J. Phys. Chem. B 2001, 105, 10159-10162
10159
ARTICLES Thermal Decomposition of Solid Cyclotrimethylene Trinitramine Maija M. Kuklja* Department of Electrical and Computer Engineering, Michigan Technological UniVersity, Houghton, Michigan 49931 ReceiVed: April 25, 2001; In Final Form: August 6, 2001
In this paper, we show how a traditional solid-state chemistry approach, applied to the essentially molecular problem of the energetic barrier for decomposition, gives qualitatively new results and, in fact, brings very new perspectives in the detonation initiation theory development at large. Quantum-chemical simulations of the thermal decomposition of solid cyclotrimethylene trinitramine (RDX) by means of the Hartree-Fock method combined with the cluster and periodic models are performed. We found that the dissociation of the RDX molecule in the bulk crystal is characterized by the different energetic barriers for cleavage of N-NO2 bonds, unlike the gas-phase molecule, where all three of the energies are equal. It is also shown that a rupture of the N-NO2 chemical bond requires less energy for an isolated molecule than for a molecule placed in the bulk of the solid. The situation changes if the molecule is close to the free surface of the crystal. In this case, less energy is required to break the bond than for a bulk molecule. Mechanisms of solid RDX decomposition, the relevant experimental data, and possible applications of the results obtained are discussed in great detail. We also discuss how the conclusion obtained can serve for the better understanding of the well-known mechanism of pore collapse, of different sensitivities to detonation initiation of porous, solid, perfect, and defective explosives, and other processes that take place in hot spots. The mechanisms of the thermal decomposition of solid energetic materials are discussed with the illustrating example of RDX.
Introduction Selected for this study, cyclotrimethylene trinitramine (C3H6N6O6), also known as RDX, belongs to the large class of molecular crystals. It is often used as a high explosive and as a propellant. The mechanisms of initiation in liquid- and gasphase explosives are fairly well understood. Much less is known about processes on the atomic and electronic level in solid explosives. It is generally believed that initiation can start in small (nano- to microsize) regions or so-called hot spots, which have the ablity to accumulate the mechanical energy of an impact or shock wave and transfer it into chemical energy to start a reaction. However, even simple questions, such as the nature of the initial step in the thermal decomposition of energetic materials, particularly RDX, are still the subject of debate.1-10 Among the many suggested initial steps in thermal decomposition, the most supported mechanism for condensedphase decomposition is N-NO2 bond rupture.11,12 Experiments on samples with isotopically labeled nitrogen also showed that the decomposition of RDX is mostly unimolecular and involves the removal of only one NO2.13 Activation energies vary from 24.7 to 52.1 kcal/mol and reported pre-exponential factors vary from 1017 to 1020 s-1 for the overall decomposition.14 Moreover, it is difficult to interpret the condensed-phase experiments because of the many possible product species. At present, the most accurate ab initio study based on gradient-corrected density functional theory found an activation barrier of 34.2 kcal/mol for the N-NO2 dissociation mechanism of gas-phase RDX.14 * E-mail:
[email protected].
The •NO2 radical formation is attributed to N-NO2 bond breakage as a result of UV radiation.15 In solution, the molecule has C2V symmetry, but in the solid state, the NO2 groups are not symmetrically equal.16 This has been confirmed by the crystal structure determination of RDX, which shows that the molecule has C1 symmetry.17 The RDX molecule is locked into a chair configuration; consequently, there are two “axial” NO2 groups and a single “equatorial” NO2 group per molecule. Quantum-chemical simulations of the thermal decomposition of solid RDX at the Hartree-Fock (HF) level are presented in this investigation. Our main objective was to study energy barriers for the RDX molecule decomposition via the rupture of one of the N-NO2 chemical bonds. In particular, we were looking for an effect of a crystal environment, such as the bulk and the surface, on the energetics of the process. That is, we studied the initiation chemistry in the RDX molecule as a function of the molecule’s surroundings. It is shown that the cleavage of the N-NO2 chemical bond requires less energy for the isolated molecule than for the molecule placed in the bulk of the solid. The situation essentially changes if the molecule is located near a free surface of the crystal. In this case, less energy is required to break the N-NO2 bond than for both the bulk crystal molecule and the isolated molecule. Results of Calculations, and Discussion Our calculations are performed by means of the standard HF method for a periodic system (the band structure problem) by the code CRYSTAL95/98.18 For the present work, we used the
10.1021/jp011563f CCC: $20.00 © 2001 American Chemical Society Published on Web 10/02/2001
10160 J. Phys. Chem. B, Vol. 105, No. 42, 2001
Kuklja TABLE 1: Calculated Energies for the N-NO2 Bond Dissociation in an RDX Moleculea model
I (R ) 1.3505)
II (R ) 1.3985)
III (R ) 1.3921)
gas phase isolated bulk: MCb bulk: MCc bulk: UC surface: MC surface: slab
1.61 (37.15) 1.31 (30.18) 2.01 (46.39) 2.11 (48.72) 2.27 (52.36) 1.44 (33.16)
1.53 (35.14) 1.77 (40.91) 1.82 (41.97) 1.82 (41.97) 1.93 (44.52) 1.49 (34.25) 1.49 (34.25)
1.54 (35.40) 1.76 (40.79) 1.71 (39.34) 1.84 (42.36) 1.64 (37.92) 1.52 (35.14)
a Values are given in eV (kcal/mol). I-III denote different N-NO 2 groups. R is the corresponding initial bond length in Å.17 Ab initio study based on gradient-corrected density functional theory found an activation barrier of 34.2 kcal/mol for the N-NO2 dissociation mechanism of gas-phase RDX.14 b Molecular cluster consists of nine RDX molecules. c Molecular cluster is in the form of the RDX unit cell.
