Molecular dynamic insight into octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) and the nano-HMX decomposition mechanism

Herein, we demonstrate the use of large-scale reactive molecular dynamics simulations to identify the influence of nanostructures, size effects, and temperature for the decomposition processes of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). The bulk-phase and six types of HMX nanoparticle (30–70 Å) systems were investigated at two high temperatures (2000 K and 3000 K). The evolution of the potential energy (PE) and total number of molecules (TM) of HMX crystals and their six nanoparticle systems were analyzed and addressed, and it was revealed that the nanostructure has a great accelerative effect on the thermal decomposition of HMX. The temperature distribution, initial decomposition process, and main intermediate and gas products were traced, and showed that the initial decomposition of HMX nanoparticles is triggered by the dissociation of the N–NO2 bond. With the increase in temperature, the total amount of gas molecules in HMX nanoparticles rapidly increases, which shows that the high temperature can accelerate the decomposition rate for HMX nanoparticles.


Introduction
Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) has been widely used as an explosive and rocket propellant, and its initial chemical processes have been investigated for many years. There has been a great deal of research over the years to investigate the initial chemical processes of HMX. 1-20 There are two main factors that can affect the initial decomposition mechanism of HMX: (1) different external stimuli, and (2) the change in the explosive itself. Ge et al. 1,2 studied the initial decomposition mechanism of HMX dependent on the impact velocity of shockwave loading. Sharia et al. 3 commented on the revealed differences between solid and gas phase decomposition that proved that the crystalline eld affects the bondbreaking processes in molecules, and molecular materials are strongly dependent upon the molecular environment. Defects and deformations play an important role 4,5 in initiating chemical reactions in energetic materials by facilitating their degradation, and can consist of vacancies, 6-8 crystalline polymorphs, [9][10][11] dislocations, 12,13 charged particles, 14,15 and electronic excitations. 16,17a,b,18-20 Nanoscale energetic materials can reduce the number of defects compared to conventionally sized energetic materials. The nano-structure may lead to high-shock initiation pressure 21 and less sensitivity of the energetic materials. [22][23][24][25][26][27][28] The combustion rate can be controlled by changing the particle size of nano-explosives. [29][30][31][32][33] It has been proven that nanoHNS (2,2 ′ ,4,4 ′ ,6,6 ′ -hexanitrostilbene) and nanoTATB are more sensitive than production grade explosives under a short duration pulse. 34,35 The shock sensitivities of nano-sized HMX particlecontained samples are obviously lower due to the more regular particle surfaces. The detonation velocities of the nanosized HMX particle-contained samples are higher, which is caused by the larger specic surface area of the nano-sized particles. 36 The apparent activation energy as well as the thermal decomposition temperature of dense spherical nano-HMX particles were markedly decreased. 37 Liu et al. 38 studied the adiabatic initial decomposition processes of molecular explosive HMX nanoparticles with diameters of 1.4-2.8 nm at high temperatures from 2400 to 3000 K. Zhu et al. 39 employed ReaxFF molecular dynamics (MD) to simulate the physicochemical properties accompanying some transitions of HMX nanoparticles at low temperatures. While nano-HMX has been studied for more than ten years, its pyrolysis mechanism at high temperature and closer to the actual nanoscale is unclear. Therefore, it is necessary to study the mechanism of pyrolysis at high temperature with a relatively larger nanoscale.
In this study, we demonstrate the use of large-scale reactive molecular dynamics simulations to identify the inuence of nanostructures, size effects, and temperature for the initial decomposition mechanism of HMX. Herein, we simulated bulkphase and six types of HMX nanoparticle (30-70Å) systems at two high temperatures (2000 K and 3000 K). The initial decomposition pathways, the evolution of the small molecule products, and the evolution of the potential energy were investigated.

