular information, as a function of spatial location in a



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material, will provide insight into how chemical reactions are coupled with transport processes in these materials. For example, a microscope that provides molecular information as a function of location, in a manner analogous to reflected light for optical images or secondary electrons for SEM images.

2.2.2. Analysis of Data from High-Level Content Experiments

Information

The overall objectives of experimental work with energetic materials are: (1) to develop a qualitative understanding of the underlying reactive processes and (2) to create mathematical models of the reactive processes. To achieve these objectives requires the extensive development and use of numerical algorithms. High-level information content experiments provide large amounts of data that must be analyzed to glean relevant information on the underlying reactive processes. This requires both the application of transformation algorithms to convert raw data to the desired information format, and the use of analysis algorithms to extract the chemical, physical, and temporal information from the data. Developing mathematical models of the underlying reactive processes and comparing these models to data collected from the high information content experiments provide a test of the postulated reactive processes. The optimized models that characterize the underlying reactive processes provide a basis for development of models that can be used to characterize the response of materials in larger-scale systems. To summarize, the experiments must provide information that can track the chemical and physical state of the sample as a function of time. They must also provide information that can be used to identify and track the progress of the rate-controlling reactions in the decomposition process. The experiments should also provide information on the identities and amounts of condensed-phase products and morphological changes that occur in the sample during the course of an experiment. To extract an understanding of the underlying reactive processes and the associated reaction kinetics, a numerical simulation method must be used to analyze the data. The method must allow one to postulate various reaction schemes, numerically simulate the reaction rates for the postulated reaction scheme, and compare the numerical results with the data from the experiments. Feedback between experiments and numerical simulations provide guidance to selecting new experimental conditions.

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2.3. New Mass Spectrometry-Based

Experimental

Protocol

A mass spectrometry-based experimental protocol, developed in our laboratories, addresses the experimental requirements for examining the decomposition of energetic materials in the condensed phase. The protocol uses new instrumental methods and numerical algorithms for data analysis and simulation of physicochemical processes in the condensed phase. A schematic diagram outlining the experimental methods and numerical algorithms and the types of information obtained by each is shown in Fig. 1. As illustrated in the diagram, the overall goal is to develop a model of the thermal decomposition processes based on the underlying fundamental reactions and the associated reaction kinetics. 2.3.1. Qualitative Models Require Both Chemical and Spatial Information Understanding the underlying reactive processes requires identifying the compounds and determining how fast they are formed as a function of experimental conditions. For reactions in the condensed phase, the development of dissipative structures may play a significant role in determining the rates of reaction. Therefore, it is important to determine the spatial characteristics of these features and how they may change during the course of an experiment. This requires determining the morphological characteristics of the samples during the course of an experiment in addition to the time-dependent chemical information on the reactants and products. The simultaneous thermogravimetric modulated beam mass spectrometry instrument The simultaneous thermogravimetric modulated beam mass spectrometry (STMBMS) instrument provides the main source of information on the thermal decomposition processes. It was designed to conduct experiments that would provide information on both the identities and rates of formation of the compounds involved in the reactive processes that control the decomposition of energetic materials. The instrument and the obstacles presented by using mass spectrometry have been described in detail previously 7-9 ; the STMBMS enables: (1) identification of compounds in a mixture; (2) quantitative measurement of each of the identified compounds; (3) control of rate of vaporization of condensed-phase species;


Instruments & Algorithms STMBMS Thermal Decomposition Experiments

T

TASHOWData Analysis Algorithms

Ifo@to$s

I

x_i REMKIN Compilation & Analysis Algorithms


Information Obtained

1. Raw Mass Spectra of Products vs. time. 2. TGA Data. 3. TOF Velocity Spectra.

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Instruments

High resolution FTICR Mass Spec

Ion formulas Molecular structure. 1. Identities of products 2. Rates of formation of products. 3. Pressure of gases in reaction cell. 4. Vapor pressure of condensed phase reactants and products. 5. All as a function of time. 1. Structural changes of sample. 2. Morphology of microscopic material features. 1. Identification of high MW products. 2. Reactions at interfaces. 3. Spatial maps of chemical compounds. 4. Chem analysis of microstructures.

1. Underlying fundamental reaction mechanisms. 2. Arrhenius parameters for fundamental reactions. 3. Rate of heat generation. 4. Quantitative assessment of damage

Optical & Scanning Electron Microscopy

J Surface Analysis Ion beam & laser microprobes.

fsfcrasfe^

Model of Thermal Decomposition Based on Underlying Fundamental Reactions and Associated Reaction Kinetics. Fig. 1. Experimental protocol used to study thermal decomposition processes of energetic materials in the condensed phase.

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(4) control of the pressure of gaseous compounds formed in the reactions and contained in the reaction environment; (5) collection data that provides simultaneous information on all compounds. The STMBMS instrument (Fig. 2) incorporates several features to provide the desired information. The decomposition experiment is conducted in a reaction cell that is fitted with well-characterized exit orifice that can be used to control the rate of flow of gases out of the reaction cell. Varying the size of the orifice allows the pressure of gases within the reaction cell to be controlled. The simultaneous measurement of the rate of force change (mass loss and thrust) and the mass spectra of the gases exiting the reaction cell provides the rates of formation of compounds formed during

it>S-*-",h"i' IH'llorts

Modulating Wheel

540 l/s Turbo

Reaction Cell

Microbalance

Fig. 2. Schematic of STMBMS instrument. An experiment is conducted with the STMBMS instrument by placing the sample in the reaction cell, closing the reaction cell with a cover containing an orifice of desired diameter, mounting the reaction cell in t h e instrument on top of t h e thermocouple probe t h a t is seated in a microbalance, and then evacuating the instrument. The data is collected by heating the sample and collecting data on the rate of force change due to gas exiting the cell with the microbalance and collecting the mass spectra of the mixture of gaseous compounds exiting the cell with a modulated beam quadrupole mass spectrometer. The pressure of the gaseous compounds in the reaction cell may range from 10~ 6 to 10 3 torr, depending on experimental conditions.



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thermal decomposition. The time-of-flight velocity spectra of the neutral gases that exit the reaction cell are used to determine whether ion signals measured with the quadrupole mass spectrometer are parent or daughter ions. Thus ion signals at a specific m/z value, measured with the mass spectrometer, can be associated with a compound that evolves from the reaction cell. Enhanced product identification and molecular structure determination Three methods are used to help identify the compounds that evolve from the reactive processes. Two of these provide additional information to assign formulas to the ions that make up the mass spectra of the evolving compounds. The third method sorts ion signals into groups of m/z values that are associated with each compound. In the first method, isotopically-labeled analogues of the energetic materials are synthesized (deuterium, 1 3 C, 15 N, and 1 8 0) and the corresponding isotopic shifts, recorded in the STMBMS experiments, are used to determine the formulas of the ions. In the second method, high resolution and high mass accuracy measurements are made using a Fourier Transform Ion Cyclotron Resonance (FTICR) mass spectrometer. These two methods provide the information needed to determine the formulas of the ions in the mass spectra. The FTICR mass spectrometer provides a more rapid means of determining the formulas, eliminating the need to synthesize isotopicallylabeled analogues. The third method employs a correlation analysis of the temporal dependence of the ion signals in the mass spectra to sort the ion signals into groups whose m/z values represent the mass spectra of the individual compounds that evolve from the reaction cell. Quantification of the data After the compounds are identified and ion signals from the mass spectra are assigned to represent each compound, the data are quantified using the TASHOW analysis algorithm. The ion signals, measured with the mass spectrometer, and the rate of force change, measured with the microbalance, are used to determine the sensitivity parameters that relate the measured ion signals to the number density of the corresponding compound in the reaction cell as a function of time. 7 ' 9 This analysis may be used to calculate rates of reaction, partial pressures, and other related properties. At this point in the analysis, the following information is available to construct a

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qualitative model of the decomposition process: (1) (2) (3) (4) (5)

identities of the compounds involved in the decomposition process; rates of formation of the compounds; pressure of gases in the reaction cell; vapor pressure of condensed-phase compounds; all data as a function of time.

Morphological features Morphological features of the condensed-phase samples: surface roughness, grain structure, and bubbles can play an important role in the decomposition process. Because these features cannot be examined in situ during the course of a decomposition experiment, the morphological characteristics are determined by stopping the reaction at various stages of the decomposition process and removing the sample for examination by optical microscopy and scanning-electron microscopy (SEM). Some energetic materials form products that are nonstoichiometric, polymeric-like and have a low volatility; these are called nonvolatile residue (NVR). In many cases the NVR reacts with the remaining reactant or other decomposition products. Optical and SEM examination has shown that these NVRs may be located on the surface of particles, in reactive regions within solid grains, or on the walls of the reaction cell. Knowing the geometrical characteristics of these morphological features is often important for understanding and modeling the reactive process. While optical and SEM pictures provide valuable information about the structures created during the decomposition process, they do not provide information about the chemical compounds that are involved in the reactions at these localized regions. To improve our understanding of the role that interactions between chemical reactions and morphological features play in the decomposition process, we must probe the nature of the chemical reactions that occur at the boundaries of these morphological features. We are developing surface analysis methods such as secondary ion mass spectrometry (SIMS) and laser desorption mass spectrometry (LDMS) to examine these features in energetic materials. 10 2.3.2. Development of Mathematical Models Once a qualitative understanding of the underlying processes that control the thermal decomposition of an energetic material is obtained, the next



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task is to formulate this understanding into a set of mathematical expressions to characterize the thermal decomposition process. This task requires using the qualitative model of the decomposition process to construct the set of differential equations that represents the reaction rates of the underlying reactive processes, then solving this set of differential equations, and finally, determining the values of the parameters for the reaction model by comparing the results of the calculations to experimental data. This method is basically a numerical simulation method in which a reaction scheme is postulated, a mathematical representation of the reaction scheme is constructed, a guess for the reaction parameters in the model is made, and the model is solved. The model simulates a decomposition experiment. The reaction scheme and its associated parameters are iterated to capture the various features of the reactions that appear in the data from the thermal decomposition experiments. Further details are provided below.

2.4. Comparison Experiments

of Conventional

Thermal

Decomposition

So far we have (1) summarized the scientific issues that must be addressed to understand the underlying reactive processes of energetic materials in the condensed phase, and (2) outlined the experimental challenges that must be addressed and described the development of one experimental protocol intended to meet these experimental challenges. Later in this chapter, it will be shown how this work has led to a new understanding of reactions in the condensed phase. While this experimental protocol provides new opportunities to understand the underlying reactive processes in energetic materials, it is relatively expensive and unique. The highly-specialized equipment is not as accessible as the other methods previously used to examine the thermal decomposition of energetic materials in the condensed phase. In this section we provide a brief summary of the other methods and assess their strengths and weaknesses in meeting the experimental challenges for studying the thermal decomposition of energetic materials. Thermal decomposition experiments have been used extensively to probe the reactions of energetic materials. In general the various experimental methods may be grouped according to the type of data provided. One group focuses on measuring the overall behavior of a sample by measuring a global property, such as heat flow or mass loss. The second group focuses on identifying the products formed during a decomposition experiment.

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2.4.1. Global Measurements Standard thermal analysis methods such as thermogravimetric analysis (TGA), differential thermal analysis (DTA) and differential scanning calorimetry (DSC) have been used extensively to characterize the thermal behavior of energetic materials in the condensed phase. n ~ 1 4 The DTA and DSC methods track the heat flow as a sample is heated and are useful for detecting phase changes and the onset of decomposition of an energetic material. TGA measures the mass of the sample as it is heated and reveals when reactions occur that release gaseous decomposition products and result in a loss of sample mass. Thermal analysis methods are excellent for characterizing the behavior of simple, well-defined processes such as phase transitions or simple chemical transformations. However, for complex processes, such as those that occur during the decomposition of energetic materials, thermal analysis methods do not provide sufficient information to unravel the underlying processes as discussed by Pinhiero et al. The global nature of the measurement (i.e., total heat flow or total mass loss) is determined by the summation of all the underlying processes at any particular time during an experiment, providing a limited amount of information on the underlying processes. The thermal behavior of propellants and explosives has also been characterized by time to explosion experiments. In these experiments, such as the one-dimensional time to explosion (ODTX) experiment, 15 a sample is heated using a predefined isothermal boundary condition, and the time until the sample explodes is recorded. This has provided useful information for handling explosives, but, due to the limited amount of information collected during an experiment, this method has been of limited value in determining the underlying reactive processes that occur during the thermal decomposition process.

2.4.2. Product Identification

Measurements

To complement the global experiments and provide insight into the reactive processes that occur during the decomposition of energetic materials, a number of different types of spectroscopic methods have been used over the years. Some methods, such as mass spectrometry, have identified a broad range of different compounds formed during the decomposition process; other methods, such as electron spin resonance, 16 ' 17 have identified a more limited range of species, such as radicals.



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Infrared spectroscopy (IR) and mass spectrometry (MS) have been used extensively to identify products formed during the decomposition of energetic materials. MS has been used to identify the gaseous products that evolve during the decomposition process, while IR has mostly been used to probe the products formed in the condensed phase. IR spectroscopy can be applied over a wide range of experimental conditions: high-pressure, 18 ' 19 in thin films,20'21 during combustion, 22 ~ 24 in shocked materials, 25 and at very low temperatures. 26 ' 27 Depending on the specific experiment, IR may provide information ranging from individual steps in a decomposition reaction, 28 to a more detailed set of reaction kinetics. 19 While this information is often useful, the extent of the data is somewhat limited, making it difficult to develop complete reaction schemes and the associated reaction kinetics from the data. For applications to experiments focused on understanding the underlying reactive processes in the condensed phase at low and moderate temperatures, IR lacks some of the molecular specificity provided by mass spectrometry-based methods. Mass spectrometry measurements were some of the first experiments to identify the products formed in the thermal decomposition of energetic materials. 29 " 31 Analyzing gaseous thermal decomposition products with mass spectrometry can be done by either admitting the gas mixture directly into the mass spectrometer or by first chromatographically separating the mixture before introducing the gas into the mass spectrometer. Both methods have limitations. If the mixture of the reactant and its decomposition products is admitted into the mass spectrometer, it is difficult to associate individual ions with the corresponding decomposition products. For example, it has been shown8 that using appearance potential measurements developed to examine hydrocarbons 32 is not adequate to distinguish ions that originate from products formed in the thermal decomposition of HMX from ions formed by the fragmentation of sublimed HMX in the mass spectrometer. HMX fragments into daughter ions using electron energies of 12.5eV (~3eV above its estimated appearance potential). 8 - 33 If the mixture is chromatographically separated prior to entering the mass spectrometer, it is difficult to obtain time-dependent information to characterize the behavior of the sample. The sensitivity of the mass spectrometer varies for different species, which also makes it difficult to obtain quantitative data. Finally, depending on the type of mass spectrometer used for the measurements, there can be uncertainty in the identification of ions because of uncertainties in the exact mass of the ion: N 2 0 = 44.0083 and

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C 0 2 = 43.9898 would both be measured as m/z = 44 with most types of mass spectrometers, making the two compounds indistinguishable. Mass spectrometry provides useful information for identifying products, but may not clearly identify the thermal decomposition products. 3. Condensed-Phase Reactive Processes 3.1. Evidence

for Complex

Processes

In examining the decomposition of energetic materials, one may ask, what evidence suggests that their decomposition is controlled by a complex set of coupled reactive processes. The answer may be found in the general features of experimental results from two sources: a historical examination of the results from a wide range of different experiments and the results from STMBMS experiments on a number of different compounds. During the 1980s, Schroeder undertook an extensive examination of the entire literature on the thermal decomposition of energetic nitramine compounds. 34 ^ 36 This review of the wide range of results from both nominally similar and different types of experiments revealed a high degree of variation in the results. For example, in some decomposition experiments with RDX and HMX the major products were C H 2 0 and N2O. In other types of experiments, HCN and NO2 were the major products. Similarly, an accelerating type of "autocatalytic" behavior was reported in some cases but not in others. To describe the reactive processes in these older experiments, a unimolecular decomposition framework was used, and the experimental observations were attributed to a particular bond-breaking sequence of the reactant. For example, in experiments in which HCN and NO2 were observed, it was argued that N-NO2 bond fission was the rate-limiting step; whereas in experiments in which CH2O and N2O was observed, it was argued that fission of a C-N bond in the ring of the molecule was the rate-limiting step. These arguments also assumed that once the first bond in the molecule ruptured, the remaining bonds would rearrange rapidly and lead to the final reaction products. Additionally, in many experiments the temperature dependence of the experimental observable (i.e., weight loss, heat generation) was determined and reported as an activation energy, assuming that an Arrhenius expression described the underlying reaction. Schroeder reported 36 that the activation energies from these experiments varied widely. This variation in activation energies is not surprising if the decomposition process is controlled by an underlying set of coupled nonlinear



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reactive processes. For these types of processes, even slight variations in experimental conditions (e.g., the extent of confinement of gaseous decomposition products with the sample) can lead to variations in the identities of the products, as well as how fast the products are formed. This complex behavior was examined in the early 1970s by Batten for the case of RDX decomposition, 37-41 in which it was found that the decomposition of RDX below its melting point was controlled by a complex autocatalytic-like process. The results showed that a nonvolatile residue is formed during the decomposition and the addition of gases such as C H 2 0 increase the reaction rate. Batten also demonstrated that the past decomposition history of the sample can affect the subsequent decomposition processes. Our STMBMS experiments performed on a range of different types of energetic materials provide more detailed evidence for the complex nature of the thermal decomposition process. The compounds that we have investigated using STMBMS are listed in Table 1. We have studied the nitramines, Table 1.

Compounds studied with STMBMS methods. C-Nitro, Azoles, and Others

Nitramines

NO,

N0 2 0,N.

r

-N-. 0 2 rT ^>k^ N0 2

"N^

M> 02N^

^N

^ N

X

N0 2

x

N0 2

H

CL-20

RDX

OoNk

NO,

24DNI TATB

OpNs

N

.NO, ^N'

I—N-N0 2

fJ02 0?N-

NO, 0 2 NK

^ ^

v

N02

OpN'

HMX

^

^Nv "NO,

TNAZ

NTO

K6

N0 2

-N-NO

NO

-Nk

qVW* NO, TNCHP

0,N"

.N^/Ns

N-N O.N—V./Ô N I H

N0 2 "NO,

ONDNTA

NDNAZ

Ammonium perchlorate

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RDX and HMX, most extensively. The thermal decomposition of all these compounds exhibits two common features, which show that their thermal decomposition is controlled by a complex set of coupled reactions. First the temporal behaviors of the rate of evolution of the gaseous decomposition products are never what is expected for a simple first-order decomposition reaction, in which the rate of reaction falls as the sample is depleted. Indeed, for most of the compounds listed in Table 1, there is an induction period, characterized by low rates of evolution of gaseous products, followed by an accelerating rate of reaction. In addition, the identities of the products and their rates of evolution are very sensitive to the extent of confinement of gaseous decomposition products in the reaction environment; higher pressures typically increase the rate of reaction. Second, a nonvolatile residue is always created during the decomposition process. Its presence is usually associated with higher rates of reaction. These two general features clearly indicate that the thermal decomposition behavior of these materials in the condensed phase is controlled by a set of complex nonlinear reactive processes.

3.2. HMX Decomposition

Processes

The decomposition of HMX provides a good example of the types of processes that occur in the condensed phase. An illustration of the features that are observed using the experimental protocol, outlined above, is shown in Fig. 3. The temporal behavior of the rates of formation of two of the main decomposition products (CH2O and N2O) indicates a complex process and is completely different from the exponential decay that is expected for a simple first-order reaction. Their behavior is more indicative of a nucleation and growth reaction or what is commonly referred to as an "autocatalytic" reaction. The temporal behaviors of the rates of evolution of the products can be divided into three stages: an induction period, an acceleratory period, and a late stage (2000 to 3800 s, 3800 to 5800 s, and 5800 to 7000 s, respectively in Fig. 3). The identities of the products and the temporal behaviors of their rates of formation provide information that can be used to guide the development of models of the reactive processes that control decomposition. The SEM pictures in Fig. 3 illustrate how spatial features can play an important role in controlling the decomposition process. The micronsize shell-like structures formed during the decomposition of HMX in the solid phase are remnants from reactive regions that were formed during


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49

Fig. 3. Illustration of the gas evolution rates and the morphological structures created during the thermal decomposition of an HMX particle. The graph shows the rate of evolution of two products formed during the decomposition of a single particle of HMX that was heated to and held at 235° C. To examine the morphological structures that are created during the decomposition, the reaction was stopped at the "sample point". To expose the morphological structures that grow within the particle, about half of the HMX remaining after decomposition was stopped is removed by sublimation. The particle was cut in half to expose the interior of the particle for SEM analysis. Pictures A through C show increasing magnifications of the particle interior. In picture B the material in the upper left portion of the picture is the HMX that remains in the particle (note the granular structure). The lower right portion shows the structures of nonvolatile residue that is formed via reactions within the HMX grains. Picture C shows that the NVR forms both strands and shell-like structures.

the decomposition process. Localized decomposition within these regions suggests that several types of spatially-dependent processes may play a role in the overall reactive process. The rate of transport of products within the condensed phases can play an important role in controlling the rates of reaction. For example, in the localized micron-size reaction regions in solid HMX, which appear to be bubbles contained within the solid HMX, the gaseous decomposition products from the bubble may diffuse into the surrounding lattice. As a result, this process may control the reaction rate by transforming crystalline HMX into a molten solution in which the HMX may react more rapidly.

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The SEM pictures of HMX also illustrate the role that interfacial boundaries may play in controlling the decomposition process. New surfaces are created at interfacial boundaries within the HMX particle. Initially, a grain structure is created within the particle (upper left of Picture B), which forms a new reaction environment on the surface of the grains. As the decomposition progresses, another type of reaction environment is created at the interfacial boundaries in the micron-size reaction regions, associated with the formation of bubbles within the grains. The formation of strands of NVR (Picture C) appears to be associated with reactions that occur at the grain boundaries, whereas the shell-like structures appear to be associated with the formation of bubbles within the grains. Both the development of the morphological features associated with the creation of interfacial boundaries and the transport of reactants and products in the vicinity of these boundaries illustrate the important role that spatial features can play in controlling the underlying nature of the reactive processes and the rates at which these processes occur. Isotopic scrambling experiments and deuterium kinetic isotope effects (DKIE) using isotopically-labeled analogues of HMX 42 and RDX 43 have provided further information on the sequence of bond-breaking steps that occur in the various reaction channels during the decomposition process. This provides further evidence of the complex nature of the decomposition process.

3.2.1. General Nature of Condensed-Phase Reactions in Energetic Materials The experimental protocol developed to investigate the decomposition of energetic materials in the condensed phase has been applied to examine a relatively wide range of different types of energetic compounds, which are listed in Table 1. Data with the level of detail shown above for HMX has been collected on most of these compounds. All of the compounds listed in Table 1 exhibit complex nonlinear reaction behavior. The degree of complexity varies from compound to compound. The most complex processes are observed in HMX 14 ' 42 ' 44 ' 45 and AP. 4 6 - 4 8 The decomposition of both materials involve tightly-coupled interactions between the chemical reactions and the spatial aspects of the morphological features created in the particles during the thermal decomposition process. The least complex processes are observed in the decomposition of K6 and TNCHP. 49 ' 50 The presence of the keto group in K6 appears to promote a more direct reaction to the gaseous decomposition products.



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Decomposition of TNCHP has a number of similarities to the decomposition of RDX and HMX in terms of the chemical reactions involved, but is not complicated by morphological issues associated with the solid phase, since it melts at approximately 170°C and is relatively stable in the liquid phase. The complexity of the decomposition process for the other compounds falls somewhere in between these two groups. Types of processes that control decomposition in the condensed phase Examination of the data from experiments with the compounds listed in Table 1 show that a wide range of processes can be a factor in the decomposition process. The types of processes that may contribute to the overall decomposition behavior include the following: (1) Phase changes. Solid-solid, melting, and vaporization all may play a role in controlling the rate of decomposition. (2) First-order reactions. The direct reaction to the gaseous decomposition products can play a role, but it is unlikely to be the sole reaction pathway in the condensed phase. (3) Formation of solutions. Mixtures of the reactant with its decomposition products may occur in either the solid or liquid phase, creating solutions of the components. (4) Reactions of parent compounds with decomposition products. These appear to be the main rate-limiting reactions for decomposition in the condensed phase. (5) Secondary reactions of products. All of the decomposition processes involve secondary reactions of the products. For nitramines, the creation and decomposition of the mononitroso analogue of the reactant appears to play an important role in their decomposition. (6) Nucleation and growth of bubbles. For compounds that remain solid at higher temperatures, such as HMX, AP, and TATB, the nucleation and growth of reaction regions within the solid, which forms microscopic bubbles, can be very important in controlling the decomposition process. (7) Reactions on surfaces and interfacial boundaries. Several compounds that remain solid at relatively high temperatures (>170°C) react on the surface of the particles by nucleating and growing an NVR on the surface of the particles. This behavior has been observed for 24DNI 51 ' 52 and RDX. 53 ' 54

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(8) Formation and growth of new morphological structures. For compounds that remain solid at higher temperatures, such as HMX, AP, and TATB, the growth of new morphological features creates dissipative structures that play a role in controlling the rates of reaction. The relative importance of these different processes depends on the intrinsic properties of the energetic compound and raises an interesting question: How do the molecular structure, crystal structure, and morphological characteristics of these materials determine which types of reactive processes will play a role in the overall decomposition process? Spatial dimensions of reactivity Is it possible that the physicochemical properties of the material may determine spatial dimensions of reactivity? The development of spatiotemporal structures is associated with some of the underlying decomposition processes in an energetic material. The spatial structures may be characterized by cellular units: volumes of material in which a physicochemical reactive process occurs within the volume and is controlled by a combination of chemical reactions, transport of species within the volume, and the development and growth of interfacial boundaries. This concept is similar to a unit cell used to represent crystal structure or a grain structure in a metal, except that the volume contains a reactive system on a microscopic scale. This concept is also similar to nucleation and growth concepts used to describe solid-state reaction chemistry of inorganic compounds. 55 Using this concept of a reactive unit cell, it may be possible to characterize and categorize the underlying reactive processes in an energetic material with a set of reactive cellular units with several different discrete and representative dimensions. For example, for HMX there may be one cellular unit to represent the reactions in bubbles and another to represent reactions at grain boundaries, essentially forming a hierarchy of cellular subunits. Within this framework, a reactive unit cell may be defined as a volume of material that contains a reactive system with self-contained chemical, physical and morphological features. Thus, characterizing the reactions in a reactive unit cell can be used to describe the overall behavior of any size sample, assuming appropriate heat and mass transfer processes can be properly characterized.



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3.2.2. Decomposition of Composite Materials Up to this point, discussion has focused on reactive processes in energetic compounds, however, the same general ideas can be applied to the reactions of composite energetic materials such as propellants and explosives. In this case, the chemical nature of the reactants, the morphological structure of the material, and interfacial boundaries are determined by the material design and manufacturing processes. For example, a binder or plasticizer that may be included with the energetic compound will (1) create new boundaries between the binder and energetic compounds, and (2) create potential interactions between the plasticizer and its decomposition products with the energetic compound or the binder. Understanding these processes requires the same type of information that is required for the individual energetic compounds. Hence the framework developed to examine and characterize energetic compounds may be used to characterize more complex propellants and explosives, which are composite materials with a cellular structure. 3.3. Characterization of Decomposition and HMX Case

Processes:

RDX

3.3.1. Development of a Conceptual Framework to Represent and Analyze Decomposition Processes Characterization of the complex processes that control the thermal decomposition of energetic materials requires a framework on which to build and test new concepts. Historically, a basic concept has been used to represent, analyze, and understand the experimental observations from thermal decomposition experiments. This concept may be expressed as "the harder you drive something the more likely it will happen." This concept was formulated into a model to characterize chemical reactions by Arrhenius, 56 in which the amount of energy available drives a chemical reaction. We have established a new framework to integrate the data derived from high information content experiments with concepts derived from everyday, anecdotal, and scientific experience. The framework consists of a suite of concepts that are built on parallel representations of two types of natural phenomena. The resulting framework is designed to achieve two main objectives: (1) develop an understanding of the underlying processes; (2) form the basis for predicting the behavior of the decomposition processes over a range of physical conditions.

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The suite of concepts borrows from two widely-used models: Darwinian evolution of biological systems and physicochemical control of hightemperature combustion. While both models characterize complex reactive systems, they are quite different, focusing on substantially different phenomena, but providing complementary means to represent and analyze thermal decomposition processes. The Darwinian evolution model provides a means to represent sets of interacting processes, which are not necessarily elementary reactions, and analyze how these processes compete and spawn new processes over a range of controllable environmental conditions. In contrast, the high-temperature combustion model provides a framework to represent the physical processes and chemical reactivity at a more fundamental level, associated with elementary processes, and creates mathematical representations of the underlying behaviors. A conceptual framework being developed to represent, analyze, and understand the decomposition of energetic materials draws from general features of the models for both metabolic pathways and high-temperature combustion. The general Darwinian approach used to characterize metabolic pathways forms the basis for describing the general competitive nature of the reactions that occur in the condensed phase of energetic compounds at low and moderate temperatures. Once the general nature of the underlying reactive processes is determined, physical and mathematical features, similar to those used in the high-temperature combustion model, are applied to further test the original reaction concepts and to develop a deeper understanding of the reactions. Many details of this conceptual framework are still under development. However, in the course of its development, the underlying concepts have been used to represent and analyze the decomposition of four energetic compounds: 24DNI, NDNAZ, RDX, and HMX. The use of the conceptual framework is illustrated with a discussion of the decomposition of the cyclic nitramines: RDX and HMX.

3.3.2. Reaction Pathways: Solid-Phase Reactions, Nonlinear Processes, Feedback Loops and Autocatalysis The Darwinian model has been used to construct a qualitative depiction of the competing processes that control the thermal decomposition of RDX and HMX over a range of conditions. It is based on data collected using the mass spectrometric experimental protocol and is illustrated in Fig. 4. The


Solid HMX/RDX Pristine solid/crystal

,

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Liq.

HMX/RDX 5


r»~

'

OST/I1CN t

T

Solid

NO t

NO. i ll.O

T

T

Completely damaged'

I ! Minor Products

l

CHj Hfi' 0

"CHj Hfi' HjC, 0

(7/.0

~CHj H,C%

0

•*-

CH 2 0 + HjO * CO + NjO

N;N-C

Pressure Fig. 4. Reaction diagram showing the underlying reactive processes t h a t control t h e decomposition of HMX and RDX.

competing reaction pathways are gleaned from the analysis of extensive sets of experimental data on the decomposition of R.DX43,53'54-57-58 and HMX 42,44.45 i n t h e c o n ( i e n s e d phases. Typical data for HMX is shown in Fig. 3. The representation of the decomposition process for RDX/HMX, shown in Fig. 4, describes the general set of reactions and interconnections between the main reaction pathways. It also contains a set of pressure and temperature scales, whose purpose is described below. Illustrations of how the reactive processes were gleaned from the data have been described previously 53 for several of the pathways. The reactants are listed in the upper left corner. The products detected using the experimental protocol are listed in the two boxes. The species that are denoted as "Exit Products" are compounds that have been involved in the reactive processes within the reaction environment, but eventually leave the reaction environment and are detected without undergoing further reaction. Several of these products (i.e., H2O, CO, N2O) are considered nonreactive under the conditions of the experiment, whereas the others can

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continue to react. The amount of each reactive species observed depends on the competition between the various reaction pathways that dominate under different sets of reaction conditions. The species listed as "minor products" are also formed in reactive processes, but represent only a small fraction of the total amount of products formed during decomposition. While only minor species, these compounds provide valuable insight into the nature of the underlying processes, since their time-dependent rates of formation track the various underlying behaviors, such as the decomposition of the NVR. The reaction at the top of the diagram represents a relatively direct reaction pathway between the reactants and exit products. This reaction represents the elimination of HONO from the RDX or HMX to form oxy-s-triazine in the case of RDX, and the subsequent reaction of these products to HCN, NO, N 0 2 and H2O. This reaction is first order in the amount of reactant, and is the only pathway whose reaction rate is consistent with a unimolecular decomposition process. The bond-breaking sequence of this reaction has been determined via DKIE and isotopescrambling experiments. 43 The five circles shown in the reaction diagram represent the main nonlinear reactive processes that occur in RDX and HMX. These reactions are described as cycles, as is done for biochemical pathways, in order to track and illustrate how the different reaction pathways are interrelated. The arrows connecting the different reaction cycles show how various compounds move between the different reaction cycles. This movement of compounds between reaction cycles also illustrates the coupling and extent of nonlinearity that occurs during decomposition. The five reaction cycles can be divided into two groups with similar features. One group represents chemical reactions at the molecular level. The second group represents complex physicochemical processes involving multiple phases, reactions at interfacial boundaries, and emergent phenomena. The three reaction cycles representing the chemical reactions play a major role in the decomposition of RDX and HMX in the molten or liquid phase. The chemical reaction cycles include the NO Cycle, the Nitroso Cycle and the C H 2 0 / N 0 2 Cycle. The NO Cycle involves the reaction of NO with RDX or HMX to form the mononitroso analogue of these compounds. Isotope-scrambling experiments 43 have shown that this is the primary reaction leading to the formation of hexahydro-l-nitroso-3,5-dinitro-5-triazine (ONDNTA) from RDX in the liquid phase. NO can originate from several different sources.



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For example, during the decomposition of RDX in the liquid phase, NO produced by the direct reaction (OST/HCN) provides the initial source of NO to form ONDNTA. Note that, as the DKIE lowers the rate of the direct reaction, the rates of the NO Cycle and Nitroso Cycle may also be reduced if the direct reaction is the primary source of NO. The Nitroso Cycle is more complex. The mononitroso analogues of RDX and HMX may be formed initially by reacting with NO. Once formed, the decomposition of the mononitroso analogue can itself be quite complex. Thermal decomposition studies of ONDNTA 59,6 ° have shown that N 2 0 , H2O, and CH2O are the major products formed during its decomposition. However, a large portion of each ONDNTA molecule is incorporated into the nonvolatile residue. Once the NVR is present, a new pathway leading to the formation of the mononitroso analogue is created. In this case, the isotope-scrambling experiments indicate that the reaction involves the removal of an oxygen atom from the NO2 group, rather than the replacement of the NO2 groups with NO, since there is no scrambling in the N-NO bond. The C H 2 0 / N 0 2 Cycle is a facile reaction that involves reactants formed from different reaction pathways and results in the generation of a substantial amount of heat (AH = —185 kJ/mol). This type of behavior shows how the extent of self-heating of the sample may be influenced by the relative rates of the different reaction cycles since separate reaction cycles produce the CH2O and NO2 reactants in this heat-generating cycle. The two remaining cycles represent complex physicochemical processes, play a major role in solid-phase decomposition, and are responsible for morphological damage created in the material that can lead to sensitized explosives and propellants. The NVR Cycle is characterized by the creation of an amorphous higher molecular weight material that has a low volatility. Infrared spectra and thermal decomposition of the NVR indicate it has amide and cyano groups. The NVR is formed during the decomposition of HMX, RDX, and ONDNTA. In each case, the same minor products, shown in the box, are either associated with its formation or decomposition. The location in the sample where the NVR is formed differs for ONDNTA, RDX, and HMX. ONDNTA becomes molten at relatively low temperatures (125-165°C, depending on experimental conditions), and the NVR is formed in the molten mass of the sample. In contrast, the NVR nucleates and grows on the surface of the RDX particles when the sample is maintained below the melting point of RDX (~170-190°C). In these experiments, it is clear that the rate-controlling reaction involves the

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interaction between the NVR and the RDX at the surface of the RDX particle. 58 Formation of the NVR during the decomposition of HMX occurs in micron-size reaction centers, which are distributed homogenously throughout an HMX particle (the strand and shell-like structures shown in Fig. 3). In HMX, formation of the NVR may involve the reaction of HCN with CH2O under high-pressure conditions, since both of these compounds are observed at lower rates when the sample remains solid compared to when the sample is allowed to liquefy. Given the range of physical conditions under which the NVR is formed in these three compounds, it is remarkable that the reaction products associated with its formation are the same in each case. This again emphasizes the nonlinear and cyclic nature of the processes involved in the formation and decomposition of the NVR. The Solid-phase Cycle is the most complex of the five cycles. The processes involved in the Solid-phase Cycle are quite different, depending on whether the reactant is RDX or HMX. In RDX, the surface of the particles appears to roughen and undergo a morphological change. This is accompanied by the formation of the "reddish" NVR on the surface of the particle. Once the NVR is formed on the surface of the RDX particle, the rate of reaction accelerates, leading to an increase in the amount of NVR and the continued acceleration of the reaction rate. In HMX, the solid-phase processes are more complex, creating a set of morphological features as illustrated in Fig. 5. HMX first undergoes the Grain Structure Strand location

Bubbles

Flake Fig. 5. Illustration of the morphological features created in an HMX particle during the thermal decomposition process.



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P —> 5 phase transition, which creates a granular structure within the particles. This is followed by the nucleation and growth of reaction centers within the grains of HMX. The gaseous products formed in the reaction centers create bubbles, which grow in size as the reaction progresses. The smallest dimension of the HMX grains limits their maximum size, since the gas is released from the bubbles as they intersect the grain boundaries. The high-pressure conditions within the bubbles appear to favor the formation of the NVR within the bubbles as the bubbles grow. The NVR remains behind as a remnant of the reactions that have occurred within the bubble. Once a substantial amount of decomposition has occurred (~30%), the particle becomes relatively porous, allowing HMX and its decomposition products to flow within the porous structure and interact with the sample surfaces during the later stages of the decomposition process, forming flakes of NVR in the intergranular regions. What is especially intriguing about the processes involved in the Solid-phase Cycle is that there is no a priori way to anticipate their emergence from the properties of either RDX or HMX.

3.3.3. Emergent

Phenomena

The concept of emergence has been developed to describe the behaviors of complex systems and may be defined as a set of interacting components whose collective behaviors cannot be predicted from the behavior of the individual parts. 61 In examining the decomposition behavior of energetic compounds, we are confronted with similar issues. For example, can the behaviors that emerge on a larger spatial scale during the decomposition process of HMX be predicted from its underlying physical and chemical properties? If so, how? At this point, we do not have the answers to these questions. However, further examination of these systems may provide new insights into how basic chemical reactions and physical phenomena may be coupled to create systems that exhibit new and independent behaviors. From the chemical point of view, energetic materials are comprised of carbon, hydrogen, nitrogen and oxygen. From the physical point of view, energetic compounds are relatively easy to characterize. Their molecular crystal structures are readily measured and known. Calculations on the energetics and dynamics of their reactions at the molecular level have been made, 62 " 64 and calculation of their interactions at larger spatial scales are now possible. 65 ' 66 Thus, the main question becomes how do we determine the rules that control the evolution of these systems in time?

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3.4. Effects of Experimental Conditions Decomposition Processes

on

Observed

The complex physicochemical thermal decomposition reaction network, described above for HMX and RDX, can be used to understand the rules that control the competition between the various reaction pathways. This, in turn, will provide insight into the apparent discrepancies observed in experiments conducted using different experimental techniques. The reaction network can be interpreted as a diagram that illustrates the set of possible reaction channels by which a sample of HMX or RDX may decompose during an experiment. The entire set of channels is active for any given decomposition experiment; however, what is observed for a particular experiment is simply the subset of reaction channels that successfully compete and dominate the reactive process under a given set of experimental conditions. The most successful pathways will consume the RDX/HMX the fastest.

3.4.1. Reaction-Coordinate

Vectors

To provide a framework to represent and discuss the details of the reactive process, we introduce the concept of a reaction-coordinate vector. The reaction-coordinate vector represents the progress of a reaction through a set of conditions defined by an experiment. Graphically, a vector joining two points on the reaction network represents the reaction-coordinate vector. Thus, the dominant rate-limiting steps encountered, and therefore measured, by an experiment conducted under a specific set of conditions, will correspond to the reaction cycles and coupling pathways directly intersected by the reaction-coordinate vector. Reaction cycles not intersected by the vector will play only a minor role under the given conditions; the extent of contribution decreases for reaction cycles that lie farther away from the vector. For example, the line between the solid-phase cycle and point 1 represents one such reaction-coordinate vector. 3.4.2. Environmental Conditions Determine Location of Reaction-Coordinate Vector Figure 4 shows the global thermal decomposition reaction network for HMX and RDX. Depicted, are the different reactive processes: NO, ONDNTA, C H 2 0 / N 0 2 , NVR, and the Solid-phase Cycles. The complex interaction pathways connecting these distinct reaction cycles are also shown. The extent to which each reaction cycle contributes to the overall decomposition



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process is dependent on several "environmental" factors. These factors include: (1) pressure of gas in contact with the RDX/HMX, which is represented by a vertical line and increases qualitatively as one moves to the left in the diagram; (2) temperature of the RDX/HMX, which is represented by the horizontal line and increases qualitatively as one moves up in the diagram; (3) heating rate of the RDX/HMX, which is depicted by the horizontal axis in the grid surrounding the Solid-phase Cycle, with heating rates increasing from left to right in the grid; and (4) initial state of the RDX/HMX, qualitatively depicted by the two horizontal lines (labeled "pristine solid/crystal" and "completely damaged") to the left of the solidphase cycle, with initial "damage" to the RDX/HMX sample increasing as one goes down between the lines. Qualitatively, a vector connecting the "starting point" of the RDX/ HMX sample with a point formed by the intersection of the relative pressure and temperature lines can be thought of as a reaction-coordinate vector. The starting point is a point within the grid located in the upper left region of the reaction network that represents the initial state of the sample, which is determined by the heating rate in an experiment. The heating rate controls the relative amount of initial "damage" created in the sample, with slower heating rates being associated with the creation of more damage. In this context, the reaction cycles and "coupling" pathways that are intersected by this reaction-coordinate vector are indicative of the dominant decomposition processes followed during a specific thermal decomposition event. This is not to say that any processes not intersected are inactive for this specific set of circumstances. Indeed, due to the coupling of the different reaction cycles, all processes must play some role. A correct interpretation of this vector is that it depicts the dominant processes during the thermal decomposition under this specific set of circumstances, and therefore, these processes will be the ones observed during an experiment that is conducted under these same conditions. With this interpretation of the decomposition process, the apparent discrepancies observed by previous experiments may be addressed. As mentioned above, different experimental investigations have shown different sets of products. Until now, this discrepancy was thought to indicate that different unimolecular decomposition mechanisms were at play under different thermal decomposition conditions. The decomposition diagram shows that each of these different experimental results (i.e. product distributions) is correct. One may use this framework based on different "simplified" (i.e. unimolecular) reaction mechanisms to interpret the results from

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experiments collected under different sets of conditions to account for the apparent discrepancy. The reaction network expresses the idea that a single complex reactive process, with interactions between the distinct reaction cycles, is responsible for the overall decomposition. The varied experimental conditions simply serve to "shift" the reaction coordinate vector to regions of the reaction mechanism where different reaction cycles dominate the reactive process and lead to different distributions of the observed products.

3.4.3. Conditions Probed by Various Experiments The three numbers in red circles (Fig. 4) depict the regions of the global thermal decomposition reactive process network probed by several different experimental techniques. The initial state of the sample is of significant importance when determining the dominant reaction pathway. The initial state of the RDX or HMX sample at the onset of decomposition in the STMBMS and other experiments can be mapped to a point within the region formed by the initial state and heating rate parameters. This region essentially encompasses the solid-phase reaction cycle and accounts for the possible states of RDX/HMX powders or single crystals used in various experiments (grid region). At the upper left of the region is pristine RDX/HMX solid or single crystals. Rapid heating moves the sample to the right through the upper portion of the grid, corresponding to an experiment in which there is minimal damage in the solid due to nucleation and growth in the Solid-phase Cycle. Continuing towards the right in the grid, liquid-phase RDX/HMX is formed in experiments that start with pristine, undamaged RDX/HMX and the sample is rapidly heated above its melting point, to again minimize the extent of "damage" due to the solid-phase reaction cycle. The bottom left is a "fully damaged" solid/single crystal, liquid-or meltphase RDX/HMX, (i.e. RDX/HMX where the solid-phase nucleation and growth process has fully developed and an NVR has been produced). The bottom right depicts solid/single crystal, liquid-or melt-phase RDX/HMX that has become fully "reactive" (i.e. the nucleation and growth process is fully developed, and the condensed-phase RDX/HMX is completely saturated with intermediate stage decomposition products). Within this region, the possible initial states of RDX/HMX used in the thermal decomposition studies can be "mapped".



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Region 1 in Fig. 4 is occupied by TGA/DSC and vacuum laser-pyrolysis experiments. In a typical TGA/DSC experiment, a fast heating rate is used to obtain temperatures above the melting point of RDX/HMX, thereby minimizing the amount of time spent in the solid-phase reaction cycle during the heat ramp and resulting in essentially pristine liquid-phase RDX/HMX as the isothermal temperature is reached. Decomposition then proceeds in parallel by unimolecular liquid- and gas-phase processes, typically accompanied by significant RDX/HMX sublimation. The lack of high gas-confinement near the condensed-phase surface minimizes the contributions of secondary reactions between the condensed- and gas-phase decomposition products in the TGA/DSC measurements. The vacuum laser-pyrolysis experiments 67 also generate rapid heating of the solid surface, again leading to essentially pristine liquid-phase RDX/HMX at the sample surface and consistent with the reactioncoordinate vector for Region 1. There is a significant contribution to the decomposition through the OST/HCN decomposition pathway and also contributions from the NO Cycle. Interactions between these two channels are controlled by the coupling pathways. Contributions to the overall decomposition process by reaction cycles and coupling pathways that are not directly intersected by the reaction-coordinate vector decrease the farther removed from the reaction-coordinate vector the individual process lies. The parameter space depicted by Region 1 in Fig. 4 does not include all variations of the space encountered by current ongoing TGA/DSC and laser-pyrolysis experiments; it simply maps the relative parameter space that is typical of the majority of work in these types of experiments. Region 2 (Fig. 4) is the relative parameter space occupied by flashheating mass spectrometry and FTIR experiments. 68 In these experiments, very fast heating rates are used to "flash" the solid sample to isothermal temperatures ranging from just below to significantly above the melting point of RDX/HMX. This flash heating produces a sample surface temperature that initially falls within the transition region between pristine solidphase and pristine liquid-phase RDX/HMX. This creates a surface that exists as a melt or "froth" prior to the onset of significant decomposition, with minimal "damage" created by the solid-phase reaction cycle before decomposition initiates. The visual indications of a residue in these experiments, along with measurements of a mononitroso derivative of RDX (ONDNTA) indicate that there is a contribution to these experiments from the ONDNTA and NVR

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reaction cycles. Thus, results from these experiments can be mapped to Region 2, with the dominant processes lying along the reaction-coordinate vector and minor processes falling farther away from the vector. A comparison of the reaction-coordinate vectors for Regions 1 and 2 shows that ONDNTA and solid-phase decomposition contribute to Region 2 processes, 41 while the first-order OST and NO channels contribute more to Region 1 processes. Region 3 depicted in Fig. 4 is the experimental parameter space filled by the slow-heating rate sealed bulb type experiments such as those by Batten 3 7 - 4 0 and Cosgrove and Owen. 69 ' 70 In these experiments, the slow heating allows the Solid-phase Cycle to contribute significantly to the decomposition. Thus, the NVR reaction cycle is the major contributor to the rate-limiting processes controlling the overall decomposition for the solid-phase experiments and plays a contributing role in the melt-phase experiments. Summarizing: one unified picture captures the overall decomposition process. This picture is a network of complex interactions amongst different reactive processes with multiple pathways coupling the individual processes. This network captures all of the seemingly contrary results obtained in many different investigations in one unified picture. The network also provides a framework where most experiments can be mapped to distinct regions within the network. Differences among experiments can be attributed to variations in the experimental parameters which shift the dominant, rate-limiting steps to different reaction paths within one overall reaction network. 4. Reaction Kinetics While the reaction network provides a qualitative picture of the decomposition process and illustrates how various reaction pathways may compete under different sets of conditions and lead to the emergence of different observed behaviors, it falls short of the ultimate goal: predicting the behaviors of propellants and explosives over a wide range of conditions. To achieve this goal requires applying the second aspect of our conceptual framework: physicochemical control of high-temperature combustion reactions. The various reactive pathways in the reaction network must be individually characterized and represented by a set of mathematical expressions in a manner analogous to the use of elementary reactions to characterize gasphase reactions in high-temperature combustion processes. This requires



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new numerical algorithms that can be used to characterize the reaction kinetics associated with reaction networks that characterize the decomposition of the different energetic compounds and various energetic materials. 4.1. Extracting Reaction Experiments

Kinetics

from

Condensed-Phase

4.1.1. Simple Kinetics — Direct Inversion from Experiment For simple reactive processes, the reaction kinetics can be determined directly from experiments by means of an Arrhenius-type analysis. Inversion of the data from the experiment provides the required reaction rate constant and its temperature dependence. If this type of analysis is applied to thermal decomposition results from experiments with energetic compounds, the rate constant will only represent the reaction rate along the reaction-coordinate vector that represents the conditions of the particular experiment in the overall reaction network. The obvious limitation of this approach is that each reaction-coordinate vector requires its own set of reaction rate parameters. 4.1.2. Kinetics of Complex Reaction Networks The development of mathematical models to represent combustion processes is a good example of how the kinetics of complex reaction networks has been developed. In this case the reaction kinetics have been determined by two different approaches. In the first approach, experiments are conducted to investigate and measure the rate of elementary reactions, thus providing pieces to be used in the overall reaction network. In the second approach, the distribution of reactants, intermediates, and final products are measured as a function of spatial location in a flame. Then the reaction rate parameters of the elementary reactions that represent the reaction network are optimized to match the details of the experimental measurements. The conceptual framework that has been developed to investigate reactions of energetic materials in the condensed phase incorporates an approach to characterize the reaction kinetics that is analogous to the one used to characterize reaction kinetics in flames. In this approach, the timedependent rates of formation of the reactants, intermediates, and products are measured using the experimental protocol. Next, reaction schemes are postulated, sets of differential equations representing the underlying processes constructed, solved, and compared to the experimental data (Fig. 6).