Figure 1. Schematic representation of the RDX orthorhombic unit cell in accord with Pbca space group symmetry.
Figure 2. Structure of the individual RDX molecule.
6-21G split valence basis set with the scaling factor for the outer (most diffuse) Gaussian basis vector of 1.10 for all of the atoms (H, C, N, and O). In the initial calculations, we use the experimentally determined crystalline structure of RDX and the bond lengths, angles, and torsion angles of the RDX molecule.17 Then, the optimal theoretical geometry of the crystal was found by varying the three lattice constants proportionally in a hydrostatic manner until a minimum of the total energy is achieved. The configuration of the individual molecules was left unaltered in accord with the rigid molecule approximation. A cleavage of the N-NO2 chemical bond was simulated for four basic situations, placing the molecule in different environments. That is, we studied a gas-phase molecule, an isolated molecule with the “crystal configuration”, a molecule in the bulk of the crystal, and a molecule located near a surface of the crystal. For the bulk and surface calculations, two different solid-state models such as the molecular cluster and the periodic defect were used. The molecular cluster consisted of several RDX molecules with their coordinates taken from periodic calculations. Thus, the molecule with the N-NO2 group of interest was surrounded by all of the nearest-neighbor molecules as it is in the crystal. The long-range crystal field was neglected in this model because of the van der Waals nature of RDX and also because of its relatively small value. The lattice and molecule relaxation was also neglected because both of these contributions are known to be small.14,19 The RDX molecular geometry stabilization is between 2 and 6 kcal/mol for the cleavage of N-NO2 in the gas phase.14 Electronic relaxation is thus the dominant mechanism: it accounts for 6-10 kcal/mol.14 This contribution is included in our models. By using the periodic defect model, the relevant unit cell containing the molecule of interest was translated either in three crystalline directions (a molecule in the bulk) or in two directions in accord
with the slab model18 (a molecule near the surface). To simulate the bond rupture, all of the electrons and cores of the NO2 groups were removed from the crystal retaining the basis functions on the vacancies. Further, the corresponding decomposition energy was determined by the formula Ebond ) Eperfect - (Edefect + ENO2) as the difference between the energy of the perfect system and the combined energy of the defective system and an isolated NO2 group. A comparison of the obtained results, using the principle different descriptions of the solid with defects, leads to more accurate conclusions and permits the performance of a careful analysis of the process under investigation. The results obtained for the N-NO2 bond-dissociation energy are given in Table 1. First, gas-phase and isolated molecules were examined (see Table 1). In the calculations, all of the parameters of the molecule, such as bond lengths, angles, and so forth, were taken from X-ray diffraction experiments.17 Then, full optimization was performed for the gas-phase molecule, and the geometry and energies obtained were compared to the earlier study.14 No neighbors were included in the calculations (i.e., no crystalline field around the molecule was taken into account). The isolated molecule model is different from the gasphase molecule only by the change in geometry and reduction in symmetry. As follows from Table 1, the energies obtained are not equal, which is in contrast to the gas-phase molecule14 where all three of the N-NO2 groups are equivalent. Besides, it is clearly seen how two axial N-NO2 groups are distinguished from the equatorial N-NO2 group. This is in accord with the symmetry reduction. This result is consistent with our previous investigation on the electronic structure of the RDX crystal. The band structure calculations found that the RDX upper-valence band was formed by the 2p functions of N and the 2p functions of O atoms similarly to the upper-bonding states of the molecule.19,20 Also, the highest occupied molecular orbitals (HOMO) of the bulk crystal and the RDX molecule as well are dominated by the 2p states of the equatorial N-NO2 group, while the next HOMOs are formed by the atomic functions of two axial N-NO2 groups. Furthermore, we place the molecule in the center of two differently shaped quantum clusters: the molecular cluster represented by nine molecules (Table 1; bulk: MCB) and the molecular cluster in the form of the RDX unit cell of eight molecules (Table 1; bulk: MCC). The equatorial N-NO2 group is found to be the most sensitive to the presence of the crystal field in the model, and the activation energy is visibly increased. This is observed for both clusters, confirming the accuracy of the conclusion. Even more interesting, the same trend is demonstrated in the periodic model (Table 1; bulk: UC) where