Computational details
The LAMMPS molecular dynamics simulator was employed to perform simulations with ReaxFF-lg. 40 An amorphous molecular model of nano-HMX was established with the radius of 30-70Å. Each possible atomic pair was assigned a different bond order cutoff value to properly identify chemical species (standard values in ReaxFF C/H/O/N high-energy simulations). 41 The original C/H/O/N ReaxFF has been used for several nitro explosives [41][42][43][44] and nanoparticles 45,46 and it correctly provided the 30-70Å radius of nano-HMX, which was constructed from the original unit cell that was experimentally determined at room temperature. 47 The initial state of the system is shown in Fig. 1, which contains 64 molecules (S 0 , 1792 atoms, 30.28 × 23.89 × 23.65Å 3 ), and other systems are shown in Table 1 with three-dimensional periodic boundary conditions. First, we relaxed the nano-HMX by energy minimization with the conjugation gradient algorithm. To further relax the particles, with the canonical ensemble (NVT) and the Berendsen thermostat at 300 K, an MD simulation was performed for 10 ps. Then, we obtained the equilibrium nano-HMX crystal structure by an isothermal-isobaric (NPT) MD simulation at 0 atm and 300 K for 15 ps. Finally, the relaxed supercell was then used as the initial structure for six subsequent separate MD simulations. The relaxed supercell was heated from 300 to 2000 and 3000 K. Isothermal-isochoric MD (NVT-MD) simulations were then performed for 220 ps with the time step of 0.1 fs. An analysis of the products was performed with a 0.3 bond-order cutoff for all atom pairs to recognize molecular species. Within the minimum bond lifetime of 25 fs, if the distance between two atoms was less than the bond distance criterion, it was determined that the two atoms form a chemical bond. [48][49][50][51][52] Therefore, the molecular species, bond orders, and dynamic trajectory were determined every 50 fs. These data were used to analyze the molecular species, and provided detailed information regarding the decomposition process.
The FORTRAN code FindMole 53 based on the ideas of Strachan et al. 54 was used to analyze the dynamic trajectories and calculate the chemical species and their numbers. The Getpath script was used to output net reactions and their frequencies.

Results and discussion
3.1. Evolution of the potential energy (PE) and total number of molecules (TM) in the HMX and nano-HMX system Evolution of the PE and TM in the system at 2000 K and 3000 K within 220 ps is shown in Fig. 2. Initially, the curves rapidly increase and then decrease over time, indicating that energy is rst absorbed and then released during decomposition. The PE curve of HMX reaches the maximum value earlier than that of  nano-HMX, which indicated that it is necessary for nano-HMX to absorb more energy to achieve decomposition energy. As the temperature and nano-particle size increase, there is little change in the ve PE curves. This demonstrates that the nanostructure greatly affects the PE curves, while there is little effect of nano-size and temperature on the PE curves. The PE curves of the HMX system reach stability at the maximum reaction time, which can be considered as completion of   reaction. The PE curves of the HMX system decreased to equilibrium much more quickly as compared to the other nano-HMX system. The nano-size and temperature have little inuence on the equilibrium time. There is a more rapid rate in the decrease of the PE curve, and the time to reach equilibrium is shorter for the HMX system. This indicates that the decomposition of nano-HMX is slower, and the reaction time is longer than that of the nano-HMX particles, while the nano-size and temperature have little effect on the stability of the HMX systems.
There are two turning points during the initial 30 ps of HMX thermolysis, which is interesting because the potential energy can roughly characterize the overall properties of the model system. The rst turning point was at approximately 16 ps, and it may have been caused by the signicant slippage in the surface layer at approximately 16 ps. This phenomenon is consistent with the conclusion in Fig. 4. The second turning point was at approximately 20 ps, and may have been caused by the rapid dispersion of the molecules and the approach of the initial decomposition reaction. At 30 ps, the maximum potential energy corresponded to all the nano-HMX molecules completely breaking down.
The number of molecules (NM) reects the decomposition speed of the nano-HMX molecules. As Fig. 3 shows, the change in the NM in the system is similar at two high temperatures: rst, the number of molecules remains stable for a period of the reaction time. Then, the number of molecules rapidly decreases. Finally, the number of molecules decreases during decomposition. When the temperature is higher, there is less time to decomposition, indicating that the reactions are more violent at higher temperatures. The decomposition rate increases with the increase in the nano-size at high temperatures. Fig. 4 shows the temperature distribution of the 30Å nano-HMX system for 0-24 ps at 3000 K. Due to the exothermic reaction, a few hot spots emerged at 5 ps (T > 1500 K). The diffusion of atoms is accelerated due to the atomic vibration conducting heat for further decomposition. The hot spots mainly occur in the center of the nano-ball (12-16 ps) and result in a microexplosion that leads to the ball falling apart (20 ps). Microexplosions promote the transfer of matter and energy to the gas phase (22-24 ps).