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Reaction Scheme Refinement Postulate or Refine Reaction Scheme

Set or modify Parameters

No

Kinetics Parameters Optimization Yes

Does Postulated Model Capture All Features in Data?

Compare reaction scheme to experiments covering range of experimental conditions and optimize parameters.

1

Assess reaction schemes strengths and weaknesses in capturing underlying reaction processes.

Construct and Solve Equations

i Compare to STMBMS Data

T

No

Yes

Add results to database and publish.

Comparison OK? Fig. 6. Algorithm used to create mathematical models to represent the reaction kinetics of thermal decomposition processes.

The analysis procedure is divided into two primary tasks. First the reaction scheme is postulated and refined and then the kinetics parameters are optimized. Sets of differential equations are constructed to characterize the various processes in the reaction network that represent the decomposition of an energetic compound, such as the one above for RDX and HMX. The procedure used to build the model starts with a small set of differential equations that represent specific aspects of the decomposition process. The parameters for these processes are optimized by minimizing the difference between the calculations and the corresponding experimental measurements. If the differential equation for a specific aspect of the reaction network captures the features observed in the experimental measurements, it is retained in the model. If not, it is discarded and another process is postulated and tested. Using this procedure, a model of the reaction network is built. Once the reaction scheme is developed to a point where it captures most, if not all, of the features observed in the data, it is then used to assess its ability to capture the features observed in experiments collected over a range of experimental conditions. When the model can capture the behavior over a range of experimental conditions, the parameters used in the model are then optimized to provide the kinetic parameters for the different pathways in the reaction network.



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The modeling aspects of the conceptual framework for investigating the thermal decomposition of energetic materials are still under development. A higher level programming language, Mathematica®, has been used to develop the analysis methods. Papers on the decomposition of 24DNI52 and NDNAZ, 71 illustrate how models of the reaction networks are developed for complex reactive processes in the condensed phase. A new reaction modeling and kinetics (REMKIN) compiler and analysis tool is currently under development. The design goal for REMKIN is to provide a set of numerical algorithms to facilitate the development of mathematical representations of the reaction networks that control the decomposition of energetic materials. With the completion of the REMKIN compiler and analysis tool, the conceptual framework for investigating the thermal decomposition of energetic materials will be complete and new advances in our understanding of reactive processes in energetic materials in the condensed phase at low and moderate temperatures will be possible.

5. Conclusions and Future Research Understanding the physicochemical processes that control the thermal decomposition of energetic materials in the condensed phase will help to characterize the safety and aging behavior of existing explosives and propellants. This understanding will also provide new insight for designing and developing new energetic compounds. Obtaining this understanding is a challenge due to the complex nature of the decomposition processes in these materials, which occur far from equilibrium conditions. The development of a new experimental protocol to examine the complex processes associated with the thermal decomposition of energetic materials in the condensed phase has been described. The fundamental concept of the new protocol is to maximize the extent of information obtained from the experiments so as to reveal the greatest insight into the underlying reactive processes. The protocol described in this chapter is primarily based on mass spectrometric methods. However, the general concepts of using multiple instrumental methods to make simultaneous measurements on a system, with the goal of obtaining the maximum amount of temporally correlated information, is a general principal that provides guidance for creating other types of experiments to probe reactive processes in the condensed phase.

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The new experimental protocol has been used to examine a range of different types of energetic materials and has revealed new insight into the underlying reactive processes. It has been found that the decomposition of most energetic compounds is controlled by a set of coupled nonlinear physical and chemical reactive processes. These features create complex reactive systems whose behavior is characterized by the emergence of dissipative structures that play a major role in controlling the overall decomposition. Several different types of spatiotemporal structures have been observed for different materials. For example, reactions on the surface of 24DNI and RDX particles control the decomposition of these compounds in the solid phase, whereas nucleation and growth of sub-micron size reaction regions within HMX particles control its decomposition in the solid phase. The experiments have also provided new insight into the multiple reaction pathways that compete to control the evolution of the decomposition process in time. This competition and interaction between the underlying processes has been illustrated with results from the decomposition of RDX and HMX. It has been shown how the effects of temperature and pressure of the contained gaseous decomposition products can alter the reaction pathways and lead to divergent results. It has also been shown which reaction pathways are likely to dominate the decomposition process using a variety of the more conventional thermal analysis methods. These methods typically provide insufficient information to identify and characterize the underlying processes. The complex reaction behavior poses a challenge to develop a new conceptual framework that can be used to represent, develop, and convey understanding of the underlying behavior of energetic materials. While this is a new challenge in the field of energetic materials, understanding similar types of processes have been of great interest in the more general scientific community. The entire set of behaviors observed in the decomposition of energetic materials in the condensed phase falls under the new science, born over the past several decades, of nonequilibrium processes. This new science uses concepts such as dissipative structures and self-organization and describes processes in terms of unidirectional time and irreversibility.6 This context has been used to characterize a range of different phenomena, including complex chemical systems, such as the well-known Belousov-Zhabotinski chemical oscillator reaction. Use of these concepts will most likely play an important role in the characterization of decomposition processes of energetic materials in the future.



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More recently, Wolfram has developed a description of complex processes in his book "A New Kind of Science".72 It uses cellular automata to explore the behavior of complex systems and categorizes the evolution of these systems using a set of rules to guide the evolutionary progress. Some rules lead to the rapid development of simple, repetitive and predictable structures; others evolve as complex unpredictable patterns. This behavior illustrates that, for some set of rules, one can develop mathematical representations that predict the future state of the system, but with other sets of rules this is not possible and the system is not computationally reducible. Thus, the only way to characterize the evolution of the computationally irreducible system is to let it evolve and examine its structure at the time of interest. These concepts developed by Wolfram72 for cellular automata may be applied to the characterization of the decomposition processes in energetic materials by allowing the physicochemical processes to represent the rules that guide the evolution of the system and using the corresponding set of differential equations to compute the evolution of the system. This is essentially the process that has been developed for the numerical simulation features of the experimental protocol described in this chapter. A set of chemical reactions and physical processes are postulated (the rules to control the process), the evolution of the system is computed, and the results are then compared to the experimental results to determine if the chemical reactions and physical processes (the rules) describe the observed results. From one point of view, the high-information content experiments developed in the experimental protocol can be considered an experimental implementation of the computational processes (rules), which guides the evolution of a system. Basically, a non-silicon analogue computer. One of the main challenges remaining from the scientific viewpoint is connecting the behavior of the nonequilibrium reactive processes to the chemical and physical properties of the compounds (i.e., chemical functionality, molecular and crystal structure, and constitutive properties). The ability to meet this challenge is in its infancy, for it requires first identifying the underlying reactive processes and then determining how these underlying processes are linked to the molecular, physical, and constitutive properties of the material. Currently, this is being approached by collecting data from high-information content experiments on a diverse set of different compounds and carefully examining the data to uncover correlations between decomposition behavior and the properties of the compounds. Until now, most experiments that have examined the underlying detail of reactions of energetic materials in the condensed phase at low and

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moderate t e m p e r a t u r e s have focused on individual pure compounds. However, development of new experimental methods now allow the interactions of ingredients t h a t make u p explosive and propellant formulations to be examined in more detail. This should provide a more fundamental understanding of how the ingredients interact and what effects these interactions have on the mesoscale mechanics and aging behavior of these materials.

Acknowledgments T h e development of the new experimental protocol and its applications to the examination of energetic materials is the result of contributions of many people at Sandia National Laboratories over the past twenty years. Contributors include: Mr. N. Toly, Mr. J. Collins, Mr. J. Damico, Mr. M. Mitchell, Mr. D. Puckett, Dr. T. Land, Dr. L. Minier, Dr. K. Anderson, Mr. R. Hannush, Ms. L. Johnston, Ms. J. Wood, Ms. S. Mack, Ms. D. Wiese-Smith, Ms. E. Cooper, and Dr. S. Maharrey. Many advances in our understanding were through discussions and collaborations with Dr. Surya Bulusu (U.S. Army, A R D E C ; deceased). T h e work has been supported over t h e years by U.S A r m y / D O E M e m o r a n d u m of Understanding (MOU), the Army Research Office, DoD Office of Munit i o n s / D O E MOU, and United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94-AL85000. T h e author thanks Dr. G. Anderson, Dr. W . Alzheimer, Mr. P. Gildea, Mr. Tom Hitchcock, Dr. S. Johnston, Dr. R. Carling, Dr. A. Ratzel, Dr. F . Tully, and Dr. D. Hardesty for support and encouragement for this work within Sandia. Finally, we t h a n k Dr. R. Shaw for his long-term support and encouragement in our efforts.

References 1. B. Asay, P. M. Dickson, B. F. Henson, L. Smilowitz, L. Tellier, N. Glassmaker and M. Greenfield, Large Scale Annular Cookoff Experiment (LASC), in PSHS Meeting, Coca Beach, Florida, CPIA, 1999. 2. S. K. Chidester, C. M. Tarver, L. G. Green and P. A. Urtiew, Combust. Flame 110(1-2), 264-280 (1997). 3. H. S. Johnston, Gas Phase Reaction Rate Theory, Modern Concepts in Chemistry, eds. Bryce Crawford Jr., W. D. McElroy and C. Price (The Ronald Press Company, New York, 1966). 4. B. Bhushan, A. Halasz, J. Spain, S. Thiboutot, G. Ampleman and J. Hawari, Environ. Sci. Tech. 15(36), 3104-3108 (2002). 5. X. E. Zhao, E. J. Hintsa and Y. T. Lee, J. Chem. Phys. 88(2), 801-810 (1987).

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6. I. Prigogine, The End of Certainty: Time, Chaos and the New Laws of Nature, 1st edn. (The Free Press, 1996), pp. 57-72. 7. R. Behrens, Rev. Sci. Instrum. 58(3), 451-461 (1987). 8. R. Behrens, Int. J. Chem. Kinet. 22, 135-157 (1990). 9. R. Behrens, Int. J. Chem. Kinet. 22, 159-173 (1990). 10. S. Maharrey, B. Bastasz, R. Behrens, A. Highley, S. Holier, G. Kruppa and J. Whaley, Appl. Surf. Sci. 2 3 1 - 2 3 2 , 972-975 (2004). 11. R. N. Rogers, Thermochim. Acta 3, 437-447 (1972). 12. S. L. Rodgers, M. B. Coolidge, W. J. Lauderdale and S. A. Shackelford, Thermochim. Acta 177, 151-168 (1991). 13. G. T. Long, S. Vyazovkin, B. A. Brems and C. A. Wight, J. Phys. Chem. B23(104), 2570-2574 (2000). 14. G. F. M. Pinheiro, V. L. Lourenco and K. Iha, J. Therm. Anal. Calorim. 67, 445-452 (2002). 15. C. M. Tarver, R. R. McGuire, E. L. Lee, E. W. Wren and K. R. Brein, in 17th Symp. (Int.) on Combustion, Pittsburgh (The Combustion Institute, 1978), pp. 1407-1413. 16. M. D. Pace, J. Energetic Mater. 3, 279-291 (1985). 17. M. D. Pace, J. Phys. Chem. 95, 5858-5864 (1991). 18. E. Catalano and C. E. Rolon, Thermochim. Acta 6 1 , 53-71 (1983). 19. P. J. Miller, S. Block and G. J. Piermarini, Combust. Flame 83(1-2), 174-184 (1991). 20. T. R. Botcher, D. J. Beardall, C. A. Wight, L. M. Fan and T. J. Burkey, J. Phys. Chem. 100(21), 8802-8806 (1996). 21. K. L. Erickson, W. M. Trott and A. M. Renlund, in Proc. 10th Int. Detonation Symp., ed. J. M. Short (Office of Naval Research, Boston, MA, 1993), pp. 340-346. 22. T. B. Brill, P. J. Brush, S. A. Kinloch and P. Gray, Philos. Trans. R. Soc. London, Ser. A: Phys. Sci. Eng. 15(339), 377-385 (1992). 23. S. T. Thynell, P. E. Gongwer and T. B. Brill, J. Propul. Power 12(5), 933-939 (1996). 24. J. Wormhoudt, P. L. Kebabian and C. E. Kolb, Combust. Flame 111(1-2), 73-86 (1997). 25. W. M. Trott and A. M. Renlund, Appl. Opt. 24(10), 1520-1525 (1985). 26. L. R. Ryzhkov and J. M. McBride, J. Phys. Chem. 100(1), 163-169 (1996). 27. L. R. Ryzhkov and J. M. McBride, J. Am. Chem. Soc. 119(21), 4826-4833 (1997). 28. T. R. Botcher and C. A. Wight, J. Phys. Chem. 97(36), 9149-9153 (1993). 29. A. J. B. Robertson, Trans. Faraday Soc. 45, 85-93 (1949). 30. S. Bulusu and R. J. Graybush, in 39th Congress on Industrial Chemistry, Brussels, Belgium, 1966. 31. W. L. Ng, J. E. Field and H. M. Hauser, J. Chem. Soc, Perkin Trans. II, 637-639 (1976). 32. F. W. Lampe, J. L. Franklin and F. H. Field, J. Am. Chem. Soc. 79, 6129-6132 (1957). 33. M. Farber and R. D. Srivastava, Chem. Phys. Lett. 80, 345-349 (1981).

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34. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data Preliminary Comments on Autoacceleration and Autoinhibition in HMX and RDX Decomposition (US Army Ballistic Research Laboratory, 1984). 35. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data: Product Distributions from HMX and RDX Decomposition (US Army Ballistic Research Laboratory, 1985). 36. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data: Activation Energies and Frequency Factors for HMX and RDX Decomposition (US Army Ballistic Research Laboratory, 1985). 37. J. J. Batten and D. C. Murdie, Aust. J. Chem. 23, 737-747 (1970). 38. J. J. Batten and D. C. Murdie, Aust. J. Chem. 23, 749-755 (1970). 39. J. J. Batten, Aust. J. Chem. 24, 945-954 (1971). 40. J. J. Batten, Aust. J. Chem. 24, 2025-2029 (1971). 41. J. J. Batten, Aust. J. Chem. 25, 2337-2351 (1972). 42. R. Behrens and S. Bulusu, J. Phys. Chem. 95(15), 5838-5845 (1991). 43. R. Behrens and S. Bulusu, J. Phys. Chem. 96(22), 8891-8897 (1992). 44. R. Behrens, J. Phys. Chem. 94, 6706-6718 (1990). 45. R. Behrens, S. Mack and J. Wood, in JANNAF 17th Propulsion Systems Hazards Subcommittee Meeting, Vol. 1, CPIA Publication 681 (1998), pp. 21-44. 46. R. Behrens and L. Minier, in 33rd JANNAF Combustion Meeting, CPIA Publication 653 (1996), pp. 1-19. 47. L. Minier and R. Behrens, in JANNAF 17th Propulsion Systems Hazards Subcommittee Meeting, CPIA Publication 681 (1998). 48. A. I. Atwood, K. J. Kraeutle, T. P. Parr, D. M. Hanson-Parr, R. Behrens, L. Minier and A. Rutzel, in 49th JANNAF Propellant System Hazards Subcommittee Meeting, CPIA (1999). 49. R. Behrens and S. Bulusu, in 29th JANNAF Combustion Meeting, Vol. II, CPIA Publication 573 (1992), pp. 453-463. 50. R. Behrens and S. Bulusu, in Fall 1992 Meeting of the Materials Research Society, Vol. 296 (1992), pp. 13-24. 51. L. Minier, R. Behrens and S. Bulusu, in Decomposition, Combustion and Detonation Chemistry of Energetic Materials (Materials Research Society, Boston, MA, 1996). 52. R. Behrens, L. Minier and S. Bulusu, in 34th JANNAF Combustion Subcommittee Meeting, CPIA Publication 662 (1997), pp. 549-567. 53. R. Behrens and S. Maharrey, in Combustion of Energetic Materials, eds. K. K. Kuo and L. T. DeLuca (Begell House, New York, 2002), pp. 3-21. 54. S. Maharrey, D. Wiese-Smith and R. Behrens, in Proc. 38th JANNAF Combustion Meeting, Chemical Propulsion Information Agency, Destin, FL (2002), pp. 373-386. 55. M. E. Brown, D. Dollimore and A. K. Galwey, Reactions in the Solid State. Comprehensive Chemical Kinetics, Vol. 22, eds. C. H. Bamford and C. F. H. Tipper. (Elsevier Scientific Publishing, Amsterdam, 1980), p. 340. 56. S. Arrhenius, Z. Phys. Chem. 1, 110 (1887). 57. R. Behrens and S. Bulusu, J. Phys. Chem. 96(22), 8877-8891 (1992).

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58. S. Maharrey, R. Behrens and L. Johnston, in 19th PSHS Meeting, Chemical Propulsion Information Agency, Monterey, CA (2000), pp. 17-32. 59. R. Behrens and S. Bulusu, in Proc. Materials Research Society, Vol. 296 (1993), pp. 13-24. 60. R. Behrens and S. Bulusu, in Challenges in Propellants and Combustion 100 Years after Nobel, ed. K. K. Kuo (Begell House, Inc., New York, 1997), pp. 275-289. 61. J. Bickle, Minds Much. 11, 467-481 (2001). 62. C. C. Chambers and D. L. Thompson, J. Phys. Chem. 99(43), 15881-15889 (1995). 63. D. Chakraborty, R. P. Muller, S. Dasgupta and W. A. Goddard, J. Comput. Aided Mater. Des. 8, 2-3 (2002). 64. C. J. Wu and L. E. Fried, J. Phys. Chem. A13(101), 8675-8679 (1997). 65. D. C. Sorescu, B. M. Rice and D. L. Thompson, J. Phys. Chem. B103(32), 6783-6790 (1999). 66. D. Bedrov, C. Ayyagari, G. D. Smith, T. D. Sewell, R. Menikoff and J. M. Zaug, J. Comput. Aided Mater. Des. 8, 2-3 (2002). 67. T. R. Botcher and C. A. Wight, J. Phys. Chem. 98(21), 5441-5444 (1994). 68. P. E. Gongwer and T. B. Brill, Combust. Flame 115(3), 417-423 (1998). 69. J. D. Cosgrove and A. J. Owen, Combust. Flame 22, 13-18 (1974). 70. J. D. Cosgrove and A. J. Owen, Combust. Flame 22, 19-22 (1974). 71. K. Anderson, J. Homsy, R. Behrens and S. Bulusu, in 11th Int. Detonation Symp., Vol. 1 (1998), pp. 239-245. 72. S. Wolfram, A New Kind of Science, 1st edn. (Wolfram Media, Inc., 2002).


CHAPTER 3 S T U D Y OF ENERGETIC MATERIAL C O M B U S T I O N CHEMISTRY BY PROBING MASS SPECTROMETRY A N D M O D E L I N G OF F L A M E S Oleg P. Korobeinichev Institute of Chemical Kinetics and Combustion Siberian Branch Russian Academy of Sciences 630090 Novosibirsk, Russia

Contents 1. Introduction 2. Experimental Techniques 2.1. Microprobe and Molecular Beam Mass Spectrometric Techniques 2.2. Coupled Mass Spectrometric and Laser Technique 2.3. Mass Spectrometric Technique for Studying the Kinetics and Mechanism of Thermal Decomposition of EMs and their Vapors 3. Validating the Method of Probing Flames with Narrow Combustion Zones 4. Flame Structure of AP and AP-Based Composite Propellants 5. RDX and HMX Flame Structure 6. Flame Structure of ADN and ADN-Based Propellants 7. Conclusions References

75 77 78 79 80 81 83 88 91 97 98

1. I n t r o d u c t i o n Progress in the understanding of energetic material (EM) combustion will arise from a clearer picture of the chemistry and physics t h a t take place in flames. We now recognize t h a t the combustion of E M s is a complex multistage process based on t h e chemical transformations in t h e condensed a n d gas phases. Much more detailed information about the combustion chemistry of E M s is required. It is important to understand the combustion chemistry because this is the type of information a propellant formulator or a chemist 75

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may use to tailor and/or improve the performance of the propellant. 1 The theories of Zel'dovich2 and others on combustion of gun powder and explosives have played an important role in the development of the combustion theory of EMs. But, due to their simplified assumptions about the EM combustion mechanism and kinetics of reactions, they could not obtain satisfactory agreement with experiments on burning rates and their dependence on pressure and initial temperatures. New developments in advanced numerical methods and experimental techniques have enabled progress in the understanding of EM combustion chemistry, kinetics and mechanisms of chemical reactions in flames, and the derived combustion models much better describe the characteristics of burning EMs and the structures of their flames. Studies of EM combustion have mostly investigated physical characteristics and neglected chemistry because of the experimental difficulties of studying chemical reactions in EM combustion waves. These difficulties are due to the high reaction rates (reaction times in condensed phases are of the order 10 _ 1 -10^ 5 s), the high temperatures (up to 3000K in the flame zone), the narrow spatial zones (of the order of 1 0 - 3 mm in the condensed phase and 10 _ 1 -1 mm in the gas phase), the high burning rates, and the short time available for experiment (0.1-10 s). The difficulties are increased by the presence of heterogeneity and multiple ingredients. Although studies of combustion have been intensively conducted for about 60 years, only during the last decade has appreciable progress been achieved. Our knowledge of the combustion chemistry of EMs comes mostly from flame structure studies. 3 These studies allow us to identify species in flames and to measure temperature and species concentration and their spatial distributions. 3 ~ 16 Analysis of the data on EM flame structures provides information on the composition of the condensed phase reaction products that are produced by EM thermal decomposition on the burning surface. These analyses, in turn, enable understanding of reactions in the condensed phase and their mechanisms. On the other hand, the chemical structure of the EM flame also provides information on the mechanisms and kinetics of gas-phase chemical reactions of further transformations of products emerging from the surface. These reactions are responsible for heat release in flames. The principal methods applied to the investigation of chemical and thermal flame structures of EMs are: (1) probing mass-spectrometry (PMS), 4 ^ 9 (2) spectroscopic methods 1,10 ~ 16 for absorption and emission, including planar laser induced fluorescence (PLIF), spontaneous Raman scattering (SRS), coherent anti-Stokes Raman spectroscopy (CARS), and (3) the micro thermocouple technique. 17 Systematic studies of EM flame structures

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using laser spectroscopic methods have been done mainly by Parr and Hanson-Parr 11,13 ' 14,16 and Vanderhoff et al.10'15 Spectroscopic methods are relatively non-intrusive; but there are many species in flames (very often the key species) which cannot be detected spectroscopically (see the chapter by Dagdigian). For example, the spectra of important species may be inaccessible because of wavelength or apparatus sensitivity limits. Until recently there were few studies of EM flame structure. The improvement of experimental techniques, however, along with the development of flame-structure modeling and the rise of interest in EM combustion chemistry, has significantly increased the number of studies and their results have been used to understand EM combustion chemistry, to create chemical kinetics mechanisms of reactions in EM flames, and to develop EM combustion models. This paper describes briefly the PMS method for EM flame structure studies and presents the results of the application of this method to EMs such as AP, RDX, HMX, ADN and some composite solid propellants (SP).

2. Experimental Techniques Probing mass spectrometry (PMS) is one of the most effective and universally used experimental techniques for studying EM flame structures. Heller and Gordon 18 performed some of the first studies using a capillary probe to sample a double-base propellant flame at 10-20 atm. The closest approach of the probe to the burning surface was 1 mm; the surface was held at a constant position using a gold wire or quartz fiber restraint upon the propellant strand, which was pushed from below by a compressed spring. We developed an improved method19™21 allowing the detection in situ of many species in the flame and the determination of their concentrations and their spatial distributions. In this improved method, a burning strand of EM moves with a velocity exceeding the burning rate toward a probe so that the probe continuously samples gaseous species from all the zones including those next to the burning surface. The probe ensures free gas-dynamic expansion of the sample accompanied by a rapid decrease in temperature and pressure and, hence, freezing of the mixture composition, which allows detection of atoms and free radicals. A skimmer placed after the probe cuts out the central part of a supersonic jet: free from possible heterogeneous and catalytic reactions on internal hot walls of the probe. The sample is then transported to the ion source of a time-of-flight (TOF) or quadruple mass spectrometer (again, the beam is not permitted to collide with the apparatus). Mass

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spectra of samples are recorded with simultaneous filming of the probe and the burning surface. We have described the electronic system for stabilization of the EM burning surface using microthermocouples. 20

2.1. Micro-probe and Molecular Beam Spectrometric Techniques

Mass

Two types of apparatus have been developed to study flame structure. The sample is transported to an ion source (1) as a molecular flow using a microprobe (MPT) with an inlet orifice of 10-20 micron, or (2) as a molecular beam (MBT) using a sonic probe with an inlet orifice of 20-200 micron. The microprobe has high spatial resolution and only slightly disturbs the flame, allowing the study of flames with a narrow combustion zone of 0.1mm or less. Radicals, however, may recombine and unstable species, including EM vapors, may decompose and react on the inner hot walls of the probe and deposit on the cold parts of the probe walls. So EM vapors, very important EM gasification products, may not be detected using this setup. Molecular beam mass spectrometric (MBMS) sampling 21 allows detection of radicals and other unstable species but disturbs the flame more strongly and therefore has reduced spatial resolution. We reported 19 the first use of MPT to study the solid propellant (SP) flame structure of ammonium perchlorate (AP) and polymethylmetacrylate. MPT was further applied to the study of EM flame structures with narrow combustion zones using AP and AP-based composite propellants. Figure 1 is a sketch of the MBMS system, 4 ~ 7 which has been used to examine the flame structures of AP, RDX, HMX, ADN, GAP and some composite SP. It includes a molecular beam sampling system, a time-of-flight mass spectrometer (type MSKh-4), a combustion chamber, a scanning system, a data acquisition system and an experiment controller based on CAM AC equipment and a computer. The sampling probe (item 3) is a 25-mm high cone with a 50-degree external angle, a 40-degree internal angle, and a 50-100 micron diameter orifice at the apex (at l a t m ) . The probe produces a molecular beam, which passes to an ion source (item 4). The ignition spiral (12) is automatically removed from the combustion zone after ignition. The EM flame is scanned using a control system and a stepper motor (13) to move the burning strand (14) at a speed of less than 20mm/s. A thermocouple (15) measures temperature profiles. To study the flame structure at high pressure by MBMS, we use a quartz probe with an inner angle of 40 degrees and an orifice of 50 microns at 3 atm, 20 microns at 6 atm and wall thickness near the probe tip of 25 microns. We


Fig. 1.

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MBMS system for studying the name structure of EMs with TOFMS.

visualize the combustion using a video camera (Panasonic NV-M3000EN). CAMAC equipment assisted the measurement of peak intensities of selected masses as a function of time. It is not always possible, however, to predict which peaks will be found in a mass spectrum. To reveal unpredictable peaks in the mass spectrum an oscilloscope (LeCroy 9310AL with a memory of 1 MB) was used. This allowed detection of singular mass spectra within short time intervals of 0.01 s. To stop data acquisition at the time of probe contact with the burning surface, a special device was designed and manufactured: an end switch of the stepper motor moving the sample to the probe was used as a sensor keeping a record of contact. Video recording of the ADN strand burning surface and probe was performed simultaneously with mass spectra recording. The synchronization of the two measurements was achieved by allowing the contacts of the stepper motor end switch to close at the moment of probe contact with the strand-burning surface. The latter was accompanied by light diode luminescence simultaneously with the stoppage of step frequency generator, which starts the oscilloscope. The light diode luminescence was recorded by video camera. 2.2. Coupled Mass Spectrometric

and Laser

Technique

The MPT technique was also developed by Litzinger et al.8,9'22'23 to study laser-supported combustion (LSC) using a triple quadruple mass spectrometer 15 and an ionization energy of 22 eV. Laser-supported

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combustion enables studies at lower pressures in which the chemical reaction zones in the EM flame are spread and the errors in flame concentration profiles measured by the probe are reduced. It is generally believed that the flame zone width should be greater than the probe tip dimensions. But, in LSC, one must ensure that the probe does not shield the burning surface from the laser, reducing the energy to the surface, and that the probe is not heated by the intercepted laser beam. This inadvertent heating may increase the rate of chemical reactions in the extracted sample. Laser irradiation is widely used for the study of EM ignition. A recent paper by Yang et al.24 is devoted to comprehensive analysis and modeling of laser-induced ignition of RDX. Generally, the only measured characteristics of laser-induced ignition are ignition delay and surface temperature of EM as a function of heat flow. Unfortunately there are no experimental data on the gasification products and species concentrations as functions of time. The available data 9 ' 22 have been obtained using MPT and do not contain information about EM vapors in the narrow (0.1mm) zone near the EM surface. This near-surface information is necessary for understanding the mechanism of EM ignition and its transition to combustion on a molecular level, and for development of comprehensive ignition and combustion models. We have described experiments for study of ignition and combustion of EMs supported by CO2 laser irradiation using MBMS. 25 The tip of the probe was 100-150 microns from the sample surface. This distance is close to the value of the sampling shift ZQ (see below). So the probe sampled the products evolving directly from the EM surface during its ignition and its combustion as a function of time. The beam of the laser made a small angle to the surface, excluding possible probe shielding of the EM surface from the laser beam. Positioning was controlled with the help of a video camera. The tip of the probe was heated to the temperature of the burning surface to prevent clogging of the sampling orifice by reaction products.

2.3. Mass Spectrometric Technique for Studying the Kinetics and Mechanism of Thermal Decomposition of EMs and their Vapors Probing mass spectrometry can also be successfully applied to the study of kinetics and mechanism of the thermal decomposition of an EM and its vapors. The thermal decomposition of EM is one of the most important stages of its combustion; hence knowledge of the kinetics and reaction mechanism of EM thermal decomposition under different conditions (including the temperature at the burning surface) is


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necessary for development of EM combustion models. Such information can result from using Rapid-Scan FTIR spectroscopy, SMATCH/FTIR, and T-Jump/FTIR — all methods developed by Brill26 and by the method of differential mass-spectrometric thermal analysis (DMTA) developed in our laboratory. 27 These methods give information about the products of EM decomposition including EM vapors (e.g., the molecules HMX, RDX, etc.) as well as their rates of evolution. We have described the setup for mass spectrometric investigations (e.g., MBMS) of the kinetics of EM thermal decomposition under the non-isothermal conditions approximately similar to those present in the condensed phase in the vicinity of the EM burning surface.27 The EM sample was applied to a metal ribbon located in flow reactor near the tip of the probe and heated by electrical current at 100-1000 K/s. This technique also can be used for obtaining calibration coefficients for EM vapors.

3. Validating the Method of Probing Flames with Narrow Combustion Zones Quantitative results of the mass spectrometric probing technique for EM flame structure depend on the performance of the probe. Detailed studies 2 8 - 3 1 have been carried out to validate the probe method when the ratio of the flame zone width, L\>, to the probe tip outside diameter, d, is close to one. The studies were made for a preheated (T = 533 K) AP flame32 where the burning zone was about 0.1mm wide at 0.6 atm. Distortions caused by the probe can be divided into external and internal ones: the external ones being hydrodynamic and thermal. The probe acts as a sink for matter and heat, which causes distortions of temperature and species concentration profiles.33'34 Errors were determined 28 ' 29 ' 35 by measuring perturbations in the velocity field in one-dimensional gas flows using submicron particles and a pulsed laser. The flow starts deviating from onedimensional type at a distance depending on the sampling factor, which is defined by the equation a^ = AQ/-K(1^VQ. Here Q is the sink flow rate, d0 is the probe orifice diameter, and w0 is the flow velocity. The velocity fields and stream lines near the orifice of a probe have been calculated from Rosen's disk sink model. 33 This model can be used to evaluate measurement errors. Probe-error estimates have also been carried out for a real flame. A preheated AP flame with Lb ~ 0.1mm was used, but we were unable to find reliable data on the AP flame chemical structure. Model experiments were, therefore, performed with a methane-air flat flame with argon additive having a 0.5 mm burning zone width. A

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special quartz probe was used (subsequently referred to as a macroprobe) with an outside tip diameter equal to the flame zone width of 0.5 mm and with a probe orifice of do = 0.012 mm. This probe and flame were similar in such dimensionless parameters as do(ao)05 / L^, L^/d ss 1 and Red w 1 to those used in the case of the AP flame (Re d is the Reynolds number of the flow determined from the probe outside diameter). According to similarity theory, the equality of these numbers for the model flame and probe and the AP flame and real probe allows us to use the results from the former to study the latter. The following methods were applied to study the structure of the model flame: (1) microthermocouple technique (MT) using II-shaped platinum-platinum/rhodium thermocouples (wire diameter of 0.02 mm) for measuring temperature profile; (2) probe mass-spectrometry measuring methane concentration profiles by macroprobe and quartz microprobe with do = 0.06 mm, d = 0.12 mm; (3) Spontaneous Raman Scattering (SRS) spectroscopy for measuring methane and nitrogen concentration profiles. The comparison of the results of measuring methane concentration profiles in the model flame by probing methods and non-intrusive diagnostics showed that the error of the probe technique in finding concentrations at the burning surface was less than 10%. When the tip of the probe diameter was reduced 7 times, the change in concentration was about 15%. Concentration profiles of methane measured with a probe agree within 15% with the undisturbed profiles, if the first profile is shifted toward the burner by a value close to ZQ, the calculated shift of the sampling point with respect to the unperturbed flow. Calculations 35 based on simplified assumptions of the flame and flow perturbations (using Rosen's model 33 ) provided the following values: ZQ « OAdo(ao)0'5 and A « 0.3do(ao) 0 ' 5 , where A is a samplingzone width representing spatial-sampling resolution. At mass-spectrometric study of preheated AP flame structure do was 0.012 mm and «o = 75. After applying appropriate corrections for the sampling point on the concentration profiles (ZQ shift), the error in finding concentrations by the probe method was less than 15% of its maximal value. The sampling zone width was within ±15% of the AP flame zone width. This error is reasonably small for quantitative modeling of AP flame structure data. We note, however, that Smith 36 gives other formulas for the shift. In judging these experiments, one must be aware that the thermal disturbance of a flame by a probe strongly depends on the shape, wall thickness, and composition of the probe. Specification of these probe characteristics is frequently omitted in published work. Estimation of the thermal disturbances should be carried out by comparison of temperature


Chemistry

83

profiles in a flame measured by thermocouples located both close to the tip of a probe and far from it. If the difference in these profiles is small, the thermal disturbances of the flame by the probe is likely to be small. To reduce thermal disturbances, one should use probes made of quartz or alumina, with an angle of opening of a cone less than 30-40 degrees and with thin (about 100 microns) walls, especially near the tip of the probe. Making these probes is difficult. Large wall thickness may be the cause of significant disturbances reported in some work. 8,38 Composition distortions in MBMS sampling has also been considered and discussed by Knuth. 39 Validations of the MBMS method for determination of product composition of SP combustion at high temperatures and pressures (40atm) typical of combustion chambers of rocket motors have been reported in Refs. 40-42. Estimation of internal distortions of sample inside-probe and skimmer were performed by the numerical solution of the full set of unsteady Navier-Stokes equations for axially-symmetric flows of compressible gas. The combustion products of stoichiometric mixtures of ammonium dinitramide (ADN)-polycaprolactone (pPCLN) at 4MPa were chosen as the object of investigation. The gas dynamics and chemical kinetics were simulated to assess the correctness of sampling. We showed that, during the sampling from flames, the relative change in concentrations for most of the stable species does not exceed 3% and, for H 2 and O2, it does not exceed 12%. Results of experiment and calculation are in good agreement.

4. Flame Structure of A P and AP-Based Composite Propellants The homogeneous condensed mono-propellants: AP, RDX and ADN have been examined in detail. They have simple chemical structures, so they provide good models for studying combustion mechanisms. They are also the main components of commonly-used composite solid propellants so knowledge of their combustion mechanisms is essential to developing compositesolid propellant combustion models. An AP flame preheated to 533 K was studied at 0.6 and 1 atm using MPT 3 2 and MBMS. 21 Figure 2 presents the results of some peak intensity profile measurements obtained with MBMS probing of an AP flame preheated to 533 K at 1 atm. 21 These experiments showed detection of mass peaks for m/e equal to 83 and 100 — characteristic of perchloric acid. Thus, these experiments provided the experimental support of the hypothesis that perchloric acid is the main AP gasification product in the combustion wave and plays a key role in the AP combustion mechanism. This result laid the

84

O. P.

a

i 0.4-

r

n

°

Korobeinichev

H20

02

"°—cr5~~° o

P^T5~

1

HCI

NO 0.1

sv-

NH 0

ctior

102 a. 4-1 o

NO, —rlSn

0.2 1.1 o_

o

nfc —ss 4 - j n o_

r—

1.3

Cl2 CIOH N20

£ o r " £ A -i 2

Fig. 2.

)) ^ a-o—o——o—' N2 I i—iH0 0.2 1.1 1.3 Distance from burner surface (mm)

Distance from burner surface (mm)

AP flame structure (points are for experiment and lines are for calculation).

foundation for modern models of the combustion of AP. Chlorine dioxide and fragmentary ions of perchloric acid contribute to mass peak 67. We estimate that, at L = 0 to 0.05 mm, the contribution of perchloric acid to the intensity of mass peak 67 is about 50%. This means that the concentration of chlorine dioxide and perchloric acid are approximately equal near the burning surface. Because of this near-equality, when analyzing MPT data, we assumed that half of the intensity of mass peak 67 came from chlorine dioxide in the flame and the other half from chlorine dioxide formed by heterogeneous catalytic decomposition of perchoric acid on the probe walls. Radicals, like HO2, also recombined on the probe walls. Other species concentrations were determined using the measured calibration coefficients of individual species and mass-peak intensities obtained using MPT to study AP flames at 0.6 atm and 533 K. The ratio between the intensity of the perchloric acid peaks with m/e 83 and those of chlorine dioxide with m/e 67 (the latter being obtained with regard to the fact that the peaks with m/e 83 from perchloric acid contributes to the peaks with m/e 67) is shown in Table 1. This ratio (the intensity of the perchloric acid peaks with m/e 83 is equal to those of chlorine dioxide with m/e 67) was used when correlating the data obtained in setup No. 1, under which conditions chloride dioxide resulting


Chemistry

85

Table 1. Species mass peaks intensities (in relative units) at different L in AP flame (a setup with molecular-beam sampling). L (micron)

0 230 290 310 200

100 65 190 230 130

50 140 280 270 180

150 10 90 160 90

200 0 20 80 30

250 0 0 0 0

from heterogeneous catalytic decomposition of perchloric acid on the probe walls into CIO2 and HO2 contributes to a peak with m/e = 67. Using the results of measuring calibration coefficients by individual species and mass peak intensities of the species obtained in the experiments in setup No. 1 studying AP flame structure at 0.6 atm (533 K), species concentrations were found. Profiles of species concentrations and temperature versus the distance from the burner surface L are presented in Fig. 2. Concentration profiles in an AP flame show the following two-zone structure: in a narrow (~fl.lmm wide) zone, NH 3 , HCIO4 and C10 2 concentrations fall and N 0 2 concentrations rise, and in the next wide (~1.5mm wide) zone N 0 2 concentrations fall while NO and 0 2 concentrations rise. Figure 2 also represents modeling results for the same flame structure (lines) 43 ' 44 performed using a mechanism incorporating 80 reactions. The reduced mechanism is presented below. C10 3 = C10 + 0 2 ,

(1)

NH 3 + CI = NH 2 + HC1,

(11)

C10 2 + CI = 2C10,

(2)

OH + HNO = H 2 0 + NO,

(12)

2C10 = Cl2 + 0 2 ,

(3)

HC10 4 = 0 H + C10 3 ,

(13)

C10 + NO = Cl + N 0 2 ,

(4)

HCIO4 + HNO

CIO + NH 3 = NH 2 + C10H,

(5)

0 H + HC1 = H 2 0 + C1,

(6)

N 0 2 + N 0 2 = 0 2 + 2NO,

(15)

CI + 0 2 + M = C10 2 + M,

(7)

NH 3 + OH = NH 2 + H 2 0 ,

(16)

HNO + 0 2 = N 0 2 + OH,

(8)

HCIO4 + HNO

NH 2 + 0 2 = HNO + OH,

(9)

ClOH + OH = CIO + H 2 0 ,

(10)

= C10 3 + NO + H 2 0 ,

= C10 2 + N 0 2 + H 2 0 .

(14)

(17)

86

O. P.

Korobeinichev

Satisfactory agreement between the calculation and experimental results provides evidence for the suggested mechanism. Subsequent work provides a revised mechanism. 45 The obtained results were used when developing an AP combustion model. 4 6 - 4 9 Lin et al. have investigated unimolecular decomposition of perchloric acid and the related OH + C10 3 reaction 50 as well as C10 x reactions and the reaction of OH with CIO by ab initio molecular orbital and variational transition state theory calculations. It allows us to refine chemical kinetics models of reactions in AP flames. The flame structure of composite propellants based on AP (particle size less than 50 micron) and HTPB was studied at subatmospheric pressures in setup No. 1 with MPT and modeling. 51-53 Eighteen stable species (HC1, H 2 0 , CO, NH 3 , C 0 2 , HCIO, NO, 0 2 , H 2 , N 0 2 , N 2 0 , N 2 , C 4 H 6 , C 2 H 2 , CIO2, Cl 2 , HCN, HCIO4) were detected in the flame zone. No mass peaks 83 and 100 were found but HCIO4 concentration was determined as it was for the AP flame. Profiles of species concentrations and temperature in flames of model composition HTPB/AP (16/84) at 0.08 atm are shown in Fig. 3.

Fig. 3.

A P / H T P B flame structure.

Energetic Material Combustion Chemistry

87

Kinetics model includes 58 reactions and 35 species. Satisfactory agreement between the experimental and calculated d a t a was achieved. T h e reactions of oxidation of ammonia and H T P B destruction products with perchloric acid decomposition products (CIO2, ClOH, CIO, etc.) are the main reactions in the flame of composite propellants based on A P and H T P B . T h e chemical transformations in the A P / H T P B flame is shown in Scheme 1. T h e d a t a analysis of flame structure of composite propellant based on A P and H T P B (especially rich formulations) at low pressure indicates t h a t oxidation of hydrocarbon binder destruction products occurs in the flame

C4H6

+ C 1

-

»-C 4 H 5 (l,3)

/-C 4 H 5 (1,3) + CIO C4H4

C2H2 + C2H3

^ - » - CH 2 CO

CHO + C H 2 0

CO + H 2 NH,

+ C1 NH 2 + HC1

+ o2

HNO + OH +H + OH

+ NO N2H +

HC10 4

+ HNO ^ + HCO

OH

CIO,

NO

cio + o 2 + CO CI

cio2

+ CO

•

cio + co + CO Cl- HN 3 [HN(N0 2 ) 2 ]

AH = 12-14 kcal/mole > NH 3 + HN(N0 2 ) 2

The kinetics and mechanism of the secondary reactions of ADN vapor decomposition at 6 torr have been studied 85 using MBMS and modeling based on kinetic mechanism. 86 The additional experimental evidence of ADN evaporation has been obtained: NH3 concentration increased in the temperature range 430 to 530 K. The authors of paper 86 did not notice this fact because they did not take into account the contribution of the fragmentary ion of ADNV to the intensity of mass peaks 17 and 16. Also if ADN decomposition yielding DA and NH3 was the first stage of the process, the temperature dependence of DA + NH3 vapors would correspond to AiJ su bi = 25-26 kcal/mole but not to AHSU\,\ = 37 ± 3 kcal/mole. The rate constant of ADNV dissociation ADNV + M —»• NH3 + HN(NC>2)2 + M has been determined from experimental data k = 3 x 10 12 exp(—12000/RT), cm 3 mole - 1 s _ 1 . These conclusions are in good agreement with the data of Ref. 87. So the mechanism of ADN evaporation differs from that of other ammonium salts. In the case of ammonium perchlorate and ammonium nitrate, dissociative sublimation takes place, yielding ammonia and the corresponding acid. The obtained mass spectra


Chemistry

93

of ADN vapor allowed us to identify it in the "cool" flame zone at 1 and 3 atm and to measure its concentration. The temperature distribution in the wave of ADN combustion has been measured using thin thermocouples in a wide pressure range which has revealed several burning zones. The composition of ADN combustion products has been determined by the authors of paper 79 at 0.26-0.78 atm. But the purity of ADN in this study 79 was very bad. ADN combustion mechanisms suggested in Refs. 27, 78, 79, 83 are different. Thus, it is suggested in Refs. 79 and 83 that ADN reactions in the condensed phase result in ammonium nitrate. The dissociation of ammonium nitrate yielding NH 3 and H N 0 3 controls the temperature of ADN burning surface and, therefore, the burning rate. Another mechanism has been discussed in Refs. 27 and 82. It is based on the results of studying the chemical structure of the ADN flame at 1-6 atm using an MBMS and the microthermocouple technique. 27 The flame structure was found to involve three zones. At 1-3 atm a luminous flame zone was not observed. The burning rate at 1-6 atm is controlled by reactions in the condensed phase. At 3 atm a "cool" flame zone adjacent to the burning surface was found. The width of this zone is about 1-1.5 mm. The following species have been identified in the "cool" flame zone: HNO3, N0 2 , N 2 0 , NH 3 , NO, N 2 , H 2 0 and ADN vapor. The ratio between the mass peak intensities in the mass spectra of samples taken from the zone close to the ADN burning surface at 3 atm and those of ADN decomposition products 27 ' 85 are in reasonable agreement. The analysis of the mass spectra of the samples taken from the zone near the ADN burning surface at 3 atm has shown that gaseous ADN and dinitraminic acid are the key reactants in the near-surface zone. The product composition near the ADN burning surface has been determined. Gaseous ADN and dinitraminic acid decomposition in the near-surface zone results in a temperature rise of about 150 K. The second high temperature zone was found to be 6-8 mm from the ADN burning surface at 6 atm (Fig. 5). The main reaction in this zone is ammonia oxidation by nitric acid, while the temperature rise is 500 K. The combustion temperature is 1400 K and the combustion products are H 2 0 , NO, N 2 0 , N 2 . The ADN flame structure studied at a pressure of 40 atm 80 revealed the presence of three zones of chemical transformations. The first, a low-temperature ~0.1mm wide zone associated with the rise in temperature from 640 to ^970 K which is similar to the ~ 1 mm wide zone obtained in ADN burning at 3-5 atm. The second is a 1 mm wide zone associated with the rise in temperature from 970 to ^1370 K which is similar to the ~ l l m m wide zone found in the burning of ADN at 5-6 atm. The third zone is at a distance of ~ 1 to

94

O. P.

4

Korobeinichev

8

Distance from burning surface (mm) F i g . 5.

