JOURNAL DE PHYSIQUE Colloque C4, supplement au nb9, Tome 48, septembre 1987

C.F. MELIUS

Energetic Materials Division, Sandia National Laboratories, Livermore, CA 94550, U.S.A.

La detonation des materiaux Qnergetiques implique la liberation de l'bnergie chimique resultant du rearrangement des liaisons chimiques pour former des mol6cules plus stables. Une comprBhension de ces processus chimiques au niveau moleculaire demande une connaissance de la stabilite thermochimique des differents intermediaires mol~culaires qui peuvent Btre formes. Elle necessite aussi une connaissance des chemins de reaction possibles pour un rearrangement molbculaire. En particulier, on a besoin de connaitre les hauteurs de barrisres d'energie (energies d'activation) ainsi que les variations d'entropie (facteurs preexponentiels) au goulot de la &action. Pour determiner la thermochimie et les chemins de &action au cours de la d6composition, nous avons d6veloppk la nethode de chimie quantique BAC-MP4. Utilisant les calculs de corrections d'additivitb de liaison a la theorie des perturbations au 48me ordre Moller Plesset (Bond - Additivity - Corrections to goller - glesset 4th Order), on peut determiner les energies des differentes liaisons, les chaleurs de formation, les entropies, et les energies libres le long des chemins possibles de reaction. Les reactions chimiques dominantes sont fortement dependantes de la vitesse avec laquelle l'energie est portbe sur le front de choc. La thermochimie et les mecanismes de decomposition sont discut6s en fonction de la vitesse de chauffage et de la temperature. Nous distinguons dans le processus de decomposition les etapes chimiques qui sont exothermiques, de celles qui sont, par nature, endothermiques. Les resultats sont pr8senti.s pour une varietir de composes nitres comprenant les nitro-aliphatiques et les nitramines HMX et RDX.

Abstract

The detonation of energetic materials involves the release of chemical energy resulting from the rearrangement of the chemical bonds to form more stable molecules. An understanding of these chemical processes at the molecular level requires a knowledge of the thermochemical stability of the various molecular intermediates which can be formed. It also necessitates a knowledge of possible reaction pathways for molecular rearrangement. In particular, one needs to know the heights of the energy barriers (activation energies) as well as the changes in entropy (preexponential factors) at the bottleneck to reaction. To determine the thermochemistry and reaction pathways occurring during decomposition, we have developed the BAC-MP4 quantum chemical method. Using Bond- Additivity-Cofiections to Moiler-Elesset sth-order pertubation theory calculations, the various bond - energies, heats of formation, entropies, and free energies along possible reaction pathways can be calculated. The dominating chemical reactions are strongly dependent on the rate of energy deposited at the shock front. The thermochemistry and decomposition mechanisms are discussed as a function of heating rate and temperature. We distinguish those chemical steps in the decomposition process which are exothermic from those which are inherently endothermic. Results are presented for various nitro compounds including the nitro-aliphatics and the nitramines HMX and RDX.

*This work supported by the U.S. Department of Energy and the U.S. Department of Army

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987425

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Introduction

The detonation of energetic materials involves the rapid release of heat and pressure due to chemical reactions arising from the decomposition of the chemically energetic material. In particular, the decomposition products under high heating rates representative of detonation can be significantly different than the products formed during slow heating rates and low pressures. The energetics of the chemical reactions and bond breaking occumng during ignition, deflagration and detonation require a knowledge of the thermochemistry of the various molecular species that can occur. In particular, the thermal stability of the short-lived, highly reactive radical species occurring during the decomposition and subsequent chemical processes must be determined. The activation barriers of possible reaction pathways involving these intermediates must be determined as well.

A theoretical means now exists for determining the thermochemistry and reaction mechanisms occurring under these high temperature and pressure, short time scale conditions. We have developed the theoretical quantum chemical approach known as the BAC-MP4 methodl-5 to calculate the thermochemica1 properties of the molecular species. In this paper we briefly describe the theoretical method, present thermochemical results, and discuss possible decomposition mechanisms which are consistent with these BAC-MP4 calculations. Applications of this technique have been presented previously for the determination of corresponding reaction mechanisms in combustion6-7.

Theoretical Approach

Since the thermochemical stabilities of the transient decomposition species are generally not known, it is important to have an accurate theoretical method for determining their heats of formation. The BAC-MP4 r n e t h ~ d l - ~ provides such a means of obtaining thermochemical energies accurate to approximately 10 kJ-mol-l. This method can also be used to obtain estimates of activation barriers along reaction pathways, although the error uncertainty is somewhat larger.