Decomposition reaction
The calculation results showed that the main fragments are NO 2 , NO, OH, H, HNO 2 , HNO, and CO in six systems at 2000 K and 3000 K, as shown in Fig. 5. All the curves of each fragment are similar for the nano-HMX system, while they are quite different from those of the HMX system. This demonstrates that the nanostructure strongly inuences the main fragments. For all six systems, NO 2 fragments initially appeared, and the number of NO 2 molecules rapidly increased and then rapidly decreased. However, in the HMX system, the rate of decline was higher than that in the nano-HMX system. This demonstrates that NO 2 decreased more quickly for the HMX system than that for the nano-HMX system. The NO 2 totally decomposed for the HMX system, but for the nano-HMX system, there was less decrease in NO 2 , and it tended to be in equilibrium. The NO fragment rapidly increased and then reached the maximum value faster for the HMX system than that for the nano-HMX system.
The variation trend for other nitrogenous fragments such as HNO 2 and HNO was consistent with that of the NO fragment for the six systems. All the nitrogenous fragments completely decomposed to produce more stable products such as N 2 for the HMX system. However, they tended to be in equilibrium for the nano-HMX system, which demonstrates that the reaction for nano-HMX is much more complicated. The H fragment increased, while the H-R fragments decreased. Then, the H and OH fragments reached equilibrium. The number of OH fragments was larger than that of H fragments, which is abnormal.
To clarify the effect of temperature on the main intermediate products, an analysis was performed on the state of the major intermediate ( Fig. 5(b)). The maximum of all the fragments was larger at 3000 K than that at 2000 K, while there was more rapid decomposition of all the nitrogenous fragments, which totally disappeared. This demonstrates that high temperature can accelerate the decomposition for the six systems. At 2000 K, there was little CO in the bulk HMX and nano-HMX systems. More CO was generated in the nano-HMX system than that for the bulk HMX system, which may have been caused by the nanostructure. At 3000 K, the amount of CO for the bulk HMX and nano-HMX systems increased, which may have occurred because heat increases the intensity of the pyrolysis reaction.
All the curves for CO 2 , H 2 O, and N 2 of each fragment are similar to those of the nano-HMX system. However, they are quite different as compared to those for the HMX system. This demonstrates that the nanostructure strongly inuences the main products. For the HMX system, the curves for CO 2 and H 2 O initially increased, and then reached equilibrium. The curve for N 2 rapidly increased, then slowly increased, and nally increased with rapidity once more. For the nano-HMX system, the curve for H 2 O increased, and then, there was a tendency to reach equilibrium. The curves for N 2 and CO 2 monotonically increased. For the six systems, the trend of the curve height is in the following order: H 2 O > N 2 > CO 2 .
To understand the effect of temperature on the main products, the main gas products were analyzed ( Fig. 6(b)). The curves for three gas products indicate that less time is required to achieve a maximum value at 3000 K than that at 2000 K. For the six systems, the curves for three gas products initially increased, and then reached equilibrium. The equilibrium value of N 2 was larger than that of H 2 O, while the equilibrium value of H 2 O was larger than that of CO 2 . The variation tendency for nano-HMX was similar, but the tendency for variation in the nano-HMX and HMX systems greatly differed. The increased rate of H 2 O production, the main product of nano-HMX, was much higher than that of N 2 and CO 2 . Nevertheless, the trends for the growth rates of H 2 O and N 2 were very similar.
As the temperature increased, the amount of CO 2 and N 2 increased, while the amount of H 2 O slightly decreased per HMX molecule for the nano-HMX system. However, as the temperature increased, CO 2 and H 2 O decreased, while N 2 increased per HMX molecule for the HMX system. The total gas molecules were almost the same at two high temperatures for the HMX system. However, the total gas molecules rapidly increased for the nano-HMX system as the temperature increased. These results indicate that high temperature can increase the specic impulse of the nano-HMX system, which further indicates that nano-HMX may be used as a propellant (Fig. 7). The initial decomposition paths of the six HMX systems were analyzed by a MATLAB script. Table 2 shows the most frequent and important primary reactions of 30Å nano-HMX at 3000 K. As shown in Table 2 Fig. 5(b), the most likely initial reaction mechanism of nano-HMX is N-NO 2 bond breakage and NO 2 release.
This result indicates that the N-NO 2 bond is decomposed in nano-HMX. This phenomenon is consistent with the result that LEWIS used BLYP and B3LYP to explore the decomposition path of HMX in the gas phase. LEWIS found that the reaction energy barrier of N-NO 2 cleavage (40.5-41.8 kcal mol −1 ) was the lowest among four possible paths (HONO elimination, C-N bond breaking, and joint ring opening); that is, N-NO 2 cleavage was the most likely cleavage path of HMX. The most frequent of the three reactions was the release of multiple NO 2 molecules from a nano-HMX molecule, which adequately explains the rapid growth rate of NO 2 aer the initial reaction in Fig. 5. At 0.2 ps, the C 4 H 8 O 8 N 8 / C 4 H 7 ON 5 + OH + 3NO 2 reaction occurred twice. The appearance of OH adequately explains the phenomenon that OH appears earlier than H in Fig. 5, while the HNO 2 fragment in R3, R4, R7, and R8 adequately explains the phenomenon that the amount of OH is greater than H in Fig. 5.
One of the results reported by the soware is that the net ux (NF) indicates how oen the reaction is observed during the simulation time. Table 3 demonstrates the relatively higher NF of the reactions that have relatively higher NF at 2000 K and 3000 K.

