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Nature of the Enhanced Self-Heating Ability of Imperfect Energetic Crystals Relative to Perfect Ones Chuan Deng, Xianggui Xue, Yu Chi, Hongzhen Li, Xinping Long, and Chaoyang Zhang* Institute of Chemical Materials, China Academy of Engineering Physics, Post Office Box 919-327, Mianyang, Sichuan 621900, China S Supporting Information *

ABSTRACT: It is extensively deemed that the increased self-heating ability of defects relative to perfect crystals increases the sensitivity, or reduces the safety, of energetic materials. Nevertheless, the nature of such increased self-heating ability remains unclear. The present work provides insight into the origin of such ability by ReaxFF reactive molecular dynamics simulations on the thermal decay of perfect and twinned β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) under three typical heating conditionsconstant-temperature, programmed, and adiabaticthat represent various rates of heat exchange between the HMX crystal and environment. As a result, it is found that the enhanced self-heating ability stemmed from the high internal energy of the molecules around the defects, and such ability is remarkably exhibited with low heat-exchange rates between the energetic materials EMs and environment. Adiabatic heating is an extreme to exhibit the most remarkable such ability, as the superiority of the high internal energy of the molecules around the defects cannot be lowered without heat exchange. Thereby, the twin-induced shock sensitivity enhancement of HMX and a small difference in differential scanning calorimetric measurement values between perfect and twinned HMX can well be understood by means of the insight. one another. For example, two EMs have been compared: βoctahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX), which has been extensively applied in explosive formation,39 and an energetic salt, dihydroxylammonium 5,5′-bistetrazole1,1′-diolate (TKX-50),40 β-HMX is more impact-sensitive than TKX-50 (impact energy was 7 vs 20 J), whereas β-HMX is less heat-sensitive than TKX-50 [differential scanning calorimetry (DSC) decomposition peak temperature at a heating rate of 5 K/min was 275 vs 221 °C]. Furthermore, different testers may provide various sensitivity values, which can be attributed to differences in test conditions and testers’ judgment.39,41−43 In general, sensitivity is not a physical quantity although it is a crucial statistic value in engineering applications. Defects are very common in crystals, particularly for energetic crystals held by weak intermolecular interactions.26 These defects include volume, planar, line, and point defects, such as voids, twins, dislocations, and vacancies, which are inevitably generated during crystal nucleation and growth.45 These defects have attracted continuous attention owing to their significant influence on sensitivity, which is crucial to EM applications. For example, Sharia and Kuklja46 confirmed through ab initio calculations that the vacancies and voids in HMX crystals accelerate thermal decomposition by increasing surface area. This finding was supported by a reactive molecular

1. INTRODUCTION Safety is a major concern in the field of energetic materials (EMs) and involves many important complicated disciplines.1−15 The safety of EMs is generally evaluated by sensitivity, that is, the responses of EMs to various external stimuli such as impact, heat, friction, shock, and electrostatic spark.1,16−20 The evolution of an EM suffering from xternal stimulation to final combustion or detonation involves a series of complex processes, such as energy absorption and transfer, structural transformation, and chemical reaction. Thus, it is usually difficult to elucidate the detailed sensitivity mechanism involved in these processes. For example, the chemical reactions caused by external stimuli of the simplest prototype of explosives, nitromethane, have not been completely understood, even though numerous related studies have been conducted.21−25 Sensitivity is determined by many factors, including material characteristics, stimulation types, and test conditions. First, the applied EMs feature multihierarchy and multiscale. At the molecular level, sensitivity is strongly dependent on molecular stability.26,27 On the crystal scale, sensitivity is related to the molecular stacking mode in crystals and to crystal qualities (purity, perfection, shape, particle sizes and their distributions, etc.).28−32 In addition, the anisotropy of sensitivity should sometimes be stressed.33−36 Interfacial integrity can seriously influence the sensitivity of a mesostructure.37,38 Second, sensitivity relies on the type of external stimulus. Sensitivities to different types of stimuli are not always in accordance with © XXXX American Chemical Society

Received: May 10, 2017 Revised: May 20, 2017 Published: May 22, 2017 A

DOI: 10.1021/acs.jpcc.7b04518 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. Models for MD simulations: (a) p-HMX and (b) t-HMX (double red dashed line shows the boundary of twinned interface).