The BAC-MP4 approach begins with the electronic structure calculation of a given molecule using the Hartree-Fock method. This technique is used to determine the optimum molecular geometry and harmonic vibrational frequencies. Total electronic energies are then calculated at a higher level of theory using M~ller-Plesset many-body perturbation theory to fourth order (MP4). This method extends Hartree-Fock theory to include electron correlation, which is important in evaluating bond energies. We then include bond-additive corrections (BAC) to obtain heats of formation. Combining this information with the moments of inertia of the molecule and the vibrational frequencies provides the thermochemical entropies and free energies of the various decomposition and combustion intermediates. For transition state structures, the same approach is used except that a saddle point on the electronic potential energy surface is located. Comparison of BAC-MP4 and experimental heats of formation for selected molecular species of relevance to energetic materials is given in Table I. Note that the BAC-MP4 method works well for unstable and radical species as well as for the stable molecules.

Results and Discussion

A. Bond Energies

The resulting bond energies of various C-nitro, N-nitro, and 0-nitro compounds are given in Table 11. One can see from Table I1 that the more insensitive energetic materials have the larger bond energies, with NH2-CH=CH-NO2 (representative of the insensitive high explosive TATB) having the largest bond energy. Also, one can see that the bond energies are relatively localized by the

Table I. Comparison of BAC-MP4 heats of formation for various molecules with experimental values. (Energies in kJ-mol-1.)

mf,298 AH!,298 Molecule Theor. Exp. Molecule Theor. Exp.

CH3N02 CH30NO CH30N02 CH3NHNH2 NH2CHO HONO HON02 CH3CHO CO c o 2 HC(0)OH CH300H

HNCO HN3 N20 NO NO2 CH3 CH2 NH2 NH OH

Table 11. Bond dissociation energies for various C-nitro, N-nitro, and 0-nitro compounds calculated using the BAC-MP4 method. (Energies in Id-mol-1 at 298K.)

C-Nitro Compounds BDE H-Nitro Com~ounds BDE

CH3--NO2 C2H5--NO2 NH2CH2--NO2 02N-CH2--NO2 CH2=CH--NO2 CH3CH=CH--NO2 trans-NH2CH=CH--NO2 cis-NH2CH=CH--NO2 HOCH=CH--NO2 (no h.b.) HOCHzCH--NO2 (h.b.) C6H5--NO2 HC(0)--NO2

N-Nitro Compounds

0-Nitro Compounds

nature of the group, ie., nitramine (NH2N02), methyl nitramine (CH3NWN02), and dimethylnitramine ((CH3)2NN02) have similar N-NO2 bond energies (- 200 Id-mol-l). Also, when the carbon becomes unsaturated (e.g. CH2=CHNO2), the C-NO2 bond energy increases, but when the nitrogen becomes unsaturated (e.g. CH2=NN02), the bond energy decreases. As has been indicated in previous papers, the nitro-group bond energy is the weakest bond in typical energetic materials.

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B. Decomposition of Nitromethane, CH-jNOz

Nitromethane, CH3NO2, is an energetic material which can decompose to form more stable molecules. In particular, N-0 bonds are weaker than C-0 bonds; C-H bonds are weaker than N-H or 0-H bonds. This is illustrated in Fig. 1 where the heats of formations of various isomers of CH3NO2 are shown. One can see that CH3N02 is relatively unstable compared to its other isomers. However, the aci- form of nitromethane, H;?CN(O)OH, is less stable while methyl nitrite, CH30N0, has a comparable stability. Before energy can be released (as can be seen from Fig. I), multiple rearrangements must occur, involving the breaking of many old bonds and the forming of many new bonds. In Fig. 2 we present the decomposition pathways for CH3N02. One can see from Fig. 2 that rearrangement involves large activation barriers, comparable to the NO2 bond breaking energy. While the calculations indicate that there is a tight transition state structure with a high barrier for rearrangement to form CH30N0, it is possible at large bond distances for the NO2 group to flip around and recombine as ONO. Having formed the nitrite (which has a weaker CH30-NO bond energy), it can now decompose to form CH3O + NO or CH20 + HNO. This process should become more important in the high pressure regime of detonation. However, it should be noted from Fig. 2 that these initial stages of decomposition are endothermic.