Conclusions
In this work, the decomposition mechanism of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) and nano-HMX by size effect and temperature was studied by ReaxFF-lg reactive MD. The results illustrate the detailed mechanism and morphological evolution of HMX and its nanospheres. The main conclusions are as follows: (1) For the variation rate in the PE curve of HMX and nanoparticles with different sizes at different temperatures, it was found that the nanostructure greatly inuences the PE curve. However, there is little inuence of the nanosize and temperature on the PE curve.
(2) By comparing the change trend of TM in the six systems at different high temperatures, it was found that the larger the nano-size, the higher the reaction temperature, and the more intense the reaction.
(3) By analyzing the temperature distribution of nano-HMX, it was found that the heat conduction process of the entire reaction was endothermic, heat transfer, pyrolysis and heat release, and the corresponding morphological change of nanospheres was vibration-sphere dissociation and diffusion.
(4) For the variation in the main intermediate fragments and products, it was found that the nanostructure and high temperature have a strong inuence on the main fragments, while there is little inuence of nanosize on the pyrolysis reaction.
(5) At 3000 K, the initial decomposition reaction of 30Å nano-HMX is C 4 H 8 O 8 N 8 / C 4 H 8 O 2 N 5 + 3NO 2 , which occurs at a maximum frequency of 23 times at 0.2 ps. The most likely initial reaction mechanism of nano-HMX is N-NO 2 bond breaking and NO 2 release.
We expect that these theoretical studies of the reaction of HMX might stimulate further experimental studies of nanoparticle-HMX, particularly the synthesis and characterization.

Conflicts of interest
There are no conicts to declare.