S p e c i e s m o l e f r a c t i o n profiles in A D N flame a t 6 a t m , e x p e r i m e n t a l r e s u l t s .

T a b l e 2.

P r o d u c t c o m p o s i t i o n in A D N

flame.

P (atm)

L (mm)

NH 3

H20

N2

NO

N20

ADN V

HNO3

02

3 6 40

0.2 4.4 1.5

0.08 0.07 0

0.30 0.30 0.42

0.08 0.10 0.18

0.19 0.23 0.21

0.24 0.28 0.14

0.03 0 0

0.08 0.02 0

0 0 0.05

6 mm from the burning surface and is associated with N2O consumption. The temperature in it increases from 1370 to 1770 K. The width of the third zone depends on the ADN burning rate. ADN combustion product compositions at 3 and 6 atm at different distances (L) from the burning surface are shown in Table 2. The temperatures, product compositions measured at the distances L = 0.2, 4.4 and 1.5 mm at 3, 6 and 40 atm and product mass flows were used as boundary conditions in the modeling of the ADN flame using CHEMKIN Code 88 and based on the developed mechanism (98 reactions and 22 species). Part of these reactions and their rate constants have been calculated and suggested by Park et al.m The results of temperature and species concentration profile calculations 80,82,84 are in a good agreement with experimental data. The calculation has also shown the existence of a fourth zone at higher pressures, where nitric oxide decomposes to nitrogen and oxygen with a temperature rise to a value (^2100 K) close to the thermodynamic equilibrium temperature. The results of sensitivity analysis for most of the important reactions in all flame zones are presented in Table 3. ADN combustion chemistry is described in Scheme 2. The obtained data is applicable for developing an ADN combustion model.

Energetic Material Combustion Table 3.

The most important reactions in ADN flame.

Zone number 1

Chemistry

Reaction 73. NH 3 + OH = NH 2 + H 2 0 111. HN3O4 = HNNO2 + NO2 114. HNNO2 + NO2 = HNO + NO + N 0 2 134. HNNO2 + NO = HNNO + N 0 2 135. HNNO2 + NO = HONO + N 2 0 172. ADN V + M = NH 3 + HN3O4 + M

2

36. NO + OH(+M) = HONO(+M) 65. NH 2 + NO = NNH + OH 66. NH 2 + NO = N 2 + H 2 0 73. NH 3 + OH = NH 2 + H 2 0 94. HONO + OH = H 2 0 + NO2 101. N 2 0 + NO = NO2 + N 2 105. NO + NO = N 2 + O2

ADN.

- • ADN,,

-• HN(N02)2 + NH3

HN4NO3 + N 2 0 Products * N H 3 + HNO3 I zone (>3 atm):ADN v

Products

-* HN(N0 2 ) 2 + N H 3

I Products II zone (>6 atm): HNO3+NH3 III zone (>40 atm): N 2 0 IV zone (>40 atm): NO

• Products

• N 2 + V202 •

!/2N2 + V2O2

Scheme 2.

95

96

O. P.

Korobeinichev

The flame structure of the composite pseudo-propellants based on ADN and several binders, such as PCL, HTPB and glycidyl azide polymer (GAP), was studied using MBMS. 81,89 ^ 92 Combustion of stoichiometric compositions based on ADN and PCL has been studied in details. 89,91,92 The combustion of PCL/ADN (10,92/89,08) and HTPB/ADN (3/97) propellants at 1 atm is jet-like in nature. Video-recording demonstrated the presence of several brightly luminous jets of about 0.5-1 mm in diameter at the burning surface, disappearing at one site and appearing at another with a lifetime of 0.2 s. The spatial heterogeneity and non-stationary nature of the propellant combustion process is in agreement with mass spectrometric and temperature measurements. The videotape recording of ADN/PCL combustion showed that a dark zone exists near the burning surface. The width of the dark zone varies from ~ 1 mm (near the bottom of the torch) to 3-4 mm (in the region between torches). Thermocouple measurements revealed the existence of three zones in the flame (1) the narrow dark zone adjacent to the burning surface (width of the zone ~0.2-0.3 mm), where the temperature grew from ~600 to ~1150 K, (2) the dark zone (width of the zone is ~0.5 to ~3mm) where the temperature slightly increased from 1150 to 1450 K, (3) the luminous zone (torch), where the temperature increased to 2600 K at the distance of 4-8 mm. Compositions of the combustion products in the luminous and dark flame zones of propellant ADN/PCL (molecular weight PCL 1250) are presented in Table 4. The temperature of the combustion products in the luminous zone, which is equal to 2600 K, is slightly less than the calculated equilibrium temperature (2695 K), i.e. 100% completeness of combustion is not achieved. The presence of NO in combustion products confirms this conclusion. The element balance in the luminous

Table 4. Concentrations (in mole fractions) of species and temperature in flame of propellant A D N / P C L at 1 atm and of ADN at 6 atm.

Luminous zone (exp) Thermodynamic calc. Dark zone (exp)

T (K)

H20

N2

~2600

0.39

2695 0.40 ~1120

0.32

N20

NO

NH 3

0.32

0

0.10

0

0.34

0

0.01

0.11

0.20

0.20

HNO3

H2

CO

C02

02

0

0.03 0.02

0.12

0.02

0

0

0.03 0.05

0.09

0.03

0.04

0.01

0.01 0.02

0.08

0.01


Chemistry

97

zone was in satisfactory agreement (±5%) with that in the propellant. The calculated deficiency of carbon in the combustion products determined in the dark zone is equal to ~50% of the initial amount. This fact indicates that identification of carbon-containing products in the dark zone was incomplete. Besides, peaks of the following unidentified masses in the mass spectrum of species near the burning surface of the propellant have been obtained: 55, 57, 60, 67, 69, 70, 71, 73, 79, 81, 95, 108, 115. It was assumed that masses from 55 to 115 are responsible for the decomposition of PCL. For propellant HTPB/ADN (3/97) at 6atm, video-recording near the burning surface revealed a dark zone of ~0.3mm, which was in agreement with the data obtained when studying the flame structure of ADN-based sandwiches.90 The dark zone width increases up to 1.5 mm as pressure is reduced to 1 atm. Thermocouple investigations have shown temperature fluctuations of about ±400 K at 1 atm in the flame zone within 1.5-4 mm from the burning surface. Along with the temperature fluctuations, variations in the intensities of mass peaks 17 (NH3), 28 (CO, N2), 30 (NO), 46 (HNO3, N 0 2 ) , 44 (C0 2 , N 2 0) take place. The values for mass peak relative intensities of combustion products near the burning surface of ADN/HTPB 97/3 propellant and pure ADN at 1 atm are close. Analyzing the data on mass peaks intensities in the mass spectra of samples near a burning surface of ADN and ADN/HTPB at 1 atm, one can suggest that pure ADN combustion products are mainly found in the dark zone of propellant combustion, and that luminous jets are formed in the gas phase when ADN decomposition products are mixed with HTPB decomposition products. One of the explanations for the presence of luminous jets with a mean size of ~0.5-l mm at the burning surface may be the agglomeration of small ADN and (or) binder particles into larger ones at the burning surface. The combustion product composition of composite propellant ADN/HTPB 97/3 at 1 atm approaches the product composition of pure ADN combustion at 6 atm, in the content of nitrogen-containing components. So ADNHTPB interaction in flame provides an increase in final temperature and ADN combustion completeness.

7. Conclusions By the example of the study of the flame structure of AP, RDX, HMX, ADN and some propellants, the probing mass-spectrometry procedure has been shown to be an indispensable method providing important information on

98

O. P. Korobeinichev

E M chemical combustion mechanisms. Although it is limited t o some extent by pressure, flame zone width and other considerations, the results obtained with its aid have successfully been used to understand the chemical reaction mechanisms of E M combustion and to develop combustion models. Further application of this method, as well as other spectroscopic and thermocouple methods, will allow a refined and widened understanding of E M combustion mechanisms.

References 1. T. Edwards, Solid Propellant Flame Spectroscopy, Air Force Astronautics Laboratory, AFAL-TR-88-076, Edwards AFB, CA (1988). 2. Y. B. Zel'dovich, J. Exp. Theoret. Phys. 12, 498 (1942), in Russian. 3. R. M. Fristrom, Flame Structure and Processes (Oxford University Press, New York, 1995). 4. O. P. Korobeinichev, Combust. Explos. Shock Waves 23, 565 (1988). 5. O. P. Korobeinichev, Pure Appl. Chem. 65, 269 (1993). 6. O. P. Korobeinichev, L. V. Kuibida, A. A. Paletsky and A. A. Chernov, Combust. Sci. Technol. 113-114, 557 (1996). 7. 0 . P. Korobeinichev, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 335. 8. T. A. Litzinger, Y. J. Lee and C. J. Tang, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 355. 9. T. A. Litzinger, Y. J. Lee and C. J. Tang, in Proc. Workshop on the Application of Free-Jet, Molecular Beam, Mass Spectrometric Sampling, National Technical Information Service (NTIS), US, Department of Commerce, Springfield, VA, 1994, p. 128. 10. J. A. Vanderhoff, M. W. Teague and A. J. Kotlar, Absorption Spectroscopy Through the Dark Zone of Solid Propellant Flame, Ballistic Research Lab. Rept. BRL-TR-3334 (1992). 11. T. P. Parr and D. M. Hanson-Parr, in Non-Intrusive Combustion Diagnostics, eds. K. K. Kuo and T. P. Parr (Begell House Publishing, Inc., New York, 1994), p. 517. 12. J. H. Stufflebeam and A. C. Eckbreth, Combust. Sci. Technol. 66, 163 (1989). 13. T. P. Parr and D. M. Hanson-Parr, in 26th Symp. (Int.) Combustion (The Combustion Institute, Pittsburgh, PA, 1996), p. 1981. 14. T. P. Parr and D. M. Hanson-Parr, in Decomposition, Combustion and Detonation of Energetic Materials, Proc. Mat. Res. Soc, Vol. 418, eds. T. B. Brill, T. P. Russell, W. C. Tao and R. B. Wardle (1996), p. 207. 15. S. H. Modiano and J. A. Vanderhoff, in 26th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburgh, PA, 1996), p. 2017.


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16. T. Parr and D. Hanson-Parr, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 381. 17. A. A. Zenin, Fiz. Goreniya Vzryza 2, 67 (1966), in Russian. 18. C. A. Heller and A. S. Gordon, J. Phys. Chern. 59, 773 (1955). 19. O. P. Korobeinichev and A. G. Tereshchenko, Doklady Akademii Nauk USSR 231, 1159 (1976), in Russian. 20. O. P. Korobeinichev, I. N. Skovorodin, E. L. Emel'anov, K. P. Kassheev, S. V. Polozov, A. G. Tereschenko, L. V. Kuibida and V. V. Ivanov, Byulleten' Izobreteney i otkrytiy 30 (1980), in Russian. 21. O. P. Korobeinichev and L. V. Kuibida, in Flames, Lasers and Reactive Systems, Progress in Astronautics and Aeronautics, Vol. 88, eds. J. R. Bowen, N. Manson, A. K. Oppenheim and R. I. Soloukuin (AIAA, New York, 1982), p. 197. 22. B. L. Fetherolf and T. A. Litzinger, in 29th JANNAF Combustion Meeting, Vol. 2, CPIA Publication 593, (1992), p. 329. 23. Y. J. Lee, C. J. Tang and T. A. Litzinger, Combust. Flame 117, 600 (1999). 24. Y.-C. Liau, E. S. Kim and V. Yang, Combust. Flame 126, 1680 (2001). 25. A. G. Tereshchenko, O. P. Korobeinichev, A. A. Paletsky and L. T. DeLuca, in Rocket Propulsion: Present and Future, ed. L. T. DeLuca (Grafiche GSS, Bergamo, Italy, 2003), paper 24. 26. T. B. Brill, Prog. Energy Combust. Sci. 18, 91 (1992). 27. O. P. Korobeinichev, L. V. Kuibida, A. A. Paletsky and A. G. Shmakov, J. Propul. Power 14, 991 (1998). 28. O. P. Korobeinichev, L. V. Kuibida, V. N. Orlov, A. G. Tereshchenko, K. P. Kutsenogii, R. V. Mavliev, N. E. Ermolin, V. M. Fomin and I. D. Emel'yanov, in Mass-Spektrometriya i Khimia Kinetika, ed. V. Tal'rose (Nauka, Moscow, 1985), p. 73, in Russian. 29. O. P. Korobeinichev, A. G. Tereshchenko, I. D. Emel'yanov, L. V. Kuibida, V. N. Orlov, R. V. Mavliev, K. P. Kutsenogii, A. L. Rudnitskii, S. Yu. Fedorov, N. E. Ermolin and V. M. Fomin, Probe Mass-Spectrometry for Condensed System Flames Having Narrow Combustion Zones (Institute of Chemical Kinetics and Combustion, Novosibirsk, 1985), preprint No. 14, in Russian. 30. O. P. Korobeinichev, A. G. Tereshchenko, I. D. Emel'yanov, A. L. Rudnitskii, S. Yu. Fedorov, L. V. Kuibida, V. V. Lotov and V. N. Orlov, Combust. Explos. Shock Waves 21, 524 (1985). 31. I. D. Emel'yanov, O. P. Korobeinichev, A. G. Tereshchenko and L. V. Kuibida, Combust. Explos. Shock Waves 22, 168 (1986). 32. N. E. Ermolin, O. P. Korobeinichev, A. G. Tereshchenko and V. M. Fomin, Combust. Explos. Shock Waves 18, 36 (1982). 33. P. Rosen, Potential Flow of Fluid into a Sampling Probe, Applied Physics Laboratory, Johns Hopkins University, Rept. CF-2248 (1954). 34. V. V. Dubinin, B. Ya. Kolesnikov and G. I. Ksandopulo, Fizika Goreniya i Vzryva 13, 920 (1977). 35. K. P. Kutsenogii, O. P. .Korobeinichev, R. V. Mavliev and A. G. Tereshchenko, Dokl. Akad. Nauk SSSR 282, 1425 (1985), in Russian.

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36. O. Smith, in Flame Structure and Processes, ed. R. M. Fristrom (Oxford University Press, New York, 1995). 37. A. T. Hartlieb, B. Atakan and K. Kohse-Hoininghaus, Combust. Flame 121, 610 (2000). 38. T. A. Lintzinger, B. L. Fetherolf, Y. J. Lee and C-J. Tang, J. Propul. Power 11, 698 (1995). 39. E. L. Knuth, Combust. Flame 103, 171 (1995). 40. O. P. Korobeinichev, A. G. Tereshenko, P. A. Skovorodko, A. A. Paletsky and E. N. Volkov, in Proc. 18th ICDERS (2001), paper 82-1. 41. A. G. Tereshenko, O. P. Korobeinichev, P. A. Skovorodko, A. A. Paletsky and E. N. Volkov, Fiz. Goreniya Vzryza 38, 91 (2002), in Russian. 42. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereshenko and E. N. Volkov, J. Propul. Power 19, 203 (2002). 43. N. E. Ermolin, O. P. Korobeinichev, A. G. Tereshchenko and V. M. Fomin, Combust. Explos. Shock Waves 18, 180 (1982). 44. N. E. Ermolin, O. P. Korobeinichev, A. G. Tereshchenko and V. M. Fomin, Sovetski J. Khimicheskaya Phizika 1, 2872 (1984), in Russian. 45. N. E. Ermolin, Combust. Explos. Shock Waves 31, 58 (1995). 46. M. Tanaka and M. W. Beckstead, AIAA paper (1996) 96-2888. 47. M. W. Beckstead, J. E. Davidson and Q. Jing, in Challenges in Propellants and Combustion/100 Years after Nobel, ed. K. K. Kuo (Begell House Inc., New York-Wallingford, 1997). 48. H. K. Narahari, H. S. Mukunda and V. K. Jain, in 20th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburgh, PA, 1984), p. 2073. 49. N. Ilincic, M. A. Tanoff, M. D. Smooke, R. A. Yetter, T. P. Parr and D. M. Hanson-Parr, in 34th JANNAF Combustion Meeting, Vol. II, CPIA Publication 662 (1997), p. 23. 50. R. S. Zhu and M. C. Lin, Phys. Chem. Comm. 25, 1 (2001). 51. O. P. Korobeinichev, N. E. Ermolin, A. A. Chernov and I. D. Emel'yanov, Fiz. Goreniya Vzryza 28, 53 (1992). 52. O. P. Korobeinichev, N. E. Ermolin, A. A. Chernov, I. D. Emel'yanov and T. V. Trofimycheva, Fiz. Goreniya Vzryza 26, 46 (1990). 53. O. P. Korobeinichev, L. V. Kuibida, A. A. Paletsky, A. A. Chernov and N. E. Ermolin, Prep. Pap. Am. Chem. Soc., Div. Fuel Chem. 36, 1582 (1991). 54. M. B. Jeppson, M. W. Beckstead and Q. Jing, AIAA paper (1998) 98-0447. 55. O. P. Korobeinichev, A. G. Tereschenko, V. M. Shvartsberg, G. A. Makhov, A. A. Chernov and A. E. Zabolotnyi, in Flame Structure, Vol. 1, ed. O. P. Korobeinichev (Nauka, Sibirskoe otdelenie, Novosibirsk, USSR, 1991), p. 262. 56. O. P. Korobeinichev, A. G. Tereschenko, V. M. Shvartsberg, G. A. Makhov, A. A. Chernov, A. E. Zabolotnyi and I. D. Emel'yanov, Combust. Explos. Shock Waves 26, 173 (1990). 57. A. A. Chernov, V. M. Shvartsberg, N. E. Ermolin, O. P. Korobeinichev and V. M. Fomin, Prep. Pap. Am. Chem. Soc, Div. Fuel Chem. 39, 188 (1994). 58. N. E. Ermolin, O. P. Korobeinichev, L. V. Kuibida and V. M. Fomin, Combust. Explos. Shock Waves 24, 400 (1988).


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59. M. Ben-Reuven and L. H. Caveny, AIAA J. 19, 1276 (1981). 60. C. F. Melius, in 25th JANNAF Combustion Meeting, Vol. II, CPIA Publication 498 (1988), p. 155. 61. C. F. Melius, in Chemistry and Physics of Molecular Processes in Energetic Materials, ed. S. Bulusu (Boston, Kluver, 1990), p. 51. 62. N. E. Ermolin and V. E. Zarko, Fiz. Goreniya Vzryza 37, 3 (2001). 63. Y.-C. Lian and V. Yang, J. Propul. Power 11, 729 (1995). 64. R. A. Yetter, F. L. Dryer, M. T. Allen and J. L. Gatto, J. Propul. Power 11, 683 (1995). 65. J. J. Cor and J. J. Branch, J. Propul. Power 11, 704 (1995). 66. K. Prasad, R. A. Yetter and M. D. Smooke, AIAA paper (1996) 96-0880. 67. B. E. Homan, M. S. Miller and J. A Vanderhoff, Combust. Flame 120, 301 (2000). 68. T. Niioka, T. Mitani, H. Miyajima, N. Saito, T. Sohue, K. Ninomiyya and L. Aoki, The Fundamental Study of HMX Composite Propellant and its Practical Application, National Aerospace Laboratory Report, TR-875 (1985). 69. A. Zenin, J. Propul. Power 11, 752 (1995). 70. O. P. Korobeinichev, L. V. Kuibida and V. Jh. Madirbaev, Combust. Explos. Shock Waves 20, 282 (1984). 71. A. Bizot and M. W. Beckstead, in Flame Structure, Vol. 1, ed. O. P. Korobeinichev (Nauka, Novosibirsk, 1991), p. 230. 72. D. Hanson-Parr and T. Parr, in 25th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburg, PA, 1994), p. 1635. 73. C. J. Tang, Y. J. Lee, G. Kudva and T. A. Litzinger, Combust. Flame 117, 170 (1999). 74. T. P. Parr and D. M. Hanson-Parr, in 35th JANNAF Combustion Meeting, CPIA Publication 685 (1988), p. 87. 75. J. E. Davidson and M. W. Beckstead, in 26th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburg, PA, 1996), p. 1989. 76. Z. Pak, AIAA paper (1993) 93-1755. 77. B. L. Fetherolf and T. A. Litzinger, Combust. Flame 114, 515 (1998). 78. A. A. Zenin, V. M. Puchkov and S. V. Finjakov, AIAA paper (1998) 99-0595. 79. V. A. Strunin, A. P. D'Yakov and G. B. Manelis, Combust. Flame 117, 429 (1999). 80. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereschenko and T. A. Bolshova, in Combustion of Energetic Materials, ed. K. K. Kuo (Begell House Inc., New York, Wallingford, 2001), p. 486. 81. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereschenko, E. N. Volkov, J. M. Lyon, J. G. Carver and R. L. Stanley, in 32nd Int. Ann. Conf. ICT, Karlsruhe, Germany, 3-6 July, 2001, paper 123-1. 82. O. P. Korobeinichev, T. A. Bolshova and A. A. Paletsky, Combust. Flame 126,1516(2001). 83. A. E. Fogelzang, V. P. Sinditski, V. Y. Egorshev, A. I. Levshenkov, V. V. Serushkin and V. I. Kolesov, in 28th Int. Ann. Conf. ICT, Karlsruhe, Germany, 1997, paper 99-1.

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84. O. P. Korobeinichev, L. V. Kuibida, A. A. Paletsky and A. G. Shmakov, in Proc. 21st Int. Symp. on Space Technology and Sciences, Vol. 1 (Society for Aeronautical and Space Sciences, Tokyo, 1998), p. 87. 85. A. G. Shmakov, O. P. Korobeinichev and T. A. Bolshova, Combust. Explos. Shock Waves 38, 284 (2002). 86. J. Park, D. Chakraborty and M. C. Lin, in 27th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburgh, PA, 1998), p. 2351. 87. A. M. Mebel, M. C. Lin, K. Morokuma and C. F. Melius, J. Phys. Chem. 99, 6842 (1995). 88. R. J. Kee, J. F. Grcar, M. D. Smooke and J. A. Miller, Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames, Sandia Rept. SAND85-8240, Livermore, CA, 1989. 89. O. P. Korobeinichev and A. A. Paletsky, Combust. Flame 126, 151 (2001). 90. L. V. Kuibida, O. P. Korobeinichev, A. G. Shmakov, E. N. Volkov and A. A. Paletsky, Combust. Flame 126, 1655 (2001). 91. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereschenko and E. N. Volkov, J. Propul. Power 19, 203 (2003). 92. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereschenko and E. N. Volkov, in Proc. Combustion Institute, Vol. 29 (2002), p. 2955. 93. A. A. Zenin, Fiz. Goreniya Vzryza 2, 67 (1966), in Russian.

CHAPTER 4 OPTICAL S P E C T R O S C O P I C M E A S U R E M E N T S OF ENERGETIC MATERIAL FLAME STRUCTURE Tim Parr* and Donna Hanson-Parr Naval Air Warfare Center, Weapons Division Code 4T4320D China Lake, CA 93555-6106, USA * Timothy. ParrQnavy. mil 'Donna. Hanson-ParrQnavy. mil

Contents 1. Propellant Combustion Environment 1.1. Global Data 1.1.1. Burning Rates 1.1.2. Ignition Data 1.1.3. Radiative Response Function 1.2. Nature of Combustion Environment 1.2.1. Effect of Pressure on Flame Structure 1.2.2. Two-Stage Flames 2. Optical Spectroscopic Techniques Applied 2.1. Absorption and Emission Spectroscopy 2.2. Laser-Induced Fluorescence 2.3. Raman 2.4. CARS and DFWM 2.5. Uncertainties in Concentration and Temperature Measurements 3. Neat Nitramines 3.1. Deflagration 3.1.1. Laser-Supported Deflagration 3.1.2. Self-Deflagration 3.2. Ignition 4. Homogeneous Nitramine Propellants 5. Ammonium Perchlorate (AP) 5.1. One-Dimensional Counter Flow AP/Fuel Diffusion Flames 5.2. Two-Dimensional AP/Fuel Diffusion Flames 6. Summary References 103

104 104 104 105 106 106 107 107 108 108 110 110 111 112 113 113 114 117 118 119 120 120 122 123 126

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Hanson-Parr

1. Propellant Combustion Environment Some important solid propellant performance properties, such as specific impulse and flame temperature, can be easily calculated thermodynamically. However, most properties critical to the design of rocket motors, such as burning rate, pressure exponent, temperature sensitivity, combustion instability response, and hazard response, are kinetically controlled and cannot be calculated using thermochemical codes. Some progress has been made recently in developing solid propellant combustion models based on detailed chemical kinetics. These codes offer hope of being able to a priori calculate the performance of a solid propellant even before it is formulated and mixed. With the addition of quantum mechanical calculations, these predictions of propellant performance could be undertaken even before new candidate energetic materials had been synthesized. If such tools were available, it would greatly reduce the cost of developing new solid propellants, as it would reduce the costly trial and error formulation, mixing, casting, and performance evaluation work. These tools must be validated, and since they provide detailed information on species concentrations, one good way to validate the models is to make spatially-resolved measurements of species concentrations in solid propellant flames. Optical diagnostics have proven to be useful in this task, especially when combined with complementary techniques such as mass spectrometry (see the chapter by Korobeinichev). 1.1. Global

Data

1.1.1. Burning Rates In the recent past, most models of propellant combustion were validated by comparison with measured burning (regression) rate as a function of pressure (P), and sometimes as a function of both P and initial temperature (To). Much regression data is available in the literature. For example, burning rate (r) data has been measured from To = — 100°C to +150°C, and P = latm-8000 PSIA for HMX, 1 and from T0 = -50°C to +150°C, P = 100-1500 PSIA for RDX. 1 The burning rates were found to have an essentially linear pressure dependence, r = A'Pn, over most of the pressure range. It is easy to fit a two-parameter result, even with simple global kinetic models like BDP (Beckstead-Derr-Price). 2 However, good quality fits to burning rate data can be obtained with wildly differing "global" kinetic parameters and, thus, these models do not uncover the real controlling

Optical Spectroscopic Measurements

of Energetic Material Flame Structure

105

kinetic mechanism. These simple models, therefore, cannot be used to predict ignition, combustion instability (CI), or be directly used for other families of propellants for which they were not directly parameterized via fitting to measured data. From the burning rate data sets, the temperature sensitivity (ap) can be calculated: dp = (d In (r)/ 3000 c m - 1 vibrational energy begin to drop because of an excited-state predissociation. 70 The NCO radical has been detected in flames by laser fluorescence excitation. CoUisional quenching rate constants, required for correction of collisional effects at finite temperatures, have been measured both within flames71 and at room temperature. 72 A number of kinetic studies of the rates of elementary reactions of NCO has been carried out. Laser fluorescence detection of NCO has been employed in the measurement of thermal reaction rate constants. Several exemplary studies are mentioned here. Brownsword et al.73 have employed laser fluorescence excitation in the A2T,+-X2H band system to study the reaction of NCO with N atoms at 298 K. Hershberger and co-workers74 have utilized infrared transient absorption spectroscopy of the CO and CO2 products to study the product branching to N 2 0 + CO versus CO2 + N2 in the NCO + NO reaction. Gao and Macdonald 75 determined the

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room-temperature rate constant for the O + NCO reaction through timeresolved infrared absorption spectroscopy.

4.2.2. Nitrogen Dioxide (N0 2 ) This stable free radical is a primary end product in the decomposition of energetic materials containing nitro groups. As a stable product, it can be detected by a variety of methods, including conventional electron-impact mass spectrometry and infrared absorption, as described in the chapters by Korobeinichev and Brill, respectively. The electronic absorption spectrum of NO2 in the visible and near ultraviolet is extremely complex and covers a broad spectral region.76 The spectral complexity arises because of the interaction between the X2 A\ and A2B2 electronic states. There has been much progress, reviewed recently,77 in understanding the spectrum and the coupling between the two electronic states through analysis of the spectra of jet-cooled molecules. However, most of the high-resolution electronic absorption spectrum of NO2 remains unassigned. An additional factor limiting the use of laser fluorescence excitation for the detection of NO2 is the long excited-state radiative lifetimes (ranging from 40 to 200 fis).78 Nevertheless, electronic absorption spectroscopy has been used to detect NO2 above decomposing RDX. 79 CRDS has also shown utility for the sensitive detection of NO2, as illustrated by its detection in the exhaust of a diesel engine.80 An alternative approach, using infrared vibrational transitions, is an excellent detection method for NO2.

4.2.3. Amidogen (NH2) The NH2 radical is an important intermediate in the oxidation of fuel nitrogen and in the decomposition of energetic materials. The reactions of NH2 with NO and NO2 are key steps in the combustion of ADN, as well as in the thermal de-NO^ process. These reactions, which generate major chain reaction propagators H atoms and OH, are further discussed below. The ground X2B\ electronic state of NH2 possesses a bent geometry. This radical has an electronic transition, to the A2 A\ state, toward the red end of the visible spectral region. 81 The X2B\ and A2Ax electronic states become degenerate at linear geometries and form a Renner-Teller pair. There are perturbations between these two states which cause some irregularities in the electronic spectrum. The radiative lifetimes of N H 2 ( J 4 2 > 1 I ) excited levels range from 4 to 10 /is, depending on the vibrational level. 82 ' 83

Transient

Gas-Phase

Intermediates

145

Rate constants for electronic quenching by various molecules have also been determined. 82 The A-X transition can be used to detect NH2 radicals sensitively by laser fluorescence excitation 84 and has been employed for the detection of the radical in flames.85 One drawback to the use of laser fluorescence excitation detection of NH2 is its relatively long radiative lifetime, which makes this detection scheme especially susceptible to collisional electronic quenching. Laser fluorescence detection has been employed to determine rate constants for reactions of NH2. 86 Amidogen may be conveniently prepared by 193 nm photolysis of ammonia, although account must be taken of NH formed in the secondary photolysis of NH2. As discussed above, knowledge about the reactions of NH2 is important in the detailed kinetic modeling of the decomposition of energetic materials. Several product channels have been considered for the reaction with NO: NH 2 + N O ^ N 2 + H 2 0

(6a)

-> HN 2 + OH

(6b)

- • H + N 2 + OH.

(6c)

To explain experimental observations in the thermal de-NO^ process, processes (6a) and (6b) have been proposed as the major pathways for the reaction. 56 The reaction rate constant and product branching ratios have been measured by several groups as a function of temperature. 87 ~ 91 In the most recent study, frequency modulation absorption was employed to detect NH 2 . 91

4.2.4. Nitrosyl Hydride (HNO) The HNO molecule plays an important role in the mechanism of formation of nitrogen oxide pollutants in combustion, 56 as well in the decomposition of energetic materials. HNO is a closed-shell molecule in its ground electronic state. It is nonetheless included among the transient intermediates discussed in this chapter because of the weak H-NO bond and consequent ease of dissociation. The HNO molecule has an electronic transition, AlA"-XlA'®2 toward the red end of the visible spectral region, and this transition has been used to detect this species by absorption, emission, and laser fluorescence excitation. The sensitivity of laser fluorescence excitation is somewhat low because of the relatively small oscillator strength of the transition, leading to a long excited-state radiative lifetime (ca. 30//s). 93

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Infrared chemiluminescence from vibrationally-excited HNO has also been observed from the NO + HCO reaction. 94 Absorption techniques have found utility for spectroscopic studies of HNO. Pearson et al.95 have employed CRDS of the A-X electronic transition for a comprehensive study of many bound and quasi-bound vibrational levels of the A1 A" state. Through linewidth measurements, they were able to deduce the mechanism of predissociation of the quasi-bound levels. Cheskis and co-workers96 have employed intracavity laser absorption spectroscopy to probe the concentration profiles of HNO in low-pressure hydrocarbon flames doped with nitrogen oxides. A significant complicating factor in laboratory studies, e.g. measurements of reaction rate constants, of this species arises from the relatively weak H-NO bond. Schemes which have been employed for the generation of this molecule include 3-body recombination of H atoms with NO, 95 hydrogen transfer from a molecule with a more weakly bound H atom e.g. HCO + NO -> HNO + CO, 94 and the photolysis of ammonia in the presence of oxygen.97 Thus, the HNO molecule is produced in the presence of other, possibly interfering species, most commonly NO. Measurements of room-temperature rate constants for three reactions involving HNO, namely HNO + O, HNO + 0 2 and HNO + HNO, have been reported. 97 ' 98 Intracavity laser absorption 97 and photoionization mass spectrometry 98 ' 99 were employed to follow the HNO concentration. Rate constants for several other reactions of HNO of relevance to the combustion of nitramines have been estimated through theoretical methods by Chakraborty and Lin.3

4.2.5. Formyl (HCO) The HCO radical is important in the combustion of hydrocarbons and also plays a significant role in the decomposition of energetic materials. Two electronic transitions have been employed in laser fluorescence studies of this radical, namely the A2A"-X2A' transition in the red portion of the visible spectrum and the B2A'-X2 A' transition in the UV. The former transition is not particularly suitable for sensitive laser fluorescence detection of HCO since the excited state is strongly predissociated, 100 and only K' = 0 bender levels have an appreciable fluorescence quantum yield. This transition has been employed with both intracavity laser absorption spectroscopy and CRDS to detect HCO produced in the photolysis of aldehydes. 24 ' 101 The B2A'-X2A' transition 102,103 is well suited for laser fluorescence detection of HCO. Excited-state decay lifetimes have been measured for a

Transient

Gas-Phase

Intermediates

147

number of rovibrational levels, 104,105 and the excited state is subject to a Coriolis-induced predissociation, whose rate depends on the vibrational and rotational quantum numbers. Bimolecular quenching rate constants for a number of collisional partners are available for the ground vibrational level of the B2A' state. 106 REMPI has also found utility for the detection of the HCO radical. Cool and co-workers have characterized the REMPI spectrum for the transitions to both the B2A' state and the 3p 2 II Rydberg state. 107 They also showed that REMPI could be used to detect HCO in a methane/oxygen flame.20 The transition was detected by monitoring the laser-induced electron current. No mass selection was employed for detection within the flame. Rather, the HCO radical was identified from the characteristic transition wavelengths for the 2-photon electronic transition. There have been a number of reported measurements of rate constants for reactions of the HCO radical, focusing on the important HCO + O2 reaction. In most of these studies, the HCO concentration was monitored by a spectroscopic method, including diode laser infrared absorption 108 and pulsed 109 or cw 110 UV laser-induced fluorescence. Photoionization mass spectrometry has also been employed in the measurement of HCO reaction rate constants (see, for example, Ref. 111). Photolysis of acetaldehyde at 308 nm is a convenient means to generate HCO.

4.2.6. Nitrogen Hydride (HN2) This species has been proposed as an important intermediate (see Eq. 6(b)) in the thermal de-NO^ process 56 and has also been suggested as an intermediate in the decomposition of nitramines. However, this species is weakly bound and is predicted to have a very short lifetime due to unimolecular dissociation. The lifetimes for the ground vibrational levels of HN2 and DN 2 have been computed to equal 10~ 8 and 10~ 5 s, respectively.112

4.2.7. Nitroamidogen (HNNO) This species can be formed in the 3-body recombination of NH and NO and is an intermediate in the bimolecular reaction channels to form H + N 2 0 and N 2 + OH products. The 2A" state can be accessed from the reagents along a barrierless potential energy surface, while there are barriers to the formation of the more strongly bound trans and cis 2A' states. 113 Both these isomers of HNNO, isolated in a cryogenic matrix, have been observed by vibrational

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spectroscopy.114 The cis form was prepared from the trans form by photoisomerization. Detection in the gas phase has not been reported. 4.2.8. Nitrous Acid (HONO) On the basis of theoretical study of decomposition pathways of HMX and RDX, 2 ' 6 ' 115 nitrous acid is thought to be possibly formed in the initial step of the decomposition in the condensed phase or in subsequent steps. It is also one of the possible end products of the decomposition of energetic materials and has been observed by IR absorption above the surface of decomposing energetic materials. 116 Like HNO, HONO is a closed-shell molecule in its ground electronic state but is nonetheless included in this chapter because of the weak HO-NO bond and ease of dissociation. The HONO molecule has an electronic transition, A1A"-X1A', in the near UV spectral region. This transition does show resolved vibrational bands, but the excited state is predissociative, leading to OH + NO fragments. While an indirect scheme for HONO detection through this electronic transition, which involves monitoring the OH fragment by laser fluorescence excitation, has been employed to observe the formation of HONO in the UV photodissociation of 2-nitropropane, 117 the most promising method using the electronic transition is through an absorption technique. CRDS near 355 nm has recently been employed for the sensitive detection of HONO. 118 Because of difficulties in generating HONO cleanly, i.e. in the absence of NOz, there is a dearth of experimental measurements of rate constants for reactions of this species. A method to quantify HONO concentrations, through the slow HONO + HCl —> C1N0 + H 2 0 reaction, has recently been described. 119 Chakraborty and Lin 3 have estimated rate constants for a number of bimolecular reactions of HONO of relevance in the decomposition of energetic materials. 4.2.9. Methylene Amidogen (H2CN) The methylene amidogen radical is a pivotal radical in the dark zone and can be formed by the dissociation of methylene nitramine (H2CNNO2), the monomer of RDX and HMX. Marston and Stief120 reviewed the spectroscopic and kinetic data available on H2CN as of 1989. Electronimpact ionization through a sampling port in a flow tube has been employed by Stief and co-workers for the measurement of rate constants of some elementary bimolecular reactions involving H2CN. This method suffered from

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interference from vibrationally-excited N2, which has the same mass-tocharge ratio (m/e = 28) as H2CN, and the use of deuterated reagent to generate D2CN alleviated this background problem. Sensitive spectroscopic detection of H2CN for observation of this species either in decomposition processes or in kinetic studies has proven to be problematic. The vibrational frequencies have been determined for matrixisolated H 2 CN by Jacox. 121 Flash photolysis studies utilizing formaldoxime and formaldazine as precursors identified electronic absorptions in the region of 280 nm. 122 ' 123 However, the excited vibronic states of these transitions are predissociative, 124 ' 125 precluding the use of fluorescence excitation as a diagnostic for H2CN. In a coupled-cluster study by Brinkmann et al.,12e the ground X2B2 and low-lying A2Bi, B2A', and C2A1 electronic states were computationally characterized. Davis and co-workers125 observed the previously reported 123 transitions of H 2 CN near 280 nm in a molecular beam study through Rydberg atom detection of the H atomic fragment from predissociation of electronicallyexcited H2CN. Through measurement of the H-atom translational energy distribution, they found that the HCN co-fragment was formed with a wide distribution of internal energy. The measured H-atom recoil anisotropy was consistent with a vibronically-induced transition to the A2B\ state. This work showed that H2CN could be detected by laser-based techniques; however, this scheme is not amenable to kinetics studies. In our laboratory, we have employed CRDS as a sensitive absorptionbased detection method for spectroscopic and kinetic studies of H2CN. 127 The radical was prepared by 193 nm photolysis of formaldoxime (H 2 CNOH). This precursor is convenient because both photolytic fragments, H 2 CN and OH, can be spectroscopically observed in the same wavelength region: the former by the previously identified transitions near 280 nm and the latter through its A-X (1,0) band. Figure 3 presents the room-temperature absorption spectrum of H 2 CN as recorded in our laboratory by the CRDS technique. 127 Two broad features, with additional structure, can be seen. In contrast to the other polyatomic intermediates discussed above, it has not been possible to analyze the rotational structure of these features to make definitive assignments of the upper levels, even with the availability of quantum chemistry calculations for the excited electronic states. 126 In this regard, it would be interesting to obtain a jet-cooled spectrum of the radical. Room-temperature rate constants for several reactions of H2CN with atoms have been determined. Stief and co-workers reported rate constants

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0.008 CO

en Q.

0.006

i _

en a. O

0.004

(1 i _

o CO o to

0.002

278

280

282

284

286

288

laser wavelength (nm) Fig. 3. Room-temperature cavity ring-down absorption spectrum of the H2CN radical. The radical was prepared by 193 nm photolysis of formaldoxime (500mtorr), diluted in 5 torr argon. The spectrum was collected 30 /us after the photolysis laser pulse. The broad features are due to H2CN, and lines in the A—X (1,0) of the OH co-fragment of the photolysis are also observable. Lines in the Qi branch of this band are marked in the plot. Spectrum adapted from Nizamov and Dagdigian. 1 2 7

for the H + H 2 CN and N + H 2 CN reactions. 120 Our group measured the room-temperature H2CN self-recombination rate constant in 5 torr argon. 127 In addition, we also derived the rate constant for the important OH + H2CN reaction, as well as upper bounds to the room-temperature rate constants for reactions with a number of stable molecules (O2, C2H4, CO, CH4, H 2 ). Chakraborty and Lin 3 employed theoretical methods to estimate temperature- and pressure-dependent rate constants and product branching ratios for the reaction of H2CN with N 0 2 , N 2 0 , NO, and OH, as well as for the unimolecular decomposition of H2CN. 4.2.10. Methyleneimine (H 2 CNH) This transient species has been identified in the CO2 laser-assisted decomposition of RDX at pressures of 0.1 to 3 atm by Litzinger and co-workers.11 It is the simplest member of the imine family. These compounds are very reactive and normally decompose by polymerization, oxidation, or hydrolysis. The microwave spectrum of H 2 CNH has been reported, and a molecular structure for the ground electronic state derived. 128 Its infrared absorption spectrum has been investigated by both matrix isolation spectroscopy 129 and in the gas phase. All nine fundamental vibrational frequencies have

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been observed in high-resolution gas-phase experiments. ' In these studies, H 2 CNH was prepared by pyrolysis of methyl amine. In our laboratory, we have developed a spectroscopic probe for H2CNH based on an electronic transition. There has been some theoretical work to characterize the excited states of H2CNH. The ground electronic state has a planar equilibrium geometry. As in the isoelectronic ethylene molecule,132 the Si and T\ states are computed to have a nonplanar geometry, with a dihedral angle of 90° between the planes containing the CH2 and NCH moieties. 133 ' 134 The vertical excitation energies are thus greater than the excitation energies to the zero-point levels of the excited states, and it is expected that the lowest electronic transition would be spread over a broad wavelength range. The dependence of the electronic energies of the ground So and excited Si and T\ states of H2CNH upon the dihedral angle between the two halves of the molecule has been investigated computationally. 133 A conical intersection between Si and So is found near the geometry of the minimum energy of the Si state. This crossing will lead to internal conversion in the molecule, and there is enough energy in the So state to allow dissociation to yield H atom fragments. To this author's knowledge, there was no information on the electronic spectroscopy or chemical reactions of methyleneimine prior to our work. We have developed a spectroscopic probe using electronic absorption spectroscopy so that the reaction kinetics of H2CNH could be investigated. Photoelectron spectroscopic studies have shown that pyrolysis of methyl azide is a very convenient method to generate H2CNH. 135 This process occurs by loss of N 2 and a 1,2-hydrogen shift on the lowest singlet CH 3 N potential energy surface. We have employed this generation technique with CRDS to observe the Si N O , . . . , to find "initial steps" in the RDX chain of decomposition events; (4) because of these various pathways and multiphoton processes, one often finds what one seeks (e.g., OH or N 0 2 or NO) as a function of laser wavelength, pulsewidth, and intensity; (5) the first step in the decomposition can be a species not sought (e.g., O); (6) intermolecular

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interactions can change the products, even the initial steps; (7) model systems and model potentials can often lead to difficulties because details do matter with so many potential pathways separated in energy by only 1-10 kcal/mol; and (8) many of the reaction paths that lead to products have activation energies and barriers that render the "obvious path" (e.g., breaking of the weakest bond) not the one taken in the molecular decomposition process. These difficulties, plus rapid processes and potentially dangerous experiments, make energetic material research both exciting and challenging. Early references to the importance of electronic excitation for the initial steps in the condensed phase detonation process can be found in the works of Williams, 2 ^ ~2(h) Dremin 2 ^ and S h a r m a . 2 ^ - 2 ^ The relation of shock and impact sensitivity to electronic excitation is correlated with the shake-up promotion energy observed for x-ray photoelectron spectra. These excitations arise for core ionization of an atom in the time frame of ca. 10 fs, which is argued to be smaller than the transit time for a detonation wave in a solid over the dimensions of a molecule ((v = 1) C 3 H 6 (N 2 02)2NO + O

(2b) C 3 H 6 (N 2 0 2 )2NO

-v C 3 H 6 (N 2 02)2 + NO - • • • •

(3a) RDX + 226nm

- • (cycIic)-C 3 H 5 (N 2 02)2NNOOH

(3b) (cyclic)-C 3 H 5 (N202)2NNOOH -> C 3 H 5 (N20 2 )2N + HONO (3c) HONO + (226 nm?)

^ HO + NO

(4a) RDX + 226 nm

- • 3CH 2 NN0 2

(4b) CH 2 NN0 2

-> HONO or NO (or N 0 2 ) . . .

(5) RDX + 226nm

-y C 3 H 6 (N 2 02)2NONO -> NO + • • •

The most likely mechanism based on the studies of Refs. 16, 21, and 20 seems to be number (2) above. We know number (1) is out (because of the spectroscopy for NO2/NO dissociation), number (3) is unlikely because HONO probably would not give the observed distribution of degrees-offreedom energy for NO, and number (4) requires that NO be generated directly from CH 2 NN0 2 . This latter pathway would not be consistent with the results of Ref. 11 assuming CH2N2O2 were not highly excited. Mechanism (5) appears to be possible, but at present not the most likely one. I emphasize that no initial step can be definitively identified from a 10 ns experiment because the initial process, whether loss of O or isomerization or symmetric fragmentation or HONO formation or something else,

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must take place in less than 1 ps. It appears that the difference between a stable nitramine (e.g., N-nitropyrrolidine, etc.) and an "energetic" one (e.g., RDX, HMX, DMN) is that the stable species has a stable nitroso intermediate.

5. Conclusions and Future Work Firm conclusions for the behavior of energetic materials are difficult to reach, especially for excited electronic state behavior at the chemical mechanism level. Difficulties include time resolution, sample handling, and laser/matter interactions (single- and/or multiphoton behavior). I hope that the following tentative conclusions will stand the test of time. First, matrix assisted laser desorption seems to work for many different delicate systems to generate non-volatile fragile molecules in the gas phase. Second, the molecules can be cooled and isolated in supersonic expansion for LIF, TOFMS, and other sophisticated gas phase dynamics experiments. Third, at 226 nm and 10 ns time resolution, NO is generated by RDX decomposition in a characteristic rotational, rovibrational and translational energy distribution. Fourth, the most likely guess at an overall mechanism for the dissociation at 226 nm is first loss of an O atom and then loss of NO. Such an NO could be rotationally cold and vibrational^ hot in agreement with experiment. Fifth, RDX seems to be different from non-energetic cyclic nitramines (N-nitropyrrolidine) as well as other model nitro-containing species with regard to its photodissociation behavior. Sixth, 248nm, high-intensity excitation at 155°C in a non-cooled, non-beam environment seems to generate NO2. Energetically, NO2 generation is possible and not inconsistent with other results, but a number of questions concerning these experiments should be addressed. Future experiments central to the understanding of energetic material behavior in excited electronic states include: (1) fs studies, with the knowledge that these short times can add additional complications to the results; (2) studies of more energetic materials: HMX, TNAZ, DMN, and others; (3) studies of non-energetic models such as N-nitropiperidine and various N,N'-dinitropiperazines (1,2; 1,3; 1,4); (4) multi-laser experiments such that photodissociation and product detection can occur at different wavelengths;

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(5) study of gas phase solvation clusters of energetic materials (e.g., RDX(H 2 0) x , RDX(C n H 2n +2)s, etc.; and (6) multimers of energetic materials (e.g., (RDX) n , (HMX) n , etc.) to model condensed phase and bimolecular behavior. Clearly, lots of work remains to be done to unravel the chemistry and physics of energetic materials. These last research recommendations bring us full circle to the introductory paragraph of this overview. There we posed three essential questions concerning energetic materials: how are they different from other molecules and what are their decomposition pathways and kinetics? We cannot answer all these questions at present, in part because of the experimental problems and interpretational difficulties discussed in this overview. Nonetheless, we now understand much about the decomposition of energetic molecules and we have ideas of how to uncover and measure the details of this process. Both molecular and condensed phase results are clearly important: we must understand the molecular behavior first, before we can develop a clear picture of condensed phase behavior. Decomposition as a function of electronic state is an essential component of the energetic material properties. We are on the verge of uncovering these details and mostly know how to proceed effectively and judiciously. Acknowledgments These studies were supported by the U.S. Army Research Office. I would particularly like to thank Ms. Margo Greenfield for her help with a literature search on energetic materials. Ms. Greenfield and Dr. Yuanqing Guo have carefully read drafts of this manuscript and have made many helpful suggestions about the presentation and form of the final product. Dr. Richard Beyer, ARL, also helped with a literature survey through the Army Research Laboratory library facilities: this effort helped us find the more difficult-to-access references. References 1. (a) G. A. Olah and D. R. Squire (eds.), Chemistry of Energetic Materials (Academic Press, New York City, 1991); (b) Y. Tsuoboi, T. Seto and N. Kitamura, J. Phys. Chem. B107, 7547 (2003) and references to older work therein. 2. (a) H. M. Windawi, S. P. Varma, C. B. Cooper and F. Williams, J. Appl. Phys. 47, 3418 (1976); (b) J. Schanda, B. Baron and F. Williams, Acta

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7.