dynamics (MD) simulation of Zhou and Huang.47 The dislocation-induced shock sensitivity enhancement of 1,3,5,trinitro-1,3,5-triazinane (RDX) was confirmed by Armstrong and co-workers,48−50 and subsequently supported by the reactive force field MD simulation of Xue et al.31 Moreover, twins in HMX crystals have been experimentally and theoretically verified to be an evident reason for enhanced shock sensitivity.51,52 Both the dislocation and twin-induced shock sensitivity enhancements are thought to be related to the increase in free volume.31,52−56 It is generally deemed that the enhanced self-heating ability of defects causes the increased sensitivity, or reduced safety, to external stimuli, in contrast to perfect energetic crystals. However, there is little insight into such increased self-heating ability, for example, the nature of such increased ability and under what conditions it will be exhibited remarkably. These issues are crucial to the defect-sensitivity dependence of EMs. Thus, we focus on the nature of the enhanced self-heating ability of defects in energetic crystals in the present work. We performed a series of MD simulations to resemble the thermal decay of perfect and twinned β-HMX (p-HMX and t-HMX) under three typical heating conditionsconstant-temperature, programmed, and adiabatic heatingas these heating conditions possesses distinct heat-exchange rates (Rh) between the HMX crystals and the environment. Results show that adiabatic heating can highlight such high ability to the largest extent, as it distinguishes remarkably the thermal decay behaviors of p- and t-HMX. It suggests that such increased ability is exhibited more and more remarkably with decreasing Rh. Originally, the molecules around defects possess higher internal energy than those regulated in perfect crystals, and thus a lower energy barrier is required for decay. That is, the elevated internal energy by defects facilitates molecular decomposition to release energy to heat the HMX crystal itself. This is the so-called enhanced self-heating. Obviously, under an extreme condition of adiabatic heating (Rh = 0), the superiority in self-heating keeps well, because there is no heat exchange to lower the superiority of higher internal energy. Thus, a lower Rh is helpful to maintain the superiority. It is just the nature of increased selfheating ability of defects. On the basis of this insight, we can well understand a significant difference in shock sensitivity between p- and tHMX,51 while a small difference in their stability is measured by DSC at various heating rates (see Figures S1 and S2 of Supporting Information).

2. METHODOLOGIES An experimentally determined crystal structure of β-HMX at room temperature39 was adopted for MD simulations. An 8 × 4 × 5 supercell enlarged from the HMX unit (320 HMX molecules and 8960 atoms) was built as p-HMX in Figure 1a; for t-HMX, the modeling details can be found in ref 52. Briefly, according to experimental observation of the most common “cross” twins usually growing in the (101) face of β-HMX crystals, we sliced a β-HMX crystal along this face and then established a cell with 320 HMX molecules by combining the slice and its mirror together to construct an interface, as demonstrated in Figure 1b. MD simulations resembling three typical heating conditions mentioned in the Introduction were carried out for both tHMX and p-HMX for comparison. Constant-temperature, programmed, and adiabatic heating represent distinct differences in heat exchange between the related system and the environment, that is, fast, moderate, and no exchange, respectively. Both t-HMX and p-HMX were relaxed by isothermal−isochoric ensemble (NVT) MD simulations at 300 K for 5 ps for subsequent simulations. For each simulation, the temperature was controlled by a Nose−Hoover thermostat with a damping constant of 100 fs and the time step was set to 0.1 fs. For constant-temperature heating, six temperatures (1500, 1800, 2000, 2500, 3000, and 3500 K) were set for NVT MD simulations for 40 ps each. For programmed heating from 300 to 3300 K, five rates of 80, 100, 125, 166.7, and 250 K/ps were adopted. For adiabatic heating, the HMX crystals were separately preheated at 1500, 1800, 2000, and 2200 K for 0.5 ps before the subsequent microcanonical ensemble (NVE) simulations for 40 ps. All MD simulations in the present work were carried out with the LAMMPS software package57 with reactive potentials of ReaxFF-lg,58 which had previously been validated.31,47,52 The bond order files generated during the simulations were postprocessed to obtain the molecular species by the mol_fra.c code in the package. 3. RESULTS AND DISCUSSION 3.1. Constant-Temperature Heating Conditions. The molecular decay of p-HMX and t-HMX under constanttemperature heating is illustrated in Figure 2. The numbers of all chemical species in this work were normalized by the original number of HMX molecules (i.e., 320) as 100. Figure 2 shows that the p-HMX and t-HMX decay very similarly as they proceed along two decay curves similar to each other at any given temperature. In the limit of simulation time of 40 ps, both p-HMX and t-HMX are completely decomposed when they are B