Thermal Decomposition of Solid RDX the crystal was simulated by translating the unit cell with one broken bond in three crystallographic directions. Physically, it means one N-NO2 bond in each unit cell in the infinite crystal is broken. In other words, one molecule suffers one bond cleavage per seven perfect RDX molecules. From this observation, an important conclusion follows: the molecule located in the bulk crystal has a higher activation barrier for the N-NO2 rupture. Unlike the axial groups, the equatorial group is more sensitive to the crystal field potential. This result is supported by suggestions that the NO2 groups are responsible for intermolecular cohesion21 in the solid. The proposal was based on the temperature dependence of the nitrogen-14 nuclear quadrupole resonance spectra experiments. It was established that intermolecular electrostatic interactions are important because of the alternating relative positive and negative charges on the atoms comprising RDX. The oxygen atoms and amine nitrogen atoms are relatively negative while the carbon atoms and nitro nitrogen atoms carry relative positive charges.22 One of the oxygens of the axial N-NO2 groups situated in the molecular “pocket” of the neighboring molecule attractively interacts with all three of the nitrogen atoms of the nitro groups. Other oxygen atoms attract neighboring pairs of molecules through interactions with the nitro nitrogen of the equatorial N-NO2 group. Thus, cohesion results between all of the RDX molecule pairs because of oxygen affinity. Finally, we studied the activation energies for molecules (more precisely, for N-NO2 bonds) located near a surface of the crystal. We modeled this again using a molecular cluster (Table 1; surface: MC) and a periodic approach (Table 1; surface: slab). Several different clusters were used. The presence of all of the nearest-neighboring molecules of the N-NO2 bond in the given surface and under it was used as a criterion for the selection of the proper cluster. It is obvious that all of molecules (and interactions) above the given surface were missing. As is perfectly seen from Table 1, the activation energies for all three of the NO2 groups are decreased. The same conclusion follows from the periodic model calculations. The cleavage of the given bond on the (210) surface was simulated in the slab model. In doing so, the relevant unit cell was translated in two crystallographic directions, reproducing a semi-infinite system with a thickness of six molecular layers. The two-dimensional periodicity resulted again in one broken bond per unit cell, describing the simultaneous rupture of many equivalent bonds in the slab. Good agreement of the energy obtained with the value obtained by the MC model provides additional evidence for the accuracy of our conclusions. The lower energy for a molecule near a surface with respect to the bulk crystal can be understood in terms of intermolecular interactions. The molecule surrounded by other molecules is more strongly bound with the crystal than if some of the interactions are missing. Therefore, the molecule placed on the surface (or close to it) can be more easily ruptured. From this, it is reasonable to suppose that the initiation chemistry will start near the surface. The energetic barriers for all three of the bonds in this case are pretty close to each other. Hence, the comparison of activation energies hardly permits one to select a particular N-NO2 group as responsible for the first chemical reaction. This suggestion is consistent with the EPR spectra of NO2 radicals produced by UV photolysis of the RDX single crystals.15,23 It can be established where N-NO2 bond breakage takes place to form these radicals. In particular, a comparison of the direction cosines of gmax for NO2(I), NO2(II), and NO2(III) with the directions calculated from the atomic coordinates of the crystal structure suggests that NO2(I) forms by the cleavage of the equatorial N-NO2 bond and does not