E. R. Bernstein Technica Academiae Scientiarum Hungaricae 80, 185 (1975); (c) J. Schanda, B. Baron and F. Williams, J. Luminescence. 9, 338 (1974); (d) S. P. Varma, F. Williams and K. D. Moeller, J. Chem. Phys. 60, 4950 (1974); (e) S. P. Varma and F. Williams, J. Chem. Phys. 60, 4955 (1974); (f) S. P. Varma and F. Williams, J. Chem. Phys. 59, 912 (1973); (g) R. B. Hall and F. Williams, J. Chem. Phys. 58, 1036 (1973); (h) F. Williams, Adv. Chem. Phys. 21, 289 (1971); (i) A. N. Dremin, V. Yu. Klimenko, O. N. Davidoua and T. A. Zolodeva, in Proc. 9th Symp. on Detonation, Vol. I, 28 Aug-1 Sept. 1989, Portland, OR, p. 319; (j) J. Sharma, B. C. Beard and M. Chaykovsky, J. Phys. Chem. 95, 1209 (1991); (k) J. Sharma, J. W. Forbes, C. S. Coffey and T. P. Liddiard, J. Phys. Chem. 9 1 , 5139 (1987); (1) J. Sharma, APS Topical Meeting on Shocks in Energetic Materials (APS, Williamsburg, VA, June, 1991). J. C. Mialocq and J. C. Stephenson, Chem. Phys. Lett. 123, 350 (1986); Chem. Phys. 106, 281 (1986). N. L. Garland, D. H. Ladouceur and H. H. Nelson, J. Phys. Chem. A l O l , 8508 (1997). S. M. Hankin, Rapid Commun. Mass. Spectrom. 16, 111 (2002). (a) M. M. Kukija and A. B. Kunz, J. Appl. Phys. 87, 2215 (2000); (b) M. M. Kukija and A. B. Kunz, J. Phys. Chem. Solids 61, 35 (2000); (c) M. M. Kukija, E. V. Stefanovich and A. B. Kunz, J. Chem. Phys. 112, 3417 (2000); (d) M. M. Kukija, B. P. Adver, E. D. Aluker, V. I. Krasheninin, A. G. Krechetove and A. Y. Mitrofanov, J. Appl. Phys. 89, 4156 (2001); (e) M. M. Kukija and A. B. Kunz, J. Appl. Phys. 89, 4962 (2001); (f) A. B. Kunz and M. M. Kukija, Theor. Chem. Acta 384, 279 (2002); (g) M. M. Kukija, Appl. Phys. A76, 359 (2003); (h) D. Margetis, E. Kaxiras, M. Elstner, Th. Frauenheim and M. R. Manaa, J. Chem. Phys. 117, 788 (2002); (i) J. P. Lewis, Chem. Phys. Lett. 371, 588 (2003). (a) F. J. Owens and J. Sharma, J. Appl. Phys. 5 1 , 1494 (1979); (b) J. Sharma and B. C. Beard, Mater. Res. Soc. Symp. Proc. 296, 189 (1993); (c) T. R. Botcher, H. D. Landouceur and T. R. Russell, in Shock Compression of Condensed Matter — 1197, Proceedings of the APS Topical Group, eds. S. C. Schmidt, D. P. Dandekar, and J. W. Forbes (AIP, Woodbury, New York, 1998); (d) B. P. Aduev, E. D. Aluker, G. M. Belokurov and A. G. Krechetov, Chem. Phys. Rep. 16, 1479 (1997); (e) B. P. Aduev, E. D. Aluker and A. G. Krechetov, Chem. Phys. Rep. 17, 643 (1999); (f) J. J. Gilman, Philos. Mag. B 7 9 , 643 (1999); (g) C. J. Wu, L. H. Yang, L. E. Fried, J. Quenneville and T. J. Martinez, Phys. Rev. B67, 235101/1 (2003); (h) S. Roszak, R. H. Gee, K. Balasubramanian and L. E. Fried, Chem. Phys. Lett. 374, 286 (2003); (i) M. R. Manaa, L. E. Fried, C. F. Melius, M. Elstner and Th. Frauenheim, J. Phys. Chem. A106, 9024 (2002); (j) E. J. Reed, M. R. Manaa, J. D. Joannopoulos and L. E. Fried, in AIP Conference Proceedings, Part 1, 620 (2002), p. 385; (k) M. R. Manaa, R. H. Gee and L. E. Fried, J. Phys. Chem. A106, 8806 (2002); (1) L. E. Fried, M. R. Manaa, P. F. Pagoria and R. L. Simpson, Annu. Rev. Mater. Res. 31, 291 (2001); (m) M. R. Manaa and L. E. Fried, J. Phys. Chem. A105, 6765 (2001);

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12. 13. 14. 15.

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(n) E. J. Reed, J. D. Joannaopoulos, and L. E. Fried, Phys. Rev. B62, 16500 (2000); (o) M. R. Manaa and L. E. Fried, J. Phys. Chem. A103, 9349 (1999); (p) M. R. Manaa and L. E. Fried, J. Phys. Chem. A102, 9884 (1998). D. Margetis, E. Kaxiras, M. Elstner, Th. Frauenheim and M. R. Manaa, J. Chem. Phys. 117, 788 (2002). J. P. Lewis, Chem. Phys. Lett. 371, 588 (2003). H. Zuckermann, G. D. Greenblatt and Y. Haas, J. Phys. Chem. 9 1 , 5159 (1987). (a) X. Zhao, E. J. Hintsa and Y. T. Lee, J. Chem. Phys. 88, 801 (1987); (b) D. S. Anex, J. C. Allman and Y. T. Lee, in Chemistry of Energetic Materials, eds. G. A. Olah and D. R. Squire (Academic Press, New York City, 1991); (c) A. M. Wodtke, E. J. Hintsa and Y. T. Lee, J. Phys. Chem. 90, 3549 (1986). M. Hiskey (LANL) and R. Behrens (SRI), personal communication. E. R. Bernstein, in Atomic and Molecular Clusters, ed. E. R. Bernstein (Elsevier, New York, 1990), p. 551. R. Cohen, B. Brauer, L. Grace and M. S. de Vries, J. Phys. Chem. A104, 6351 (2000). (a) A. Meffert and J. Grotemeyer, Ber. Bunsenges. Phys. Chem. 102, 459 (1998); (b) K. W. D. Ledingham and R. P. Singhal, Int. J. Mass Spectrom. Ion Processes 163, 149 (1997), and references therein; (c) R. J. Conzemius and J. M. Cepellen, Int. J. Mass Spectrom. Ion Proc. 34, 197 (1980) and references therein. H.-S. Im and E. R. Bernstein, J. Chem. Phys. 113, 7911 (2000). (a) T. Burgi, T. Droz and S. Leutwyler, Chem. Phys. Lett. 225, 351 (1994); (b) E. R. Bernstein, Annu. Rev. Phys. Chem. 46, 197 (1995); (c) E. R. Bernstein, in Chemical Reactions in Clusters, ed. E. R. Bernstein (Oxford, New York, 1996), p. 147; (d) R. Compargue, Atomic and Molecular Beams: The State of the AH 2000(Springer, Berlin, 2001); (e) G. Scoles, Atomic and Molecular Beam Methods, Vols. I, II (Oxford, New York City, 1988, 1992); (f) D. M. Lubman, Lasers and Mass Spectrometry(Oxiord, New York City, 1990). A. G. Suits and R. E. Continetti, Imaging in Chemical Dynamics, ACS Symposium Series 770 (ACS, Washington, DC, 2000). (a) H. L. Dai and R. W. Field, Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping (World Scientific, Singapore, 1995); (b) A. B. Meyers and T. R. Rizzo, Laser Techniques in Chemistry, XXIII of Techniques of Chemistry (Wiley, New York City, 1995); (c) G. Hall and B. J. Whitaker, J. Chem. Soc, Faraday Trans. 90, 1 (1994); (d) M. Motzkus, S. Pederson and A. H. Zewail, J. Phys. Chem. 100, 5620 (1996). H.-S. Im and E. R. Bernstein, J. Phys. Chem. A106, 7565 (2002). C. Capellos, in 12th Int. Detonation Symposium, eds. J. M. Short and J. L. Maienschein (OCNR, Arlington, CA, 2003), p. 813. R. Behrens (SRI) and M. Hisky (LANL), personal communication. H.-S. Im and E. R. Bernstein, unpublished results.

CHAPTER 7 G A S - P H A S E KINETICS FOR P R O P E L L A N T C O M B U S T I O N MODELING: REQUIREMENTS AND EXPERIMENTS William R. Anderson U.S. Army Research Laboratory Aberdeen Proving Ground, MD 21005-5069, USA

Arthur Fontijn High- Temperature Reaction-Kinetics Laboratory The Isermann Department of Chemical and Biological Engineering Rensselaer Polytechnic Institute Troy, New York 12180-3590, USA

Contents 1. Introduction 2. Propellant Models and their Gas-Phase Chemistry Inputs 2.1. Primary Features of Propellant Combustion and their Relation to the Gas-Phase Mechanism 2.2. Gas-Phase Chemistry Issues of Primary Significance 2.2.1. First-Stage Chemistry 2.2.2. Dark Zone Chemistry 3. Experimental Input Data 3.1. Elevated Temperature Techniques for Obtaining Kinetic Data on Individual Reactions 3.1.1. Thermostated Reactors 3.1.2. Shock Tubes. Comparison of Techniques 3.1.3. Reaction Mechanisms 3.2. Examples of Results with Significant Impact on the Models 3.2.1. 0 + N 2 0 3.2.2. H + N 2 0 3.2.3. H + NH 3 NH 2 + H 2 3.2.4. H + N 0 2 , C H 3 N 0 2 191

192 195 196 200 200 210 218 218 218 221 222 223 223 224 225 226

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3.2.5. H + NO 3.2.6. N + CO2, N 2 0 , 0 2 3.2.7. NH + C 0 2 , H 2 0 3.2.8. NH 2 + NO 3.2.9. CN + OH 3.2.10. NCO + NO N 0 2 4. Conclusions Acknowledgment References

& A.

Fontijn

227 228 229 230 231 232 233 234 234

1. Introduction One of the most important characteristics of a propellant is its onedimensional burning rate and the dependence thereof on pressure and unburnt propellant temperature. Burning rate is controlled by propellant formulation. During the last ~15 years, one-dimensional models of solid propellant combustion have shifted from those using one or a few global gas-phase reactions to those including all the species and reactions thought to be important to the gas-phase flame. This means tens of species with associated thermodynamics and hundreds of elementary chemical reactions with associated kinetics. The overall gas-phase reaction rate must be properly predicted to obtain the rate of heat transfer to the condensed phase material; this heat transfer controls the rate of conversion of condensed phase material to initial gas-phase intermediates. Accurate kinetics mechanisms, consisting of the many possible elementary steps that can occur across a range of temperatures, pressures, and mixture ratios pertinent to propellants, are necessary to achieve success in predicting burning rates for the large variety of chemical ingredients that can be used. a Here we review the current status of the relevant gas-phase chemistry with emphasis primarily on solid propellants used in gun and rocket applications and recommend how to further the ability to model their combustion.^ 1 During the mid to late 1980s it was first recognized, largely due to the modeling efforts of Hatch 2 and Melius,3 that it had become feasible a

T h e term "gas phase mechanism" includes not only the elementary reactions and their kinetics parameters, but also the thermodynamics of the species. The latter can be critically sensitive input parameters. Some crucially important data, in particular heats of formation of some key radicals and molecules and even of some important propellant ingredients, are not well known. b A t one point there is also a very brief discussion of liquid rocket fuels which could be fruitfully studied.

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193

to develop models of propellant combustion that include a detailed gasphase description of the chemical kinetics and transport properties of the flame gases. It was recognized that a large number of elementary reactions would have to be understood for proper modeling. The best way to determine kinetics parameters for an elementary reaction is by experimental study under conditions designed to carefully isolate the reaction, when possible. Section 3 of this chapter will focus on methods by which this may be done. However, it is not possible to do this for every reaction. Also, if one focuses only on individual reactions, one may overlook key reactions of such intricate systems. Not only are isolated reaction studies of interest, but also more complex systems of reactions pertaining to intermediates of propellant combustion. A number of investigators decided that a "hierarchical approach" to development of submodels was appropriate, both for the chemistry and the physics of propellant combustion. For the gas-phase chemistry, this meant stable, small molecule fuel/oxidizer pairs, whose mechanisms were subsets of propellant mechanisms, were selected for study and arranged from simplest to most complex. These molecules are intermediate species formed during the decomposition and combustion of key propellant ingredients. The hierarchical organization clarified why certain chemical systems are of interest. Further discussion of the hierarchical approach, concentrating mainly on nitramine gas-phase mechanisms, is found in Ref. 4. This chapter is confined to propellants consisting of C, H, N, and O. AP and metallized propellants are not discussed. We focus on nitrate ester and nitramine-based propellants. These ingredients produce copious amounts of NO2 and/or N 2 0 oxidizers at intermediate combustion stages. Therefore, the detailed gas-phase propellant mechanisms are similar to those for modeling NO^ emissions formation and abatement processes during combustion of other fuels. Pollutants such as NO^ are of growing import to the Army since increased concern is being placed on the environmental impact of its weapons systems, vehicles, and programs. We will briefly mention some techniques which have been used to study global kinetics along with a few references pertinent to propellant combustion: low pressure burner stabilized flame,5 thermally initiated shock tube, 6 high pressure turbulent flow reactor, 7 and static reactor 8 techniques. Typically, a mechanism of many elementary steps (commonly referred to as a "complex" or "detailed" mechanism) is used to model results. The best work uses sensitivity analysis to single out the key reactions controlling the

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& A.

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observed global results. Frequently, a new key reaction may be postulated and fits to the data made to extract its rate coefficients. The assumed reaction, however, may be incorrect or errors may occur in ancillary input data. For this reason, it is always important to compare results from a variety of techniques; when they agree, this lends confidence. Global kinetics approaches not only lend a check that all important reactions are included, but often yield rate coefficients for key reactions that cannot be isolated experimentally. Theoretical chemistry (e.g. ab initio or density functional approaches for determination of potential energy surface features, coupled with transition state, QRRK, and RRKM theories for estimation of rate coefficients) has also played a major role in the development of gas-phase propellant mechanisms.0 These techniques have greatly improved during the last two decades and calculated thermodynamic and kinetic parameters can be close to the best experiments. Theory can help assign proper products for isolated reactions. Agreement of the rates of key elementary reactions lends confidence that experiments are being interpreted properly — especially helpful in global kinetics experiments where assumptions for the key reactions are often made. In many cases elementary reaction kinetics cannot be experimentally measured. For example, it is possible only in a few cases to create a sufficiently pure gas-phase sample of solid propellant ingredients or their major, large radical breakdown products at known concentration. Some theoretical studies which have produced estimates for the initial reactions in the mechanisms of the ingredients RDX and HMX are mentioned in Sec. 2. In Sec. 2, the primary features of solid propellant combustion are described and gas-phase chemistry issues pertinent to various combustion zones within typical propellant flames are discussed. Sensitive elementary reactions are highlighted and discussion of which are in most need of further work is given. Ingredients and burning rate modifiers of highest interest are also discussed along with the current availability of reaction mechanisms. In Sec. 3, experimental techniques to obtain data for individual reactions at temperatures pertinent to the models are discussed. Several examples where these techniques have been successfully applied to reactions of interest to propellant modeling are given.

c

Sometimes experimental input is needed to scale key theoretical parameters to achieve the best kinetic descriptions.


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2. Propellant Models and their Gas-Phase Chemistry Inputs Models of solid propellant combustion which include detailed gas-phase chemistry and transport properties first began to appear in about the mid-1980s. All have used a one-dimensional assumption and the phase boundaries are assumed to be sharp, flat surfaces. Until recently all such models considered three phases: solid, liquid, and gas, and assumed that one or a few global reactions, with associated kinetics parameters, occur within the liquid layer.d Unfortunately, it has proven impossible to be certain what reactions or other processes occur within the near-surface condensed-phase region, let alone the proper formulation of rates. This is because of nearly insurmountable experimental obstacles to probing the condensed phases6 due primarily to: (1) inability to extract quantitative data from condensedphase spectra; (2) micron thickness and roughness of the reaction zone; (3) large temperature gradients; (4) short burn times of the propellants; and regression of the surface in the laboratory reference frame; (5) no actual propellant burns in one-dimensional, steady-state fashion; (6) high pressure; and (7) reactions continuing during sampling. Three groups that developed 3-phase models for RDX combustion used the same rate coefficients for liquid RDX consumption but assumed different products. 3 ' 10 ' 11 Because the thermodynamics of the reactions chosen are quite different, the heat feedback to the condensed phases varies greatly among these models. There are also significant differences in the assumed physics (e.g. whether bubbles form). Because all the efforts have achieved excellent agreement with experimental burning rates, the modeling solutions are not, apparently, unique (see the chapter by Miller). The community has oft-times referred to such models as "first principles" approaches, but this term may cause misunderstanding about how uncertain the assumptions are. These difficulties have led to slow application of such models to new ingredients: three-phase modeling has been applied mostly to single ingredients and simple mixtures. A few years ago, Miller and Anderson of ARL presented a two-phase approach to prediction of propellant burning rate and gaseous flame structure. The phases were condensed (solid or liquid) and gas, and the model

d

More reactions could be included: the situation is not computationally limited. Thermogravimetric mass spectrometer experiments, like those of Behrens, 9 allow condensed-phase kinetics of energetic ingredients to be measured; but the temperature range is well below combustion. This method is mainly relevant to slow reactions important for shelf life, slow cookoff, and safety. e

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was applied to a few pure ingredients and simple binary mixtures. 1 2 More recently, they have successfully applied the approach to several fielded nitrate esters, 1 3 and nitramine/energetic binder type propellants. 1 4 T h e approach uses two main inputs (besides the gas-phase chemistry): (1) a semi-empirical pyrolysis "law" is assumed applicable t o a broad range of propellants within a given class; this law relates the burning rate to the surface temperature; and (2) the mixture of gaseous species evolved from the surface for each propellant ingredient. (Miller and Anderson refer to this mixture as the "surface products" — not to be confused with "equilibrium products" which are obtained in the burnt gas region.) T h e pyrolysis laws have been measured for several major propellant types, classified according to ingredients, by Zenin. 1 5 Qualitative guidance for the surface products to use for each ingredient comes from pyrolysis experiments and chemical intuition. Ultimately, Miller and Anderson had to rely on comparison with experimental burning rates to guide selection, which is basically a fitting procedure. Once the "best" set is found, this is fixed and used for the mixture of ingredients in actual propellants along with the pyrolysis law appropriate for the propellant type. In this way, the model can be used for propellant predictions. The approach has been used successfully for about ten actual fielded and developmental propellants, based on nitrate ester or nitramine energetic ingredients. Besides needing the gas-phase mechanism for either the two- or three-phase approach, the two-phase approach would benefit from more reliable information about the surface products evolved by the pure ingredients. We will return to this issue later in this section. More discussion of the two-phase model is given by Miller in this volume.

2 . 1 . Primary Relation

Features of Propellant Combustion to the Gas-Phase Mechanism

and

their

Features typically observed during combustion of a solid propellant are shown in Fig. 1. W h e n initial propellant t e m p e r a t u r e s are close to ambient, most solid propellants cannot undergo sustained, steady-state combustion at pressures below about 5-10 a t m . Pressures in guns range from about 100 to 5,000 atm; for missiles/rockets they range from 5 to 100 a t m . So "low pressures" for guns means below 500 a t m . T h e idealized combustion picture in Fig. 1 uses a cylindrical strand in a pressurized vessel. An inhibitor on the side a n d / o r flowing inert gas causes the propellant to b u r n at one end only. T h e schematic has been drawn with a "dark zone" (DZ) — a nonluminous gas-phase region observed between the condensed-phase surface


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Propellant Strand 3000 2000

!

1000

Distance Fig. 1. Idealized schematic of a burning solid propellant strand with a dark zone. In typical experiments, the strand is oriented vertically, but it is shown rotated 90° clockwise here to make the correlation to the temperature profile clear.

and the luminous flame (burnt gas region). The DZ consists of intermediate combustion species at intermediate temperature while the luminous flame consists of equilibrium products at the final temperature/ The burning rate is that at which the solid surface regresses as the combustion wave moves through the propellant (assuming steady combustion has been reached). Most gun propellants exhibit a DZ at low pressures. In Fig. 1 the temperature within the solid is ambient — typically about 293 K. At the propellant surface, heat transfer from the gas-phase to the condensed phase causes gasification to occur yielding the initial gas-phase intermediates. In a very narrow region near the surface, a rapid, exothermic, global reaction rapidly converts the initial gas-phase intermediates to DZ intermediates. Coupled with this reaction is a strong upward gradient in the temperature profile. The near-surface region is also often called the "first stage flame". At the end of the first-stage flame, the comparatively low reactivity of the major DZ intermediates causes their concentrations and the temperature profile to linger at plateau levels for a time, often referred to as the "DZ ignition delay". This chemical delay, coupled with convection, causes formation of

f

T h e trace species — e.g. radicals and atoms — will not be at equilibrium at the leading edge of the luminous flame, though the major species are. Thus, the temperature there may be ~100 K different from the adiabatic flame temperature, even in model calculations.

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the DZ. The global reaction slows due to the low reactivity of DZ intermediates as the concentrations of trace radicals and, perhaps, temperature slowly build. At some point the chemical rates rapidly increase, the conversion of DZ intermediates to (nearly) equilibrium products quickly occurs, and heat is released, driving the temperature upwards to nearly the adiabatic limit. The thin region at the end of the dark zone where this occurs is called the "second-stage" flame. At the end of the second-stage flame, the temperature is high enough that the gases typically become luminous; this luminous region is often called the "luminous flame". It appears likely that 1 6 , 1 7 the primary factor causing DZ formation is the chemical delay between formation of the slowly reacting intermediates and their sudden, rapid conversion to near-equilibrium products at the end of the DZ. The DZ ignition delay time and gas-phase convective rate are the major determining factors of the DZ length. The state-of-the-art model of Ref. 16 is in good agreement with the measured DZ structure of actual propellants. There is, however, only scant experimental evidence with which to compare, especially for nitramine propellants. As will be discussed in Sec. 2.2.2(a), more experiments are needed. For some propellants, no DZ is observed at any pressure. Rather, the luminous flame seats itself very close to the condensed-phase surface (not shown in Fig. 1). The corresponding temperature profile rises slowly just below the propellant surface, then smoothly in a narrow region just above the surface to nearly the adiabatic limit. The corresponding species profiles also exhibit no plateau regions. The entire flame is luminous except for the very thin, cool region near the surface. We will discuss our suspicions below as to why no DZ occurs, at least for some propellants. Most solid propellants of U.S. Army interest fall into two major types based upon the chemically-energetic ingredients they contain: nitrate esters (R-O-NO2) and nitramines (R1-, R2-N-N0 2 ). Some of the gas-phase species which occur along the major chemical pathways within the main regions of the flames are discussed here. Much of the gas-phase kinetics study in this field has been related to combustion of these species. Chemistry in the near-surface, first-stage flame is considered first. For both nitrate esters and nitramines, the most important small fuel molecule in this region is CH2O. For nitrate esters containing nitrocellulose (NC), pyrolysis experiments suggest that CHOCHO and HCOOH are also important, though these have not received much consideration except in very recent combustion models. For nitramine propellants HCN also plays a central role. The most important small oxidizer molecules are nitrogen oxides.


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For both nitrate esters and nitramines, NO2 plays a central role; HONO may also be present: as a direct product of the condensed-phase material, or along the gas-phase pathways from nitrogen oxides. For nitramines, N2O also plays a major role. In first-stage flames of most propellants nearly all the N 0 2 and HONO, and a small fraction of the N 2 0 , are converted to NO, the majority of the N2O is converted to N2, and most of the C-containing species except HCN are converted to CO and CO2, with concomitant heat release. Various studies conclude that, during combustion, all nitrate esters and nitramines have major chemical pathways through NO; HCN is also important for nitramines. NO and HCN survive the first-stage flame in most propellants because there are few species present in the mixtures that will react rapidly with them and the equilibrium products, N2, H2O, CO, and CO2, can only form slowly. This blocks the immediate full heat release of the gaseous mixture, resulting in an intermediate temperature region, the DZ (see the plateau in the temperature profile of Fig. 1). When no DZ is formed, it is probably not because little NO and/or HCN are formed in the first stage. Rather, for certain ingredients, it is likely that a species is formed in the surface region or first-stage flame that can cause rapid conversion of these intermediates to final products. Corresponding temperature profiles have sharp, smooth upward gradients and the final temperature is reached close to the surface (not shown). In some cases, this new species may be NHX [x = 0,1,2,3). NH 3 typically leads to N, NH, and/or NH2 formation. These three species react very rapidly with NO, even at low temperatures, quickly leading to formation of final product N 2 . Thus, no DZ is formed. M30 propellant is an example. It contains a large amount of nitroguanidine (NQ), a known NH 3 precursor. Propellants using ingredients which form HNCO and other intermediates might behave similarly. (See also the discussion of NH 3 and HNCO flame chemistry and their precursors, such as NQ, as burning rate modifiers in Sec. 2.2.1(c).) When a DZ forms, it contains only a few major species. 16 ' 17 For nitrate esters, there are six major species present: H 2 , H 2 0 , NO, N 2 , CO and C 0 2 ; traces of CH4, C 2 H 4 , and CH 2 0 may also be found. For nitramines, there are also large amounts of HCN, a few percent of N 2 0 , and (perhaps) NH 3 . Model calculations suggest that the trace species, especially N 2 0 and NH 3 , could play important roles. Typical temperatures in propellant DZs are about 1200-1600 K. Because of the difficulty of measurements in propellant flames, there is a high degree of uncertainty in the DZ mixture ratios and temperatures. This makes checks of DZ models difficult. Even for the best data sets, at least one of the majority species is

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missing. For example, some researchers used sample extraction into evacuated vessels, hence the H 2 0 concentration cannot be measured because of significant condensation on the walls and must be inferred by mass balance, relying on the assumption that it is the only significant missing species. The trace species concentrations have high uncertainties for all propellant types. Finally, for nitramine propellants, there are very few data sets for which the majority species concentrations are well established. The dearth of data for nitramines may be because their associated flames are less steady, more flickering, than the better behaved nitrate esters. (Even for the best case of a "steady-state" propellant flame exhibiting a DZ, the DZ is inherently easily perturbed because the second-stage flame is not stabilized against a solid surface. Thus, some nickering even in the most carefully arranged experiments is common, and most measurements of DZ length are an average.) Recent work shows that the DZ chemistry at low pressures is much more important to the burning rates at high pressures than had previously been appreciated (see the introduction of Sec. 2.2.2). The DZ and its associated chemistry, therefore, deserve renewed, vigorous attention. 2.2. Gas-Phase

Chemistry

2.2.1. First-Stage

Chemistry

Issues

of Primary

Significance

(a) Small molecule issues common to a wide variety of propellants Some of the sensitive reactions pertinent to the small fuel/oxidizer species chemistry in the first stage of propellants are presented in Table 1. Much of what is presented in Table 1 regarding reactions important for nitrate ester propellants comes from a recent modeling effort.13 See in particular the sensitivity tables in Ref. 13 which refer to M10, a propellant consisting primarily of highly-nitrated nitrocellulose. The model in that case has the propellant evolving large amounts of C H 2 0 and NO2, as well as HCO, CH 2 , and CO, into the first-stage flame zone. As discussed in the introduction to Sec. 2, the list of species evolved for a given ingredient in the Miller and Anderson model is highly empirical, obtained by choosing (based on decomposition experiments and intuition) a set of species emitted from the surface (the "surface product set"). Once product sets are found which properly predict the burning rates for pure ingredients, these sets are fixed and used to model propellants according to the ratios of the ingredients in the propellant mixture. The product sets, of course, determine which reactions drive the model results. Excellent results


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Table 1. Sensitive reactions for small molecules commonly observed in the first stage of solid propellant combustion chemistry. Comments

Reaction Type: RH + N 0 2 = R + HONO * 0 H 2 O + N 0 2 = HCO + HONO * CHOCHO + N 0 2 = products * HCOOH + N 0 2 = products * H 2 + N 0 2 = HONO + H

Type: Major first-stage species decomposition reactions * N 2 0 ( + M ) = N2 + O ( + M ) Extremely sensitive for propellant combustion. Well-established, except M-efficiencies for only a few species are measured. * N 0 2 (+ M) = NO + O ( + M) [as above] HONO (+ M) = OH + NO (+ M) Others (general) * HCO + NO2 = H + C 0 2 + NO * HCO + N 0 2 = CO + HONO C H 2 0 + (H, OH) = HCO + (H 2 H 2 0 ) H + N 0 2 = OH + NO See Sec. 3.2.4. H + NO (+ M) = HNO ( + M) See Sec. 3.2.5. H + HNO = H 2 + NO * HONO + OH = H 2 0 + N 0 2 C H 2 C O (+ M) = CH 2 + CO (+ M) * CH 2 + NO = H + HNCO Others (nitramine) * H 2 CN + (H, OH) = HCN + (H 2 , H 2 0 ) * H 2 CN + M = HCN + H + M H 2 CN + NO2 = products H 2 CN + N 2 0 = products HCO + NO = HNO + CO * HCN + O = NCO + H * HNC + OH = HNCO + H Highly sensitive for 1 atm RDX. * HNC + O = products HNCO + H = NH 2 + CO NCO + M = N + CO + M * NCO + OH = NO + CO + H * CN + OH = NCO + H NH 2 + NO = NNH + OH NH 2 + NO = N 2 + H 2 0 * NNH + O = NO + NH N + NO = N 2 + O N + H 2 = NH + H NH 2 + H = NH + H 2

Example of a reaction studied and settled by the TSiOx community. See Sec. 3.2.8. Highly sensitive for 1 a t m RDX. The N O x community is also interested.

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(Continued)

Reaction

Comments

* H + N2O = N2 + OH

Extremely sensitive for propellant combustion; see Sec 3.2.2 for remaining issues. Moderately sensitive for nitramines and all propellant dark zones.

* H + HNO = NH + OH NH + O = NO + H

' T h e s e reactions need further study. Currently many of these are included in propellant combustion models only via crudely estimated rate coefficients. Efforts on these are especially desirable.

were obtained by including HCO, CH 2 , and CH3 radicals for some nitrate ester ingredients. The radicals appearing in future surface product sets might change. However, because of the ubiquitous nature of CH2O in the first-stage chemistry, HCO is expected to remain in future models: HCO, for example, will result by H atom abstractions from CH2O by H, OH, and N 0 2 . Thus, the branching of the reaction of HCO + NO2 is likely to remain high on sensitivity lists. CH 2 and CH 3 are more likely to be removed and their reactions would decline in importance. (Evidence does suggest that traces of CH4 are present in nitrate ester DZs. More complete models include CH 4 and sensitivity to CH 3 reactions will remain if this is done; see Sec. 2.2.2(b).) Reactions of the form RH + N 0 2 = R + HONO, where R represents a free radical, are usually sensitive in first-stage propellant combustion, and in experiments involving pertinent R H / N 0 2 mixtures. This results from the high concentrations of fuels and N 0 2 , and the radical source nature of this type of reaction. A few reactions of this type are grouped at the top of Table 1. Modeling has shown that such reactions with RH equals CH 2 0 or H 2 are sensitive examples; we expect that similar CHOCHO and HCOOH reactions will be sensitive when these species are included in future nitrate ester modeling. It is difficult to predict what the products of their reactions with N 0 2 will be, especially for the latter because several of the bonds have similar energies. Small molecule reactions peculiarly sensitive for nitramine propellant modeling are shown in the last section of Table 1 which is heavily influenced by a sensitivity calculation for pure RDX at 1 atm. 18 Note that many of the reactions involve HCN and its subsequent chemistry is particularly important for nitramine combustion.


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A significant controversy concerns HCN chemistry. The Emory group 19 has suggested the important pathways are 8 :

HCN + M = HNC + M, HNC + O = NH + CO, HNC + OH = HNCO + H.

(1) (2) (3)

If this is correct, then the competition between HNCO + H = NH 2 + CO NH 2 + NO = NNH + OH or N 2 + H 2 0

(4) (5a,b)

and HNCO + OH = NCO + H 2 0 NCO + NO = N 2 0 -f CO or N 2 + C 0 2

(6) (7a,b)

can be very important in propellant combustion modeling; also note the possibly sensitive radical versus non-radical branching of reaction (5). Alternatively the Stanford group 20 has suggested, based on shock-tube experiments on HCN/HN03/Ar mixtures, that the sequence above may be unimportant and only HCN + OH = CN + H 2 0

(8)

need be considered. Were the Reaction (8) used, the reactions involving HNCO, NH 2 , and/or NCO might not matter. However, they would still matter to modeling of propellants with burning rate modifiers, as discussed in Sec. 2.2.1(c). (b) Major propellant ingredients In this section we present a listing of some major ingredients being used in propellants. By "major" ingredients we mean compounds at 5 weightpercent or more. Additives are also used in typical propellants at the percent level to enhance shelf life (stabilizers) or to suppress muzzle flash/blast (high overpressure and luminosity at gun exit due to re-ignition of rich s

I n Sec. 2, reaction equations contain the = symbol, indicating that the reaction can occur in both directions. This is common in modeling and modeling programs. By contrast, in Sec. 3 the —• symbol is used instead, indicating that only the reaction in the direction of the arrow is considered and the data given pertain to it; obtaining such data is the goal of elementary reaction kinetics studies.

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Major propellant ingredients and burn rate modifiers of interest.

Homogeneous propellant ingredients NC NG DEGDN

Heterogeneous ("filled") propellant ingredients NQ ADN RDX HMX CL20

Binders

Modifiers

"Inert" CAB Energetic GAP BAMO-AMMO BNMO-NMMO

urea NQ TAGN TAGAzT DINGU

exhaust gases as they mix with air). Propellant combustion modelers currently ignore additives. Solid propellants are called homogeneous or heterogeneous. Homogeneous propellants are fully mixed on a microscale; heterogeneous ones are not. Heterogeneous propellants contain energetic crystalline ingredient — finely powdered and the size of the particles is carefully controlled. The powder "fill" is mixed with a binder and the mixture formed into the desired shape. Homogeneous, heterogeneous, and binder ingredients are presented in the first three columns of Table 2. Homogeneous propellants are further classified as "single base" or "double base". Single base propellants are composed mainly of NC (nitrocellulose), an energetic polymer. Double base propellants are composed mainly of NC and NG (nitroglycerine). Some energetic fill ingredients of interest are listed in the second column of Table 2. Triple base propellants generally use NC and NG as the binder and NQ (nitroguanidine) as fill. The nitramines RDX, HMX, and CL20 have received much attention recently as fill materials in attempts to make so called "low-vulnerability" propellants (propellants with a high threshold for shock initiated detonation). Finally, ammonium dinitramide (ADN) has received attention recently for possible missile/rocket applications because propellants made from it yield relatively little smoke. Some typical binder materials are listed in the third column of Table 2. These are used for "filled" propellants. Binders are divided into "inert" and "energetic". An inert binder is composed of hydrocarbon polymer or is based on hydrocarbon-oxygen linkages (e.g., ether structures). An inert binder usually cannot burn without the presence of the oxidizing fill material. An example is CAB (cellulose acetate butyrate). Energetic binders are polymers based on hydrocarbon-oxygen structural features but also


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containing azide or nitrate moieties. These nitrogenous moieties increase the combustion energy. Most of the combustion models using detailed chemical mechanisms are for pure RDX and HMX. All these combustion models have relied heavily on the earliest detailed mechanism developed by Melius.3 He used rate coefficients for a few reactions based on theoretical (BAC-MP4) calculations of transition states and estimates for most of the reactions involving RDX or its larger fragments. In Yetter's later variations, much of the small molecule chemistry was revised.21 However, Yetter adopted most of the reactions of RDX and its large fragments from Melius' original mechanism. Combustion models of HMX thus far have simply used the RDX mechanism with kinetics for HMX and its large fragment reactions estimated based upon analogy with Melius' similar RDX reactions. Better theoretical calculations were highly desirable for the RDX and HMX chemistry. Potential energy surfaces (PES), and results of some dynamical studies have recently been provided by three groups. 22 ^ 24 The situation is much improved, although comparison of results from those groups suggests that there are some differences that could lead to different predictions regarding the reaction pathways. One of the three groups 22 has calculated kinetics parameters for both RDX and HMX and a second 23(c) for HMX (that is, they, performed TST and RRKM calculations based upon their PES) and provided detailed gas-phase mechanisms. These mechanisms have not yet been used in solid propellant combustion models. PES calculations and some gas-phase experiments on ADN have been performed by the Emory group yielding kinetics for the initial steps. 25 Their results were used to model the structure of an ADN gas-phase flame over the burning solid by taking the measured mass flux (inferred from the observed burning rate) and near-surface mixture (assumed to be the premixed reactants) as inputs. 26 The same kinetics were also used by that group in three-phase modeling 27 and by Miller and Anderson in their semi-empirical approach (unpublished). The earlier workers were unable to achieve agreement with experiment — computed burning rates were at least an order of magnitude too low.27 Miller and Anderson achieved agreement in preliminary results but had to assume that the surface product mixture evolved from ADN chang function of pressure (and, thus, surface temperature). Smooth burning rate versus pressure curves were observed for most other ingredients, which suggests that usually there is little change in decomposition mechanism with pressure; this in turn suggests that there is little change in surface products. The assumption

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that there is no change has worked well in all other cases Miller and Anderson have modeled. So our need to relax this assumption for ADN is unsettling. However, unlike most other ingredients, ADN exhibits a long plateau region and two sharp changes in gradient in its burning rate curve; thus, relaxation of the constant surface product set assumption may be correct for this special case. Further cross-checking of gas-phase flame structure is needed to determine efficacy of the semi-empirical modeling solutions. The Emory group has also done theoretical calculations on a model monomer for polymeric GAP energetic binder. 28 Further calculations on GAP and the related BAMO-AMMO and BNMO-NMMO energetic binders would be desirable. Theoretical calculations similar to those for RDX, HMX, and ADN have not been attempted for NQ or the nitramine CL20. Nor have they been attempted for any of the burning rate modifiers listed in the last column of Table 2, discussed in the next section. The community would greatly benefit from such work. Efforts would not only provide combustion modelers the necessary gas-phase mechanisms, but would probably also provide guidance regarding estimates about the condensed-phase breakdown. (c) Burning rate modifiers Burning rate modifiers replace a large fraction of the ingredients in a propellant to reduce or to increase the burning rate without adversely affecting energy content, shock sensitivity, etc. Successful use of modifiers is one of the most important topics in formulation science. A brief discussion of several possible modifiers of interest, and suggested reasons for their effects, are given below. To include modifiers in modeling, we must understand them as well as the major ingredients. Several burning rate modifiers are listed in the last column of Table 2. Two of these, TAGN and TAGAzT (also called TAGZT), contain significant numbers of NHX moieties in their structure; and they are known to produce copious NH 3 , amongst other species, upon pyrolysis. Miller and Anderson, in their earliest work with the new semi-empirical approach, modeled some simple binary mixtures of NG where small amounts of "dissolved" gas phase molecules such as H2, N2, CH 2 0, and NH3 were included. 12 We found that, whereas all the other species that we tried had only a modest effect on the NG burning rate, addition of a small amount of NH 3 produced a strong increase in the burning rate. We knew that NH2 and NH, the typical products of elementary reactions of NH3 in combustion, react much more


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rapidly with NO than the other species commonly occurring in nitrate ester combustion. We wondered whether this would lead more rapidly to the final product N2 and concomitant increased heat release near the propellant surface. The radical chain branching product channel of the NH2 + NO reaction (5a), that is NNH + OH, and consequent increase in the radical pool, is extremely important in this regard. Detailed analysis of the comparative model solutions (that is, NG with versus without NH 3 ) shows that this NHX chemistry, resulting in conversion of NO to N2, and the concomitant radical pool increase is, in fact, responsible for the predicted NH3 burning rate enhancement. Therefore, it is likely that the presence of the NHZ moieties in TAGN and TAGAzT is the primary reason for the increase in burning rates commonly obtained with these modifiers. NH3 plays a central role in "Thermal deNO^", 29 an industrial process whereby NO pollutant is removed from industrial furnace exhaust gases by mixing NH 3 into them under the proper conditions. The main reaction responsible is the fast reaction NH2 + NO (5a,b). This chemistry led Miller and Anderson to postulate its similar role in the propellant modifiers and to study the effects of the idealized "propellant" NG + NH3. There is a similar NO x removal process, RAPRENO x , in which HNCO is used. 30 For HNCO, under conditions in which H is the primary flame radical present, the most important reactions are HNCO+H = NH2 + CO (4), followed by NH 2 reacting with NO (5a,b). If this were the main pathway for HNCO removal, one would expect that an idealized HNCO "additive" would increase burning rate, similar to the effect of NH 3 . If the breakdown occurred mainly in the DZ, that pathway would be followed because our modeling concludes that in the DZ [H] » [OH]. H is normally the major flame radical under such rich conditions. However, near the propellant surface — the first-stage combustion region, where changes in heat release have their greatest effect on burning rate — there is almost always considerable NO2 and H + N 0 2 = OH + NO,

(9)

converting H to OH, is one of the fastest reactions known. Due to reaction (9), Miller and Anderson find that, near propellant surfaces, even though the overall mixture is usually quite rich,h [OH] is typically much larger than [H]. Under these conditions, the reaction HNCO + OH = NCO + H 2 0 (6) is the main removal pathway of HNCO. There is also h

T h e mixture is especially rich when one considers that the NO formed may not be very reactive, driving the effective equivalence ratio 3 1 quite high.

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a large concentration of NO present, so that the subsequent reaction of NCO with NO rapidly follows. NCO + NO yields N 2 0 + CO or N 2 + C 0 2 (7a,b), all of which are stable, non-radical products: this pathway results in radical loss and slows the global reaction. Anderson, therefore, suggested recently that the presence of HNCO near propellant surfaces might reduce propellant burning rates. 32 Preliminary modeling on NG/HNCO mixtures bears this out. 33 Curiously, this may happen even though the HNCO may reduce DZ length or eliminate the DZ altogether, because the HNCO chemistry converts NO to N 2 . Elimination of the DZ is desirable because it may reduce gun ignition delay (not to be confused with DZ ignition delay). 34 Because HNCO may reduce propellant burning rates, we seek modifiers that will produce it upon decomposition. Urea is known to break down to equal amounts of NH 3 and HNCO during combustion and is used in the NOj, removal process NOÔUT. 30 Indeed, this compound has been used as a "coolant" — a modifier thought to reduce burning rate by its thermochemistry. Now it appears this result may be due to kinetics. It is not clear, a priori, whether addition of NH3 together with HNCO would produce a burning rate increase, decrease, or no effect. Preliminary modeling of NG/NH3/HNCO mixtures suggests the effects of the HNCO overwhelm those of the NH3. 33 Thus, the strong burning rate decreases observed for urea, which probably produces equivalent amounts of both, are likely due to the chemical effects of HNCO on the radical pool. Other compounds suitable as propellant ingredients which may produce NH 3 or HNCO upon combustion are being sought. Nitroguanidine (NQ) is a candidate for NH3 production. Indeed, Oyumi et al. have shown NQ produces copious NH3 upon pyrolysis.35 Curiously, NQ can be used to reduce burning rate. Williams et al. suggested that, for NQ and a number of similar ingredients, this may be due to the formation of a residue inhibiting mass flux at the burning surface.36 Alternatively, the result may simply be due to the lower energy of NQ which may overwhelm its kinetic effects. If used in small amounts, NQ might, instead, increase burning rates. 12 The issue is further complicated by the production of HNCO during NQ pyrolysis.35 As noted above, even small concentrations of HNCO retardant may overwhelm the effects of the NH3. These ideas on the chemistry of NQ are supported by Miller and Anderson's modeling of M30, a propellant which contains considerable NQ. The model correctly predicts that no DZ is produced at any pressure. Detailed analysis confirms that this result is caused by the breakdown of the major ingredient NQ to NHX, amongst other species; and

Gas-Phase Kinetics for Propellant Combustion Table 3.

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Reactions important for modeling NH3 and HNCO producing additives. Reaction

NH3 producing additives NHa;+H = NHa:_i+H2 NrLs + OH = N H . - i + H 2 0 NH X + NO = products HNCO producing additives HNCO + H = NH 2 + CO HNCO + OH = NCO + H 2 0 NCO + NO = N 2 0 + CO NCO + NO = C 0 2 + N 2

Comments

x = 0-3 x = 0-3 x = 0-2

Most likely pathway in first-stage flame. More detailed discussion in Sec. 3.2.8 for NH 2 . Most important HNCO path in dark zone. Most important HNCO path in first stage. Primary NCO removal in first stage. Branching ratio in need of study. See Sec. 3.2.10.

the NH^ causes rapid conversion of NO to N2, preventing DZ formation (to be published).1 Isocyanates (R-NCO) might produce HNCO during combustion and be useful burning rate reduction modifiers. Brill, however, has pointed out that, although such compounds are frequently used during binder curing processes, they are currently thought too toxic for propellant formulation. Brill also suggested that another compound, DINGU, which produces copious HNCO upon pyrolysis, might be acceptable. 38 The importance of NH3 and HNCO as intermediates produced during combustion of propellants with modifiers suggests further elementary reactions that are of concern in the first stage of combustion for those propellants. These are listed, with comments, in Table 3. (d) Some related areas for future development Some nitrogen-containing, liquid fuels are used with inhibited red fuming nitric acid as oxidizer. In the past, hydrazine and its alkylated derivatives have found use, but monomethylhydrazine (MMH) has received most attention. 39 An MMH mechanism has been developed by Catoire et al.40 All the reactions of MMH and of its larger fragments need further study. Many of the rate coefficients are estimated, and the pressure dependence of the 'Bright orange flame emission directly above the propellant was always observed by Miller upon combustion of M30 in his strand burner. 3 7 Hot NH 2 is a strong emitter of yellow-orange emission, and there is little Na in the formulation, another common yellow-orange emitter. Of course, the observation of excited state emission by a given species is only suggestive of the presence of the ground state species, and no spectra were taken; nevertheless, this observation supports NH 2 formation during M30 combustion.

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unimolecular reactions is unknown. An MMH mechanism is being used in a vortex rocket engine model. 41 Diamino and amine azide compounds are being studied as possible replacements for the hydrazine compounds. Experimentalists should be vigilant about the results of theoretical estimates for new intermediates produced by the preceding solid propellant ingredients and burning rate modifiers. The models use the assumption that H2CNNO2 and H 2 CN are key intermediates produced during combustion of RDX and HMX. Of these species, only H 2 CN has received experimental study. Lack of a simple source and diagnostic for H 2 CNN0 2 has deterred study. Even for H 2 CN few kinetic data are available. Formerly, mass spectroscopy has been the only readily applied detection method. Recently, however, Nizamov and Dagdigian 42 (see the chapter by Dagdigian) have used intracavity ring-down spectroscopy to study kinetics of a few reactions at room temperature. This diagnostic tool will enable more studies.