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red and black curves overlay each other at each temperature, implying similar decay mechanisms for p-HMX and t-HMX. At each temperature, the potential energy increases initially and then decreases. In particular, higher temperature causes more rapid increase and subsequent reduction, corresponding to the decay mechanism of HMX: the first endothermic stage is NO2 partition and the subsequent exothermic stage is formation of small stable molecules. From the viewpoint of the evolution of HMX molecules, main intermediates, and products and potential energy, we can confirm the similar decomposition mechanism of p-HMX and t-HMX during constant-temperature heating. Furthermore, such similarity can be verified by kinetic analysis. Zhou and Huang47 assumed the thermal decomposition of HMX to be pseudo-first-order reaction processes and successfully explained its thermal behaviors. Here, such assumption was also made and the rate constant (k) at each temperature can be determined from the evolution of the number of HMX molecules, which are fitted to the first-order decay expression as follows:

Figure 2. HMX decay at various conditions of constant-temperature heating.

heated at no less than 1800 K; and at the lowest temperature of 1500 K, most of the HMX molecules remain. A more detailed analysis of chemical reactions involved in the decay was conducted, and the results are demonstrated in Figure S3. The main intermediate (NO2) and the main products (N2, water, and CO2) evolved in very similar ways for both p-HMX and tHMX, as two curves overlay each other at each temperature. Meanwhile, the figure shows the initial increase and then decrease of NO2 in HMX decay, suggesting that decay suffers from the initiation of N−N break, which is consistent with previous experimental and simulated observations.46,47,59 Potential energy is another important indicator showing chemical reaction mechanism. As demonstrated in Figure 3, the

ln(Nt /N0) = −kt

(1)

where N0 and Nt are the numbers of HMX molecules at times 0 and t, respectively, and t and k are in units of picoseconds and (picosecond)−1, respectively. The linear fitting of t−ln N shows high correlation coefficients. For example, the t−ln N plot of tHMX at 1500 K possesses a correlation coefficient of 0.992 (seeFigure S4). All k fitted at various temperatures are listed in Table 1. The k values of p-HMX and t-HMX are close to each other at any temperature. In the range 1500−3500 K, the k of p-HMX is not always lower than that of t-HMX. For instance, the k values of p-HMX are larger than those of t-HMX at 1800, 2000, and 3000 K, whereas the reverse is true at the remaining temperatures. The relative differences below 22% in the table suggest the similar kinetics of t-HMX and p-HMX. Furthermore, by Arrhenius equation and the data in Table 1, we obtain the apparent activation energies of thermal decay of p-HMX and t-HMX, 114 and 109 kJ/mol, which are very close to each other too. No significant difference in the evolution of chemical species and potential energy, or in kinetic parameters of heated p-HMX and t-HMX, at various constant temperatures is found. This also suggests that the twins in the HMX crystals cannot obviously enhance thermal sensitivity, or decrease thermal stability, under constant-temperature heating conditions. 3.2. Programmed Heating Conditions. MD simulations for programmed heating were performed to confirm whether the twins in the HMX crystal can reduce thermal stability. Five pairs of curves in Figure 4 show that both p-HMX and t-HMX are completely decomposed during the increase in temperature from 300 to 3300 K at various heating rates. Comparisons of the two curves in each pair show that the decay of t-HMX is a little faster than that of p-HMX at most times, as the red curve (t-HMX) is below the black curve (p-HMX). This small

Figure 3. Evolution of potential energy per molecule at various temperatures.

Table 1. Decay Rate Constants of p-HMX and t-HMX under Various Constant-Temperature Heating Conditions temperature (K) kp‑HMX (ps−1) kt‑HMX (ps−1) [(kt‑HMX − kp‑HMX)/kp‑HMX] × 100

1500

1800

2000

2500

3000

3500

0.09 0.08 −11

0.41 0.50 22

0.89 1.05 18

4.51 3.80 −16

9.48 9.74 3

15.69 14.15 −10

C


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HMX, a lower temperature is required for t-HMX to decay at the same degree for any heating rate.

Figure 4. Evolution of HMX decay at various programmed heating rates.

difference is not observed in the constant-temperature heating simulations (Figure 2) and could be attributed to a little higher potential energy of t-HMX, which can lower the energy barrier for HMX thermal decay and increase decay velocity. Essentially, p-HMX is more stable than t-HMX. A ReaxFF-lg calculation gives a potential energy value of t-HMX of 7.2 kcal/mol per molecule higher than that of p-HMX. If we attribute the increased potential energy by twins to the molecules in the four layers around the twin interface, this value will increase to 10.5 kcal/mol. This increase in potential energy can also be supported by the potential evolution in Figure 5. Thus, the

Figure 6. Dependence of HMX molecular numbers versus temperature at various heating rates.