C. HONO Elimination from Nitro-Compounds

In Fig.3 we compare the energies of decomposition for 0-, N-, and C-nitro compounds. In each case, the molecule can undergo simple bond scission to form NO2 or can undergo a five-centered elimination to form HONO. The trend from left to right is an increase in the endothermicity of the decomposition process, as was previously mentioned for Table 11. This trend is consistent with the trend toward more insensitive expiosives to the right. In particular, having an unsaturated C attached to the nitro group, as in the nitroaromatics, greatly increases the endothermicity of the initial decomposition step.

The BAC-MP4 calculations provide not only bond energies but also geometries and frequencies which can be used to obtain entropies, A S's, and free energies, AG's. These thermochemical properties can be used in molecular dynamics, such as transition state theories, to determine rate constants for decomposition. As an example, Fig. 4 shows a comparison between theory and expeement for the rate constant of the five-centered elimination of HONO from nitroethane

CH3CH2N02 + CH2CH2 + HONO = 68 kJ-mol-l

The theoretically determined unimolecular rate constant (with an effective energy barrier of 172 kJ- mol-I and a pre-exponential A factor of 1011.9 sec-I at 600K) is consistent with the experimental datag. At high temperatures, the experimental data differs from the theoretical curve due to the simple bond fissioning of the NO2 group,

which is not included in the theoretical calculation. The high temperature experimental slope (250 kJ-mol-1) is consistent with the calculated CH3CH2-NO2 bond energy of 244 Id-mol-1 and a pre- exponential A factor of 1016.6 at 800K. It is important to note that the significantly larger A factor (by more than four orders of magnitude) for simple bond scission suggests that under the rapid heating rates occurring at the shock front during detonation (corresponding to very high effective temperatures) breaking apart of the molecule to form NO2 should be the f ist step in the decomposition process. While this step may be immediately followed by abstraction of a hydrogen

Heats of Formation of Nitromethane and Its Isomers

H~C'ANOH +47 HzCO + HNO

H ~ C N (O +1 0 HEON=O

-1 29

-189

Fig. 1. Heats of formation of various isomers and decomposition products of nitromethane, CH3N02, based on BAC-MP4 heats of formation at 298K.

Decomposition of Nitromethane

Fig. 2. Calcualted unimolecular decomposition pathways for the reaction of CH3N02, based on BAC-MP4 heats of formation at 298K for stable species and transition state activated complexes.

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CH30N02 + CH30

4 163

-85 CH30N02 + CH,O

+ HONO

CH3NHN0, + CH2NH

+ HONO

CH3CH2N02 + CH2CH2

+ HONO

CH2CHN02 + CH2CH

+ NO,

7 283

J CH,CHNO, + HCCH

+ HONO

Fig. 3. Comparison of decomposition pathway energies for CH30N02, CH3NHN02, CH3CH2N02, and CH2=CHN02 calculated using the BAC-MP4 heats of formation at 298K. For each molecule, the top energy value represents the bond dissociation energy for N02,the middle energy value represents to barrier height for the five-centered elimination to form HON0,and the bottom energy value represents the heat of dissociation for formation of HONO. (Energy in kJ-mol-1.)

1000 I T (K)

Fig. 4. Comparison of experimental and theoretical decomposition rate constants for nitroethane, CH3CHzNOz. Theoretical curve represents the five-centered HONO elimination, calculated using the BAC-MP4 method. Experimental data is taken from Ref. 8.

atom or the formation of a nitrite and subsequent formation of NO of HNO (due to the very high pressures), these initial steps are endothermic and require additional chemical reactions to provide heat feedback to the shock front.

D. Autocatalyzed Decomposition By Radicals

An alternative to unimolecular bond breaking is radical-assisted attack on the molecule. This is indicated in Fig. 5 for H atom attack on nitromethane, CH3N02. One can see from Fig. 5 that the net bond breaking energies for this reaction is small, on the order of 20 k~-mol-1, corresponding to the activation energy for hydrogen atom addition. The overall bond breaking process is exothermic, given the presence of the H atoms. From Fig. 5 one can see that H atom attack on the energetic molecule produces new radicals, i. e., OH and CH3, which can further attack the energetic molecule, producing a possibly rapid chain of exothermic chemical reactions.