2.2.2. Dark Zone Chemistry Prior to Miller and Anderson's modeling of the burning rates of several nitrate ester propellants, 13 many thought that the chemistry controlling the DZ length was not likely to affect the computed burning rates. Careful analysis of the solutions in Ref. 13 shows that this notion is wrong. Because the final flame zone at low pressures is separated from the propellant surface by the DZ, the burning rates at those pressures are quite insensitive to the reactions controlling DZ length (below about 300 atm in Ref. 13). In spite of our expectations, we found that the burning rates at high pressure are very sensitive to those same reactions. As pressure increases, the DZ collapses and the equilibrium products are close to the propellant surface. Previously, modelers thought that some short plateau region would probably be present in the gas phase temperature profile, blocking heat released in the second-stage flame from reaching the surface. In fact the computed solutions above 300 atm exhibit no plateau region. From the species profiles we found that, although the conversion of N 0 2 and HONO to NO precedes that of NO to N 2 , the conversion of NO to N 2 begins fairly close to the surface; the structured portion of those species' flame profiles is quite narrow. The concept of heat transfer characteristic distance, i.e. distance for 1/e falloff in effectiveness of transfer, helps to characterize results. 13 Considerable NO to N 2 conversion occurs within the heat transfer characteristic distance of the surface at high pressure, but not at low pressure. The reactions responsible for the conversion at high pressure are the same as those


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responsible for controlling the DZ length at lower pressures. To summarize: though the burning rate results at low pressures are not sensitive to the DZ reactions, they become highly sensitive to them at high pressures. Because only scant test data are available, the DZ formation should be studied and the DZ model improved. To guide this effort, we are reviewing the model and comparing it to the few available appropriate propellant combustion studies. 16 (a) Simplified DZ model A simplified model for propellant DZs is used to test the relevant chemical submechanisms. The approach and chemistry are also discussed elsewhere. 16 ' 17 ' 43 Composition and conditions of the DZs of nitrate ester and nitramine propellants were discussed towards the end of Sec. 2.1. Measured conditions at the leading edge of the DZ (e.g., temperature, pressure and mixture ratio) are used as inputs to an adiabatic, time-dependent chemical kinetics-only model to calculate the chemical ignition delay time of the DZ mixture. We assume adiabatic, convective plug flow; diffusion and conduction are ignored because the major species concentrations and temperature are fairly constant across the length of the DZ. The computed ignition delay is compared to experimental results by converting the measured DZ length to an equivalent ignition delay time using the convective gas flow rate. The latter in turn is computed using an estimated average molecular weight of the gases, the measured pressure, DZ temperature, and solid propellant burning rate, and a continuity assumption between solid and gas phases. The current model agrees with the available experimental data, but there are few measurements on solid propellants that provide all the information necessary to test the DZ model: the mixture ratio and temperature measured at the leading edge of the DZ and the DZ length, the propellant density, and burning rate at the pressure of interest. Thus the model has not been well tested. Heller and Gordon 44 studied three NC/NG propellants. For one of these, all data needed to test the DZ model was provided except the H2O concentration; that quantity is derived by a mass conservation assumption. The needed physical data for several other nitrate ester propellants was provided in the work by Aoki and Kubota 45 ; but the DZ mixture composition was not measured. One of Aoki and Kubota's propellants was similar to the key one of Heller and Gordon. Comparison with other works suggests the DZ mixtures do not vary strongly amongst such similar nitrate ester propellants (see results of Refs. 13, 44, 46, 47 compared in Table 4 of Ref. 13a).

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Therefore, it is reasonable to use the Aoki and Kubota DZ physical data for that one, but with the Heller and Gordon initial DZ chemical composition, as a further test of our DZ mechanism. A pleasing aspect of each of these two data sets is that both provide a measure of DZ ignition delay (length) over a range of pressures from about 10-35 atm. Another very important point regarding the Heller and Gordon data is that equilibrium conditions for the final gas phase products may be calculated starting with either the initial solid propellant composition or the DZ mixture. The results should be equivalent. They thus provide an important validity check on the DZ condition measurements. The adiabatic flame temperatures and equilibrium concentrations obtained in the two ways are, reassuringly, consistent. For nitramine propellants, fewer well-defined test data are available. In prior works, 17-43(b) comparisons were made with data from Kubota 48 on his own formulations of experimental HMX-binder propellants. It now appears the DZ mixture ratio in those experiments was not extracted reliably from the results and the data may have to be discarded. The main problem is that H 2 0 could not be measured and no HCN was observed. The lack of HCN in the DZ should be viewed with suspicion because it is known to form in copious amounts during HMX pyrolysis49 at the surface temperatures observed in Ref. 48. HCN has been observed in combustion experiments on other HMX propellants (see the review in Ref. 17). HCN is relatively stable; gas-phase models of solid nitramine combustion indicate it would survive through the first stage into the DZ. Because Ref. 48 leaves two major species concentrations unknown, the extraction of the complete mixture ratio is impossible. We have found only one data set 50 that can be used for nitramine propellant for an RDX-GAP mixture at f atm. A 400 watt CO2 laser beam impinges on the surface to heat the solid to obtain sustained, steady-state combustion of the propellant at this low pressure. Unfortunately, it is quite uncertain how much laser energy is absorbed into the propellant; some may go into the gas phase and some may reflect off the surface. Due to this absorption, the energy in the DZ is larger than in an equal mass of the solid phase propellant. Thus a consistency check like that performed with the nitrate ester propellants is not possible. Equilibrium calculations do at least show that the computed flame temperature of the DZ mixture is much larger than for the solid propellant, as one would expect. The current DZ chemistry submechanism is in good agreement with available experimental results for both nitrate ester and nitramine propellant types. The check for nitrate ester propellant DZs is reassuring, but at


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least one more complete data set, similar to Heller and Gordon's, should be obtained. For nitramine DZ chemistry, the available tests are not sufficient. Further measurements relevant to DZs for this propellant type should be made over a range of pressures similar to that used for the nitrate esters. The measurements should be made without heating-assisted combustion, e.g. using a CO2 laser. It is important to ascertain how much HCN is present without the laser assist because pyrolysis studies indicate that the branching to HCN versus CH2O formation in the condensed phases is strongly affected by temperature. 49 The [HCN] in the DZ is as important to know as [NO], because the HCN reactivity is similarly low. Modeling indicates that HCN formed in the first stage also contributes to the DZ formation. The temperature at the leading edge of the DZ should be measured as precisely as possible because the modeling calculations are extremely sensitive to temperature. In addition to measurements on propellants, the kinetics of reacting idealized DZ mixtures should be studied. Measurements on actual propellants, e.g. in strand burners, provide key information regarding actual conditions (initial temperature and mixture ratio). However these are clearly not the most desirable experiments for kinetics mechanism tests because the exact initial conditions cannot be controlled, or known, nearly so accurately as in a kinetics apparatus. For example, there are fairly wide error limits on measured species concentrations and temperature from experiments on propellant DZs. Calculated DZ ignition delays are quite sensitive to some of these input DZ conditions, especially the N 2 0 concentration and temperature. Also mixture ratios in kinetics apparatus usually can be varied easily while changing the DZ conditions cannot be done in a straightforward, controllable manner. Varying gaseous mixture ratios would provide a measure of global mechanism reaction orders for the components of the DZ mixture. Kineticists have found for many other chemical systems that such data provide stringent tests of proposed mechanisms. Such experiments could, for example, help resolve the issue about HCN chemistry discussed in Sec. 2.2.1(a). Relevant measurements would be most easily obtained in shock-tube experiments, perhaps by obtaining mixture ignition delay times; though possibly other techniques might be used. Experimentalists interested in pursuing this idea should note that the reactant concentrations likely to be required are quite high. This point could bring safety and collider vibrational energy transfer issues into concern.

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(b) Sensitive reactions in DZ submechanisms A listing of reactions to which DZ calculations are known to be sensitive is presented in Table 4. Parts of Table 4 highlight reactions of particular importance to nitrate ester and nitramine propellants. Comments in the table identify reactions needing the most work because of high sensitivity and poorly characterized rate coefficients. The last four reactions in Table 4 are no longer included in our reaction mechanisms. If included in DZ models, the first three of these reactions became reversed and were highly sensitive, in the models, because they were incorrectly predicted to be important radical sources. These three reactions are discussed further in the next few paragraphs. The results highlight how modeling of global reactions can yield important mechanistic insights. The last reaction is not included in current models because its rate is uncertain, but it is likely to be negligible. Our early effort at DZ modeling 17 highlighted the possible significance of the first of these now-discarded reactions, N + C 0 2 = N O + CO.

(10)

The rate coefficient expression used was from Ref. 51, which had been commonly used in DZ and other combustion modeling. The reaction reverses in DZ modeling, producing radicals, because there is considerable NO and CO in DZ mixtures, but no other significant source of N atoms. Although early modeling yielded good agreement with experiment when this reaction was used and the reaction was highly sensitive, a critical literature review reported in Ref. 17 brought its importance into question. The reaction was tentatively removed in spite of adverse effects on agreement with experiment and revisions were made to the models. Later efforts, discussed in Sec. 3.2.6, have yielded strong evidence that the reaction is too slow to be important under any condition, so it has been permanently discarded. It was also checked against later static reactor experiments, see a few paragraphs below. Rohrig and Wagner 52 performed shock-tube experiments on the reactions of NH with H2, CO2, and H2O. This was the first indication that the latter two reactions occur; they suggested that these proceed as NH + C 0 2 = HNO + CO,

(11)

NH + H 2 0 = HNO + H 2 .

(12)

Recent thermostated reactor work by Fontijn et al.53 yielded NH + H 2 rate coefficients in accord with those of Rohrig and Wagner, indicating

Gas-Phase Kinetics for Propellant Combustion Table 4.

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Sensitive reactions controlling propellant dark zone structure. Comments

Reaction

Relevant to both nitrate ester and nitramine propellant DZs Extremely important for dark zones of nitrate ester * HNO + NO = N 2 0 + OH propellants. High T study needed; challenging. * HNO + HNO = N 2 0 + H 2 0 See comments in Table 1. * N 2 0 ( + M ) = N2 + 0 ( + M ) Entire T range needs study. Likely to require high * N 2 0 + NO = N 2 + N 0 2 [NO], therefore complex modeling, N 2 0 ( + M = NO) likely to interfere. (Efficiency for M = NO in N 2 0 ( + M ) is a likely, desirable by-product of such a study.) NH + NO = H + N 2 0 H + N 2 0 = N 2 + OH See Table 1 and Sec. 3.2.2. H + HNO = H 2 + NO H + HNO = NH + OH NH 2 + NO = NNH + OH See Sec. 3.2.8. NH 2 + NO = N 2 + H 2 0 See Sec. 3.2.8. Primarily relevant to nitrate-ester propellant DZs * HNO + N 0 2 = HONO + NO H + NO(+M) = HNO(+M) See Sec. 3.2.5. N 0 2 O M ) = NO + O ( + M ) H + NO2 = NO + OH See Sec. 3.2.4. 0 + N 2 0 = NO + NO Reversed under dark zone conditions, modest radical source. See Sec. 3.2.1. N + NO = N 2 + OH NO + H = OH + N : :

C H 3 + N O = H 2 CN + OH CH 3 + NO = HCN + H2O

Primarily relevant to nitramine CO + O (+ M) = CO2 (+ M) CO + N 0 2 = NO + C O a HCN + O = NH + CO * HNC + O = NH + CO * HNC + OH = HNCO + H HNCO + H = NH 2 + CO NCO + NO = N a O + CO * NCO + N 0 2 = products

This reaction pair is sensitive only if CH4 trace species is considered in the starting mixture (best models include it). propellant

DZs

See Sec. 3.2.10. See Sec. 3.2.10.

Reactions discarded from recommended combustion mechanisms N + C 0 2 = NO + CO It is now established that this reaction does not occur with fast enough forward rate to any products to be of significance in combustion. See Sec. 3.2.6. NH + C 0 2 = HNO + CO This reaction occurs with a significant forward rate, but not to the products shown. See Sec. 3.2.7.

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(Continued) Comments

Reactions discarded from recommended combustion mechanisms (Continued) * NH + H2O = HNO + H2 This reaction occurs with a significant forward rate, but not to the products shown. See Sec. 3.2.7. * CO + N2O = CO2 + N2 The rate coefficient expression for this reaction is highly controversial. Our opinion is that it should be discarded from combustion mechanisms. ' T h e s e reactions need further study, currently many of these are included only via crudely-estimated rate coefficients. Efforts on these are especially desirable.

that the respective techniques give correct results. However, if the products shown for reactions (11) and (12) are included in nitrate ester DZ models, the global rates are over-predicted by several orders of magnitude. This results from H + NO (+ M) = HNO (+ M)

(13)

H + HNO = H 2 + NO

(14)

and

having, very roughly, equal forward and reverse rates in DZs. This creates significant traces of HNO. Because the DZ mixtures also contain much CO and H2, and there is no other significant source of NH, reactions (11) and (12) reversed, producing NH radicals, when included in early DZ models. They were predicted to be so fast that they overwhelmed other sources of radicals. The result was that the predicted chemical delay time in the DZ, and hence the DZ length, was much too short, indicating no DZ would exist. This result is strongly contrary to experiment, suggesting that reactions (11) and (12), with the products as shown, are incorrect, as further discussed in Sec. 3.2.7. Further insight into reactions (10)-(12) is available from modeling of the isothermal static reactor experiments of Diau et al.,8 who studied H2/NO and H2/CO/NO mixtures diluted in Ar at 900-1225 K. Three example runs for the latter mixtures are given in their Fig. 2. Our (WRA) modeling results are qualitatively similar for each. Results for their case B, run 8 are presented here, see the present Fig. 2; conditions are constant pressure 0.930atm, constant temperature 1000K, and initial mole fractions of H 2 , NO, CO of 0.0263, 0.0161, 0.0430, respectively. Excellent agreement of base


0.5

1.0 Time, 101 s

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1.5

Fig. 2. Comparison of experimental 8 and modeling results (this work) for a H 2 / C O / N O / A r mixture at 1000K. Note the different timescales in (a)-(d). (a) Experimental results (points) and modeling result using baseline mechanism (curve). (b) Modeling result when N + CO2 = NO + CO (10) is added to the baseline mechanism, using experimental forward k(T) from Ref. 51 and thermodynamics to compute the rate of the assumed reverse reaction. (c) Modeling result when NH + H 2 0 = HNO + H 2 (12) is added to the baseline mechanism, using experimental forward k(T) from Ref. 52 and thermodynamics to compute the rate of the assumed reverse reaction. (d) Modeling results when NH + CO2 = HNO + CO (11) is added to the baseline mechanism, using experimental forward k( T) from Ref. 52 and thermodynamics to compute the rate of the assumed reverse reaction.

mechanism predictions with experiment for [CO2] is achieved, see Fig. 2(a). However, when N + CO2 = NO + CO (10) is added, using k from Ref. 51, the predicted CO2 production rate becomes about two orders-of-magnitude too fast, see Fig. 2(b). If instead NH + H 2 0 = HNO + H 2 (12) is added, using k\2(T) from Rohrig and Wagner, 52 the predicted rate is about three orders too fast, see Fig. 2(c). Finally, if NH + C 0 2 = HNO + CO (11) is added instead, using fcn(T) from Rohrig and Wagner, the predicted rate is four orders too fast, see Fig. 2(d). The suspicions raised by the

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preceding observations on dark zone and static reactor modeling spurred the isolated reaction experiments and ab initio studies discussed in Sees. 3.2.6 and 3.2.7.

3. Experimental Input Data 3.1. Elevated Temperature Techniques for Obtaining Kinetic Data on Individual Reactions Accurate information on individual reactions, which together govern global propellant combustion processes, can best be obtained in isolation from competing reactions, when possible. Techniques for providing such environments have originally been developed for at, or near, room temperature studies. Till about 1970 little information was available on individual energetic materials (EM) combustion reactions at temperatures of interest. Since then apparatus has been developed that operates on the same principles as the room temperature methods, but different materials have allowed temperatures up to around 1800 K to be reached. Thermostated reactors, used with optical spectrometric monitoring for the determination of reactant concentrations, are particularly relevant for EM reactions (Sec. 3.1.1). Thus, information on the kinetics of many of the reactions of interest to modelers can now be obtained at or near the temperatures of interest. Most of the processes which can be isolated are between atoms, or other small transient species, and a second, molecular, reactant. The equipment to be discussed is particularly suited for observations on such reactions. However, reactions between transient species can, and have in some cases, also been studied. Simultaneously with these developments, shock-tube techniques, which were typically used for multi-reaction environments observations above about 2000 K, have undergone refinements to allow measurement on isolated reactions below that temperature. This approach is discussed in Sec. 3.1.2. These technique developments are not unique to EM combustion. Thus, e.g., fossil fuel combustion and related NO^ (NO, N0 2 ) pollution generation and abatement models also require input data on elementary reactions at realistic temperatures. These have been investigated in the same type of apparatus. 3.1.1. Thermostated Reactors Isolation of individual reactions is achieved in these reactors by introducing small concentrations of two reactants in a large excess of inert bath gas.


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Usually Ar or He are used for this purpose, while N2 can sometimes also be useful. Under these conditions, the pressure and temperature of the bath gas are essentially the pressure and temperature of the reaction, which thus can be varied independently of the reactant concentrations. Several versions of this type of apparatus exist. Of these, high-temperature photochemistry (HTP) reactors have been most frequently used for EM studies at temperatures of interest. In that type of reactor, atomic or other small transient species are generated from a parent compound, the photolyte, by means of a flash lamp or pulsed laser. 53-55 These species are used as the rate-limiting reactants. Their relative concentration as a function of reaction time gives the reaction rate at the particular concentration of the second reactant, i.e. of the reactant present-in-excess, and of the bath gas. Varying these latter two parameters then allows determination of the rate coefficients. Since the limiting reactant is present in small concentrations, so is the product concentration limited, which usually prevents interference from secondary reactions. The transient species concentration is monitored by fluorescence or, occasionally, light absorption. A schematic of an HTP reactor is shown in Fig. 3. A ceramic reaction tube, surrounded by SiC resistance heating elements and soft ceramic insulation, is contained in a vacuum chamber. The use of these materials has allowed the «1800K maximum temperatures to be reached. The reaction tube has four holes at right angles which face windows in the chamber. Two windows at opposite ends are used for the photolysis and diagnostic radiation beams. At a third hole, a photomultiphier tube (PMT) and associated electronics is used to measure the fluorescence intensity, which is proportional to the transient species concentration. The observed reaction zone is thus delineated by the intersection of the photolysis beam, the diagnostic radiation, and the field of view of the PMT. Consequently, the measurements are made in an essentially wall-less reaction zone. The diffusion times of the reactants to the walls are long compared to the times during which the reactions are observed. A movable water or air-cooled inlet tube is used to minimize the exposure time of the reactants to high temperatures. The bath gas, Ar or N2, flows in from the upstream (bottom) reactor plate. The flows are sufficiently slow that mixing of the reactant and bath gases is at least 99% complete before the photolysis pulse. Observed reaction times are in the order of 10~ 4 to 10 _ 1 s, short compared to the gas residence times, i.e. these are real-time observations. The photolysis radiation repetition rate is such as to allow essentially complete replacement of the gas mixtures between pulses.

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REACTION TUBE HEATING RODS

SHIELDED THERMOCOUPLE CW RESONANCE LAMP hv, H ( 2 P - 2 S )

NH3orCH4 + nd 2 REACTANT

MULTI-CHANNEL SCALER/COMPUTER

Fig. 3. Schematic of a high-temperature photochemistry reactor. The reactor is shown as configured for H-atom reaction measurements.

Flash lamps, emitting in the UV and vacuum UV (VUV) regions of the spectrum, have been used as photolysis sources. The flashes tend to interfere with diagnostic equipment; pulsed lasers are, therefore, preferred. The principal atomic reactants of interest in EM reaction models, O, H, and N, all have resonance lines in the VUV. Their concentrations are conveniently monitored by excitation of fluorescence resulting from cw microwave discharge flow lamp radiation. The PMT output is then fed to multi-channel sealer-based electronics to produce the fluorescence intensity versus time plots, which yield the reaction rates. Many flashes are needed for accurate data. For di-, or poly-atomic species detection, e.g. NH, NCO, lasers are often needed. Pulsed dye lasers have been employed for this purpose. As each pulse of these yields only one point for the intensity versus time plots, variable time delays are used in those experiments. Details of the operation of HTP reactors and the data analyses have been discussed in many original papers, e.g. Refs. 53-55. Other diagnostic techniques could in principle also be employed in HTP experiments


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and have sometimes been used in lower temperature apparatus. The major requirement is that the diagnostic equipment can be placed outside the vacuum housing and not be significantly interfered with by radiation from the hot reaction tube walls. Several laser-based techniques would be suitable. Some of these have been used in flame research and in practical devices, and hence can be compatible with high-temperature observations. 56 (See also the chapter by Dagdigian.) For atomic and diatomic reactants in HTP-type reactors, there would be little advantage in using more laborious diagnostics. However, those techniques could become essential when extending the research to larger reactant species and to quantitative product measurements. Several reactions have been studied in thermostated tubular electricaldischarge fast-flow reactors (EDFFR). There, reaction time is determined from the flow velocity and the distance traveled and a steady state is obtained at each cross-section of the reaction tube. Optical techniques have been used there as well, but, importantly for product analysis, mass spectrometry can readily be employed with such reactors. The latter allows determination of the masses of the reactants and the products in one experiment, as well as for investigation of reactions between transient species.57 However, in EDFFR reactors, the reactants come in contact with the heated walls, which in many cases leads to dissociation of reactants or products in the temperature regime of EM interest. Thus their use in EM-oriented research has been limited. For the study of metallic species, involved in e.g. metallized solid propellant combustion, a thermostated fast-flow reactor has been developed, which allows measurements over the same temperature range as the HTP reactors. 58 It has also been used for product identification by mass spectrometry. 59

3.1.2. Shock Tubes. Comparison of Techniques Shock tubes are the most appropriate tool for obtaining kinetic information at temperatures above about 2000 K. In shock tubes, similar spectrometric transient reactant species detection methods as above are often used. By additionally monitoring the concentrations of simple intermediate products, information on the reaction channels has sometimes been obtained and the observed rates can then be associated uniquely with a particular reaction. 60 ~ 62 Tn most shock-tube experiments, the transient reactant species are produced as a result of thermal dissociation. This typically leads to a multiple reaction situation, requiring complex modeling to extract

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kinetics results. However, in the temperature domain of interest, the shock waves can occasionally be used to heat gases to selected temperatures where only specific small transient species are produced. Reactions of these species are thus isolated. Similarly, a high-temperature undissociated gas mixture can be generated in which flash- or pulsed laser-photolysis then produces the desired transient reactants. In such photolysis shock tubes (PST) an environment is thus also created for the study of isolated elementary reactions. PST is typically suitable for the temperature range 700-2200 K. 6 3 - 6 5 This range partially overlaps that of the thermostated reactors. It is therefore interesting to compare HTP and PST. In HTP work, the reactant gases become premixed and reach operating temperature while flowing to the observed reaction zone. PST uses premixed gas and provides very rapid heating. This results in shorter required survival times of thermally unstable species than in HTP. Neither PST nor HTP can be used at temperatures where significant dissociation occurs within the required time range. The indicated maximum temperatures can, therefore, often not be employed. However, because of the shorter residence times, PST can always be used to reach higher temperatures than HTP. At those temperatures, direct PST measurements are clearly to be preferred over extrapolation of HTP results. However, a wider rate coefficient range has been covered by HTP, from « 1 0 - 1 0 (which corresponds to reaction upon every collision) to « 1 0 - 1 7 cm 3 molecule^ 1 s _ 1 , as compared to « 1 0 _ 1 0 to «10~ 1 4 cm 3 molecule" 1 s _ 1 for PST. HTP has also been used for termolecular reactions, which has apparently not been attempted by PST. The capability of HTP reactors to work down to about 300 K, and with modification below that temperature, can yield important mechanistic information. In practice, the two techniques well complement each other and agreement between results obtained from both reactor types has usually been good. 66 ' 67

3.1.3. Reaction Mechanisms Many of the elementary EM reactions studied thus far have been atom reactions for which there is often little doubt about the products. If there are potentially alternative channels, thermochemistry is often used to define the actual reaction paths. Variation of the pressure, which is approximately determined by the bath gas concentration, allows one to distinguish between ter- and bi-molecular reactions. In several cases, the importance of the


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bimolecular channels increases with temperature. For polyatomic reactants, product identification becomes more difficult. The same type of optical diagnostic techniques as used for the reactants can sometimes still be used to identify simple products. In some lower temperature experiments, even tri-atomic products have thus been monitored, and branching ratios have been determined. 68 ' 69 Some reactions lead to chemiluminescent products, which are thus readily identified.70 To obtain experimental evidence, over wide temperature ranges, that even identified product paths are unique is at best very time-consuming and often not possible. However, it is especially here that theoretical calculations, such as by ab initio and quantum-RRK methods, can be very helpful. Moreover, the modeling of global experiments can sometimes reveal that an expected intermediate product cannot have formed to a significant degree. Several examples in Sec. 3.2 illustrate the ways by which information from various sources can be combined to yield the desired product information. The theoretical methods can also reveal what the likely intermediates and transition states along the reaction paths are, as also illustrated in that section. A detailed discussion of that topic, i.e. of microscopic kinetics, is beyond the scope of the present chapter. 3.2. Examples of Results on the Models

with Significant

Impact

3.2.1. 0 + N 2 0 This reaction has two channels O + N 2 0 - • 2NO, 0 + N 2 O ^ N 2 + 02,

AF 2 ° 98 = - I S O k J m o r 1 1

AF0 9 8 = - 3 3 1 k J m o r .

(15a) (15b)

Till fairly recently the accepted wisdom was that, from at least 1200 to 3200 K, both reactions occur with essentially the same rate coefficients, i.e. the branching ratio is about 50%, independent of temperature. However, most studies were made above 1700 K and no direct measurements were available below that temperature. Extrapolation down to dark zone temperatures of the results of a 1992 shock-tube study of N 2 0 pyrolysis suggested that k15 = k15a + fc15b had to be revised upward for that regime for which also fc15b > fci5a.71 A kinetic modeling study further showed that some ancillary chemistry, upon which the earlier evaluations were based, was not in accord with subsequent information.72

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An HTP study of fcis around HOOK then showed these rate coefficients to be much larger than previously assumed, though a factor 4 lower than the long extrapolation of the 1992 shock study would suggest. 73 This result, combined with those high temperature data that survived a critical evaluation based on current knowledge, then led to 7 2 fc15a (1370-4080K) = 1.5 x 10" 1 0 exp(-13,930K/T) and k15h (1075-3340 K) = 6.1 x 10" 1 2 exp(-8,020K/T) cm 3 molecule" 1 s" 1 . This indicates that channel (15b) dominates below 1840 K and (15a) dominates above that temperature.

3.2.2. H + N 2 0 This reaction is one of the most sensitive in propellant combustion modeling. Its principal path is AiJ^g = - 2 6 1 k J m o r 1 .

H + N 2 O ^ N 2 + OH,

(16)

The HTP observations yielded74 k16 (750-1310 K) = 7.3 x lO" 1 0 exp(—9690K/T) cm 3 molecule -1 s _ 1 . These are shown in Fig. 4, where they are compared to the 720 to 1120 K EDFFR results from Albers et al.75 T,K „

1500

1000

700

500

400

2.0

2.5

10

V

(/> 3 O 0>

1I U0-13

10-14

o E CO

E °. 10-" J*

10-16

0.5

1.0

1.5 1

1000/T, K"

Fig. 4. Plot of the rate coefficients obtained for the reaction between H and N2O. (•) H T P ; (—) fit to H T P work; (—) results of Albers et al.,75 discharge/fast flow reactor.


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There is excellent agreement in that temperature range. The lower temperature data show considerable curvature, as confirmed in several subsequent studies. 76 ' 77 The interpretation of this curvature has led to much debate. Marshall et al74'76 made BAC-MP4 and transition state calculations and found that the following detailed mechanism agreed with the data H + N 2 0 -> HNNO - • NNOH -> N 2 + OH.

(16')

The curvature was attributed to tunneling through the barrier for the HNNO —> NNOH transition. However, quantum-RRK calculations by Dean and Bozzelli et al.7S'79 suggested instead that collision-induced stabilization of the HNNO intermediate is responsible. While Marshall et al. did not observe any pressure affect, Dean and Bozzelli expect that more extensive pressure-dependence measurements at the lower temperatures would show that stabilization occurs. Ab initio calculations by Diau and Lin have led to the conclusion that the adduct stabilization is more significant than tunneling, with the latter increasing in importance at lower pressures. 80 However, they 80 consider the tunneling to be predominantly through the barrier for the H-atom addition step in (16'). Direct experimental evidence for a pressure effect remains desirable, but will be very difficult to obtain in view of the small rate coefficient values at the lower temperatures. 3.2.3. H + NH 3 ^ NH 2 + H 2 The reaction H + NH 3 -> NH 2 + H 2 ,

AH2°98 = ^ k J m o P 1

(18)

has frequently been studied, because of its interest not only to EM but also to various other problems, such as NO^ pollution prevention. Good agreement has been obtained by various techniques, as well as by ab initio studies. The work has been thoroughly reviewed by Michael,81 who, with his co-workers, also covered the widest temperature range, by using a PST technique. 82 They measured fc17 (910-1780 K) = 3.0 x 10" 10 exp(-8067K/T) cm 3 molecule -1 s _ 1 . This result is essentially the same as obtained from an HTP 6 7 and an EDFFR 8 3 study for the lower part of this range. Extension of the data to 470 K leads to 6 7 , 8 1 kn (490-1780 K) = 9.0 x l O " 1 9 ( T / K ) 2 4 0 exp(-4991K/T) cm 3 molecule- 1 s" 1 . This expression is also well-matched by various theoretical approaches. 84,85 The nearly thermoneutral H + NH 3 reaction is further of interest in that it represents one of the relatively rare examples where a reaction and

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Fontijn

its reverse NH 2 + H 2 - • NH 3 + H,

AiJ2°98 = - 1 7 k J m o r 1

(-17)

could both be measured. This was achieved indirectly by Sutherland and Michael86 on the assumption, apparently valid for their mild NH3-photolysis conditions, that in their PST experiments the initial [NH2] and [H] are equal. No observation of NH 2 was required under those conditions. An equilibrium constant was obtained, which, combined with kn, led to k-n (900-1620 K) = 5.4 x 10" 1 1 exp(-6492K/T) cm 3 molecule" 1 s" 1 . At the lower end of this temperature range, these results agree with those from the direct EDFFR study of Hack et al.,83 where the NH 2 was produced from the NH 3 +F reaction and observed by LIF. A recent shock-tube study for the 1360-2130 K temperature domain also gave very good agreement. 87 In that work, the NH2 was produced by N2H4 dissociation and its concentration was monitored by a novel frequency modulation technique. Computational studies 84 ' 85 again well describe these results. 3.2.4. H + NO2, CH3NO2 The reaction H + N 0 2 -> OH + NO,

AH%98 = - 1 2 4 k J m o r 1

(9)

has recently been studied from 1100 to 1650 K in a shock tube. 88 There the chemical isolation was achieved by producing H atoms from the thermal dissociation of C2H5I, rather than by photolysis. In addition to monitoring [H], rate coefficients were also obtained from 1250 to 2000 K by monitoring of the OH product, combined with chemical simulation. This yielded statistically overlapping data, as had lower temperature studies. It can, therefore, be concluded 88 that kg (195-2000 K) = 1.5 x 10~ 10 cm 3 molecule" 1 s" 1 . Thus, (9) is a very fast reaction, the rate coefficients of which approach gas-kinetic collision values and show no observable ( N 2 + H 2 0 ,

Aif2°98 = 2 kJ mol - 1 ,

(5a) -1

AH%98 = - 5 2 4 k J m o i .

(5b)

Reaction (5a) is also often written as leading to N 2 + H + OH, since under most conditions the NNH dissociates rapidly to N 2 + H. Theoretical studies have shown the reactions to proceed sequentially through NH 2 NO and HNNOH intermediates. 79 ' 96 Both the rate coefficients and the branching ratios have been the subject of considerable problems, originating from an inadequate knowledge of secondary reactions in complex environments. 97 ' 98 There now are consistent results for the total rate coefficients determined by (i) Silver and K o l b " from 294 to 1220 K in an EDFFR, using LIF to monitor the NH 2 , (h) a modeling study of Miller and Glarborg 97 for the NO, N 0 2 , N 2 0 , and NH 3 profiles from atmospheric pressure N O / N H 3 / 0 2 / H 2 0 / N 2 mixtures in a quartz plug flow reactor, (iii) a theoretical study by Miller and Klippenstein, 96 (iv) the extrapolation of a 1716-2507 K, 1.3-1.8 bar


Modeling

231

shock-tube study by Hanson, Bowman as., 9 8 of CH 3 NH 2 /NO/Ar mixtures, where a cw frequency-modulated narrow line (here 597.4 nm) laser absorption technique 98,100 was used to monitor the NH 2 , j and (v) a similar study by Hanson c.s. 101 from 1262-1726 K, where C 6 H 5 CH 2 NH2 was used instead as the NH 2 precursor. By combining their results with low temperature studies the latter, most recent, work led to k5 (200-2500 K) = 1.1 x 1 0 - 8 ( T / K ) - 1 2 0 3 exp(106K/T) cm 3 molecule" 1 s^ 1 . The reaction thus has a negative temperature dependence, in accord with the formation of intermediates. The branching ratio a = k5&/(k5a + fc5b) has been determined largely by the same groups. The Stanford group obtained it from [NH2]-time profiles and extensive modeling. 101 ' 102 The result is in agreement with the theoretical 96 and modeling 97 studies by Miller et al, indicating an increase in a from about 0.1 at 300K to 0.7 at 2000K. Deppe et al.,62 in a shocktube study, observed the product H and OH concentrations directly by, respectively, atomic resonance absorption and narrow laser line absorption. Their measurement of 50% at 1500 K is in accord with the other studies; at 2800 K, a approaches 90%.

3.2.9. CN + OH Individual reactions of CN and OH radical species have been studied at temperatures up to 1500 K in HTP reactors. 103,104 Shock-tube studies have included the reaction between these radicals CN + OH -> NCO + H,

AiJ2°98 =

97kJmor1

(21a)

CN + OH ^ HCN + O,

Aff° 98 =

gOkJmol" 1

(21b)

CN + OH -> NH + CO,

Aff° 98 =

227kJmor1.

(21c)

In that work 105 HCN/HN0 3 /Ar mixtures were used. The first compound served as CN source, the second as OH source. Both were monitored by cw narrow laser line absorption. The measurements gave fc21 (1250-1860 K) = 6.6 x TO"11 cm 3 molecule 1 s 1 . Reaction (21a) is thought to dominate in this temperature range, with (21b) becoming of increasing importance at higher temperatures.

JThe frequency modulation led to an order of magnitude increase in sensitivity for NH 2 over their earlier cw narrow laser line absorption technique.

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3.2.10. NCO + NO, N 0 2 The reactions NCO + NO -> N 2 0 + CO, NCO + NO - • N 2 + C 0 2 ,

AiJ2°98 = -278 kJ m o h 1

(7a)

1

(7b)

Ai72°98 = - 6 4 3 k J m o r

were studied, by techniques similar to HTP, by Atakan and Wolfrum106 from 294-1260 K and by Becker et al.107 from 290-1098 K, respectively. A shock-tube study in the 2380 to 2660 K range used narrowline absorption to monitor the NCO reactions. 108 These data, combined with further low temperature studies, yield k7 (294-2660 K) = 2.3 x 1 0 - 6 ( T / K ) ^ 1 7 3 exp(-384K/T) cm 3 molecule -1 s" 1 , independent of pressure. This reaction thus has a strongly negative temperature dependence, related to the formation of an OCN-NO intermediate complex. It can decompose to N 2 0 + CO or via a cyclic OC(0)NN intermediate form N 2 + C 0 2 . 1 0 7 Both channels are significant over the temperature range investigated. No accurate branching ratio information appears to be available at temperatures of EM interest. However, Hershberger c.s.68 made a determination from 296-623 K. They found 44 ± 7% to follow Eq. (7a), and 56 ± 7% to lead to the channel (7b) products, independent of temperature. These authors used UV laser photolysis, combined with time-resolved, narrow-line, infrared diode laser absorption spectrometry of the reactants and products. Their narrow line technique has an advantage over LIF in that absolute product concentrations can be more readily obtained. The method becomes increasingly less sensitive with temperature, which has, thus far, precluded its use at higher temperatures for kinetic studies. If this problem could be overcome, possibly by use of multi-pass cells, their method could become a valuable addition to the existing techniques for branching ratio measurements. Another NCO reaction important for the reduction of a heteronuclear reactive N-compound directly or indirectly to N 2 is NCO + N 0 2 -» N 2 0 + C 0 2 ,

A# 2 ° 98 = - 4 6 7 k J m o r 1

(22)

where the product channel shown is thought to be dominant. The N 2 0 formed can be reduced to N 2 via the H + N 2 0 reaction, discussed in Sec. 3.2.2. Wooldridge et al. measured reaction (22) in a PST experiment near 1250 K, with cw narrow laser line absorption monitoring of the NCO. 65 Juang et al. measured it from 294 to 774 K using laser photolysis-LIF. 109 The two data sets can be combined 109 to yield fc22


Modeling

233

(294-1250K) = 6.4x KT 1 0 (T/K)-°- 6 4 6 exp(164K/T) cm 3 molecule" 1 s" 1 . The product channel given is thought 65 to be dominant, apparently based on the 298-500 K III laser diode study of Park and Hershberger, 69 which indicated a 92% contribution for it.

4. Conclusions Modeling using kinetics mechanisms composed of elementary gas-phase reactions has greatly improved the understanding of propellant combustion. We have described: (i) why studies to improve our understanding of propellant combustion, especially the gas-phase structure and mechanisms, are of interest; (ii) methods to study kinetics of the relevant elementary reactions in isolation, thus increasing realism of the mechanisms; (iii) the current status of understanding of all these issues; and (iv) directions for future research that are likely to be most fruitful. The advances in propellant combustion modeling and in understanding of the associated gas-phase mechanisms have been achieved by a number of factors: (a) the increased sophistication of both propellant and kinetics modeling techniques; (b) the ability to perform measurements on isolated reactions at combustion temperatures; and (c) the possibility to study reactions by powerful new theoretical chemistry techniques. These factors have also contributed to the progress of chemical kinetics itself, from rate coefficient information to increased insight into mechanisms as exemplified by several of the investigations discussed in Sec. 3.2. For some, perhaps most, ingredients, it is not certain what the initial large fragments are. The reactions producing large fragments likely occur in the condensed phase and/or near-surface gas-phase regions. Because their vapor pressures are not high, many ingredients likely decompose, rather than vaporize. Which initial gas species are formed is clearly a major concern — it defines what gas-phase reactions must be considered. Suitable techniques for condensed-phase kinetic studies at temperatures relevant to propellant combustion have yet to be developed (a problem not limited to propellant research). One promising new technique that has yet to be applied to solid ingredients at combustion conditions is molecular dynamics modeling. However, problems of properly describing the potentials and handling the sampling of the very large numbers of atoms involved must be solved (see the chapter by Rice). We have shown that a fair number of the gas-phase reactions of importance are now well characterized, but similarly detailed information is

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W. R. Anderson & A. Fontijn

needed for many more reactions. Most of the reactions studied are bi-, or ter-molecular processes of small species. Such reactions lend themselves best t o the newly-developed experimental techniques. However, gas-phase kinetics of the decomposition of larger molecules, which can occur in bubbles in a surface melt layer or in the first stage flame, must also be known. And, as for the condensed phases, the large molecules involved must be identified (cf. Sec. 2.2.1(b)). Of the larger propellant components, few have sufficient vapor pressure and stability to survive into the first-stage flame. RDX is an exception. A molecular beam-infrared multiple photon dissociation study of its dissociation p a t h s 1 1 0 has been made, b u t no r a t e information is apparently available. Another possibility is NG. Kinetic experiments on these would be useful if sufficiently pure gas-phase samples at appropriate conditions can be prepared.

Acknowledgment A F t h a n k s A R O for support under grant DAAD19-03-1-0046.

References 1. An earlier review of propellant gas-phase chemistry focusing on the subset of reactions pertinent to dark zones may be found in: W. R. Anderson, in U.S. Army Workshop on Solid-Propellant Ignition and Combustion Modeling, eds. R. W. Shaw, D. M. Mann and M. S. Miller, U.S. Army Research Laboratory Technical Report, ARL-TR-1411, July 1997. 2. R. L. Hatch, in 23rd JANNAF Combustion Subcommittee Meeting, Vol. I, CPIA Pub. 457 (1986), p. 157. 3. C. F. Melius, in Chemistry and Physics of Energetic Materials, NATO ASI Series, Vol. 309, ed. S. Bulusu (Kluwer Academic Publishers, Norwell, MA, 1990), p. 51. 4. R. A. Yetter, F. L. Dryer, M. T. Allen and J. L. Gatto, J. Propul. Power 11, 683 (1995). 5. (a) R. C. Sausa, W. R. Anderson, D. C. Dayton, C. M. Faust and S. L. Howard, Combust. Flame 94, 407 (1993); (b) D. T. Venizelos and R. C. Sausa, Proc. Combust. Inst. 28, 2411 (2000). 6. M. Rohrig, E. L. Peterson, D. F. Davidson and R. K. Hanson, Int. J. Chem. Kinet. 28, 599 (1996). 7. M. A. Mueller, R. A. Yetter and F. L. Dryer, Int. J. Chem. Kinet. 3 1 , 705 (1999). 8. E. W. Diau, M. J. Halbgewachs, A. R. Smith and M. C. Lin, Int. J. Chem. Kinet. 27, 867 (1995). 9. R. Behrens, this volume.

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10. Y.-C. Liau and V. Yang, J. Propul. Power 11, 729 (1995). 11. J. E. Davidson and M. W. Beckstead, J. Propul. Power 13, 375 (1997). 12. M. S. Miller and W. R. Anderson, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (American Institute of Aeronautics and Astronautics, Reston, VA, 2000), Chap. 2.12. 13. (a) M. S. Miller and W. R. Anderson, J. Propul. Power 20, 440 (2004); (b) M. S. Miller and W. R. Anderson, CYCLOPS, a Breakthrough Code to Predict Solid-Propellant Burning Rates, U.S. Army Research Laboratory Technical Report, ARL-TR-2910, February 2003. 14. M. S. Miller and W. R. Anderson, Prediction of Advanced Nitramine Propellant Burning Rates with the CYCLOPS Code, U.S. Army Research Laboratory Memorandum Report, ARL-MR-552, March 2003. 15. (a) A. A. Zenin, J. Propul. Power 11, 752 (1995); (b) A. A. Zenin, Study of Combustion Mechanism of Nitramine-Polymer Mixtures, Final technical report to the European Research Office of the U.S. Army, London, England, contract no. N68171-97-M-5771, November 1998; (c) A. A. Zenin, Study of Combustion Mechanism of Nitramine-Polymer Mixtures, Final technical report to the European Research Office of the U.S. Army, London, England, contract no. N68171-99-M-6238, August 2000; (d) A. A. Zenin, Study of Combustion Mechanism of Nitramine-Polymer Mixtures, Final technical report to the European Research Office of the U.S. Army, London, England, contract no. N68171-01-M-5482, May 2002. 16. W. R. Anderson, N. E. Meagher and J. A. Vanderhoff, to be published. 17. J. A. Vanderhoff, W. R. Anderson and A. J. Kotlar, in 29th JANNAF Combustion Subcommittee Meeting, Vol. II, CPIA Pub. 593 (1992), p. 205. 18. W. R. Anderson (1998), unpublished results. 19. M. C. Lin, Y. He and C. F. Melius, Int. J. Chem. Kinet. 24, 1103 (1992). 20. S. T. Wooldridge, R. K. Hanson and C. T. Bowman, Int. J. Chem. Kinet. 27, 1075 (1995). 21. R. A. Yetter, unpublished; however, the mechanism may be obtained from Yetter or many of the currently active modelers in the field (e.g. W. R. Anderson, M. W. Beckstead, V. Yang, or Y.-C. Liau). Version 2 is also quoted in full in Y.-C. Liau, Numerical Analysis of RDX Monopropellant Combustion with Two-Phase Subsurface Reactions under Steady and Transient Conditions, Ph.D. Thesis, Pennsylvania State University, University Park, PA, 1997. 22. (a) D. Chakraborty, R. P. Muller, S. Dasgupta and W. A. Goddard, III, J. Phys. Chem. A104, 2261 (2000); (b) D. Chakraborty, R. P. Muller, S. Dasgupta and W. A. Goddard, III, J. Phys. Chem. A105, 1302 (2001). NOTE: The combined mechanism for RDX and HMX combustion may be obtained by contacting those authors. 23. (a) S. Zhang and T. N. Truong, J. Phys. Chem. A104, 7304 (2000); (b) S. Zhang and T. N. Truong, J. Phys. Chem. A105, 2427 (2001); (c) S. Zhang, H. N. Nguyen and T. N. Truong, J. Phys. Chem. A107, 2981 (2003).

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CHAPTER 8 G A S - P H A S E D E C O M P O S I T I O N OF ENERGETIC MOLECULES Donald L. Thompson Department of Chemistry University of Missouri-Columbia 601 South College Avenue Columbia, MO 65211, USA

Contents 1. Introduction 2. Theoretical Methods 2.1. Simulations and Rate Calculations 2.2. Potential Energy Surfaces 3. The Chemistry 3.1. Basic Reaction Pathways 3.2. Experiments 3.3. Nitromethane 3.4. Methyl Nitrite 3.5. Dimethylnitramine 3.6. TNAZ 3.7. RDX 4. Concluding Remarks References

241 244 244 249 252 252 253 254 259 261 264 265 269 271

1. I n t r o d u c t i o n Determining the rates and mechanisms of the chemical decomposition of energetic materials is extraordinarily difficult. T h e y rapidly react upon heating or shocking to produce radicals which are hard to detect and rapidly undergo subsequent reactions. Furthermore, most energetic materials begin to chemically decompose in condensed phases the liquid phase, or a less characterizable melt phase. In some cases chemical reactions accompany or immediately follow melting. W h e n reaction begins in the solid phase, it is 241

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at defect sites where hot spots can form, which likely involve liquid centers where reaction or gasification occurs. These complexities greatly frustrate experimental studies of the chemistry which is far from simple. Even the chemical decomposition reactions of isolated energetic molecules are quite complicated and difficult to study, and thus they are still far from being fully understood. Because many of the gaseous products and much of the energy are produced in gas-phase reactions it is critical that we understand them. This chapter describes our understanding of the gas-phase unimolecular decomposition of some important energetic molecules and the role that theory and computations have played in achieving it. The bedrock of any scientific field is a body of experimental data, but science progresses by a cooperative interplay of theory and experiment. Given the difficulties in experimental studies of the reaction kinetics of energetic molecules, theory must play a central role. Theory is, of course, hindered by the size and complexity of the molecules and must be used judiciously; nevertheless, it is an indispensable part of the effort to unravel the reaction mechanisms. The emphasis here, in large part due to the state of our knowledge, is on the initial steps of the decomposition of a few representative molecules. The efforts, creativity, and progress in experimental kinetics and dynamics have over the past several decades been directed at more accurate and refined measurements of isolated elementary chemical reactions and energy transfer processes, e.g., those associated with changes involving a single transition state or stabilization of an excited species. This concentrated focus gave impressive progress in refined temporal and energy measurements and control of elementary chemical processes. At the same time, little progress has been made in monitoring and probing complex chemical processes that unfold over relatively long times (>/^s) and involve branching sequences of reaction pathways with a corresponding series of wells and transition states. We still attempt to map out this sort of chemistry by patching together individual elementary steps. We often have very accurate information for some steps, but for others we can only speculate within the context of a postulated mechanism not always well founded or confirmable. This is the way that reaction mechanisms have been developed for the past century. We can use measured data along with theoretically-predicted information and chemical intuition in models to reproduce the observed results. Computer modeling is the only modern major advance in methods for formulating mechanisms for complex chemical reactions. An excellent example of what can be done with this approach is the modeling of the complex

Gas-Phase Decomposition

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chemistry of flames where it has been used quite successfully (see Miller's chapter in this volume). However, in many cases modeling is not satisfactory because of the lack of accurate data for critical steps in the mechanism. A full understanding of the temporal evolution of the chemistry of the complete decomposition of an isolated molecule as large and complex as RDX is greatly hindered by the pivotal but transitory roles of radicals that must be inferred rather than observed and, although progress is being made as Dagdigian discusses in his review of radical reactions in this volume, what we know with certainty is dwarfed by what we do not know. Some very good state-of-the-art experiments have been done (although only relatively few, given the importance of the field) that provide important data for the decomposition reactions. Although valuable, and well executed and interpreted, the experiments provide much less than is needed confidently to postulate complete mechanisms for the sequential, branching chemical decomposition of these molecules. Most of the experiments rely upon some harsh excitation process (e.g., laser pumping, shock waves) to initiate decomposition that results in the small molecules and radicals that are detected much later. The complicated chemistry occurring between the start and the end of the decomposition must then be postulated by some sort of modeling which can lead to erroneous conclusions because there are so many undetermined parameters needed to describe the complicated chemistry. Nevertheless, the experiments have provided some specific, though in some cases controversial, information that provides a basis for postulating mechanisms for the initial steps in the decomposition reactions of such important energetic molecules. This chapter focuses on the rates and mechanisms for the initial unimolecular reactions of NM, DMNA, TNAZ, and RDX. The goal is to delineate what is known, how we learned it, and what is uncertain or simply unexplored about the reaction mechanisms for the decomposition of isolated energetic molecules. This chapter is best read within the context of the overall volume. For example, the work reviewed here overlaps with Rice's review of ab initio PES calculations, and is closely linked with the radical reactions discussed by Dagdigian, and the flame chemistry described by Miller. I will attempt to point out these links to help the reader gain an overall perspective. I hope that this review not only informs but also inspires more work. The chapter is a two-part review: Theory and Chemistry. In the next section I describe the current state of theoretical methods used to study the kinds of chemistry discussed in Sec. 3.