Next, we study the kinetics of the programmed heated decay. First, the initial time and temperature for HMX decay at various heating rates are analyzed. As shown in Table 2, the initial time Table 2. Initial Times and Temperatures for HMX Decay under Programmed Heating Conditions heating rate (K/ps) 250

Figure 5. Evolution of potential energy per molecule under programmed heating conditions.

initial time (ps) initial temp (K)

2.28 870

initial time (ps) initial temp (K)

2.34 885

167 p-HMX 3.3 850 t-HMX 3.3 850

125

100

80

4.4 850

5.5 850

6.58 826

4.3 837.5

5.3 830

6.5 820

and temperature for p-HMX decay are respectively shorter and lower than those for t-HMX decay at the highest heating rate of 250 K/ps. At 167 K/ps, the initial time and temperature for pHMX and t-HMX decays are the same. For the remaining rates, the initial time and temperature for the p-HMX decay are respectively longer and higher than those for the t-HMX decay. In general, the initial time for the decay can be seen as the delay time for HMX decomposition. The prolonged delay time at lower heating rate shows higher thermal stability of p-HMX relative to t-HMX. In practice, for example, in DSC examination, the samples are usually heated from several to tens of kelvins per minute, which is much lower than the simulation rates. Therefore, presumably, the thermal stability of

elevated potential energy of the initial 7.2 kcal/mol caused by the twins is maintained for a period before the energy peaks are reached. This delay facilitates the t-HMX decay, thus possessing a bit higher velocity. After the peaks, the potential energies of pHMX and t-HMX evolve similarly, with almost no differences. The increased potential energy by twins of t-HMX, which favors easier decay, should lower the decay temperature at a given decay degree. The dependence of HMX molecular percentage versus temperature in Figure 6 supports this conjecture. As demonstrated in the figure, in contrast to pD


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3.3. Adiabatic Heating. Unlike the cases of constanttemperature and programmed heating, the temperature evolution of adiabatic heating cannot be easily evaluated and can only be derived from NVE MD simulations. As illustrated in Figure 7, all simulations do not reach the assigned

t-HMX can be differentiated from that of p-HMX by DSC analysis. Thermal decay of HMX initially undergoes an endothermic and then an exothermic process, which can be reproduced by the potential energy evolution. Potential energy evolution curves in Figure 5 each include first an increase and then a decrease, corresponding to a first endothermic and then exothermic process. By fitting the data around the peaks of curves (see Figure S5), we obtained the peak times and temperatures listed in Table 3. At each heating rate, the peak Table 3. Peak Times and Temperatures for HMX Decay under Programmed Heating Conditions heating rate (K/ps) 250 tp (ps) Tp (K)

10.0 2795

tp (ps) Tp (K)

10.0 2808

ΔTp (K)

13

167 t-HMX 13.6 2569 p-HMX 13.7 2587 Difference 18

125

100

80

17.1 2439

20.2 2322

24.6 2267

17.4 2470

20.5 2349

24.3 2247

31

27

−20

Figure 7. Temperature evolution of adiabatic systems.

temperatures after 0.5 ps NVT MD simulations for preheating. In contrast to the case of preheating at 1500 K with a slight temperature increase, preheating at other simulation temperatures decreases at first and increases subsequently. In addition, higher preheating temperature leads to higher temperature increase. As time proceeds, the temperature of t-HMX increases faster than that of p-HMX, showing the higher self-heating ability of t-HMX. Next, the evolution of reactants, intermediates, and products is investigated. As demonstrated in Figure 8, higher preheating