Reaction of CH3N02 + H 240 7

HONO + CH3

-120 1 - CH3OH + NO

Reaction Coordinate Diagram

Fig. 5. Calculated reaction pathways for the reaction of CH3N02 + H + products, based on BAC- MP4 heats of formation at 298K for stable species and transition state activated complexes.

E. Changes in Bond Energies Due to Radical Formation

The bond energies within a molecule change when a radical is formed from the original molecule. This was illustrated in the previous section in which the addition of a hydrogen atom greatly weakened the C-N bond and the N-0 bonds. In general, for radical species, one must also consider a barrier to dissociation in addition to the bond energy. However, the net bond breaking energy can be significantly smaller than in the stable molecule, as was discussed in ref. 5. This is illustrated in Fig. 6 for HMX where the bond breaking energies have been estimated from smaller prototype molecular species4. In the HMX molecule, the weakest bond is N-N02, which is -200 kJ-mol-1. However, once the NO2 group has left, the resulting second-nearest-neighbor bond energies become very weak (e.g., the C-N bond breaking energy is -75 kJ-mol-1). Similarly, if a H atom has been removed, the second-nearest-neighbor bond energies also become very weak (e.g., the N- NO2 bond energy is negative with only a 8 M-mol-I barrier for leaving).

C4-348 JOURNAL DE PHYSIQUE

Bond Breaking Energies of HMX

Initially I 110

"2C /N -Nee '8 - CH.

8 0

C-N = 75 C-H = 138 \L/cH~-~ \ J

After NO, >N-N ?HZ I co

Removal H2C /N -NeO \ry - CH,

d&o O? 0 N-N = * \f

C-N = 117

After H / 'CH -N\/

Removal GN- N 0.- I

y"-' ,o

H2C /N - Ne0 'y-cn2

Fig. 6. Bond breaking energies of (a) HMX, (b) HMX after a nitro group has been removed, and (c) HMX after an H atom has been removed. Energies in k~-mol-1. Note that when a radical center is present (indicated by a dot), the second-nearest-neighbor bonds become significantly weaker.

F. Decomposition Pathways

In Fig. 7 we show the high heating rate, gas phase decomposition mechanism for HMX based on BAC-MP4 bond energies and activation baniers5. The order of bond breaking and the bond breaking energies are indicated in the figure. The net products are HCN, NO;?, and H atoms. The initial step of breaking the N-N bond can occur either by direct bond scissioning (which dominates at high heating rates) or by autocatalyzation of the nitramine by the H atoms formed from the decomposition of the H2CN in step #7. The H atoms, NO2 and HONO can react rapidly to form N02, NO, and HzO.

Decomposition of HMX At High Temperatures

+ #n ( A E) : Position, Order, and Energy

of Chain Bond Breaking (Energy in kJ-mol-1)

Fig. 7. Decomposition mechanism of HMX at high temperatures. Final products are HCN, N02, and H atoms.

G. Ignition of HMX

In this section we presents results of modelling the ignition process for nitramines. We solve for the time-dependent coupled chemical reactions. Thirty-two chemical species and over one hundred chemical reactions were used. The chemical reactions were a combination of the mechanisms presented above along with those from flame codes that modelled HCN and C2N2 combustion9.l0. First, we consider ignition at a constant pressure of 1 atmosphere. The temperature profile, given in Fig. 8, indicates a three stage ignition process. The resulting species concentration profiles are given in Fig. 9. The fist stage, which is endothermic (the temperature decreases slightly) represents the decomposition of the gaseous RDX. The first ignition step represents the conversion of NO2 to NO. The second ignition step corresponds to the major heat release, forming the final products of combustion. Next, we consider ignition at constant volume with pressures representative of solid densities. The resulting temperature profile, given in Fig. 10, also indicates a three-stage ignition. However, the species concentration profiles, given in Fig. 11, indicate a change in mechanisms. The two ignition stages observed at low pressures have combined into the second ignition step while a new step, involving the pressure stabilized HONO and HNO species, now occurs as the f i s t ignition step. Thus, under the high pressure conditions representative of detonation, many-body reactions (which are not treated adequately under usual flame conditions) must be considered. However, it should be noted that the initial stage of decomposition is still endothermic.