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2. Theoretical Methods 2.1. Simulations

and Rate

Calculations

The theoretical focus here is on rate calculations which rely predominantly upon classical mechanics, so I mention the strengths, limitations, and caveats that attend the approximations in the various classical approaches. I only briefly review these and provide references to more in-depth treatments of the methods for those who wish to understand the methods at a deeper level. We have previously reviewed practical methods for computing rates of processes based on the classical approximation. x~3 In the standard classical trajectory approach, initial conditions are selected from the appropriate probability density distributions and the time evolution of the system is followed by numerical integration of Hamilton's equations of motion with the forces given by an assumed potential energy surface (PES). The physically significant results are averages of ensembles of trajectories. The crucial issue is how well these averages correspond to reality. Classical trajectories have been used extensively over the past four decades to study reaction dynamics, but there are still some significant practical problems in their application even when the classical approximation is valid. These problems fall into two main categories: (1) the practical application of classical simulations to compute rates, and (2) the formulation of accurate global PESs. Classical simulations must be augmented with other methods to calculate rates when straightforward trajectory calculations are not feasible, which is often the case when the rates are extremely fast or extremely slow. First I discuss the problem of computing rates with methods based on the classical approximation. Classical trajectory calculations have played a central role in the evolution of our understanding of chemical reactions in the gas phase. This is mainly because they are the only practical approach available to us because quantum mechanical methods for treating rate processes are still limited to systems no larger than about a half dozen atoms. Although progress is being made in extending the methods to larger systems, it appears that we will need to continue to depend upon classical methods for the foreseeable future for molecules of the sizes of interest in energetic materials. We really have no alternative to classical methods and they have some important features that make them attractive for certain problems: they provide insight into reactions at the level of atomic motions, by allowing visualization that is not obtainable from quantum mechanical calculations.


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The classical approximation is not valid for all rate processes and chemical reactions. Obviously, the main approximation is the neglect of interference effects, which are most explicitly manifested by tunneling. However, tunneling is likely not important in most practical applications of energetic materials, although it could play a role in aging of materials. Interference effects are most important at low energies, for light atoms, and in lowdimensional systems and they can dominate processes occurring at energies near threshold or, more generally, processes with very low probabilities due to energy requirements rather than entropy factors. Thus classical mechanics can overestimate the probability of close passages over an energy barrier. Fortunately, quantum effects are most significant at the microscopic level and they tend to be averaged out at the macroscopic level. Because we are usually most interested in averaged properties (e.g., thermal rates) of many-dimensional systems at relatively high energies, the classical results are often accurate enough. However, in treating the dynamics of reactions of polyatomic molecules, aphysical behavior of zero-point energy (ZPE) can be a problem. The ZPE of a large molecule can be sufficient to cause reaction if it flows into the reaction coordinate modes. This is especially true for energetic materials because the molecules usually have relatively low dissociation energies and many degrees-of-freedom. Because the ZPE in a classical simulation can flow among the molecular modes without quantum mechanical constraints, it can contribute to reaction as it cannot in nature. This aphysical behavior is less important at high energies where the quantum-classical correspondence is generally valid. Classical dynamics simulations determine the atomic-level mechanism and fundamental dynamical behavior of reactions. Furthermore, they are often the only option for treating reactions with non-statistical dynamics. However, for most rate calculations one can use a statistical theory such as Ramsperger-Rice-Kassel-Marcus (RRKM) theory 4 or Variational Transition-State Theory (VTST). 5 A statistical rate theory is valid if energy flow to the reaction coordinate modes is faster than reaction. The statistical assumption can break down at high energies because the rate of reaction can be so fast that energy transfer cannot maintain a statistical distribution of energy. At energies near reaction threshold the reaction rates tend to be much slower than the energy transfer, thus the statistical approximation is usually valid. The rates at low energies can be so slow that following trajectories long enough to observe reactions is not practical, then one must turn to a statistical theory. Alternatively, classical trajectory calculations can be performed at higher energies and the results extrapolated

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to lower energies. Correctly extrapolating to lower energies may not be straightforward. As the energy approaches the reaction threshold, the probability of reaction decreases and one must use larger ensembles or longer simulation times (in the case of unimolecular processes) in a MD simulation to compute a good estimate of the rate. For simulations of unimolecular reactions and reactions in condensed phases, the practical limitation is the length of time that the numerical integration of the equations of motion is stable. This time is roughly determined by the highest frequency modes of the molecule which determine the integration step size that must be used. Trajectory integrations are usually accurate for times no longer than tens of picoseconds. Thus in practice MD simulations of unimolecular reactions are usually carried out at energies well above the reaction threshold so that a sufficient number of reactions are observed for statistically significant estimates of the rate. Often this means that the MD simulations are at such high energies that the reaction rate is faster than the intramolecular vibrational energy redistribution (IVR) rate. Thus the rate of reaction is controlled by the rate of energy flow into the reaction coordinate modes and the reaction dynamics are non-statistical. Clearly we must consider other methods if we are to cover the entire range of problems of interest in simulating the chemistry of energetic materials. At energies near the reaction threshold E* the statistical and dynamical rates are the same and usually obey the Ramsperger-Rice-Kassel (RRK) equation

* = «(l-f).

(1)

but as the energy increases they diverge, with the statistical rates larger than the dynamical rates. 6 We have demonstrated this behavior for several systems, including DMNA 7 and RDX. 8 Transition-state theories (including RRKM) give upper limits to the true rates. A transition-state theory rate is an upper limit because all trajectories that pass through the transition state are counted and thus there is an overestimation of the rate because, in nature, some of those trajectories recross the transition state and return to the reactant region rather than go on to products. Because MD calculations must be carried out at energies where a statistically significant number of events can be observed on the timescale for which the numerical integration is stable, the rates are often in the dynamical regime. The only sure way to determine if the dynamics are


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statistical or non-statistical is to compare the MD and transition-state theory rates for the same PES. Normally practical applications of transitionstate theories such as RRKM are based on harmonic motions, thus it is not clear whether differences in dynamical and statistical rates are due to non-statistical behavior or differences in the PES. Below we will describe a Monte Carlo statistical theory approach we have developed that can be used to compute statistical rates for the same PES as used in a classical trajectory calculation. We need a variety of methods to compute the rates and unravel the mechanisms for the decomposition of energetic materials. With the focus on unimolecular decomposition reactions, we have developed practical methods to treat rate processes for various conditions. 3 These methods include quasiclassical trajectory simulations (the basic method), Monte Carlo variational transition-state theory (MCVTST) for calculating statistical rates for realistic PESs, intramolecular dynamics diffusion theory (IDDT) for treating rate processes in the intrinsically non-RRKM regime, and semiclassical approaches for incorporating tunneling effects into MD and MCVTST calculations. The rate coefficient k for a chemical reaction can be written as the flux through a dividing surface S that separates the phase space T into reactant and product regions

*=W-

(2)

where F is the appropriate probability density function: a delta function for the microcanonical ensemble and the Boltzmann factor for the canonical ensemble. The integral in the numerator is over the region of the dividing surface, which rigorously is a hypersurface in phase space but which, in practice, is usually taken to be a function of a few critical coordinates in configuration space. The variable v± is the velocity perpendicular to S. The integral in the denominator is over all the reactant phase space V. However, this equation illustrates the modern ideas of classical theoretical treatments of rate processes. In practice, the problem comes down to how one solves the integrals and evaluates the flux from reactants to products. In principle, in a classical trajectory calculation of a reaction rate one would determine the time evolution of an ensemble by solving the Liouville equation; however, this is not possible and in practice we compute rate constants by Monte Carlo averaging ensembles of individual trajectories obtained by numerically integrating Hamilton's equations of motion. The

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methods for performing Monte Carlo classical trajectory calculations are now more or less standardized and we have previously described them in detail. 1 ~ 3 It is worthwhile, however, to mention some aspects of how they are applied. The initial conditions for classical trajectories are selected such that the simulated ensemble corresponds to the experimental conditions of interest. When state specificity or non-statistical behavior is important, e.g., at low energies or for non-statistical excitations, a quasiclassical approximation is used. Here the initial conditions are selected assuming a distribution of energy among quantum levels and the coordinates and momenta are assigned values according to the appropriate probability density functions. For statistical systems the initial conditions can be selected assuming a random distribution of energy for a continuum of classical states, i.e., for a classical microcanonical distribution. Once the initial conditions are set the time evolution of the system is determined by numerical integration of Hamilton's equations of motion for the assumed PES. Equation (2) is based on the assumption that the rate of reaction corresponds to the flux through a hypersurface in phase space that divides reactants and products. In classical trajectory calculations of rates this assumption is not needed because one can begin trajectories in the reactant phase space and propagate them into the product phase space. The averaging over the reactant phase space is usually done by selecting the initial conditions for the trajectories from the appropriate probability density distributions by Metropolis Monte Carlo sampling.9 This sampling procedure assumes that the reactants randomly occupy the classical phase space, that is, the dynamics of the reactants are ergodic. The reaction rate is determined from the outcomes of the deterministic classical trajectories that have ergodic initial conditions. Thus, the results include the effects of any dynamics in the phase space between the reactants and products, that is, for passage through the transition state region. The usual Metropolis sampling procedure neglects the ZPE of the reactants; however, a method to take it into account has been presented. 10 This entails a Markov walk in the reactant phase space that is begun at a convenient location such as the equilibrium geometry where the total energy is all kinetic. A warm-up sequence, usually tens of thousands of steps, is used to walk the system to some random point far from equilibrium. Then, as the walk is continued, phase space points along the sequences are used as initial conditions for trajectories, which are integrated to determine the fate of the system for that particular phase space point.


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The Metropolis Monte Carlo procedure provides an estimate of the classical phase space integrals in Eq. (2). Alternatively, in the quasiclassical approximation the integrand in Eq. (2) is based on quantum mechanical constraints and is assumed to be separable; that is, the averaging is over individual dynamical variables (e.g., vibrational and rotational modes in the case of molecules), for which values can be randomly selected by the Monte Carlo von Neuman rejection technique. 11 In the case of unimolecular reactions the microcanonical rate constant is calculated in a manner analogous to how it is determined experimentally: the first-order decay rate is given by the slope of plot of In N(t) as a function of t. The lifetimes are fitted to

where N(t) is the number of unreacted molecules at time t and N(t = 0) is the number of reactant molecules in the ensemble. This means that the trajectories must be integrated for times in the order of one lifetime, r ~ 1/fc. If the energy barrier to reaction is large it may be necessary to perform the simulations at relatively high energies so that a significant fraction of the ensemble decays.

2.2. Potential

Energy

Surfaces

Most of the MD simulations of unimolecular dissociation reactions of energetic molecules have been carried out by using approximate PESs constructed by using arbitrary analytical functions parameterized with empirical and quantum chemistry results. For the most part the general forms of the potentials are derived from standard anharmonic force fields with the changes in forces and energies corresponding to isomerization, bond breaking, and bond formation being built into the formulism with ad hoc switching functions.2 Switching functions are analytical expressions that can be used to fashion the shape of the potential along specified directions, e.g., the internal coordinates along the reaction path. This approach provides a facile way to introduce specific realistic features while providing the flexibility to accurately describe the reactant, products, and transitionstate properties. In many cases, these PESs are sufficiently accurate to realistically model the chemistry; however, developing them requires meticulous fitting of many parameters as one adjusts for specific features and the overall behavior of the surface.

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Serious drawbacks to this approach are the enormous labor required to adjust the functions and the inherent inflexibility of any analytical function. In fact, this is the case for any global formulism used to describe the full range of configurations available to a system at energies for which reaction can occur. The recent developments in quantum chemistry, especially in density functional theory (DFT) methods, have now made it feasible to compute energies and forces sufficiently fast that one can bypass fitting the energies with analytical functions and compute the forces on the fly while integrating the equations of motion. There is still a limit on the size of the system for which this is practical and still the need for scaling of the quantum chemistry energies and forces because direct dynamics simulations are not yet feasible with high-level ab initio methods. This new capability is being most usefully employed in statistical theory rate calculations. These qualifying statements about the utility of direct ab initio MD simulations pertain to the current status of computational chemistry, however, it is clear that eventually this will be the common approach. Thus, we need to focus on developing efficient methods for incorporating ab initio energies and forces into classical simulations. One always pushes the limits of a method and there will continue to be a need to introduce scaling of ab initio points because lower-level quantum chemistry calculations, that may not be chemically accurate, will allow studies of a wider range of systems. The fitting methods must be sufficiently flexible to give accurate fits, with or without scaling, of ab initio points to produce a global fit or provide local fitting within the context of a direct dynamics simulation. Local fitting with polynomials meets these criteria. We first proposed local fitting in the 1970s based on cubic splines12 which are efficient and accurate if a sufficiently dense grid of points is used. Although cubic splines have been used in a number of applications, they have been replaced by other similar methods that require fewer points. Chief among these is a method introduced in 1994 by Ischtwan and Collins13 based on interpolating moving least-squares (IMLS). 14 We have recently presented an improved IMLS fitting method. 15,16 This new IMLS fitting approach is accurate and easily applied and could provide a general method for both global fitting and fitting on-the-fly in direct dynamics simulations. In the latter case, one wants an efficient method for interpolating points in regions of configuration space previously visited by the trajectories and where points have been calculated and saved so that new ab initio points are calculated only where there is not a sufficiently dense grid to give an


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interpolated point of sufficient accuracy for the next integration step. The IMLS methods will facilitate the use of ab initio PESs in MD simulations for systems for which quantum chemistry is reliably accurate, thus generalizing simulation codes and eliminating the need for formulating classical PESs. This is, perhaps, the most important challenge in the development of predictive theoretical chemical dynamics methods, except for the development of practical rigorous quantum mechanical methods. We have developed automatic interpolation methods that are highly efficient and accurate for polyatomic molecules, and that can be eventually used in a blackbox configuration requiring limited theoretical expertise to generate ab initio-b&sed chemical dynamics simulations. Fits using different-degree IMLS identifies regions where additional data points are needed, so an algorithm is used automatically to determine how to improve the fit to a preset accuracy. This method achieves much higher quality fits with many fewer ab initio points than other methods. To date we have focused on unimolecular dissociation reactions in relatively simple, small 3-atom (N 2 H -» H + N 2 ) 1 5 and 4-atom molecules (HOOH - • 20H), 1 7 but the method is, in principle, applicable to systems of any size because it scales economically with the number of atoms. One approach was inspired by a dual-level method proposed by Nguyen et al.18 in which they fit low-level quantum chemistry results corrected by a few high-level points to obtain a scaled PES. Our method eliminates the need for the low-level quantum chemistry calculations by using an analytical function which we refer to as the zeroth-order PES VQ. The VQ is a rough approximation to the actual potential V. We then use an IMLS method to fit the difference A ^ = V — VQ, which is a relatively smooth function and requires relatively few points to achieve a good fit. Obviously, AV is smoothest if it matches geometries at the critical points of the actual potential, which is easily done because one can readily determine the critical points on the high-level ab initio potential using standard techniques available in many quantum chemistry codes. We have tested this method by fitting a global PES for H2O2, with particular focus on the bond-fission to give 20H and the internal hindered rotation. It can be used with any local polynomial fitting method (and we have tested it for the modified Shepard 13 and the second-degree IMLS (SD-IMLS) method we recently introduced 15 ). We find that employing the zeroth-order PES greatly reduces the root-mean-square errors of the global and reaction path fits by both the modified Shepard and the SD-IMLS methods. Since the latter does not require gradients, as does the former,

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it will be the preferred method in most applications, especially in direct dynamics simulations. 3. The Chemistry 3.1. Basic Reaction

Pathways

There are two broad classes of reactions that are responsible for the initial unimolecular decomposition of a polyatomic molecule: simple bond-fission and molecular elimination. A simple bond-fission reaction, which produces radicals, occurs along a reaction path with no exit barrier; i.e., there is an energy barrier to the reverse reaction and the potential along the reaction path has the shape of a Morse function. The reaction coordinate is mainly composed of the internuclear distance of the bond that breaks, although it may also involve some other coordinates to describe the structural differences of the product fragments in isolation and in the parent molecule. The reaction coordinate of a molecular elimination reaction is usually a linear combination of several internal coordinates. Concerted reactions often involve significant intramolecular rearrangement (e.g., atom transfer, isomerization) prior to or accompanying the arrival of the system at the transition state. Molecular elimination reactions frequently have multicenter transition states involving several atoms (often four or five) arranged in a ring structure. Thus, they involve significant electronic rearrangement with the breaking and formation of several bonds and significant repulsion between the molecular products in the exit channel. An energy barrier to the reformation of the parent molecule from the molecular products is common. Many polyatomic molecules undergo unimolecular decomposition by simple bond-fission and concerted molecular elimination reactions relatively close in energy. This is the case for many nitro and nitramine compounds. Usually it is clear which bond rupture is most likely, e.g., C-N in nitroalkanes and N-N in nitramines. One should, however, consider more than one possible molecular elimination reaction. Completing bond-fission and molecular elimination reactions that have similar energy requirements may also have significant pressure (or caging) effects due to qualitative differences in the potentials along the reaction paths. The reasons mentioned above (i.e., speeds of the reactions, detection difficulties, pressure effects) make discrimination among the possible reaction channels difficult. Quantum chemistry methods are usually not capable of the accuracy necessary to determine which path has the lowest barrier. This


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is illustrated by the continuing lack of agreement about the mechanisms for the gas-phase decomposition of several nitro and nitramine molecules, which we review later in this section.

3.2.

Experiments

We begin with a brief discussion of key experiments that have provided the basis for continuing efforts to unravel the decomposition mechanisms. It is important to understand what they do and do not provide. Observations of chemical reactions in molecular beams ensure collisionless conditions. In the case of unimolecular dissociation it is necessary to employ an alternative excitation process, e.g., laser excitation. Lee's group has studied a wide range of unimolecular reactions in molecular beams using infrared multiple-photon pumping to provide the excitation energy to the molecules.19 The drawback to this method is that the level of excitation is not directly determinable. The translational-energy probability distribution for each of the products was measured by time-of-flight mass spectroscopy. By assuming statistical reactions and the reaction energetics, the branching ratios of the decomposition reactions were determined and an estimate of the level of internal excitation of the reactant molecules was obtained. The statistical assumption should be valid for their conditions. Based on numerous studies using almost every available experimental and theoretical method, it is clear that exciting the vibrational motions of a polyatomic molecule by rapid laser pumping, overtone excitations, or other means rapidly produces a statistical distribution of internal energy. The intramolecular vibrational energy redistribution (IVR) is much faster than chemical reactions because of strong mode mixing (not chaos as often assumed) that sets in at quite low levels of excitation and increases as the excitation energy reaches levels at which unimolecular decomposition can 2D

occur. These IRMPD experiments have been enormously beneficial in illucidating certain (albeit, limited) aspects of unimolecular dissociation reaction mechanism, particularly those where there are competing decomposition pathways. These paths may be simple bond-fission or concerted reactions, either molecular elimination or rearrangement followed by a bond rupture — often the case for energetic molecules. While it is generally agreed that NO2 elimination by simple bond-fission is the dominant initial reaction in most nitro and nitramine compounds, in many cases there is evidence of a competitive concerted reaction such as HONO elimination,

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nitro-nitrite rearrangement followed by O-N bond rupture, or ring fission in cyclic molecules. Thus, there is the likelihood of changes in the relative importance of the reactions with changes in temperature, pressure, and physical phase. The IRMPD experiments probe the reactions only for specific conditions; other means of excitation may lead to different decomposition mechanisms. Shock-tube experiments provide data for high temperatures and for a wide range of pressure. Shock tubes have not been used to a large extent to study energetic molecules but are well suited for probing the chemistry for conditions (i.e., high temperatures and pressures) approaching those in practical applications. For example, shock tubes provide a means of studying the pyrolysis of compounds under controlled conditions, with greater control and detection than is possible in flames. Spectroscopic and other techniques can be used to monitor reactant and products in shock tubes, but on a relatively long time scale (~/xs). Interpretation of the data requires fitting to a complex kinetics model. These gas-phase experiments are far removed from those corresponding to practical conditions where a condensed-phase material is subjected to high heat or mechanical shocks leading to combustion or detonation. Similarly they probe conditions very different from some of the experimental techniques from which we have learned so much about the chemistry, experiments such as fast heating and slow heating which have been so deftly used by Brill and Behrens. However, although we know there are links among, and overlap of the observations from, these various methods, the links are not always obvious because we are working with only pieces of the puzzle.

3.3.

Nitromethane

From both the standpoint of theory and experiment, nitromethane is a good prototype for energetic molecules. It is a small molecule — an important consideration in theoretical studies; it also undergoes the reactions typically observed or proposed in mechanisms for larger nitro and nitramine compounds, and it has been studied extensively both experimentally and theoretically. Thus, we have a better understanding of nitromethane decomposition than for other energetic materials although there remain some critical points still unresolved (see Rice's chapter). In 1972 Glanzer and Troe 21 carried out a study of the gas-phase decomposition kinetics of nitromethane using shock heating over the range 900-1400 K. They monitored only the concentrations of CH 3 N0 2 and N 0 2 .


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They proposed the mechanism: CH3NO2 - • CH 3 + N 0 2 ,

(Rl)

CH 3 N0 2 + M -> CH 3 + N 0 2 + M,

(R2)

CH 3 + N 0 2 - • CH 3 0 + NO.

(R3)

In 1979 Perche et al.22 studied the pyrolysis of nitromethane in a bulb over the temperature range 676-771K. They identified the following secondary products: CO, NO, CH 4 , H 2 , C 2 H 6 , CH 3 OH, HCN, C 0 2 , CH 2 0, H 2 0 , and N 2 . They proposed a mechanism involving 28 reactions. Hsu and Lin 23 performed shock-tube studies of the pyrolysis of CH 3 N0 2 over the temperature and pressure ranges, respectively, 940-1520 K and 0.4-2 atm. They monitored only NO and CO. They proposed a mechanism involving 37 reactions. Their data, when combined with those of Kutschke and co-workers24 show a sharp upturn above 1000 K in the Arrhenius plot. Later experiments by Choudhury et al.25 also gave a curved Arrhenius plot, although the curvature was much smaller. Also, the measured rate was more than an order of magnitude smaller than that based on the Hsu and Lin mechanism. These studies provide the backdrop for the more recent work of Zhang and Bauer 26 who carried out shock-tube experiments of the decomposition CH 3 N0 2 over the temperature range 1000-1100 K. They proposed a mechanism of 99 reactions with 41 chemical species that also accounts for the data reported earlier by Hsu and Lin, 23 Glanzer and Troe, 21 and Perche et al.22 They found that the pyrolysis involves chain reactions and that about 40% of the CH 3 N0 2 decay is due to secondary reactions — preventing determination of the unimolecular decay rate of CH 3 N0 2 . Zhang and Bauer 26 suggested that measurements are needed for a wider temperature range in which more intermediates and products are monitored. We think that it is also important to study the lifetimes, decay channels, and bimolecular reactions of some key radicals (especially H, OH, CH 3 , and N 0 2 ) in the postulated mechanisms (see the chapter by Dagdigian). For example, we agree with Zhang and Bauer that "N0 2 is an important intermediate in the decomposition of nitro compounds. A clear understanding of its kinetics is crucial for elucidating the mechanism of the overall conversion."27 The importance of reactions of N 0 2 with other radicals is also illustrated by the analysis of nitromethane high-temperature decomposition data by Glarborg, Bendtsen, and Miller.28

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The initial decomposition reaction of nitromethane in the gas phase is controversial because of the interpretation of IRMPD experiments carried out in Lee's laboratory in the mid-1980s. Wodtke et al.29-30 studied nitromethane by infrared laser excitation in a molecular beam. They explained their data by two primary unimolecular dissociation reactions: reaction (Rl) and CH3NO2 - • CH3ONO* - • CH3O + NO.

(R4)

They concluded that the branching ratio for the isomerization bond-fission reaction (R4) to the simple bond-fission reaction (Rl) is 0.6 ± 0.2. This has not been supported by other experiments and most ab initio calculations predict that the simple bond-fission reaction has a somewhat lower energy barrier (see Rice's chapter for a thorough discussion of the ab initio studies). The differences in the energy requirements are in the range 2-6kcal/mol near the limits of accuracy of quantum chemistry. One ab initio calculation 31 predicts that the isomerization channel is slightly lower in energy. This difference agrees with that assumed by Wodtke et al.29 in their analysis of the IRMPD/molecular beam data in which they used the early semi-empirical results of Dewar et al.32 Subsequent ab initio calculations have all predicted the simple bondfission reaction to be lower in energy. Recent ab initio calculations by Hu et al.33 predict that simple bond-fission to give CH3 + NO2 is favored by 2-3kcal/mol over the isomerization pathways: CH3NO2 —> irans-CHsONO and CH3NO2 —> CTS-CH2N(0)OH. It has been followed up by another ab initio study by Nguyen et al.3i in which the emphasis was on determining both the energy barriers and the natures of the transition states, tight or loose, which could determine the relative importance of competing reaction pathways so close in energy. Based on results computed by using CCSD(T) and CASSCF in conjunction with DFT (B3LYP) Nguyen et al. concluded that the barrier for CH3NO2 -> CH 3 + N 0 2 is 60 ± 2kcal/mol and that for the isomerization reaction CH3NO2 —> CH3ONO is at least 6kcal/mol higher. These calculations predict a tight transition state for the isomerization reaction; the influence of this on the kinetics needs to be determined. To summarize: the energy barriers are sufficiently close that quantum chemistry has yet to convincingly settle the matter of the branching ratio for the nitromethane dissociation. The computed values of the energy barrier to the simple bond-fission reaction are consistently around 60 kcal/mol,


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so the discord centers on the energy barrier for concerted molecular elimination. Given the variation in the energies calculated with the high-level ab initio methods, the conclusion by Wodtke et al.29 that the branching ratio of the isomerization bond-fission (to CH3O + NO) to the simple bondfission (to CH3 + NO2) is about 0.6 might yet be confirmed by ab initio calculations. Also, because the energy barriers are comparable, the structures of the transition states may be most important in determining the relative importance of the two reaction channels. Given the established general reliability of the IRMPD/molecular beam method, we cannot, on the basis of the current ab initio results, dismiss the Wodtke et al.29 conclusion and it is worthwhile to continue looking for other explanations for why the nitro-nitrite isomerization channel has not been observed in other experiments. The experiments that have been reported are not definitive enough to decide the matter. All of them depend on analyses of data that do not have sufficient information to provide a definitive mechanism. Clearly, it would be useful to have experimental confirmation of the Wodtke et al. work, the sole experiment on the decomposition of isolated nitromethane molecules. The analysis by Wodtke et al.29 has been faulted because it was based on semi-empirical quantum chemistry, some of which have subsequently been shown to be inaccurate. For example, Nguyen et al.34i argue that this is why Wodtke et al.29 reached their conclusion. Glarborg et al.28 did a careful analysis of the existing shock-tube data for the dissociation of nitromethane. They discuss the limitations of these experiments for determining the decomposition mechanism. They point out that the experiments by Hsu and Lin 23 detected only secondary products and that Zhang and Bauer 26 did not observe the temporal evolution of the chemical species but only the composition of the products. This is a general problem in chemical kinetics — reaction mechanisms are still determined more or less in the same way as they were at the end of the nineteenth century: by postulating a series of reactions that lead to the observed final products. As for other energetic materials, following the initial decomposition steps of nitromethane there is a build up of radicals that strongly influence the subsequent chemistry. The interpretation of IRMPD/molecular beam data may also be liable to errors because the analysis depends on statistical rate theory (RRKM) to work backwards from the data collected down the beam after several sequential reactions have produced a number of product species. One way to address this would be to use molecular dynamics to simulate the entire

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sequential branching chemistry following the initial excitation of the reactant molecule. If (and this is a significant IF) accurate PESs for the complete dissociation were available, one could presumably compute the raw data measured in the IRMPD/molecular beam experiments. An initial effort along these lines using assumed forms for the PES has been made. Rice and Thompson 35 performed classical trajectory calculations to study the unimolecular dissociation mechanism for nitromethane and to interpret the IRMPD results. They constructed three PESs that differ in the energy barrier to the nitro-to-nitrite isomerization, but for which the C-N bond dissociation energy is the same (60 kcal/mol). The energy required for the simple C-N bond rupture channel is 59.5 kcal/mol which appears to be well established; the role, however, of the concerted reaction channel is not firmly established. Wodtke et al.29 predicted the energy barrier to isomerization CH 3 N0 2 -> [CH3ONO]* - • C H 3 0 + NO to be 55.5 kcal/mol, which is lower in energy than C-N bond-fission. To study the possible role of the CH3O + NO reaction channel, Rice and Thompson considered PESs with isomerization barriers of 216 kcal/mol (to essentially prevent the reaction), 55.1 kcal/mol (corresponding to the estimate of Wodtke et al.29), and 47.6kcal/mol (based on the MINDO/3 calculations reported by Dewar and Ritchie 36 ). The highest barrier (216 kcal/mol) that Rice and Thompson 35 considered was chosen to prevent dissociation via the isomerization/N-0 bondfission pathway, thus (predictably) most of the decay is by simple C-N bond-fission. Interestingly they found that a small percentage of reactions did result in CH3O + NO products formed by a mechanism in which there is near dissociation to CH3 + NO2 but then a recombination to form a [CH3ONO]* complex that subsequently undergoes O-N bond-fission. This does not account for the branching ratio determined by Wodtke et al.29 The other PESs, with more reasonable barriers to isomerization of 47.6 and 55.1 kcal/mol, allow decomposition by a similar mechanism; that is, simple C-N bond-fission to form CH 3 + N 0 2 , interrupted by recombination, which is then followed by dissociation. The dynamics calculations show that, for these model PESs, there are three main decomposition pathways: CH3NO2 - • [CH 3 N0 2 ]* - • CH 3 + N 0 2 ,

(R5)

CH 3 N0 2 -v [CH3ONO]* -> CH3O + NO,

(R6)

CH 3 N0 2 — [CH3ONO]* -> CH 3 + N 0 2 .

(R7)

The calculated branching ratio (CH3O + NO/CH3 + N 0 2 ) for the PES with the 47.6 kcal/mol barrier is in agreement with the experimental value and


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the ratio computed with the PES with the 55.1kcal/mol barrier is about an order of magnitude smaller. The computed average product translational energies (which are directly measurable in a beam experiment) for reaction (R6) are higher than for the other two channels. The product energies for reactions (R5) and (R7) are similar and thus probably not distinguishable experimentally. These classical trajectory studies, even on model PESs, can determine possible reaction pathways. They can be used to compute the raw experimental data (i.e., what is directly observed rather than information derived by analysis) and serve as a valuable tool in interpreting experiments. The Rice and Thompson 35 calculations suggest that there may be three decomposition pathways and that the experiment by Wodtke et al.29 would not have distinguished between reactions (R5) and (R7). However, if both occur it could affect the analysis of various experiments and, certainly, the conclusions about the transition state for the nitro-nitrite isomerization. High quality ab initio calculation could be critical in finally resolving the mechanism (i.e., transition states) for the initial steps in the decomposition of nitromethane. Also, it would be useful to revisit the problem with MD simulations in light of the new experimental and theoretical results that have appeared since the Rice and Thompson 35 work was done; for example, we can now develop a more accurate PES. 3.4. Methyl

Nitrite

Given the role of methyl nitrite in the chemistry of nitromethane, we review what is known about its decomposition. Also, many nitro and nitramine compounds can isomerize to the -ONO form. The pathway for the conversion of a nitro or nitramine compound to the nitrite form involves the rotation of the N 0 2 group to exchange the C-N or N-N bond, respectively, for a C - 0 or N - 0 bond. The simplest case is the conversion of nitromethane to methyl nitrite, CH3ONO —> CH3ONO, which we discussed above. The barrier to simple bond-fission to produce CH3O + NO is sufficiently low (^41kcal/mol) 3 7 that the isomerization is immediately followed by the decomposition. This was an observation of Wodtke et al.29 in their IRMPD molecular beam experiments on the decomposition of nitromethane. For the pyrolysis of methyl nitrite He et al.38 proposed a mechanism that consists of 16 reactions with the initial unimolecular steps being: CH3ONO -> CH3O + NO

(R8)

CH3ONO -y C H 2 0 + HNO.

(R9)

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Experiments 37 ' 38 show that the simple bond-fission reaction (R8) is at least an order of magnitude faster than the concerted molecular-elimination reaction (R9). The latter involves a four-center transition state, thus a small Arrhenius A factor. He et al.3S gives the values: A = 6.3 x 10 1 5 s^ 1 and E& = 41.2 kcal/mol for reaction (R8) and A = 4.0 x 1 0 1 3 s _ 1 and E.A = 38.5 kcal/mol for reaction (R9). These parameters were taken from the kinetic modeling of the shock-tube decomposition of nitromethane by Zhang and Bauer. 26 Vazquez and co-workers39 have carried out a series of theoretical studies of the unimolecular dissociation of methyl nitrite via simple bond-fission, reaction (R8), and concerted molecular-elimination, reaction (R9). They performed quantum chemistry calculations to determine the barriers for the two decomposition channels. They predicted the barrier to N - 0 bondfission reaction (R8) to be 39.29 kcal/mol and that for the formation of C H 2 0 and HNO by reaction (R9) to be 43.64 kcal/mol. The disagreement with experiment may again illustrate a case where competing reactions are sufficiently close in energy that predicting their relative importance may be beyond current theory. The rates calculated using an analytical PES based on these barriers and by direct dynamics are in accord with experiment because there is a significant entropy effect in the molecular elimination reaction, that is, the differences in the transition state structures leads to frequency factors to give rates in agreement with experiment. The first dynamics studies of methyl nitrite focused on the cis-trans isomerization as a model for a chemical reaction in which non-statistical effects were anticipated because of the low density of states and low energy barrier for the process. The initial investigations of this were the experimental studies by Bauer and co-workers,40 who studied the intramolecular conversion by using NMR spectroscopy. This, and the subsequent theoretical studies, addressed the fundamental problem of non-statistical behavior of a reaction under conditions where the rate of reaction is fast relative to the rate of intramolecular vibrational energy redistribution (IVR). Shock waves are inherently non-statistical and it is reasonable to assume they leave in their wake (at least for very short times) excited molecules with non-equilibrium distributions of internal energy, but it is not established that nonequilibrium processes occur. In any case, understanding the flow of energy among the phonon modes, within the molecular modes, and between the phonon and molecular modes in condensed phases is critical to an atomiclevel understanding of the response of energetic materials to perturbations such as mechanical shocking (for a discussion, see the chapter by Dlott).


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Comparisons of experimental rates with statistical theory predictions for methyl nitrite reported by Lazaar and Bauer 41 indicated that some of the vibrational phase space is only weakly coupled to the reaction coordinate. Preiskorn and Thompson, 42 using a PES based on ab initio calculations, 43 performed a classical trajectory study of the influence of the distribution of excitation energy on cis-trans isomerization. More recently, MartinezNunez and Vazquez 44 extended these studies using a PES based on higherlevel quantum chemistry calculations. These trajectory studies confirm the conclusions of Lazaar and Bauer that the reaction path is isolated from some of the molecular modes and provide a much more detailed picture of the intramolecular mode couplings and their influence on reaction. The isomerization rate is significantly increased when energy is initially placed in the CON bending, ONO bending, CO stretching, or NO stretching modes. Although these processes are not true chemical reactions, they do illustrate the importance of taking into account the possibility of non-statistical effects.

3.5.

Dimethylnitramine

Dimethylnitramine (DMNA) is the simplest experimentally-studied nitramine. It is often used as a prototype for the larger, more important nitramines because it undergoes the same sorts of reactions that have been postulated for RDX and HMX and it presents a much more tractable problem to theorists than do the larger compounds. Its decomposition has not proven easy to unravel because it presents the same basic problems in determining the dominant reaction path when two or more are close in energy and where variations in conditions can cause changes in the mechanism. Based on thermochemistry there are three possible initial unimolecular decomposition reactions for DMNA: (a) simple bond-fission: (CH 3 ) 2 N-N0 2 - (CH 3 ) 2 N + N 0 2 ,

(RIO)

(b) nitro-nitrite rearrangement followed by O-N bond-fission: (CH 3 ) 2 N-N0 2 - • (CH 3 ) 2 NO-NO - • (CH 3 ) 2 NO + NO, and

(Rll)

(c) HONO elimination via a 5-center transition state: (CH 3 ) 2 N-N0 2 -> CH 3 N=CH 2 + HONO.

(R12)

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Although there is still need for further experiments before final conclusions about a mechanism can be reached, it appears that reaction (RIO) is the first step in the thermal decomposition of DMNA. A wide range of values for the activation energy has been reported. However, it appears that the true value is probably in the range 43-46 kcal/mol and that the bond energy is 43.3 kcal/mol. 45 Lloyd et al.45 reported Ea = 45.5 kcal/mol based on thermal pyrolysis experiments. Experiments by Lazarou and Papagiannakopoulos 46 made measurements for IRMPD in a reaction cell that showed that the decomposition occurs via reaction (RIO), for which the enthalpy of reaction is 46.5 kcal/mol. Their analysis indicated that the average excitation energy of the molecules was 12 ± 3 kcal/mol above the dissociation limit. However, there is experimental evidence that other reactions may participate in the initial break up of DMNA. In a very early experimental study, Fluornoy 47 reported the results of static-bulb thermal pyrolysis experiments that showed that ~ 8 0 % is converted to dimethylnitrosamine, (CHs^NNO. This, of course, does not provide direct information about the initial reaction. McMillen and co-workers48 studied the decomposition of DMNA by using pulsed laser heating and determined the activation energy to be in the order of 30 kcal/mol which they attributed to reaction (Rll). Their thermal data, which are fitted by a rate constant expression with a low Arrhenius A factor, have a dependence that is too low to be explained by the simple bond rupture reaction (RIO). They concluded that the isomerization/bondfission reaction (Rll) is an important initial step in the decomposition at low (~500K) temperatures which is not in accord with Lloyd et al.45 No experimental data have indicated that HONO elimination, reaction (R12), is a competitive initial reaction in the decomposition of DMNA. Although it is frequently mentioned in discussions and even included analyses of the decomposition of nitramines such as RDX and HMX, there is no solid experimental evidence to establish that HONO elimination occurs in thermal decompositions of nitramines; however, it appears to be firmly established as an initial step in the decomposition of nitroalkanes, e.g., nitroethane and 2-nitropropane. 30 There have been estimates of ~ 38 kcal/mol as the lower bound for the activation energy for reaction (R12), 49 which would suggest that it would be competitive with reaction (RIO) unless the energy advantage is overridden by a small frequency factor. Johnson and Truong 50 have performed high-level quantum chemistry calculations for the reaction. Their calculations give 43.5 kcal/mol for the barrier to HONO elimination.


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As this brief overview shows, our understanding of the thermal decomposition of DMNA is still rudimentary and further experiments are needed. In particular, experiments should be directed at determining the importance of reaction (Rll). This kind of reaction has been suggested for other nitro and nitramine decompositions, but without clear conclusions about its likely importance. The only exceptions, to our knowledge, are the IRMPD experiments of Wodtke et al.30 and the much earlier work by Spokes and Benson. 51 We also believe that additional experiments are needed before the HONO elimination channel can be accepted as an important initial reaction. (We discuss the evidence for it in RDX decomposition below, as does Rice in another chapter in this volume.) Zhang and Bauer 52 have presented a critical analysis of the decomposition mechanisms for several nitro and nitramine compounds including DMNA. Their conclusions, more substantially illustrated by results of a sensitivity analysis study than those given here, are essentially the same — more experiments are needed to resolve the mechanisms. The resolution of this problem will likely require a combination of experiments, theoretical calculations, and modeling. All of the experimental techniques probe the chemistry under poorly-defined conditions, late in the chemistry, and only for a very limited number of species. Quantum chemistry has reached the stage where we can compute energies for relatively large molecules, although for one as large as DMNA we are limited to only a few points on the PES. Nevertheless, electronic structure calculations can provide vital information about reaction pathways. But to fully link this information to experiments we must calculate rates for the experimental conditions. For experiments such as IRMPD, it may be necessary to compute the raw data such as product energy distributions. Classical trajectory simulations can be used to compute information for the individual elementary reaction steps. Then one can use this and other established information in modeling calculations to study the overall decomposition to again compute quantities directly comparable to measured basic quantities. Sumpter and Thompson 53 reported a classical trajectory study of DMNA in 1988. They included the HONO elimination channel with a barrier of 38 kcal/mol in an empirical PES for which the N-N bond energy was 46kcal/mol. They concluded that HONO elimination plays a very minor role in the thermal decomposition of DMNA. Theoretical and computational methods have improved significantly since these early calculations were done and now it would be feasible to perform a much more meaningful dynamics study of the system.

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TNAZ

Studies by Oyumi and Brill 5 4 - 5 6 of TNAZ decomposition using rapid heating of the solid show that NO2 is the initial and most abundant decomposition product and that the other products of the overall reaction include NO (second most abundant), HCN, H 2 CO, CO, C 0 2 , and HONO. 55 The implication is that one or both of the reactions shown in Fig. 1 initiates the decomposition. Anex et al.57 used IRMPD to study TNAZ in a molecular beam with product detection by time-of-flight quadrupole mass-spectrometry. They also found that the decomposition begins with the loss of NO2, although they could not determine the relative importance of reactions (R13) and (R14) or the details of the branching following the loss of N 0 2 . They proposed a mechanism of several steps beginning with N 0 2 elimination from the C- and N-sites on the ring. They found no evidence for HONO elimination or nitro-nitrite rearrangement. Zhang and Bauer 58 carried out single-pulse shock-tube experiments that show that the decomposition is first order. They determined the high-pressure unimolecular rate constant to be k^ = io 1 3 - 9 6 ± 0 - 3 6 _1 exp[(—39.45 ± 2.36)/RT], where k is in s and the activation energy is in kcal/mol. Infrared (IR) analysis of the reaction products showed that NO, N 0 2 , CO, C 0 2 , HCN, and H 2 CO are the major products, and HONO and H 3 C-C=CH are minor products; and tentative evidence for N 2 0 . A following experiment by Bauer and co-workers59 determined the primary products of a quenched reaction sample to be CO, HCN, H 2 CO, and NO. Thermodynamic calculations predict that the equilibrium mixture should primarily be composed of C 0 2 , N 2 , and H 2 . They concluded that the TNAZ

0,N

(R13)

r--No2

\

NO2

+ NOz

-NO, NO, 0,N

(R14) + N0 2 NQ2

Fig. 1.


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decomposition is kinetically driven under these experimental conditions. Zhang and Bauer 58 proposed a mechanism of several steps beginning with NO2 elimination from the C- and N-sites on the ring, which differs in some details from that proposed by Anex et al.57 Because of its size, all of the quantum chemistry calculations for TNAZ have used DFT. 6 0 ~ 6 3 All predict the N-N bond energy, reaction (R13), to be lower than the C-N bond energy, reaction (R14) — but by only 2-3 kcal/mol. The most recently reported 63 predictions are 38 kcal/mol for reaction (R13) and 41 kcal/mol for reaction (R14). These values compare favorably with the experimental activation energy of 39.4 kcal/mol determined by Zhang and Bauer 58 for gas-phase TNAZ decomposition, but DFT may not be sufficiently accurate to distinguish between the two channels. Calculations have also been done for HONO elimination. The DFT results predict only 1 kcal/mol difference in the reactions occurring at the C-NO2 and the N - N 0 2 sites, i.e., 44 and 45kcal/mol, respectively. Highlevel ab initio calculations are needed to definitely determine the initial decomposition reaction.

3.7.

RDX

The initial steps in the decomposition of RDX are not clearly established although a lot of evidence suggests that simple N-N bond-fission plays a crucial role in the decomposition. Other unimolecular reactions may occur under certain conditions, but are likely inhibited by condensed-phase effects because they involve concerted molecular elimination with large volumes of activation. Apparently there are several possible first reactions with comparable energy barriers and which one actually occurs depends on the conditions (physical phase, heating rate, etc.). The results of a number of ab initio quantum chemistry calculations lead to different conclusions depending on the level of theory. The elucidation of the mechanisms for the initial stage of the chemical decomposition of RDX, as is the case for other cyclic nitramines, is frustrated by the complexity of the chemistry and its strong dependence on the experimental conditions; however, a great deal of progress has been made as illustrated by the reviews given in the chapters by Brill and by Behrens. The first experimental determination of the activation energy was done by Robertson 64 in 1949 for liquid RDX over the temperature range 213-299°C with the result Ea = 47.5kcal/mol. Analysis of the products showed N 2 0 , N 2 , NO, CO, C 0 2 , H 2 , H 2 0 , H 2 CO, and a solid residue.