time and temperature for p-HMX decay are a little longer and higher than those for t-HMX decay, suggesting the higher stability of p-HMX. Nevertheless, the thermal stability superiority of p-HMX is still limited. The temperature differences are below 31 K, which is very small relative to the absolute simulation temperatures of over 2000 K. Besides, Table 3 shows that lower heating rate causes lower peak temperature for the decay. Such a tendency is similar to that observed in the DSC curves of p-HMX. For example, Figure S1 exhibits an increasing order of peak temperatures of 551.3, 553.7, 556.8, and 560.5 K when the heating rate increases from 2.5 to 5, 10, and 20 K/min. Thus, our programmed heating simulations can resemble the DSC analysis. Subsequently, these peak temperatures and corresponding heating rates, as well as the Kissinger and Ozawa methods, were applied to calculate the apparent activation energies for the HMX decay, similar to that in Mitchell et al.60 The calculated apparent activation energies for p-HMX and t-HMX decays are 68.9 and 65.5 kJ/mol (by the method of Kissinger)61 and 105.2 and 101.9 kJ/mol (by the method of Ozawa).62 These values are close to the simulated value by ReaxFF of 136.8 kJ/mol,47 lower than that simulated by an ab initio method of 200.3 kJ/ mol59 and other experimental determinations of 109.2−522.4 kJ/mol [by differential thermal analysis (DTA) and DSC experiments].63−65 The relatively higher activation energy of pHMX (above 3.4 kJ/mol by the Kissinger method and 3.3 kJ/ mol by the Ozawa method) suggests that t-HMX is a bit energetically favored for thermal decay. Furthermore, we examined the evolution of the main intermediate (NO2) and products (H2O, N2, and CO2) against time and temperature (Figures S6 and S7). Results show that the evolution of these chemical species proceeds in a similar way to that of the HMX decay in Figure S3. The amount of NO2 generated from the N−N bond break during the endothermic process of t-HMX is a bit more than that of p-HMX, because t-HMX decays a little faster than p-HMX. Overall, p-HMX is a bit more stable than tHMX, particularly at a low heating rate.

Figure 8. Decay evolution of HMX molecules.

temperature causes faster HMX decay, and t-HMX decays faster than p-HMX distinctly for all four adiabatic heating conditions. At the preheating temperature of 1500 K, both pHMX and t-HMX are not completely analyzed. Approximately 70% and 44% of HMX molecules are left in p-HMX and tHMX after 50 ps NVE MD simulations, respectively. For preheating at 1800 K, the time for complete decay of HMX E


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The Journal of Physical Chemistry C molecules in t-HMX is shorter by 7 ps than that in p-HMX. With respect to preheating at 2000 and 2200 K, t-HMX decomposes remarkably faster than p-HMX. This finding is much different from the cases of constant-temperature heating (almost no difference in Figure 2) and programmed heating (small differences in Figure 4). Similarly, the intermediates and products of t-HMX in each case proceed faster than those of p-HMX, as shown in Figure S8. Nevertheless, each of these chemical species evolved with a similar tendency for both t-HMX and p-HMX. For preheating at 1500 K, only NO2 molecules are generated, and t-HMX produces more NO2 molecules than p-HMX. When the adiabatic heating starts from 1800 K, in addition to NO2, N2 and H2O molecules are generated and increase continuously within the time limit of simulations. Also, more molecules are derived from t-HMX decay than from p-HMX decay. Such faster evolution of these molecules can also be found when HMX crystals are preheated at 2000 and 2200 K. At 2200 K, the stable CO2, N2, and H2O molecules increase first and then decrease because of the very high temperature. Therefore, tHMX and p-HMX undergo similar decay mechanisms, with differences only in decay velocities. Furthermore, evolution of the potential energy per molecule is discussed to provide insight into the evolution of related systems. As demonstrated in Figure 9, the potential energies of

Table 4. Rate Constants for Different Initial Temperatures preheating temperature (K) kp‑HMX kt‑HMX

1500

1800

2000

2200

0.00472 0.01134

0.03129 0.06216

0.10348 0.17863

0.20161 0.43089

versus 1/T. The small difference in activation energy of 7.6 kJ/ mol should be attributed to the similar decay mechanisms of tHMX and p-HMX. Therefore, t-HMX is more sensitive to thermal stimuli, or less thermally stable, than p-HMX under adiabatic heating conditions. 3.4. Comparison of p-HMX and t-HMX Decays under Three Types of Heating Conditions. The preceding analyses and discussion indicate that t-HMX and p-HMX possess almost the same stability when heated at constant temperature. When programmed heating is employed, t-HMX shows a little lower stability than p-HMX. t-HMX is evidently less stable than p-HMX when they are adiabatically constrained. Thus, various heating modes possess different abilities to distinguish the thermal stability of t-HMX and p-HMX. The thermal decay of HMX crystals is intrinsically attributed to heating temperature and duration and crystal structures. Therefore, we summarize the temperature evolution under various heating conditions in Figure 10. The difference of t-

Figure 9. Evolution of the potential energy per molecule.