J. Phys. Chem. B, Vol. 105, No. 42, 2001 10161 significantly change its orientation in the lattice. The radicals NO2(II) and NO2(III) are consistent with cleavage of the axial N-NO2 bonds if a rotation of 60° about the O-O direction of each NO2 radical occurs. NO2 radicals are known to rotate about the O-O direction at liquid nitrogen temperatures.24,25 Thus, it was concluded that there is no select N-NO2 position where NO2 radicals form in UV-irradiated RDX. The single-crystal EPR spectra are consistent with NO2 radical formation at both the axial and equatorial N-NO2 positions of the parent molecule.15 As follows from the energetic considerations obtained in our study, the essential difference of 8-15 kcal/ mol appears if the molecule is displaced from the bulk crystal to its surface, and no preference can be made for the equatorial or the axial NO2 group decomposition. Conclusions and Applications We have investigated the mechanism of the solid-phase molecular decomposition of RDX. Among all of the possible reaction pathways, we considered only that which was most supported by experiments: the N-NO2 bond rupture channel. The ab initio HF method, combined with two essentially different solid-state models, a molecular cluster and a periodic defect, was applied to this problem. A range of molecular clusters and unit cells were probed to ensure that the final conclusion did not depend on the computational methods. We have found that the energy for RDX N-NO2 dissociation was strongly dependent on the environment of the molecule. Thus, an isolated RDX molecule with crystal geometry exhibits some differences in energies for the cleavage of the equatorial and the axial bonds against all of the equal energies for the gasphase molecule. This is due to bond-length changes and symmetry reduction. Furthermore, the equatorial bond of the molecule inside the crystal is sensitive to the crystal field and is characterized by the visible increase in energy compared to the gas-phase dissociation energy. Finally, significantly lowered energy barriers by 8-15 kcal/mol are obtained for the molecule placed near the surface. On the basis of energetic considerations, no preference can be made for the equatorial or the axial NO2 group decomposition. The results obtained are supported by experimental data and previous theoretical investigations. Two important conclusions follow from our study: the molecule in the crystal has different energetic barriers for cleavage of the N-NO2 bonds, and a molecule located near the surface can more easily dissociate than a molecule buried in the bulk crystal. These may have applications in explaining the detonation initiation behavior of explosive materials. Socalled hot spots are known to be associated with lattice defects such as vacancies, voids, pores, cracks, dislocations, and others. They can trigger a fast chemical reaction and explosion. It is well established that defective solids, particularly RDX, typically have a high concentration of imperfections even at low temperatures and are much more sensitive to initiation than are high-quality (perfect) crystals. Our results lead us to the suggestion that one of the reasons for initiation on hot spots is the reduced energetic barrier for the decomposition of molecules placed on defects. Obviously, the surface-induced effect must be taken into account when initiation mechanisms are studied. A good illustrating example is the well-examined pore collapse mechanism. The analysis performed on energetic barriers for the decomposition of RDX molecules, placed in different environments, may help with the consistent interpretation of the existing experimental data and with providing useful insights for the understanding of the mechanisms for detonation initiation in explosive molecular solids. Besides fundamental interests,
10162 J. Phys. Chem. B, Vol. 105, No. 42, 2001 the conclusions drawn are of great practical importance for safety issues, for the control of the sensitivity of explosive crystals to detonation initiation, for the storage and handling of energetic materials, for the prevention of accidental explosions and fires, and also for the manufacturing of efficient and safe explosive sensors. Acknowledgment. This work was performed under the financial support of MRI at LLNL under contract with DOE and of the U.S. Office of Naval Research under Contract No. N00014-91-I-1953. References and Notes (1) Chakraborty, D.; Muller, R. P.; Gasgupta, S.; Goddard, W. A., III. J. Phys. Chem. A 2000, 104, 2261. (2) Lewis, J. P.; Glaesemann, K. R.; VanOpdorp, K.; Voth, G. A. J. Phys. Chem. A 2000, 104, 11384. (3) Im, H.-S.; Bernstein, E. R. J. Chem. Phys. 2000, 113, 7911. (4) Guo, Y.; Thompson, D. L. J. Phys. Chem. B 1999, 103, 1059910603. (5) Long, G. T.; Vyazovkin, S.; Brems, B. A.; Wight, C. A. J. Phys. Chem. B 2000, 104, 2570-2574. (6) Cardao, P. A.; Gois, J. C.; Campos, J. A. Shock Compression of Condensed Matter. AIP Conference Proceedings; American Institute of Physics: Melville, NY, 2000; No. 505, pp 853-856.
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