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The basic conclusions of Robertson have withstood time and many subsequent experiments. Many others have since reported values for the activation energy close to the Robertson value, and the accepted value of Ea is 47 to 48kcal/mol. Excellent reviews were written by Schroeder 65 ' 66 in 1985; unfortunately these are not generally available. He compiled and critically evaluated all of the data, including much that are contained only in government laboratory reports. Although the details of the RDX decomposition mechanism are far from resolved, there is evidence that can be used to limit the number of initial reactions that have to be considered. Clearly, simple N-N bond-fission eliminating NO2 must be considered as a likely first step. Another initial reaction that remains an active candidate for the mechanism is the elimination of HONO following the transfer of a H-atom from carbon to oxygen. A single gas-phase experiment has been interpreted to predict that concerted ring fission (RDX —> 3H2C-N=N02) is an important route for the initial dissociation of RDX. No direct experimental studies to confirm this pathway have been carried out. There is good evidence concerning some of the early products of the decomposition regardless of the initial step. Clearly, methylenenitramine, H2C-N=N02, is likely produced if not in the first, then in a subsequent step, and it can dissociate to H 2 CN + N 0 2 , HCN + HONO, or N 2 0 + H 2 CO. Also, some experiments (see the chapter by Behrens) provide evidence that nitrosoamines are formed early in the decomposition, and then dissociate to yield radicals and smaller molecules. The end result of the chemistry is a set of relatively stable small gaseous molecules. The challenge is to understand how all of this occurs for various conditions. The most direct study of RDX molecular gas-phase decomposition is the IRMPD experiments of Zhao et al.67 Zhao et al. concluded that the initial decomposition involves two competing reactions: simple bond-fission eliminating NO2 and triple bond-fission giving 3CH 2 NN0 2 . They determined the branching ratio of ring fission to simple N-N bond-fission to be approximately two. The ring-fission reaction has not been definitely observed in other experiments. Nevertheless, given the reliability of this experimental approach, which has been widely applied, 68 it is not easy to dismiss the possibility that the ring-fission reaction occurs under collision-free gas-phase conditions. Recently, Long et al. 69 used thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) to study the thermal decomposition of RDX in open and closed (or pierced) containers. They determined the


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activation energy as a function of the extent of decomposition. Evaporation, with Eg. ~ 23.9 kcal/mol, was prevalent in the open pan experiments. When RDX was heated in a closed container it decomposed in the liquid state with Ea ~ 47.8 kcal/mol, which corresponds to the generally-accepted values for simple N-N bond-fission. A gas-phase decomposition channel with E& ~ 33.5 kcal/mol was also observed. Long et al. suggested that this reaction might be concerted ring-fission to produce H 2 C=N-N02, as observed by Zhao et al.67 There is a decrease in the value of E& as the decomposition proceeds, which they interpreted to be due to competition between the simple N-N bond-fission reaction (liquid phase) and the concerted molecular elimination ring fission reaction (gas phase). Thompson and co-workers 70-73 developed empirical PESs to determine what the barrier height to the ring fission channel must be to account for the branching ratio measured by Zhao et al.67 They took the N-N bond dissociation energy to be 48 kcal/mol, and used a PES formulation that permitted variation of the barrier height for ring fission without significant changes in other features of the surface. They carried out a series of studies using this model to investigate the branching reactions. Their studies, which included classical trajectories, 70 ' 71 Monte Carlo variational transition-state theory (MCVTST), 72 and classical diffusion theory, 73 show that for this model the barrier to ring fission must be about 37 kcal/mol in order to obtain the experimentally-observed branching ratio of 2. Wight and Botcher 74 suggested that the ring fission reaction was not observed in other experiments because it has a large volume of activation and does not occur in condensed phases where the environment cages the fragments and causes recombination. Guo and Thompson 75 tested this idea by using the model PES in MD simulations of RDX decomposition in liquid xenon as a function of pressure. The results showed that pressure effects on ring fission are considerably greater than on simple bond rupture, which supports Wight and Botcher's suggestion. The extensive studies of condensed-phase decomposition of RDX for slow-heating conditions (see the chapter by Behrens) suggest that the initial reaction for those conditions is most likely HONO elimination. Much earlier, Zuckermann et al.76 had carried out experiments in which a pulsed C 0 2 laser was used to dissociate RDX and HMX in seeded supersonic nozzle beams and OH radicals detected by laser-induced fluorescence. Their results indicate that OH(X2IT) is produced in the primary unimolecular dissociation of these molecules. However, they could not determine the mechanism by which the OH is produced. They point out that OH may be formed

D. L.

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either directly or by rapid dissociation of hot, nascent H O N O eliminated from RDX. Capellos et al.77 observed the formation of O H ( X 2 £ ) in experiments in which RDX was photolyzed at 2 4 8 n m and suggest t h a t the.initial photolysis leads t o elimination of vibrationally-hot H O N O , which absorbs a photon and dissociates to O H ( X 2 E ) and NO. Because the initial excitation is electronic, it is not clear how these results correlate with thermal excitation experiments or to shock-induced explosions. Presumably, the dissociation could occur after intersystem crossing to the ground state (see the chapter by Bernstein). Recently, Chakraborty et al.7S reported the results of ab initio D F T calculations t h a t predict t h a t RDX can decompose by elimination of 3HONO molecules plus 1,3,5-triazine at approximately 40kcal/mol. (For a more complete discussion of q u a n t u m chemistry predictions of decomposition pathways, see t h e chapter by Rice.) In 1990 Melius 7 9 proposed a detailed model for the decomposition of RDX based on B A C - M P 4 thermochemical calculations t h a t remains more or less intact in light of subsequent experiments and calculations. He predicted t h a t the decomposition channel initiated by NO2 elimination proceeds by t h e steps shown in Fig. 2. N 0 2 , H 2 C N , and 2 H 2 C = N - N 0 2 are formed and this mechanism is not consistent with the molecular beam experiments of Zhao et al.67 Recent ab initio results of C h a k r a b o r t y et al.7& predict 3 9 k c a l / m o l for Step 1 ( N - N bond-fission), which may be low (B3LYP D F T often underestimates barrier heights). However, Long et al.69 determined the value of the activation energy for N - N bond-fission in liquid

Stepl 49 kcal/mol

Step 4 2 kcal/mol

Step 2 28 kcal/mol

H2

N

O O

/ Step 3 16 kcal/mol Fig. 2.


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RDX to be 47.8 kcal/mol. The Chakraborty et al.78 calculations predict that the ring opening, Step 2, requires 26.4 kcal/mol, again in accord with the earlier prediction by Melius.79 However, the ab initio results predict that the next step involves H-atom migration (8.7kcal/mol), followed by HCN elimination (which requires 16.2kcal/mol). 78 The Zhao et al67 experiments provide the only extensive study of the decomposition of RDX in the gas phase, but the conclusions continue to be questioned by many. There is no other experiment that leads to the conclusion that ring fission is a competitive initial step. The conditions studied in other experiments that have been reported to date differ too much to assign much significance to comparisons.

4. Concluding Remarks We have attempted to describe the current state of knowledge of the decomposition chemistry of nitromethane, methyl nitrite, DMNA, TNAZ, and RDX. These were selected to illustrate what is known about the decomposition mechanisms of energetic molecules in the gas phase. They are not only representative of energetic materials but are also probably the most studied. Our focus is on the initial decomposition reactions; however, we have also discussed the subsequent chemistry. As our discussion shows, the initial reactions are not firmly established in most cases and thus conclusions about the mechanisms for the complete decompositions are premature. The state of affairs we describe for these energetic molecules is representative of that of the broader field of reaction kinetics of large molecules — we are still in a primitive stage of not only understanding these complex reaction mechanisms but also in having the experimental and theoretical techniques to study them. We still do not know what reaction initiates the thermal decomposition of RDX and other important energetic compounds even though they have been known for over a century and in widespread use for more than half a century. For obvious reasons much of the experimental work has focused on the condensed-phase chemistry and considerable progress has been made in describing it (as several other chapters in this volume demonstrate). The gas-phase studies have provided activation energies that are sufficiently accurate to be of practical use in modeling, however, the specific reactions are not clearly established. This is in large part because, for most of these molecules, two or three reaction pathways are too close in energy for experiments to clearly distinguish which one is occurring, and which one actually

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occurs apparently depends on the specific conditions of the experiment. Also, complicating the analysis of an experiment is the prompt presence of radicals that result in chemistry that is very complex and very fast. Similar problems apply to many areas of chemistry besides energetic materials. In general, we do not yet have available the experimental or theoretical techniques that allows us to resolve the details of how a reactant or mixture of reactants undergo a series of branching reactions. The main focus, and thus the greatest progress, over the past half century has been on accurately determining the microscopic details of how elementary reactions occur. Experiment and theory have worked together to reach a point now where we can measure and compute highly-accurate minute properties of reactions involving small molecules. However, little effort has been devoted to developing techniques that would allow us to confidently postulate even the major pathways in the decomposition of a molecule as small as nitromethane. We still develop such mechanisms very much the same way Bodenstein did in the 1890s, although we now have computers and so can make fewer assumptions. For the chemistry discussed in this chapter, the experiments are modern only in the sense that they employ lasers, and in rare instances molecular beams, but otherwise they use traditional approaches such as bulbs, shock tubes, etc. In all cases, there is considerable modeling required to analyze the data. Thus, the emphasis has to be on obtaining more data, particularly the identification of transient species and their temporal appearance. Confirming the conclusions of some studies is needed, particularly in cases where conclusions must now be based on a single experiment. The main role that theorists can play at this point is to provide, based on high-level quantum chemistry calculations, energetics for species and transition states. The systems are sufficiently large that these are demanding problems, however, they are feasible (as illustrated by the discussions in the chapters by Rice and Fried et al.). By a synergistic process involving experiments (such as those described here and in the chapters by Dagdigian and Bernstein), theory can both guide and interpret the information needed to postulate mechanisms for the overall decomposition of energetic molecules in the gas phase. The quantum chemistry results can be used in MD and other methods for rate calculations to directly link theory to experiment, and to make predictions of data that are difficult or impossible to measure. In particular, the use of direct dynamics methods, although still in the developmental stage, will likely play a crucial role in developing a detailed understanding of the sequential, branching


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decomposition of energetic molecules. T h e realization of the methods to accurately predict rate processes in isolated molecules will lay the groundwork of improved methods for treating chemistry in condensed phases — the kinds of problems addressed by Rice in her chapter. Furthermore, the results directly feed into the modeling studies of the sort discussed by Miller in his chapter.

References 1. L. M. Raff and D. L. Thompson, in The Theory of Chemical Reaction Dynamics, Vol. 3, ed. M. Baer (CRC, Baca Raton, FL, 1985), p. 1. 2. T. D. Sewell and D. L. Thompson, Int. J. Mod. Phys. B l l , 1067 (1997). 3. D. L. Thompson, Int. Rev. Phys. Chem. 17, 547 (1998). 4. See, e.g., K. A. Holbrook, M. J. Pilling and S. H. Robinson, Unimolecular Reactions (Wiley, New York, 1996). 5. See, e.g., D. G. Truhlar, B. C. Garrett and S. J. Klippenstein, J. Phys. Chem. 100, 12771 (1996). 6. D. V. Shalashilin and D. L. Thompson, J. Chem. Phys. 105, 1833 (1995). 7. D. V. Shalashilin and D. L. Thompson, in Highly Excited States: Relaxation, Reactions, and Structures, eds. A. Mullins and G. C. Schatz (American Chemical Society, Washington, DC, 1997), p. 81. 8. (a) D. V. Shalashilin and D. L. Thompson, J. Phys. Chem. A 1 0 1 , 961 (1997); (b) Y. Guo, D. V. Shalashilin, J. A. Krouse and D. L. Thompson, J. Chem. Phys. 110, 5521 (1999). 9. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys. 2 1 , 1087 (1953). 10. For a comprehensive review, see: A. J. Marks, in Modern Methods for Multidimensional Dynamics Computations in Chemistry, ed. D. L. Thompson (World Scientific, Singapore, 1998), pp. 580-617. 11. See e.g., J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods (Chapman & Hall, London, 1964). 12. D. R. McLaughlin and D. L. Thompson, J. Chem. Phys. 59, 4393 (1973). 13. J. Ischtwan and M. A. Collins, J. Chem. Phys. 100, 8080 (1994). 14. For a review of this and related methods, see: G. C. Schatz, in Reaction and Molecular Dynamics, Lecture Notes in Chemistry, Vol. 14, eds. A. Lagana and A. Riganelli (Springer, Berlin, 2000), p. 15. 15. G. G. Maisuradze and D. L. Thompson, J. Phys. Chem. A107, 7118 (2003). 16. G. G. Maisuradze and D. L. Thompson, J. Chem. Phys. 119, 10002 (2003). 17. A. Kawano, Y. Guo, D. L. Thompson, A. F. Wagner and M. Minkoff, J. Chem. Phys., in press. 18. K. A. Nguyen, I. Rossi and D. G. Truhlar, J. Chem. Phys. 103, 5522 (1995). 19. For a review of this method and a discussion of some early studies, see: P. A. Schulz, Aa. S. Sudb0, D. J. Krajnovich, H. S. Kwok, Y. R. Shen and Y. T. Lee, Annu. Rev. Phys. Chem. 30, 379 (1979).

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20. (a) T. D. Sewell, D. L. Thompson and R. D. Levine, J. Phys. Chem. 96, 8006 (1992); (b) T. D. Sewell, C. C. Chambers, D. L. Thompson and R. D. Levine, Chem. Phys. Lett. 208, 125 (1993). 21. K. Glanzer and J. Troe, He.lv. Chim. Acta 55, 2884 (1972). 22. (a) A. Perche, J. C. Tricot and M. Lucquin, J. Chem. Res. Synop. 304 (1979); (b) ibid 3219 (1979); (c) A. Perche and M. Lucquin, J. Chem. Res. Miniprint 3257 (1979). 23. H. S. Hsu and M. C. Lin, J. Energet. Mat. 3, 95 (1985). 24. (a) A. Toby and K. O. Kutschke, Can. J. Chem. 37, 672 (1959); (b) A. R. Balke and K. O. Kutschke, Can. J. Chem. 37, 1462 (1959). 25. T. K. Choudhury, W. A. Sanders and M. C. Lin, J. Phys. Chem. 93, 5143 (1989). 26. Y.-X. Zhang and S. H. Bauer, J. Phys. Chem. B 1 0 1 , 8717 (1997). 27. Y.-X. Zhang and S. H. Bauer, J. Phys. Chem. A104, 1207 (2000). 28. P. Glarborg, A. B. Bendtsen and J. A. Miller, Int. J. Chem. Kinetics 3 1 , 591 (1999). 29. A. M. Wodtke, E. J. Hintsa and Y. T. Lee, J. Chem. Phys. 84, 1044 (1986). 30. A. M. Wodtke, E. J. Hintsa and Y. T. Lee, J. Phys. Chem. 90, 3549 (1986). 31. R. P. Saxon and M. Yoshimine, Can. J. Chem. 70, 572 (1992). 32. M. J. S. Dewar, J. P. Ritchie and J. Alster, J. Org. Chem. 50, 1031 (1985). 33. W.-F. Hu, T. J. He, D.-M. Chen and F.-C. Liu, J. Phys. Chem. A106, 7294 (2002). 34. M. T. Nguyen, H. T. Le, B. Hajgato, T. Veszpremi and M. C. Lin, J. Phys. Chem. A107, 4286 (2003). 35. B. M. Rice and D. L. Thompson, J. Chem. Phys. 93, 7986 (1990). 36. M. J. S. Dewar and J. P. Ritchie, J. Org. Chem. 50, 1031 (1985). 37. L. Batt, R. T. Milne and R. D. McCulloch, Int. J. Chem. Kinet. 9, 567 (1977). 38. Y. He, W. A. Sanders and M. C. Lin, J. Phys. Chem. 92, 5474 (1988). 39. (a) E. Martinez-Nunez and S. A. Vazquez, J. Chem. Phys. 109, 8907 (1998); (b) E. Martinez-Nunez and S. A. Vazquez, J. Am. Chem. Soc. 120, 7594 (1998); (c) E. Martinez-Nunez and S. A. Vazquez, J. Chem. Phys. I l l , 10501 (1999). 40. (a) S. H. Bauer and N. S. True, J. Phys. Chem. 84, 2507 (1980); (b) K. I. Lazaar and S. H. Bauer, J. Phys. Chem. 88, 3052 (1984); (c) S. H. Bauer and K. I. Lazaar, J. Chem. Phys. 79, 2808 (1983); (d) S. H. Bauer, Int. J. Chem. Kinet. 17, 367 (1985). 41. K. I. Lazaar and S. H. Bauer, J. Phys. Chem. 88, 3052 (1984). 42. A. Preiskorn and D. L. Thompson, J. Chem Phys. 91, 2299 (1989). 43. J. A. Darsey and D. L. Thompson, Chem. Phys. Lett. 145, 523 (1988). 44. E. Martinez-Nunez and S. A. Vazquez, J. Chem. Phys. 107, 5393 (1997). 45. S. A. Lloyd, M. E. Umstead and M. C. Lin, J. Energ. Mater. 3, 187 (1985). 46. Y. G. Lazarou and P. Papagiannakopoulos, J. Phys. Chem. 94, 7114 (1990). 47. J. M. Fluornoy, J. Chem. Phys. 36, 1106 (1962).

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48. (a) P. H. Stewart, J. B. Jeffries, J.-M. Zellweger, D. F. McMillen and D. M. Golden, J. Phys. Chem. 93, 3557 (1989); (b) S. E. Nigenda, D. F. McMillen and D. M. Golden, J. Phys. Chem. 93, 1124 (1993). 49. R. Shaw and F. E. Walker, J. Phys. Chem. 81, 2572 (1977). 50. M. A. Johnson and T. N. Truong, J. Phys. Chem. A103, 8840 (1999). 51. G. N. Spokes and S. W. Benson, J. Am. Chem. Soc. 89, 6030 (1967). 52. Y.-X. Zhang and S. H. Bauer, Int. J. Chem. Kinet. 31, 655 (1999). 53. B. G. Sumpter and D. L. Thompson, J. Chem. Phys. 88, 6889 (1988). 54. Y. Oyumi, T. B. Brill, A. L. Rheingold and T. M. Haller, J. Phys. Chem. 89, 4317 (1985). 55. Y. Oyumi and T. B. Brill, Combust. Flame 62, 225 (1985). 56. Y. Oyumi and T. B. Brill, Combust. Flame 68, 209 (1987). 57. D. S. Anex, J. C. Allman and Y. T. Lee, in Chemistry of Energetic Materials, eds. G. A. Olah and D. R. Squire (Academic Press, New York, 1991), pp. 27-54. 58. Y.-X. Zhang and S. H. Bauer, J. Phys. Chem. A102, 5846 (1998). 59. C.-L. Yu, Y.-X. Zhang and S. H. Bauer, J. Mol Struc. (Theochem) 432, 63 (1998). 60. P. Politzer and J. M. Seminario, Chem. Phys. Lett. 207, 27 (1993). 61. C. F. Wilcox, Y.-X. Zhang and S. H. Bauer, J. Mol. Struc. (Theochem) 528, 95 (2000); ibid. 538, 67 (2001). 62. C. A. Thompson, J. K. Rice, T. P. Russell, J. M. Seminario and P. Politzer, J. Phys. Chem. A101, 7742 (1997). 63. S. Alavi and D. L. Thompson, J. Chem. Phys. 119, 8297 (2003). 64. A. J. B. Robertson, Trans. Faraday Soc. 45, 85 (1949). 65. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data: Product Distributions from HMX and RDX Decomposition, Technical Report BRL-TR-2659 (US Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, 1985). 66. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data: Activation Energies and Frequency Factors for HMX and RDX Decomposition, Technical Report BRL-TR-2673 (US Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, 1985). 67. X. Zhao, E. J. Hintsa and Y. T. Lee, J. Chem. Phys. 88, 801 (1988). 68. P. A. Schulz, Aa. S. Sudb0, D. J. Krajinovich, H. S. Kwok, Y. T. Shen and Y. T. Lee, Annu. Rev. Phys. Chem. 31, 379-409 (1979). 69. G. T. Long, S. Vyazovkin, B. A. Brems and C. A. Wight, / . Phys. Chem. A104, 2570 (2000). 70. T. D. Sewell and D. L. Thompson, J. Phys. Chem. 95, 6228 (1991). 71. C. C. Chambers and D. L. Thompson, J. Phys. Chem. 99, 15881 (1995). 72. D. V. Shalashilin and D. L. Thompson, J. Phys. Chem. A101, 961 (1997). 73. Y. Guo, D. V. Shalashilin, J. A. Krouse and D. L. Thompson, J. Chem. Phys. 110, 5521 (1999). 74. C. A. Wight and T. R. Botcher, J. Am. Chem. Soc. 114, 8303 (1992). 75. Y. Guo and D. L. Thompson, J. Phys. Chem. B103, 10599 (1999).

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76. H. Zuckermann, G. D. Greenblatt and Y. Haas, J. Phys. Chem. 9 1 , 5159 (1987). 77. C. Capellos, P. Papaiannakopoulos and Y.-L. Liang, Chem. Phys. Lett. 174, 533 (1989). 78. D. Chakraborty, R. P. MuUer, S. Dasgupta and W. A. Goddard III, J. Phys. Chem. A104, 2261 (2000). 79. C. F. Melius in Chemistry and Physics of Energetic Materials, ed. S. N. Bulusu (Kluwer, Dordrecht, 1990), p. 21.

CHAPTER 9 MODELING THE REACTIONS OF ENERGETIC MATERIALS IN THE CONDENSED PHASE Laurence E. Fried and M. Riad Manaa Lawrence Livermore National Laboratory L-282, 7000 East Ave. Livermore, CA 94550, USA

James P. Lewis Department of Physics and Astronomy Brigham Young University N319 ESC, P.O. Box 24658 Provo, UT 84602-4658, USA

Contents 1. Introduction 2. Chemical Equilibrium 2.1. Thermodynamic Cycle Theory of Detonation 2.2. High Pressure Equations of State (EOS) 2.3. Example Applications 3. Atomistic Modeling of Condensed-Phase Reactions 3.1. Molecular-Dynamics with Bond-Order Potentials 3.2. Molecular-Dynamics with Quantum Mechanical Methods 3.3. Quantifying the Energetics of Reaction Pathways 3.4. Electronic Excitations in Shocked Explosives 4. Conclusions References

275 278 278 280 283 287 288 290 295 296 297 298

1. I n t r o d u c t i o n Energetic materials are unique for having a strong exothermic reactivity, which has made t h e m desirable for b o t h military and commercial applications. Energetic materials are commonly divided into high explosives, 275

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propellants, and pyrotechnics. We will focus on high-explosive (HE) materials here, although there is a great deal of commonality between the classes of energetic materials. Although the history of HE materials is long, their condensed-phase properties are poorly understood. Understanding the condensed-phase properties of HE materials is important for determining stability and performance. Information regarding HE material properties (for example, the physical, chemical, and mechanical behaviors of the constituents in plastic-bonded explosive, or PBX, formulations) is necessary for efficiently building the next generation of explosives as the quest for more powerful energetic materials (in terms of energy per volume) moves forward.1 In addition, understanding the reaction mechanisms has important ramifications in disposing of such materials safely and cheaply, as there exist vast stockpiles of HE materials with corresponding contamination of earth and groundwater at these sites. 2 In modeling HE materials there is a need to better understand the physical, chemical, and mechanical behaviors from fundamental theoretical principles. Among the quantities of interest in plastic-bonded explosives (PBXs), for example, are thermodynamic stabilities, reaction kinetics, equilibrium transport coefficients, mechanical moduli, and interfacial properties between HE materials and the polymeric binders. These properties are needed (as functions of stress state and temperature) for the development of improved micro-mechanical models, 3 which represent the composite at the level of grains and binder. 4 Improved micro-mechanical models are needed to describe the responses of PBXs to dynamic stress or thermal loading, thus yielding information for use in developing continuum models. Detailed descriptions of the chemical reaction mechanisms of condensed energetic materials at high densities and temperatures are essential for understanding events that occur at the reactive front under combustion or detonation conditions. Under shock conditions, for example, energetic materials undergo rapid heating to a few thousand degrees and are subjected to a compression of hundreds of kilobars,5 resulting in almost 30% volume reduction. Complex chemical reactions are thus initiated, in turn releasing large amounts of energy to sustain the detonation process. Clearly, understanding of the various chemical events at these extreme conditions is essential in order to build predictive material models. Scientific investigations into the reactive process have been undertaken

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over the past two decades. However, the sub-yus time scale of explosive reactions, in addition to the highly exothermic conditions of an explosion, make experimental investigation of the decomposition pathways difficult at best. More recently, new computational approaches to investigate condensedphase reactivity in energetic materials have been developed. Here we focus on two different approaches to condensed-phase reaction modeling: chemical equilibrium methods and atomistic modeling of condensedphase reactions. These are complementary approaches to understanding the chemical reactions of high explosives. Chemical equilibrium modeling uses a highly simplified thermodynamic picture of the reaction process, leading to a convenient and predictive model of detonation and other decomposition processes. Chemical equilibrium codes are often used in the design of new materials, both at the level of synthesis chemistry and formulation. Atomistic modeling is a rapidly emerging area. The doubling of computational power approximately every 18 months has made atomistic condensed-phase modeling more feasible. Atomistic calculations employ far fewer empirical parameters than chemical equilibrium calculations. Nevertheless, the atomistic modeling of chemical reactions requires an accurate global Born-Oppenheimer potential energy surface. Traditionally, such a surface is constructed by representing the potential energy surface with an analytical fit. This approach is only feasible for simple chemical reactions involving a small number of atoms. More recently, first principles molecular dynamics, where the electronic Schrodinger equation is solved numerically at each configuration in a molecular dynamics simulation, has become the method of choice for treating complicated chemical reactions. Recent developments, however, indicate that the use of transferable bond-order reactive empirical potentials may also be a viable option in studying condensedphase reactions. Please refer to the chapter by Rice for a more detailed discussion. Chemical reactions may also occur through diabatic processes involving several electronic states. The importance of such diabatic reactions on the overall chemistry of energetic materials is still a matter of debate. 6 ' 7 In addition to chemical equilibrium methods and atomistic modeling of reaction pathways on the ground electronic state, we also review recent work on the effect of high pressure and defects in modifying the excited electronic states of energetic materials.

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2. Chemical Equilibrium The energy content of a HE material often determines its practical utility. Accurate estimates of the energy content are essential in the design of new materials 1 and for understanding quantitative detonation tests. 8 The useful energy content is determined by the anticipated release mechanism. Since detonation events occur on a (is timeframe, chemical reactions significantly faster than this may be considered to be in an instantaneous chemical equilibrium. It is generally believed that reactions involving the production of small gaseous molecules (C0 2 , H 2 0 , etc.) are fast enough to be treated in chemical equilibrium for most energetic materials. This belief is based partly on success in modeling a wide range of materials with the assumption of chemical equilibrium. 9-12 Unfortunately, direct measurements of the chemical species in the detonation of a condensed are difficult to perform. Blais et al.13 have measured some of the species produced in detonating nitromethane (NM) using a special mass spectroscopic apparatus. These measurements pointed to the importance of condensation reactions in detonation. The authors estimate that the hydrodynamic reaction zone of detonating base-sensitized liquid nitromethane is 50 (i in thickness, with a reaction time of 7 ns. The hydrodynamic reaction zone dictates the point at which the material ceases to release enough energy to drive the detonation wave forward. Reactions may continue to proceed behind the reaction zone, but the timescales for such reactions are harder to estimate. Typical explosive experiments are performed on parts with dimensions in the order of 1-10 cm. In this case, hydrodynamic confinement is expected to last for roughly a (is, based on a high-pressure sound speed of several cm/(is. Thus, chemical equilibrium is expected to be a valid assumption for nitromethane, based on the timescale separation between the 7 ns reaction zone and the (is timescale of confinement. The formation of solids, such as carbon, or the combustion of metallic fuels, such as Al, is believed to yield significantly longer timescales of reaction. 14 In this case chemical equilibrium is a rough, although useful, approximation to the state of matter of a detonating material. 2.1. Thermodynamic

Cycle Theory of

Detonation

Thermodynamic cycles are a useful way to understand energy release mechanisms. Detonation can be thought of as a cycle that transforms the unreacted explosive into stable product molecules at the Chapman-Jouget (CJ) state 15 (see Fig. 1). This is simply described as the slowest steady-state


279

ChapmanJouget

Energy

O Unreacted

"O

Combustion in air

Volume Fig. 1. A thermodynamic picture of detonation: the unreacted material is compressed by the shock front and reaches the Chapman-Jouget point. From there adiabatic expansion occurs, leading to a high volume state. Finally, detonation products may mix in air and combust.

shock state that conserves mass, momentum, and energy. Similarly, the deflagration of a propellant converts the unreacted material into product molecules at constant enthalpy and pressure. The nature of the CJ state and other special thermodynamic states important to energetic materials is determined by the equation of state of the stable detonation products. A purely thermodynamic treatment of detonation ignores the important question of reaction timescales. The finite timescale of reaction leads to strong deviations in detonation velocities from values based on the Chapman-Jouget theory. 16 The kinetics of even simple molecules under high-pressure conditions is not well understood. High-pressure experiments promise to provide insight into chemical reactivity under extreme conditions. For instance, chemical equilibrium analysis of shocked hydrocarbons predicts the formation of condensed carbon and molecular hydrogen. 17 Similar mechanisms are at play when detonating energetic materials from condensed carbon. 11 Diamond anvil cell experiments have been used to determine the equation of state of methanol under high pressures. 18 We can then use a thermodynamic model to estimate the amount of methanol formed under detonation conditions. 19 Despite the importance of chemical kinetic rates, chemical equilibrium is often nearly achieved when energetic materials react. As discussed above, this is a useful working approximation, although it has not been established through direct measurement. Chemical equilibrium can be rapidly reached

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at the high temperatures (up to 6000 K) produced by detonating energetic materials. 20 We begin our discussion by examining thermodynamic cycle theory as applied to high explosive detonation. This is a current research topic because high explosives produce detonation products at extreme pressures and temperatures: up to 40 GPa and 6000 K. These conditions make it extremely difficult to probe chemical speciation. Relatively little is known about the equations of state under these conditions. Nonetheless, shock experiments on a wide range of materials have generated sufficient information to allow reliable thermodynamic modeling to proceed. One of the attractive features of thermodynamic modeling is that it requires very little information regarding the unreacted energetic material. The elemental composition, density, and heat of formation of the material are the only information needed. Since elemental composition is known once the material is specified, only density and heat of formation need to be predicted. The C J detonation theory 15 implies that the performance of an explosive is determined by thermodynamic states, the CJ state, and the connected expansion adiabat as illustrated in Fig. 1. The adiabatic expansion of the detonation products releases energy in the form of PVwoik and heat. Subsequent turbulent mixing of the detonation products in air surrounding the energetic material leads to combustion processes that release more energy. Thermochemical codes use thermodynamics to calculate states illustrated in Fig. 1, and thus predict explosive performance. The allowed thermodynamic states behind a shock are intersections of the Rayleigh line (expressing conservation of mass and momentum) and the shock Hugoniot (expressing conservation of energy). The CJ theory assumes that a stable detonation occurs when the Rayleigh line is tangent to the shock Hugoniot, as shown in Fig. 2. This point of tangency can be determined, assuming that the equation of state P = P{V, E) of the products is known. The chemical composition of the products changes with the thermodynamic state, so thermochemical codes must simultaneously solve for state variables and chemical concentrations. This problem is relatively straightforward, given that the equations of state (EOS) of the fluid and solid products are known.

2.2. High Pressure

Equations

of State

(EOS)

One of the most difficult parts of this problem is accurately describing the EOS of the fluid components. Because of its simplicity, the


281

Fully reacted Hugoniot

P Rayleigh^^^y line ^ \ ^giChapman-Jouget state

O Unreacted state •

V Fig. 2. Allowed thermodynamic stated in detonation are constrained to the shock Hugoniot. Steady-state shock waves follow the Rayleigh line.

Becker-Kistiakowski-Wilson (BKW) 21 EOS is used in many practical energetic material applications. There have been a number of different parameter sets proposed for the BKW EOS. 22 Kury and Souers8 have critically reviewed these by comparing their predictions to a database of detonation tests. They concluded that BKW EOS does not adequately model the detonation of a copper-lined cylindrical charge. The BKWC parameter set 23 partially overcomes this deficiency through multivariate parameterization techniques. However, the BKWC parameter set is not reliable when applied to explosives very high in hydrogen content. It has long been recognized that validity of the BKW EOS is questionable. 12 This is particularly important when designing new materials that may have unusual elemental compositions. Efforts to develop better EOS have largely been based on the concept of model potentials. With model potentials, molecules interact via idealized spherical pair potentials. Statistical mechanics is then employed to calculate the EOS of the interacting mixture of effective spherical particles. Most often, the exponential-6 (exp-6) potential is used for the pair interactions: V{r) = ^ — - [ 6 e x p ( a - ar/rm)

-

a{rm/rf].

Here, r is the distance between particles, r m is the minimum of the potential well, e is the well depth, and a is the softness of the potential well. The JCZ3 (Jacobs-Cowperthwaite-Zwisler) EOS was the first successful model based on a pair potential that was applied to detonation. 24 This EOS was based on fitting Monte Carlo simulation data to an analytic

282


functional form. Ross, Ree, and others successfully applied a soft-sphere EOS based on perturbation theory to detonation and shock problems. 11 ' 25 ' 26 Computational cost is a significant difficulty with EOS based on fluid perturbation theory. Brown 27 developed an analytic representation of the EOS which uses Chebyshev polynomials. The accuracy of the above EOS has been recently evaluated by Char let et al.12; these authors concluded that Ross's approach is the most reliable. More recently, Fried and Howard 28 have used a combination of integral equation theory and Monte Carlo simulations to generate a highly accurate EOS for the exp-6 fluid. The exp-6 model is not well suited to molecules with large dipole moments. Ree 10 has used a temperature-dependent well depth e(T) in the exp-6 potential to model polar fluids and fluid phase separations. Fried and Howard have developed an effective cluster model for HF. 2 9 The effective cluster model is valid for temperatures lower than the variable well-depth model, but it employs two more adjustable parameters than does the latter. Jones et al.30 have applied thermodynamic perturbation theory to polar detonation-product molecules. However, more progress needs to be made in the treatment of polar detonation-product molecules. Efforts have been made to develop EOS for detonation products based on direct Monte Carlo simulations instead of analytical approaches. 31 This approach is promising given the recent increases in computational capabilities. One of the greatest advantages of direct simulation is the ability to go beyond van der Waals 1-fluid theory, which approximately maps the equation of state of a mixture onto that of a single component fluid.32 In most cases, interactions between unlike molecules are treated with Lorentz-Berthelot combination rules. 33 These rules specify the interactions between unlike molecules as arithmetic or geometric averages of single molecule pair-interactions. Non-additive pair interactions have been used for N2 and 02- 2 6 The resulting N2 model accurately matches double-shock data, but is not accurate at lower temperatures and densities. 28 A combination of experiments on mixtures and theoretical developments is needed to develop reliable unlike-pair interaction potentials. The exp-6 potential has also proved successful in modeling chemical equilibrium at the high pressures and temperatures characteristic of detonation. However, in order to calibrate the parameters for such models, it is necessary to have experimental data for product molecules and mixtures of molecular species at high temperature and pressure. Static compression and sound-speed measurements provide important data for these models.


283

Exp-6 potential models can be validated through several independent means. Fried and Howard 29 ' 34 have considered the shock Hugoniots of liquids and solids in the "decomposition regime" where thermochemical equilibrium is established. As an example of a typical thermochemical implementation, we consider the Cheetah thermochemical code. 28 Cheetah is used to predict detonation performance for solid and liquid explosives. Cheetah solves thermodynamic equations between product species to find chemical equilibrium for a given pressure and temperature. From these properties and elementary detonation theory the detonation velocity and other performance indicators are computed. Thermodynamic equilibrium is found by balancing chemical potentials, where the chemical potentials of condensed species are functions of only pressure and temperature, while the potentials of gaseous species also depend on concentrations. In order to solve for the chemical potentials, it is necessary to know the pressure-volume relations for species that are important products in detonation. It is also necessary to know these relations at the high pressures and temperatures that typically characterize the CJ state. Thus, there is a need for improved high-pressure equations of state for fluids, particularly for molecular fluid mixtures. In addition to the intermolecular potential, there is an intramolecular portion of the Helmholtz free energy. Cheetah uses a polyatomic model including electronic, vibrational, and rotational states. Such a model can be conveniently expressed in terms of the heat of formation, standard entropy, and constant-pressure heat capacity of each species. 2.3. Example

Applications

High-pressure nuorocarbons provide a good example of the equation of state modeling based on simple exp-6 interactions. Fluorocarbons are challenging because of the highly polar and associated nature of HF as well as the scarcity of experimental data on the EOS. A reactive fluorocarbon model requires parameters for hydrocarbons, fluorocarbon, F 2 , and HF. Fried and Howard 29 determined hydrocarbon parameters with data from shock and static experiments. High-pressure EOS measurements have not been performed on F 2 . They used exp-6 parameters for F 2 as estimated by Zerilli and Jones. 35 Chemical equilibrium modeling predicts that PTFE decomposes into a fluid phase composed mostly of CF 4 , and carbon in the diamond phase. This is in agreement with shock recovery experiments. 36 This is supports the validity of chemical equilibrium modeling for shocked organic materials.

284


The traditional exp-6 model has difficulty treating "associated" fluids with strong attractive intermolecular interactions, for example, highly polar molecules. HF is known to strongly associate, 37 in the gaseous, liquid, and fluid phases. Fried and Howard 29 have determined a simple HF association model that matches both high- and low-pressure data. The model treats the associated fluid as a set of clusters. The motivation for the cluster model is to determine the simplest possible model that will match both the lowpressure static compression of supercritical HF and the shock Hugoniot of polyvinylidene fluoride (PVF2). The Fried-Howard model succeeds in this regard, although the description of individual cluster species has not been validated against experiments, due to the difficulty in measuring speciation at extreme conditions. Fried and Howard found that it is possible to match the shock Hugoniot of PVF2 without the association model, but the static compression requires an explicit treatment of association through clustered species. We show the calculated isotherms of HF in Fig. 3; the calculated shock Hugoniot of PVF2 is shown in Fig. 4. The calculations predict that PVF2 dissociates to HF and carbon. The HF model works equally well in the pressure range 0.01 to 75 GPa.

40 35 30 "J? 25 CL

BT 20 15

10 5 2

4

6

8

10

12

14

V (cc/gm) Fig. 3. Measurements of the isotherms of HF at 543, 553, 563, and 573 K (points) compared to results for the Fried-Howard model (lines).


285

80

70

^ 60 CO Q.

o ^50 40

30 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 V (cc/gm) Fig. 4. Measurements of the shock Hugoniot of PVF2 (error bars) compared to results for the Fried-Howard model (line).

We now consider how the EOS described above predicts the detonation behavior of condensed explosives. The overdriven shock Hugoniot of an explosive is an appropriate EOS test, since it accesses a wide range of high pressures. Overdriven states lie on the shock Hugoniot at pressures above the CJ point (see Fig. 2). The Hugoniot of PETN (penta-erythritol tetranitrate) is shown in Fig. 5. Fried and Howard 34 have calculated the Hugoniot with the exp-6 model and also with the JCZS 38 product library. Good agreement with experiment is found. Since the exp-6 model is not calibrated to condensed explosives, such agreement is a strong indication of the validity of the chemical equilibrium approximation to detonation. Despite the many successes in the thermochemical modeling of energetic materials, there are several significant limitations. One such limitation is that real systems do not always obtain chemical equilibrium during the relatively short (ns-jus) timescales of detonation. When this occurs, quantities such as the energy of detonation and the detonation velocity are commonly predicted to be higher than experiment by a thermochemical calculation. Partial-equilibrium calculations 14 can overcome this problem. In partialequilibrium modeling, the concentrations of certain detonation products or

286


140

'

'

'

'

1 '

'

'

'

1 '

'

'

' 1

-

120 •

\

\

100 -*

\

80

\ \

-

"A

-

\

-

Q.

o ST

60 40 20

.

0 0.2

.

.

.

i

.

0.3

.

.

.

i

.

.

.

.

:

i

0.4 0.5 V (cc/gm)

0.6

0.7

Fig. 5. The shock Hugoniot of P E T N as calculated with exp-6 (solid line) and the JCZS library (dotted line) versus experiment (error bars).

reactants are held at fixed values. This assumes a priori knowledge of the timescales of reaction and detonation. Since this information is not usually known, partial-equilibrium modeling is not fully predictive. Chemical kinetic modeling is another possible way to treat detonation. There are several well-developed chemical kinetic mechanisms for highlystudied materials such as RDX and HMX. 39,40 Unfortunately, detailed chemical kinetic mechanisms are not available for high-pressure conditions. Some workers have applied simplified chemical kinetics to detonation processes.16 The primary difficulty in high-pressure chemical kinetic models is a lack of experimental data on speciation. First principles simulations, discussed below, have the potential to provide chemical kinetic information on fast processes. This information could then conceivably be applied to longer timescales and lower temperatures using high-pressure chemical kinetics. Finally, there are several issues to be addressed in determining the EOS of detonation products. While convenient, the exp-6 model does not adequately treat electrostatic interactions. In a condensed phase, effects such as dielectric screening and charge-induced dipoles need to be considered.

Modeling the Reactions of Energetic Materials in the Condensed

Phase

287

Molecular shape is also neglected in exp-6 models. While the small size of most detonation product molecules limits the importance of molecular shape, lower temperature conditions could yield long-chain molecules, where molecular shape is more important. Also, ionization may become dominant at high temperatures or for systems with strong acids and bases. Equation of state information for molecular ions and a successful statistical mechanical treatment at high pressure do not yet exist.

3. Atomistic Modeling of Condensed-Phase Reactions Chemical equilibrium methods provide useful predictions of macroscopic detonation processes resultant product molecules. However, no details of the atomistic mechanisms in the detonation are revealed. We now discuss condensed-phase detonation simulations using atomistic modeling techniques. Such simulations are quite useful for understanding the condensedphase reaction mechanisms on the microscopic level. Numerous experimental studies have investigated the atomistic details of HE decomposition by examining the net products after thermal (lowpressure) decomposition (for example, see Ref. 41). More specifically for RDX and HMX, the rate-limiting reaction is most likely NO2 dissociation and a plethora of final products in the decomposition process have been isolated (see the chapters by Brill and Behrens for further discussion). Several theoretical studies have also been reported on the energetics of gasphase decomposition pathways for HE materials using a variety of methods. For example, we point to work on RDX and HMX where both quantum chemistry 42 ' 43 and classical simulations of unimolecular dissociation44 were used. The gas-phase results provide much insight into the reaction pathways for isolated HE molecules; however, the absence of the condensed-phase environment is believed to strongly affect reaction pathways. Some of the key questions related to condensed-phase decomposition are: (1) How do the temperature and pressure affect the reaction pathways? (2) Are there temperature or pressure-induced phase-transitions which play a role in the reaction pathways that may occur? (3) What happens to the reaction profiles in a shock-induced detonation? These questions can be answered with condensed-phase simulations, but would require large-scale reactive chemical systems (thousands of atoms). Here we present very recent results of condensed-phase atomistic simulations, which are pushing the envelope towards reaching the required simulation goal.

288


3.1. Molecular-Dynamics

with Bond-Order

Potentials

A novel approach for investigating reactions in the condensed-phase is to take advantage of the computational efficiency of empirical force fields. Although traditional analytical force fields cannot model the required variety of chemical reactions, transferable force field terms dependent on the bond order can be included to model bond-breaking/making mechanisms. These bond-order terms describe the bond-breaking/making mechanisms needed for simulating reactions. The bond order defines the strength of the bond between two atoms where larger numbers imply stronger bonds; it is a measure of the net number of bonds between a specific pair of atoms in a molecule. Bond-order potentials have been proposed early in the history of atomistic modeling; several methods exist, and each has a different prescription for defining the bond order between reactants and products. 45 Bond-order potentials have been successfully applied to simplified models of shocked energetic materials. 46 Recently, Goddard et al.47 have developed a method (called ReaxFF) for hydrocarbons and energetic materials. In the ReaxFF method, the central-force formalism is used and nonbonded interactions and Coulomb forces are included to yield smooth bond dissociations. Local perturbations to geometries such as bond angles, and torsional angles, are also added to describe complex molecules more accurately. The bond-order term, BOj, between a pair of atoms is of the form BO;7- = exp KJ'-Z u

+ exp Plirl

~

• exp

The parameters, p, correspond to the bond-order curves associated with different types of orbitals for each atom type (see Fig. 6 for the C-C case). The method yields heats of formations within 1-2 kcal/mol of experimental values. In addition, the energetics of dissociations have the same qualitative features as those obtained from quantum chemistry calculations. Recent results for ReaxFF applied to RDX demonstrate the capabilities of the model. Strachan et al.48 applied it to the initial stages of a shock-induced detonation of RDX. Parameters were developed from 40 different reactions and 1600 different equilibrated molecules, which represent potential product molecules along the possible reaction pathways. Two two-dimensional periodic slabs (each slab having 32 RDX molecules forming a perfect crystal) were impacted into each other at velocities of 2, 4, 6, 8, and lOkm/s. The results of these shock-induced detonation simulations are quite interesting. First, the products yielded from the simulations (shown in


289

ReaxFF C-C bond order vs distance -Bond order -Sigma bond - Pi bond • Double pi bond

1.5

2

2.5

C-C bond distance (A)

Fig. 6.

Interatomic distance dependence of the carbon—carbon bond order.

80 NO,

RDX shock v. = 8 km/s imp

60

o | 40

& ex OH

20

NO

H

2° com HCN(5), CN

O

MONO

n

HCO

HCNO

UJ.

10

15

20

25

30

35

40

ILL

45 •

50

mass (g/mol) Fig. 7. Mass spectrum corresponding to u i m p = 8 k m / s at time t = 4ps. Population as a function of mass for all the molecules found up to mass 50 g/mol (all species with population larger than 3 are labeled).

Fig. 7) are products that are observed experimentally under slow heating (cook-off) conditions. 49 Although the experimental conditions of slow heating differ from the detonation condition used in the simulations, it is probable that many of the products will be similar in type albeit not necessarily

290


similar in quantity. Second, the primary reactions leading to NO2, OH, NO, and N2 occur at very early stages of the simulations. Additionally, as the impact velocity increases, N2 and OH become the dominant product species at short times. Finally, the simulations show that although the barrier for the pathways leading to NO2 and HONO is essentially the same, NO2 is the main product for low shock-velocities ( < 6 k m / s ) , in agreement with experimental work by Owens and Sharma. 50

3.2. Molecular-Dynamics with Mechanical Methods

Quantum

Bond-order potentials are fast and appear to give correct qualitative results; however, there are difficulties in using them. First, many parameters must be used to correctly model the reaction pathway. Second, many quantum chemistry calculations of small systems must be done to fit these parameters. For systems like RDX and HMX, which are experimentally better characterized than most HE materials, bond-order potentials appear to work reasonably well.48 For less-known systems, for example TATB, bond-order potentials may be less accurate. In TATB, the molecular crystal is formed through hydrogen-bonding interactions and the bond-order potentials must be modified to take such weak interactions into account. Recently, quantum mechanical methods have been applied to systems with up to 1000 atoms. This is due not only to advances in computer technology, but also improvements in algorithms. A wide range of approximations can also be made to yield a variety of methods; each able to address a different range of questions based on the accuracy of the method chosen. We now discuss a range of quantum mechanical based methods used to answer specific questions regarding shock-induced detonation conditions. Atomistic simulations have recently been performed on condensedphase HMX (l,3,5,7-tetranitro-l,3,5,7-tetraazacyclooctane). This material is widely used as an ingredient in various explosives and propellants. A molecular solid at standard state, it has four known polymorphs.