Conclusions

Using the BAC-MP4 method, we have calculated the thermochemical properties of simple energetic compounds and their possible decomposition pathways. We have shown that the decomposition mechanisms are typically endothermic. Also, at high temperatures, bond fissioning is favored over rearrangement. Thus, a series of chemical reactions are required to produce the energy needed to

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ii 1 Ignition of RDX I

at 1 Atmosphere LI

Decomposition r I 2nd lgnition 1 1st Ignition I

Fig. 9. Species concentration profiles for the ignition of gaseous RDX at constant pressure for a starting condition of lOOOK and 1 atmosphere. Major chemical reactions are given at each ignition step.

Decomposition

2nd lgnition

1st Ignition

Fig. 10. Temperature profile for the-ignition of gaseous RDX at constant volume for a starting condition of lOOOK and 1000 atmospheres. Profile indicates multistage ignition.

Chemistry of RDX lgnition

At 1000 Atmospheres

4 N2 + HID+ 3 CO + Hz+ CO2

3 HONO + HNO +

Fig. 11. Species concentration profiles for the ignition of gaseous RDX at constant volume for a starting condition of lOOOK and 1OOO atmosphere. Major chemical reactions are given at each ignition step.

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propagate the detonation. Radicals can play an important role in autocatalyzing this process. The modelling of the chemical reactions is presently being used to study the ignition of energetic materials which can lead to detonation. The applicability of these reactions to the actual propagation of a shock wave, however, is still not understood due to the short time scales and high pressures involved . Much research is still needed in this area.

References

'c. F. Melius and J. S. Binkley, Twentieth Symp. (Internat.) on Comb., p. 575, The Comb. Inst. (1984).

2 ~ . F. Melius and J. S. Binkley, ACS Combustion Symposium, 249. p. 103 (1984).

3 ~ . Ho, M. E. Coltrin, J. S. Binkley, and C. F. Melius, J. Am. Chem. Soc., a, p. 4647 (1985).

4 ~ . F. Melius and J. S. Binkley, Twenty-first Symp.(Internat.) on Comb., in press.

5 ~ . F. Melius and J. S. Binkley, Proceedings of the 23rd JANNAF Combustion Meeting, October 1986. 6 ~ . A. Perry and C. F. Melius, Twentieth Symp. (Internat.) on Comb., p. 639, The Comb. Inst. (1984). - 'J. A. Miller and C. F. Melius, Twenty-first Symp.(Internat.) on Comb., in press.

8 ~ . M. Nazin, G. B. Manelis, and F. I. Dubovitskii, Russ. Chem. Rev. 37. p. 603 (1968).

'J. A. Miller M. C. Branch, W. J. McLean, and D. W. Chandler, Twentieth Symp. (Internat.) on Comb., p. 673, The Comb. Inst. (1984). ''0. I. Smith and L. R. Thorne, Western States Section1 The Comb. Inst., Oct., 1986.

Suggestion - J. BOILEAU

On pour ra i t envisager pour confirmer l e mecanisme, de ca lcu le r ou d 'essayer l ' e f f e t de l ' a d d i t i o n de divers produits s o i t generateurs de radicaux l i b r e s s o i t bloqueurs de radicaux l i b r e s t e l s que, dans ce dern ie r cas , des ~ o u d r e s u l t r a f i n e s de materiaux i n e r t e s , s i l i c e ou a u t r e .

Commentaires - M. SAMIRANT

Au cours d 'e tudes sur l e s def lagra t ions du RDX on peut de tec te r l e f r o n t d ' i n i t i a t i o n (ho t spots) e t l e f r o n t de combustion intense correspondant 1 'onde de pression. Pour une pression i n i t i a l e de quelques Kilobars on observe un de la i de 150-300 u s e n t r e l e s deux ondes, en bon accord avec l e de la i ca lcu le en t re l e s premieres d i ssoc ia t ions e t l a react ion complete.

- N. MANSON

1) La temperature que vous considerez dans vos ca lcu ls e s t - e l l e def in ie en admettant :

a . l ' e q u i l i b r e thermodynamique local ? e t b. l ' e q u i l i b r e intramoleculaire (equ ioar t i t ion des formes d ' energ ie

( t r a n s l a t i o n , ro ta t ion vibrat ion . . .) ?

2 ) Dans l e s ca lcu ls a haute pression i l sera necessaire de t e n i r compte des in te rac t ions e n t r e l e s molecules (Van der llaals e t c . . ) . Comment pensez-voUS y parvenir (emploi de fuyantes ? equations d ' e t a t ? e t dans ce dern ie r cas , lesquel l e s ?)