IVR region 1

(c)

(

c:

©D

Fig. 1. (a) Energy levels of a molecular solid. The phonon fundamental cut-off frequency or "Debye frequency" is denoted as B p , In the intramolecular vibrational redistribution (IVR) region, the density of vibrational combination and overtone states is large enough to facilitate fast energy transfer among vibrational levels. Usually the region of chemically-significant energies lies above the IVR threshold, (b) and (c) Two scenarios for phonon up-pumping that causes chemical bonds to break. In (b), a series of phonons successively pump energy up a vibrational ladder, starting with doorway vibrations (lowest energy vibrational fundamentals). When an energy above the IVR threshold is reached, the vibrational energy becomes statistically randomized among all modes. When chemically-significant energies are attained, the weakest chemical bond breaks. In (c), a highly excited coherent phonon state pumps energy directly into the chemical bond to which it is most strongly coupled, causing this bond — not necessarily the weakest bond — to break.

of states running to much higher energy (up to near the sublimation energy) representing phonon overtone and combination excitations. The lowest frequency vibrations are potential doorway modes. One way to identify a potential doorway vibration is to note the gap between the vibrational frequency and 6 D - For instance in NM, 14,15 6 D ~ 160cm - 1 and the lowest energy vibration is 480 c m - 1 . This sizeable gap indicates poor mixing between phonons and lower frequency vibrations, so NM translates or librates as an approximately rigid body. In naphthalene this gap is small.5 The top of the phonon band is ~ 1 4 0 c m _ 1 and the lowest frequency vibration, the butterfly ring deformation, is at 175 c m - 1 . Two other naphthalene vibrations, skeletal twisting modes at 212 cm""1 and 360 c m - 1 can be

Multi-Phonon

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in Energetic

Materials

309

identified as likely doorway vibrations. With larger non-rigid molecules, one or more of the lowest frequency vibrations, typically torsions, nitro rocking or skeletal bending modes, actually lie below 0 D - In this case we say a doorway vibration is amalgamated in the phonon band. This means the non-rigid molecule cannot translate or librate without undergoing considerable deformation. In HMX for example, calculations indicate there are 10 low-frequency vibrations below 160cm - 1 . 1 6 The highest energies of the 3N — 6 vibrational fundamentals are C-H and N-H stretching modes in the 2800-3500 c m - 1 range. The mid-range vibrations, typically 800-1700 c m - 1 have the longest vibrational lifetimes and the slowest VR processes. 13 ' 17 There are a vast number of combination and overtones of the higher, mid-range and doorway vibrations, as shown in Fig. 1(a), whose state density increases approximately exponentially with increasing energy. After the rediagonalization to quasiharmonic states, the remaining (last three) terms in Eq. (lb) can be used to describe dynamical processes that result in energy transfer among phonons, among vibrations, or between vibrations and phonons. There is a sizeable literature that shows how these three terms can be used to describe a variety of relaxation processes, where non-equilibrium populations of vibrations or phonons created by sudden perturbations relax back to equilibrium. 4,18 The ffph-Ph term causes phonon-phonon scattering. For instance if an impact on a colder crystal creates a bunch of non-equilibrium phonons, ffph-Ph causes them to decay into an equilibrium phonon distribution creating a warmer crystal in thermal equilibrium. ffph-vib allows an excess of vibrational energy to decay into a bunch of phonons or an excess of phonons to pump energy into molecular vibrations. It is here that the doorway vibrations play a critical role. When a perturbation such as a shock shoves adjacent molecules together, the doorway vibrations are the first vibrations excited.5 The doorway vibrations act as a conduit for mechanical energy outside a molecule to flow into modes of primarily intramolecular character. When a particular bunch of vibrations is created, for instance by phonon up-pumping or as the result of vibrational excitations produced by an exothermic chemical reaction, i?vib-vib allows energy exchange among these states and with other unexcited vibrations. Since i?Vib-vib is typically the smallest of the interaction terms in Eq. (lb), the density of vibrational states has to be relatively large for vibration-vibration energy transfer to become efficient. It is known that excitations above the energy where the state density reaches 100-1000 states/cm - 1 , termed the intramolecular

310

D. D. Dlott

vibrational redistribution (IVR) threshold, can move rapidly among many nearly isoenergetic states. 19 Chemically-significant energies, i.e. energies large enough to have a reasonable chance of breaking a covalent chemical bond, lie in the region of efficient IVR for almost all molecules with at least three C, N or O atoms. 19 For this reason it is an extremely difficult challenge to prepare a molecule with a chemically-significant amount of energy that stays localized in a particular bond for even 50 fs. Relaxations are by nature incoherent processes. An incoherent process is one that randomly affects individual excitations differently. The rate expressions for relaxation processes are usually treated well by Golden Rule formalisms,4 where the rate constant is proportional to the square of a matrix element of the operator in Eq. (2) and a density of states. For instance at OK, an excited vibration with energy Ml could relax by spontaneous emission of a lower energy vibration fuo plus a phonon 7kJphThis process would be enabled by cubic anharmonic coupling, and the rate constant /CVR would be given by,4 kvR = 36TT2 V

(Vg>y6(il

-w-

Wph),

(3)

where {VQ I w ), henceforth just (V^3^}, is shorthand for the matrix element of the cubic anharmonic Hamiltonian, I/O)

1 d 3 V(Q) 3! OQndQ^dq^

QnQuqwplL-

(4)

Q=0

Calculations using Eq. (3) can be greatly simplified if we assume that all the matrix elements for certain processes are approximately equal to an average matrix element (V^ 3 )} a v g . 1 3 ' 2 0 ' 2 1 That is because the matrix elements are difficult to calculate and are very sensitive to minute details of the potential energy surface,22~25 whereas the density of states is easier to calculate and even easier to estimate based on neutron or vibrational spectroscopy measurements. In that case, for the Q, —> UJ + wph process,

k = ^(v*)ls

J2s(n-0,-^

=^ ^ ) 1 ^ .

(5)

In Eq. (5), the summation over S-functions gives the density of states PQ /h. This is the density of states per unit energy having one phonon and one vibration whose energies Too + fiwph sum up to hfl. The usual terminology for this quantity is "two-phonon" density of states although the same term can be used to mean one phonon and one vibration or two vibrations. Equation (5) can be generalized to describe other processes using

Multi-Phonon

Up-Pumping

in Energetic

Materials

311

different matrix elements and different densities of states. For example, two of the myriad VR pathways observed for excited vibrations of NM can be expressed as, 2 6 - 2 8 i/ s (N0 2 ) -> 4 ( N 0 2 ) + /o(N02) + 3 phonons, p(N0 2 ) —> 3 phonons. In the first process, the symmetric N 0 2 stretching vibration (1379 c m - 1 ) decays by producing one quantum of N 0 2 scissors (657 c m - 1 ) plus one quantum of N 0 2 rock (480 c m - 1 ) plus three phonons adding up to 242 c m - 1 . In the language of Eq. (5) this rate constant depends on a (V^) matrix element and a five-phonon density of states p*-5) (1379 cm" 1 ). Similarly, decay of the lowest energy vibration in NM, the N 0 2 rock, by generating three phonons, would depend on a (V^4') matrix element and a three-phonon density of states p^ (480 c m - 1 ) . In using Eq. (5), one useful refinement is to use not one but rather a small number of different average matrix elements to describe a few different processes. 13 ' 21,29 ' 30 This can be done using the following ansatz. All things being equal, (V) becomes smaller as the order n becomes larger. 31 Furthermore the matrix elements (V") are generally larger when they contain more phonon coordinates q and fewer vibration coordinates Q because phonons are generally more anharmonic than vibrations. 13 These effects are, in a very approximate sense, about equivalent, that is to say changing a q to a Q, which makes a matrix element smaller, has roughly the same effect as moving up one order by adding another q.21 Thus, we can make a table of approximate matrix element ordering as follows: QQQ < QQq < Qqq < qqq,

for (W3>)

QQQQ < QQQq < QQqq < Qqqq < qqqq < Qqq and so on. Having developed this background, let us now see what it tells us about a practical example. Breaking the N - N 0 2 bond is believed to be the first step in thermal initiation of RDX in the solid state. 32 ' 33 Although we should recognize that we cannot for certain say if this remains true with shockinduced chemistry, let us still consider the possibility of impact-generated phonons breaking a N - N 0 2 bond. Breaking this bond requires an energy34 of ~140kJ/mol or equivalently ~ l l , 7 0 0 c m _ 1 per molecule. We can imagine two quite different scenarios for phonon-induced bond cleavage. The "conventional" scenario sketched in Fig. 1(b) has the phonons up-pumping doorway vibrations including N 0 2 torsion and rock, which bleed energy into the other vibrational states until the molecule has taken

312

D. D. Dlott

up a chemically-significant amount of energy. Depending on conditions, this could take anywhere from l p s to 100ps (vide infra). Due to fast IVR, this energy is rapidly redistributed in a statistical manner among many almostdegenerate vibrational states until the weakest bond is broken. On the basis of Wight's thin-film pyrolysis experiments, 32 ' 33 for RDX this is presumably the N-NO2 bond. The N-NO2 bond is broken when enough energy happens to become concentrated in the N-NO2 stretch. The well-known theory for this redistribution process, termed RRKM theory, 35 posits a random walk among isoenergetic vibrational states until the first bond breaks. In order to have a statistically reasonable chance of getting a minimum of 11,700 c m - 1 into the right state, some extra energy is required. RRKM theory shows that with more extra energy available, the needed energy gets to the right place in less time, so the chemical reaction rate increases with increasing excess energy.35 An "unconventional" scenario is depicted in Fig. 1(c). Here a highenergy phonon excitation pumps a particular bond right to the dissociation limit. 36 For this type of mode-specific chemistry the first broken bond is not necessarily the weakest bond, rather it would more likely involve the motion that is most strongly coupled to the shock-generated phonons. This scenario could potentially produce bond breaking in impacts that is completely different from what is observed with slow heating, so do not be confused that in the present example we are comparing two different ways of breaking the same bond. This hypothetical and novel bond-breaking mechanism has been termed "shock-induced bond scission" or "shear-induced chemical decomposition". 37 ' 38 The N-NO2 stretch is probably not the motion most strongly coupled to the shock front. Dick's molecular mechanics models 38 suggest that the coupling between N-NO2 rocking and phonons (in PETN) ought to be much stronger than between N-NO2 stretching and phonons, so either the N-NO2 bond must be bent to the breaking point ("sheared off") or the rocking energy must flow preferentially into the stretching mode (which seems at least reasonable) to break this bond. Working against either of these scenarios is the IVR process, which drains energy out of these coordinates and into the rest of the molecule. Thus for this unconventional scenario to be possible, the rate of energy input to coordinates that can cause bond scission must significantly exceed the IVR rate. For more than twenty years, researchers have tried without much success to achieve selective bond scission using photons rather than phonons. 39_41 Short intense tunable IR laser pulses are used to selectively deposit energy into chosen coordinates, but in almost every case IVR causes the weakest bond to break,

Multi-Phonon

Up-Pumping

in Energetic

Materials

313

thwarting the desire to achieve bond-selective chemistry. 40 ' 41 A prominent exception involves experiments on gas-phase HOD, an isolated triatomic molecule with slow IVR, where Crim's group 42 has shown it is possible to choose to break either the O-H or O-D bond using properly selected combinations of IR and UV laser pulses. The inability of lasers to accomplish much bond-selective chemistry makes many of us familiar with the laser literature pessimistic that impact-generated phonons can break one of the stronger bonds via direct bond scission. The pessimist says that if it cannot be done with a laser, an exceedingly precise tool, it cannot be done with a shock front. The optimist counters that a planar shock front creates a vast number of phonons with a great deal of momentum and a reasonable degree of coherence, all impacting a molecule along a particular direction, and the pulse duration (the shock front risetime) could be exceedingly brief. This debate continues and its resolution should be eagerly awaited by the energetic materials community. Equations (3) and (5) above describe the decay of a higher frequency vibration Q, by spontaneous emission of a phonon wph and a lower energy vibration u>. In order to treat the problem of phonon up-pumping, we have to introduce the possibility of phonon absorption.4'18 How this is done depends on how we view the phonons created by impact. 7 Heating a sample generates incoherent phonons. Incoherent means the phases of all the phonon excitations are uncorrelated, which is the usual case. A coherent bunch of phonons is one with a well-defined and enduring phase relationship among all the phonons. 43 Phonons that are generated from a thin source layer, one that is thin relative to the phonon wavelength, will at least initially all have the same phase. Various scattering processes and phonon-phonon relaxation processes will ultimately lead to dephasing of a coherent phonon bunch. Lower frequency acoustic wavepackets (sound) can travel long distances without dephasing, but with higher phonon frequencies and high phonon densities dephasing might occur within just a few picoseconds.44 One might expect a very steep shock front just one molecule wide to generate a phonon packet with a high degree of initial coherence, since the phonon amplitudes must cancel just ahead of the front and add in phase just behind the front. Another possible coherent phonon generator involves a moving edge dislocation or dynamically forming crack surface where intense bursts of phonons can be generated from a very thin interfacial source layer. The equations for incoherent pumping are well known and they express various transition rates as functions of the phonon occupation numbers.

314

D. D. Dlott

For instance, the rate constant for a representative up-pumping process involving two-phonon pumping and cubic anharmonic coupling is, 5 ' 18 fc2ph^vib = ^ < v ( 3 > } y 2 ) ( t t ) K h ( T ,

v)

_

nvib(Tj v)])

(6)

where (V^) is a matrix element of the Qqq type, p(2\£l) is the two-phonon density of states at the doorway mode frequency f), and n p h(T, V) refers to the occupation number of phonons of frequency w = fi/2 at temperature T and specific volume V, nUJ(T,V) = {exp(fruj(V)/kBT) - l } " 1 . With incoherent up-pumping, the initial vibrational population grows linearly in time, and then levels off when phonon and vibration populations equilibrate. 5 The problem of coherent pumping of vibrations by phonons has not been worked out as well as the incoherent pumping problem. However, a similar problem, coherent pumping of vibrations by laser photons, has been studied a great deal using density matrix formalisms.45 Coherent pumping becomes efficient when the pumping rate is faster than processes46 that destroy molecular coherence such as vibrational dephasing. In coherent pumping, it is the vibrational amplitude that initially grows linearly with time. 45 The initial increase in vibrational population thus grows quadradically with time. Although Eq. (6) shows that incoherent pumping can at best result in saturation, that is equal populations in ground and excited states, coherent pumping can produce highly-inverted states where the excited-state population greatly exceeds the ground-state population. 45 Coherent pumping is an exceedingly fast and efficient way of creating high levels of vibrational excitation. Several problems need to be addressed to further develop this intriguing idea. 7 Although there is a formal similarity between photon and phonon pumping of vibrations, we should not unquestioningly adopt the wellknown photon equations because in the limit of large amplitudes phonons and photons behave quite differently. We also need a better idea of what kind of phonon wavepackets are generated by shock fronts and moving edge dislocations, what is their duration, intensity, spectrum and so forth. The direction light is propagating when it hits a molecule is not very important but the direction a molecule is hit by a shock front is very significant.

3. Up-Pumping in Experiments and Simulations Direct measurements of up-pumping have proven difficult because of the problem of generating short-duration bursts of phonons that are intense enough to cause vibrational excitation in the 200-4000 c m - 1 range. In

Multi-Phonon

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Materials

315

addition, it has proven difficult to combine available techniques for highintensity phonon generation with time- and vibrational state-resolved probes. Three methods have been developed to initiate up-pumping. The Dlott group introduced "molecular heaters" which are large dye molecules embedded in a sample that can emit many phonons in a short time after optical pumping. 47 One dye, IR-165, was shown to emit tens of thousands of c m - 1 of phonon energy per molecule when pumped by near-IR picosecond pulses, to produce temperature jumps at rates up to 1012 K/s. However, this dye heater does not do a good job of mimicking an impact, and its absorption spectrum can hinder many spectroscopic probe measurements. The Fayer group 48 introduced an interesting technique where a tunable laser generates an excitation that is initially colder than its surroundings. Up-pumping then causes this excited state to heat up to the temperature of its surroundings. Shock compression seems to be the most desirable way of generating phonons for up-pumping, but achieving the combination of picosecond time resolution and state-resolved probing has proven difficult. In 1994, Chen, Tolbert, and Dlott 27 used the molecular heater method to study up-pumping in NM. Prior to that time, several theoretical works 36 ' 49,50 had calculated the NM up-pumping rate into the C-N stretching vibration, with the intent of causing the C-N bond to break. A variety of theoretical results were obtained for C-N up-pumping times, ranging from 100 ns to 1 ms. Some of these works 49 ' 50 suggested that the 1 /zs induction time in NM shock initiation was a result of 1 /us up-pumping, so in particular establishing the timescale of NM up-pumping by experiment seemed important. The IR-165 heaters generated enough phonons to ultimately raise the NM temperature by AT = 30 K. Since this heating was so rapid as to be isochoric, the pressure also rose by ^0.05 GPa. Vibrational energy was probed using incoherent anti-Stokes Raman scattering, which is likely the most precise method for detecting up-pumping. With an anti-Stokes probe, all Raman-active vibrational transitions can be monitored simultaneously, and the intensity of each transition is proportional to the product of the instantaneous population and a known Raman cross-section. 28 ' 51 However, the weak anti-Stokes signal requires extensive signal averaging, and it is easily overwhelmed by even the smallest background of light caused by high-intensity laser pumping needed to generate phonons. NM up-pumping of two doorway vibrations at 480 c m - 1 and 657 c m - 1 , that involve N 0 2 bending and rocking, along with the 918 c m - 1 C-N stretch were observed, as shown in Fig. 2. Doorway vibration pumping occurred within the apparatus time response iPgYSi) dt

d(i)PcUc + (/)fPgUgJ

(9) (10)

where Cc =

•.YCi:

c

Si * g * '

Ac

, and Ag :

:

i=l

Ygi. t=l

(lla-d) The mass and energy production terms depend on the specific chemical reaction mechanisms used and can be formulated as described below. The model accommodates the thermal decomposition of HMX and GAP, as well as subsequent reactions in the foam layer. The formation of gas bubbles due to evaporation and thermal degradation is also considered for completeness. Two global-decomposition pathways are employed for HMX, as listed in Table 1. The first reaction (Rl) is an exothermic, lowtemperature pathway, whereas the second reaction (R2) is an endothermic, high-temperature pathway. Unfortunately, uncertainties still exist about the kinetic rates of (Rl) and (R2). A parametric study is thus performed to assess the role of the condensed-phase kinetics of HMX in the overall combustion process of HMX/GAP pseudo-propellant. Two different sets of rates are available in the literature for (Rl) and (R2): one estimated by Davidson and Beckstead 34 using their combustion model and the other obtained by Brill 12 from the T-jump/FTIR experiment. Subsequent reactions among

384

E. S. Kim & V. Yang Table 1.

Subsurface chemical reactions and rate parameters.

No.

Reaction

A&'c

Eh'c

Ref.

Rl

HMX (1) ^ 4 C H 2 0 + 4 N 2 0

5.81 x 10 1 0 1.00 x 10 1 3

34,000 34,400

34 12

R2

HMX (1) -v 4HCN + 2 ( N 0 2 + NO + H 2 0 )

1.66 x 10 1 4 1.00 x 10 16 - 6

44,100 44,100

34 12

R3 R4

GAP56 ( 1 ) - • GAP56^ } + 56N 2 GAP56*1} -> 25.6HCN + 15.8CO + 14.4NH 3 + 17.8CH 2 0 + I6CH3CHO + H 2 0 + 6.4C 2 H 3 CHO + I.5C2H4 + 8CH3CHNH + 8CH 2 CHCHNH + 14.6C ( s )

5 x 10 1 5

41,500

38

1.28 x 10 1 9

53,000

38

R5

HMX(|) «• HMX ( g )

See Ref. 5

—

38

R6

C H 2 0 + N 0 2 ^ C O + NO + H 2 0

802 x T 2 - 7 7

13,730

16

R7

CH3CHO + M = C H 3 + HCO + M

81,770

38

R8

C2H3CHO + M = C 2 H 3 + H C O + M

10 1 6

97,600

38

CH 3 CHNH + M = C H 3 + H 2 CN + M

10 1 6

63,700

38

16

66,900

38

R9 R10 a

CH 2 CHCHNH + M = C 2 H 3 + H 2 CN + M

7 x 10 1 5

10

A = pre-exponential factor; ^°E = activation energy; c Units are in mol, cm, s, K, and cal.

the products of (Rl) and (R2) may occur to provide the thermal energy to sustain pyrolysis. Brill 12 examined several plausible secondary reactions and their reaction rates. Results indicate that reaction (R6) between C H 2 0 and N 0 2 is probably the most important one in the foam layer if it indeed does occur. The rate parameter of reaction (R6) was determined with shock-tube experiments. 16 Thermodynamic phase transition consisting of both evaporation and condensation of HMX, (R5), is considered to provide a complete description of the mass transfer process. The GAP sample considered in the present study is composed of 56 monomer units and is denoted "GAP56". A global, condensed-phase decomposition mechanism for GAP was established based on the experimental data reported in Refs. 74,75 and 81. There is universal agreement that GAP decomposition is initiated by the bond cleavage of the azide group releasing N 2 . 74 ~ 80 This process proceeds rapidly over a temperature range from 260 to 290°C, and has an activation energy of about 41 kcal/mol. 75 There are, however, uncertainties as to how the bond-breaking process occurs. We assume a first-order reaction with the pre-exponential factor and activation energy deduced by Sysak et al.,81 as given by reaction (R3) in Table 1. The subsequent step in the decomposition of GAP releases NH 3 . Its concentration in the gas phase increases with increasing number of -OH end groups in the polymer. It appears that H-atom abstraction involving

Combustion

and Ignition of Nitramine

Propellants

385

the -OH end group is an important channel for NH 3 formation. At this time, there are no mechanistic details which allow one to quantify the NH3 evolution as a global reaction, and thus a rate expression cannot be formulated. Since NH3 is an important source for H-atoms in the gas phase, the deficiency in predicted species concentrations caused by neglecting this step in the decomposition of GAP must be noted. Finally, a rapid, highly exothermic event takes place and releases HCN, CO, CH2O, CH2CO, CH4, C 2 H 4 , H 2 0 , and GAP oligomers, in addition to NH3. 75 In the laser-assisted combustion study of GAP polyol by Tang et al.74 the surface temperature approached 1050 K, which was about 400 K higher than those treated by Arisawa and Brill. 75 Because of this higher temperature, Tang et al.74 identified several different large molecular species using TQMS. The major ones were acetaldehyde (CH3CHO), acrolein (C2H3CHO), and different imines (CH3CHNH and CH 2 CHCHNH). In comparing the results of Arisawa and Brill 75 with those of Tang et al.,74 it appears that the GAP oligomers identified by Arisawa and Brill are likely candidates to form the imines identified by Tang et al. A species balance of the data acquired by Tang et al.74 leads to a global reaction model for the decomposition of GAP56*, which is the polymer unit that has released N 2 , as given by reaction (R4) in Table 1. Most of the gaseous decomposition products from GAP are hydrocarbons or common gases whose chemical kinetic details are readily available. However, the available information about aldehydes (CH3CHO and C2H3CHO) and imines (CH3CHNH and CH 2 CHCHNH), as well as their interactions with either HMX or its decomposition products, appears to be limited. To allow for a reduction of these species, bimolecular decomposition reactions have been formulated, with the activation energies about the differences in enthalpy between products and reactants. 38 The pre-exponential factors are assigned values that are typical for such a process. The reactions considered are listed as reactions (R7-R10) in Table 1. Note that the condensed species GAP56(i), GAP56^, and C(s) are dissolved in liquid HMX, whereas all other species are gaseous and exist in bubbles. Based on the chemical mechanism given by (R1-R6), the species production terms in Eqs. (5) and (6) can be expressed and are listed explicitly in Refs. 37 and 39.

4.3. Gas-Phase

Region

The species evolved from the propellant surface into the gas phase include vapor HMX, decomposition products of HMX and GAP, and unreacted

386

E. S. Kim & V. Yang

GAP. Since condensed and gaseous species both exist in this region, a twophase treatment similar to that described in the preceding section is employed to formulate the problem. The effect of laser absorption in the gas phase on the ignition and combustion processes of nitramine monopropellants has been extensively investigated in Ref. 40. Results indicate that only vapor RDX may absorb an appreciable amount of CO2 laser energy in the gas phase. None of the major gaseous decomposition products of RDX exhibits a noticeable absorption at a wavelength of 10.6 /jm of CO2 laser. Thus the fraction of the laser energy absorbed in the gas phase appears quite limited (less than 10%). The heat release from exothermic reactions is much more pronounced than the laser energy absorbed by the gas phase. The same argument applies to HMX as well since the decomposition species of HMX and RDX are similar With the assumption that body force, viscous dissipation, and radiation emission/absorption effects are ignored, the isobaric conservation equations for both the condensed and gas phases can be combined and written as follows: Mass dl(l-

'

-

H2Q ;

-

/

/ v . >' *••• y ^ '•• ^

* '

/'''

-

:

"

\e-

/ /

0.05

0.00

/

%/

•i i

•

co:

y ^

•••-•.

;

0.15 0.10

.

• •

.

'•.

HCNV

i

• •

-0.5

, .

i

/

0.0

0.5

1.0

1.5

2.0

.

.

.

2.5

•

.

3.0

Exp. Measurement (Korobeinichev, 1985) 0.40

.,.,,..

• • i •

'

1

•

.

'

1 1 1 . . .

1

0.35 0.30

—o-.

o

H20

•2 0.25

\°

~~

/

i t 0.20 •"•*.

0.10

/ '-

0.00 r i -0.5

o'' i i i

\ :

// \ \\o.. \

rJ3

\

y/P

\\; / C 0

"5 0.15 -

0.05

0

.^-°~ 0 ^

•.

HCNT-

NO

O ^ 6-^-• ^ - A - ' - ^ - M ^ ^ - . . -4-6-^-i-

0

- o t i~T-i-ih 6 i

i I i1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance above propellant surface, mm

Fig. 8. Distributions of major species concentrations of self-sustained combustion of RDX at 0.5 atm.

species are quite consistent with the chemical-equilibrium predictions, with the deviation being less than 2%. The combustion wave structure at 100 atm was also predicted 33 and showed a close similarity to that at 1 atm except for the shorter flame-standoff distance (6 versus 600 /zm) and molten-layer thickness

Combustion

and Ignition of Nitramine

Propellants

395

(2.1 versus 66/mi). The major difference lies in a smaller void fraction. The shorter molten-layer thickness and higher burning rate yield a shorter residence time for condensed-phase reaction. Also, high pressure tends to retard the RDX evaporation, which dominates the gasification process in the two-phase layer. As evidenced by the large ratio of HCN to CH 2 0 mole fraction, the endothermic decomposition, (R2), appears more profound at high-pressure conditions. This can be attributed to the higher surface temperature and heat transfer into the condensed phase. A similar modeling approach was applied to study the combustion characteristics of HMX monopropellant. In this chapter, the model results pertaining to the combustion-wave structure of RDX monopropellant are focused. A comprehensive description of theoretical formulation and results for combustion of HMX monopropellant can be found in Refs. 37 and 39.

6.2. Laser-Induced

Ignition

of RDX

Monopropellant

By extending the state-state model to include the transient behavior, the entire laser-induced ignition process of RDX in an argon environment has also been studied. 39,40 Figure 9 shows the predicted temporal evolution of the temperature field at an incident laser heat flux of 400 W/cm 2 under atmospheric pressure. The initial temperature is 300 K. The interface

3500 3000 X 2500

I 2000 at

ex

I 1500 H 1000 500 1 ms 0.0

0.5 x, cm

1.0

Fig. 9. Evolution of temperature field during laser-induced ignition of RDX in argon at p = 1 atm and Q'êT = 400 W / c m 2 .

396

E. S. Kim & V. Yang

between the subsurface and gas-phase regions is set to be x = 0, with negative and positive values of the x-coordinate representing the subsurface and gas phase, respectively. The surface temperature is rapidly increased to 475 K within 1 ms, due to the high intensity of laser heat flux. The profiles for t < 1 ms represent inert heating of the thin surface layer with conductive heat losses to both the solid- and gas-phase regions. The temperature rises in the gas phase at t = 2 ms are primarily caused by radiant energy absorption rather than exothermic reactions, because the extent of RDX decomposition in the gas phase is very limited at this stage of the event. At t = 2.9 ms, exothermic gas-phase reactions start to occur, and a flame appears near the propellant surface at t = 3 ms. During the time period between 3 and 6 ms, the temperature continues to increase to around 1500 K, as a consequence of the heat release by exothermic reactions. As time further elapses, a luminous flame appears, and the temperature rises to its adiabatic temperature. The luminous flame is not stationary but regresses toward the surface. There is a time lag (about 4 ms) between the first appearances of the primary and secondary flames. Figure 10 shows a close-up view of the temperature evolution in the condensed phase near the propellant surface. The transient development of thermal-wave penetration into the subsurface region is clearly observed.

550 - Ambient Gas: Ar 500

g

450

3 a

n d

™

Solve conservation eqns. in solid & liquid phases

Solve conservation eqns. in gas phase

Fig. 4. Flow chart illustrating the logic for determining the eigenvalues for the threephase problem for single-component evaporation.

with monotonic decreasing error. The solution process is obviously more complicated if molecular diffusion in the liquid phase is not neglected. 4. Models The quantitative modeling of the burning rate of solid energetic materials really began in the dark hours of World War II with, predominantly, the efforts of Parr and Crawford6 at the University of Minnesota, and Rice and Ginell7 at the University of North Carolina. These and related wartime

434

M. S. Miller

works were published in a special issue of the (then) Journal of Physical and Colloid Chemistry, Vol 54 (1950). At that time virtually all propellants, gun and rocket, used some combination of NC and NG as their energetic ingredient. Since that time composite propellants consisting of ammonium perchlorate in rubber binders (e.g., in the space-shuttle boosters) have dominated the solid rocket propellant applications, with solid composites based on HMX in polymeric binders also in use. Fielded gun propellants are still dominated by nitrate-ester propellants although composites of these conventional propellants with nitroguanidine are common. The variety of propellant ingredients exacerbates the difficulties faced by combustion modelers both because of their different mechanisms and because of the paucity of detailed experimental data available for many of them. Recent trends are toward even more rapid proliferation of new chemical ingredients such as oxetanes, with their functional-group tailorability, and azides, with their attractive environmental advantages. In addition to enhanced performance and safety, the new constraints of minimal environmental impact in manufacture, use, and demilitarization are now driving concerns in the development of new propellants. Coincident with the emergence of many promising new energetic materials, with attendant dilution of experimental characterization, is the growing urgency for theoretical guidance in the formulation of propellants incorporating these materials. It is generally true that the higher the performance required of the weapon system, the smaller will be the margin of safety in the functioning of all the components of the system, including the propellant. If having a burning-rate model was deemed important fifty years ago, it is considerably more so with today's new mix of developmental constraints and advanced ingredients. In this section, our aim is not to give a comprehensive history of burningrate modeling but, rather, to provide a sense of the conceptual development of modeling approaches. This background is essential to an assessment of future avenues of progress in the field. Three subtopics will be addressed: frozen ozone, RDX, and multi-ingredient propellants. This progression of increasing system complexity allows us to illustrate some of the detailed mechanistic challenges facing the model builder and some new approaches to realizing a workable tool for the propellant formulator.

4.1. Frozen

Ozone

Frozen ozone is the simplest chemical system falling within the scope of 3-phase self-sustained deflagration. Though simple from a theoretical point

Burning-Rate

Models and Their

Successors

435

of view, it is anything but a straightforward subject for experimental investigation. Its propensity to detonate is legendary and the attendant dangers have undoubtedly inhibited the kind of extensive measurements of burning rate that one would like for comparison with model outputs. On the other hand, a wealth of high-quality experimental data has been obtained on thermophysical properties such as specific heat, thermal conductivity, melting and boiling points, latent heats, reaction paths and rates, and equations of state. This comprehensiveness and reliability of the input database on frozen ozone, coupled with its simplicity, makes it an attractive subject for modeling despite the paucity of burning-rate data. Its conceptual simplicity encourages and enables a more thorough study of mechanisms than with any other energetic material. Frozen ozone melts at about 80 K and has a normal boiling point of 161.3 K. The rate of reaction in the condensed phase is known to be very slow compared to the timescale of self-sustained deflagration. Thus, all of the uncertainties of describing condensed-phase reactions are conveniently (and legitimately!) sidestepped. The gas-phase reaction mechanism is known with good confidence to consist of the following three reactions. 03 + M ^ 0

2

+0 + M

A # ° 9 8 15 K = +25.65 kcal/mol

(I)

0 3 + O

A

1000

a

500 0.1

0.01

Distance from Surface in Gas (cm) Fig. 17. Comparison of CYCLOPS-code predictions of dark-zone thermal structure compared with the experimental data of Vanderhoff et al.42

Table 5. Comparison of major species mole fraction in the dark zone of double-base propellant with various experimental measurements. 4 0 _ 4 2

Parameters P (MPa) Dark-Zone Temperature (K) NO CO H2 N2 H20 C02 HCN CH 4 C2H4

Heller & Gordon (1955)

Lengelle et al. (1984)

Vanderhoff et al. (1991)

1.6 1600

0.9 1500

1.7 1500

0.24 0.33 0.08 0.04 0.20 0.10 0.004 0.008 0.008

0.21 0.38 0.08 0.02 0.20 0.09 0.026 0.008

0.24

CYCLOPS (Present Model) 1.7 1543 0.25 0.32 0.08 0.004 0.19 0.10 0.004 0.009 0.001

prediction of the thermal structure in Fig. 19. This inconsistency might at first be thought to suggest that the good burning-rate prediction is simply fortuitous, but this is not necessarily the case. As we learned in the case of M10, the burning rate and the dark-zone length at low pressure may be controlled by different sets of reactions, so it is possible that the good burning-rate prediction and poor thermal structure prediction may be due

Burning-Rate

Models and Their

457

Successors

RDX/TPE Propellant @ 293K: 80% RDX, 20% BAMO/AMMO (50/50 Mix) 10

.-.

:• . . . . . : . . . : : . . |.

- . - . - - . .-.-.'.

::i ..••...•"_~v\:|..:"

—•— Data of Zenin (2000) - • - CYCLOPS: with NTRB pyrolysis law - # - CYCLOPS: with R0X/BA pyrolysis law

E u a

0.1

;:-.:.: : : . * ^ (

1 0.01 0.1

1

10

100

Pressure (MPa) Fig. 18. Comparison of CYCLOPS-code calculations of the burning rate of and R D X / T P E propellant using two different pyrolysis laws with the experimental data of Zenin. 32 2500

:

vp\

2000

U

;/

; //

U

O.

£

1000

/

-^

H

500

..

Zenin Embedded-Thermo couple Data CYCLOPS: NTRB pyrolysis law -—'

0.0

i

... . ., .;

RDX/BAMO-AMMO (10 atm, 20 C)

/ '• s"

/ / / >

o

. . . . . .

s

1500

0.5

'

1—'

1.0

•—'—'

1 '

1.5

•

'

>—

2.0

Distance from Surface (mm) Fig. 19. Comparison of CYCLOPS-code predictions of dark-zone thermal structure for an R D X / T P E propellant with the microthermocouple data of Zenin. 32

to imperfections in the chemical mechanism describing the nitramine darkzone chemistry. In all propellants with RDX, we assume that the RDX evaporates unchanged, just as I had assumed for neat RDX; however, binder ingredients are assumed to decompose in the condensed phase.

458

M. S. Miller

The foregoing examples give evidence of the promise of the CYCLOPS code in providing both reasonable predictions of burning rate as well as details of the gas-phase flame structure and detailed chemistry. At present the code is limited to certain families of propellant ingredients, but the number of families will likely increase as other systems are studied. However, perhaps more important is the growing probability that one might be able to predict pyrolysis laws from first principles considerations. Certainly, greater theoretical capabilities to predict the final condensed-phase decomposition products of propellant ingredients can be brought to bear. Thus, the CYCLOPS code may well provide the best computational vehicle for incorporating results of new theoretical approaches to the condensed-phase and surface processes. How this might be accomplished while maintaining mathematical tractability of the code is suggested in Sec. 5. In summary, the CYCLOPS code is based upon a few simple propositions. (1) The surface regression may be adequately idealized as onedimensional. This condition is probably met for most homogeneous propellants. It may also be approximately true for many composite propellants where the burning rate is not a strong function of oxidizer particle size. Surface melt layers, for example, may provide effective premixing of ingredients where the oxidizer particle sizes are not too large. (2) The surface regression may be described by a pyrolysis law, Eq. (36). I have shown that this condition has been met by a large number of neat energetic materials and mixtures of typical propellant ingredients. (3) The overall products of condensed-phase decomposition may be estimated with sufficient accuracy. Chemical balance and results of thermal decomposition experiments are sources of guidance here, though only the former can be considered as an absolute constraint because of the high probability of secondary reactions in decomposition experiments. (4) The decomposition of one propellant ingredient does not affect the decomposition of other ingredients, i.e., the decomposition of a multi-ingredient propellant may be described as the superposition of the independent decompositions of each of its ingredients. This may well be a better approximation for some ingredients than for others. Short of describing the mixture decomposition theoretically on a molecular scale, there is little recourse to this assumption. However, it is often found that significant changes in detailed combustion mechanisms have a remarkably weak influence on the burning rate, that quantity being a highly integrated consequence of myriad underlying details. CYCLOPS exploits this relative insensitivity to mechanistic details.

Burning-Rate

Models and Their

Successors

459

Finally, since the CYCLOPS code is the first code of its kind (though still undergoing development to improve robustness for general use), one can anticipate ways in which it might be put to practical use even at its current stage of development. First, the CYCLOPS code can be used to optimize ingredient proportions to achieve a target burning rate. Also, CYCLOPS could be used to explore subtle, previously unexplained effects of formulation on burning rate. For example, German-made JA2 burns about 20% faster than US-made JA2 with identical ingredient proportions. However, the two differ by different specifications on the nitrocellulose component. While the average %N for the two propellants is the same, the two materials are made from blends of two lots of NC with different %N. Because our nitrate-state-distribution Monte-Carlo code predicts that the surface products for these two propellants will be different, it will be worthwhile to see if CYCLOPS can predict the burning rate difference. Further, CYCLOPS could be used to help set manufacturing tolerances in the specifications of ingredient proportions in military propellants. The CYCLOPS code could be used to determine how any given set of tolerances will map into variations of the burning rate and these burning-rate variations could be judged by using them as inputs to interior-ballistic codes. The burning rate at low pressure has been shown to be sensitive to the heats of formation of propellant ingredients in certain cases. 29,30 To the extent that ingredient purity is reflected in the heat of formation, e.g., due to dinitroglycerine impurity in trinitroglycerine, the CYCLOPS code could be used to determine how ingredient purity affects the burning rate, thereby enabling rationalization of quantitative tolerances for these ingredients. Finally, the CYCLOPS code could determine the effect of chemical modifiers on the burning rate without mixing chemicals. Though not replacing the need to mix and test, using the code as a screening agent and test bed for ideas could improve efficiency and possibly suggest new compounds to test.

5. Challenges and Opportunities The semi-empirical aspects of the CYCLOPS code need be tolerated only until theoretical advances obviate their necessity. The next level of improvement may well come from MD descriptions of the condensed phase and surface phenomena. However, this more fundamental level of treatment will have its own set of approximations and limitations. In order to deal with condensed-phase reactions, for example, considerable progress will have to be made in the parameterization of, and experience with, reactive

460

M. S. Miller

force fields. In my judgment, one will never want to treat the gas phase, with its dozens of species and hundreds of reactions, in this way. To do so would discard more than 50 years of hard-won kinetics research gains. One will, therefore, be faced with merging the discrete and continuous descriptions into a single, tractable mathematical entity. I believe that this will be no easy task, as the MD approach is inherently time-dependent with (computationally-intensive) explicit statistical averaging and the steadystate continuum-mechanics approach outlined earlier in this work is inherently time-independent with implicit statistical averaging. The most fruitful approach may be to develop simple, idealized continuum submodels calibrated to stand-alone MD models of a limited set of phenomena. For example, a reactive-MD model of the condensed phase would provide a set of condensed-phase decomposition products needed by the CYCLOPS code. Similarly, an MD model of multicomponent evaporation and/or pyrolysis could be used to determine a pyrolysis law for CYCLOPS. Results of the continuum submodels, depending on their scope, could then be easily incorporated into either a 3-phase model or a code such as CYCLOPS, retaining mathematical tractability and efficiency. Since, prior to the development of CYCLOPS, I had made a start on incorporating multi-component evaporation into our three-phase code, it will be used as an example here of the proposed approach. 5.1. "Molecular" Continuum Model of Multi-Component Evaporation I consider that a molecule evaporating from a liquid surface (Fig. 20) is at some distance d above the surface. I further assume that the molecule

zN>

*H fF ,

LIQUID

Fig. 20. Model for continuous-phase molecular forces experienced by a molecule evaporating from a liquid surface.

Burning-Rate

Models and Their

461

Successors

follows a tubular path from deep within the liquid to points outside the liquid; the tube has radius a 0 . The conception here is that the radius of the tube is of the order of the "radius" of the escaping molecule, and what is a tortured path geometry in reality is idealized as straightened to a cylindrical path. Since the escaping molecule is at a distance r from all the molecules in the differential volume element, dV = 2nadadz, the potential energy of interaction is d one obtains 1 /

_ ^vap RT

Tout = ~ ( ^ L i q e

*

(46)

where the quantity in parenthesis is the density of molecules with energies greater than Hvap, and ve is the average velocity of those molecules with enough energy to escape the heat-of-vaporization barrier. Assuming that the molecules in the surface are equilibrated at the surface temperature, Ts, it may be shown that the average escape velocity is •0 V )

0

2

(3ve -P vi

-f>*v'.

v ^

(47)

rM0Ve)\

464

M. S. Miller

where / W

^te

(48)

W is the molecular weight of the escaping molecules, and the minimum velocity for escape ve is

The equilibrium vapor pressure is determined by equating the outward and inward fluxes at equilibrium (see arguments of Sec. 3.3.1.), viz., 4RTsrout

(50)

8RTS TW

To test the predictions of this part of the model apart from imperfections in the predicted value of the heat of vaporization, I use the experimental value of Hv&p in the vapor-pressure formulas. With no adjustment parameters at all, the standard deviation of the predicted from experimental values is 95%. Evidently, there are more serious shortcomings in the vapor-pressure model. I experimented with several empirical modifications of the model and got interesting results by using an adjustable parameter to scale the value of iJvap in computing the escape velocity of Eq. (49). This strategy results in a standard deviation of about 36%, a much improved accuracy but possibly not sufficient for use in the multi-component evaporation code. The best-fit scaling factor has a value of 0.68, i.e., the calculation is significantly improved by assuming that only 68% of the full heat of vaporization must be overcome in order to escape the liquid surface. These results are illustrated in Fig. 22. Noting the slight downward tendency of the error with increasing -Hvap in the figure, I tried using a two-parameter fit to the fraction of Hvap used to compute ve. This improved the standard deviation slightly to 30%. The model may well be further improved and placed on a more sound theoretical basis by doing molecular-dynamics studies to help inform the assumptions. For example, perhaps decreasing the minimum escape velocity improves the idealized model because molecules tend to equilibrate, on average, at a value of potential energy somewhat above that in the bulk by means of collisions in the interfacial region closest to the bulk liquid. A great advantage of this bootstrapping partnership between discrete and continuum descriptions is that, by using the same model potential in both, the physics of the evaporation process can be studied and built into the continuum model apart from the behavior of any real substance. Separate

Burning-Rate

1

1

80

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60

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40

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Models and Their

1

1

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Nonpolar Molecules Polar Molecules

465

Successors

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•

i

fi—1.0 (Fig. 19). This bond order criterion is also

e

oioiloloT N

o Fig. 18.

Tetrazenes and tetrazene bis N-oxide.

Ideas to Expand Thinking about New Energetic Materials

497

o Dinitramide ion

•N

e0A

A, 0 .

^N/

O

O

1-1

O

Nitroazoxy nitramide ion

'Ns •Ny

>]SK

N

O-

NO,

(-1)

/ / 'NNO,

TRIS (nitraza) nitrate ion N© NO,

Fig. 19.

Inorganic homologues of dinitramide.

satisfied by dinitramide as well as the tetrazene N-oxides. However in the unoxidized state, tetrazene fails to satisfy this requirement, as the bond between N2 and N3 is essentially one. The quest for more complex molecules obeying the alternating charge rule has led to the pursuit of fused ring systems and unprecedented ylides, such as those shown in Fig. 20. Unfortunately, these molecules, although they satisfy the theorists' notion of relative stability, are often highly impact sensitive, light sensitive, and of disappointing density due to a lack of efficient packing in the crystal lattice. Still, there will always be die-hard enthusiasts willing to dedicate years of their lives to such pursuits; this is, in the final analysis, a benefit to us all as the limits of both practical synthesis and theory are being tested and evolved in the course of such endeavors.

498

J. Bottaro

N'

1I

x^ •N.

O

N

N

^x.

N

I ^

DTTO (di-tetrazene tetra oxide)

N

I o

ISO-DTTO (less stable due to unfavorable charge distribution)

0

2

r N k ^ N

^ N 0

To I N N

O

1f°

X

2

/ N—INKv \

X ^> X

(^)

N I|

O

NO, Octaza-cyclooctene 1,3,5,7-tetra-oxide dianion

TTT (trinitro triazine trioxide) O

M

N

\ +N

/ N+

/

\

-N

NN

ir o Octaza pentalene dioxide Fig. 20.

Theoretical alternant charge energetic species.

(M-)

Ideas to Expand Thinking about New Energetic Materials

3.3. Idea for More

499

Density

Energy can be stored in chemical bonds, in crystal lattices, and in metastable allotropes of various elements, such as aluminum, titanium, boron, and others. Most energetic organic compounds either store oxygen that is available for the exothermic oxidation of metals, such as aluminum or magnesium, or they store energy in the form of chemically-entrained nitrogen as is seen in azides, diazoalkanes, hydrazines, and others. These familiar modalities of energy storage need not define the boundaries or limits of possibility. Metastable allotropes of certain elements, including metals have much to offer to the field of energetic materials. Carbon, for example, has three familiar allotropic forms: amorphous carbon, defined as the ground state of the element; graphite, which has a slight positive heat of formulation; diamond, whose density and significant heat of formation make it a very interesting propellant or explosive ingredient; and, finally, fullerenes, whose unusual density (2.2g/cm 3 ) and exceptional enthalpy (up to 9 kcal/carbon atom) render them as attractive in metals as fuel ingredients. Acetylenes, whose enthalpy of formation is approximately 25 kcal/atom are also of great interest, but the challenge in this instance is to develop a family of acetylenes that is stable in storage and compatible with other propellant ingredients. The alleged constraint that the density of ensembles of the first-row elements cannot exceed 2.2 g/cm 3 may well be artificial and erroneous given that diamond has a density of 3.5g/cm 3 . While it is idealistic to maintain that this can be readily attained in energetic materials, it is reasonable to assume that certain carbon/nitrogen polymers can have densities exceeding 2.5 g/cm 3 without compromising enthalpy. Any of the vast array of such possibilities promises to advance the art of propulsion as well as explosives. While this matter is the appropriate topic for an entirely separate discourse, it is of interest to display a preliminary set of novel high valency functional groups whose design obeys the requirement for alternating charge and bond orders consistently in excess of one. Such a series of materials is shown in Fig. 21. The hypothetical groups shown in Fig. 21 (with the exception of the amine oxide) are not known in the open literature. The diaza-nitrate system has been synthesized by Russian chemists in one trivial instance. The generalized addition of nitrene or nitrene equivalent to nitrosamine would be required.

500

J. Bottaro

o

f

-NR, N^ \ j,R

R2N

Hexavalent (triamino amine oxide)

O

I N

R

Trivalent (amine oxide)

R

R A M R2N

Trivalent (diaza-nitrate)

N =

N

R

Trivalent (amino tetrazole dioxide)

R\ >N R'

II 11 N + Fig. 21.

Tetravalent (triaza-nitrate) N

R

High valency energetic groups.

4. Concluding Remark The evolution of explosives and their applications is far from a linear process. Decades and even centuries typically elapsed between one significant development and the next. Furthermore, specific advances are often not

Ideas to Expand Thinking about New Energetic

Materials

501

recognized as such until tremendous periods of time had elapsed because little or no deliberate effort was exerted to advance the state of the art. This chapter is intended to stimulate the imagination for some new types of materials.

References 1. J. C. Bottaro, R. Malhotra and A. Dodge, SYNTHESIS (4) (2004) 449-500. 2. W. E. Bachmann and J. C. Sheehan, J. Am. Chem. Soc. 71, 1842 (1949); US 3,049,543 (1962 to Olin Mathieson). 3. A. T. Nielsen, US 5,693,794 (Dec. 2, 1997). 4. R. E. Davis, Org. Syn. 7, 68 (1927). 5. J. C. Bottaro, R. J. Schmitt, P. E. Penwell and D. S. Ross, US 5,254,324 (Oct. 19, 1993). 6. T. K. Highsmith, C. J. Hinshaw and R. B. Wardle, US 5,292,387 (March 8, 1994). 7. P. E. Eaton and A. Bashir-Hashemi, US 6,222,068 (April 24, 2001). 8. H. C. Mandell and G. Barth-Wehrenalp, J. Inorg. Nucl. Chem. 12, 90-94 (1959). 9. M. A. Hiskey, D. E. Chavez and D. Naud, US 6,657,059 (December 2, 2003). 10. J. C. Bottaro, R. J. Schmitt and P. E. Penwell, US 5,889,161 (March 30, 1999).


INDEX

a-HMX, 296 /3-HMX, 290, 296

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Energetic Materials: Processing and Characterization of Particles

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Recent TCM Research from China

Recent Advances in Epilepsy Research

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