p-HMX and t-HMX generally proceed similarly at each preheating temperature, with a difference in evolution rate (tHMX proceeds faster). Similar to the evolution of NO2, N2, and H2O in Figure S8, at low preheating temperatures, the potential energies increase continuously, showing gentle chemical reactions and temperature increases; when preheated at high temperatures, the rapid chemical reactions and temperature increases cause the first increase, subsequent decrease, and final increase of the potential energies. Finally, the chemical reactive kinetics was investigated. By fitting the number of HMX molecules against time (Figure 8) using the first-order decay expression (eq 1), we obtained good correlation coefficients and rate constants (Table 4). Consistent with the above analysis on the evolution of chemical species and potential energies, t-HMX decays faster by about one unit of time than p-HMX in each case. Furthermore, apparent activation energies of 141.9 and 149.5 kJ/mol for t-HMX and p-HMX, respectively, were obtained by linear fitting of ln k

Figure 10. Temperature evolution under various heating conditions.

HMX and p-HMX in heating temperature and duration determines their responses under various heating conditions. As illustrated in the figure, the temperatures under constanttemperature heating and programmed heating of t-HMX and pHMX evolved almost in the same manner; thus exhibiting almost the same thermal stability. However, the temperature evolution is obviously distinguished when adiabatic heating is employed, thereby distinguishing the stability of t-HMX and pHMX: t-HMX is less stable than p-HMX. Overall, the thermal stability difference of t-HMX and p-HMX depends on the heating mode. Intrinsically, the twins in HMX crystals increase instability as they increase potential energy (about 7.2 kcal/mol per molecule) and therefore reduce the decay barrier, which should be attributed to the higher self-heating ability of twins. F


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In practice, explosives containing imperfect and perfect HMX crystals can undergo accidental heating, which cannot be categorized into the above three typical cases. For example, in cooking off an explosive containing HMX, the explosive is heated from exterior to interior.66 In such a case, temperature gradients exist in the explosive crystals. This condition is much different from the above three typical heating cases of the simulations, in which no temperature gradient exists, as the explosive is wholly heated in no time and without internal heat exchange. However, this process can be regarded as the cooperation of programmed and adiabatic heating until combustion and/or detonation. Nevertheless, some cases are very close to the simulation conditions. For example, in DSC tests, a small quantity of sample (several milligrams) can only lead to an ignorable temperature gradient in the sample; this case is similar to programmed heating.64 Thus, it is reasonable that no significant difference in thermal stability between pHMX and t-HMX can be observed (Figure S1). In comparison, when a large bulk of sample is shocked, internal hot spots are formed by impression, and the self-heated zone can be seen under an adiabatic condition because heat is not transferred transiently. In such a case, the interior of the sample is heated adiabatically, which can be a reason for the sensitivity enhancement induced by twins.51,52 Increasing the thermal conductivity, which is an effective way to avoid hot-spot formation, is basically just increasing the Rh, thereby alleviating the advantages of hot-spot formation by defects, such as twins.51,52 This work may be complementary to very recent research on hot-spot formation of shocked erythritol tetranitrate, which showed that molecular decomposition of a defect-containing crystal occurs with significantly higher rates compared to the perfect crystal.67 That is, given that the nature of the enhanced self-heating of defects is known, such higher rates can be understood better.

Nevertheless, the role of such increased self-heating ability in HMX decay is largely determined by the rate of heat exchange with environment (Rh): higher Rh produces lesser effect on thermal stability (or smaller difference in thermal stability of tHMX and p-HMX). In contrast to p-HMX, the increased selfheating ability of t-HMX cannot be exhibited at high Rh, as the superiority of higher internal energy will instantaneously be lowered in company with the input of external heat. We performed two additional programmed heating simulations with lower Rh of 25 and 5 K/ps for further confirmation. Figure S9 verifies that heat input at a lower Rh emphasizes the energy superiority of t-HMX. We compare the evolution of total energy changes under various heating conditions in Figure 11, because the total

Figure 11. Evolution of total energy change under various heating conditions. No heat input is applied in adiabatic heating; thus the line of y = 0, showing adiabatic heating, is not shown in the figure.

4. CONCLUSIONS In summary, we performed ReaxFF reactive MD simulations on both p-HMX and t-HMX under various heating conditions to provide insight into the nature of increased self-heating ability of defects, in contrast to perfect crystals. We find that the enhanced self-heating ability originates from the high internal energy (potential energy) of the molecules involved in defects, and such ability is remarkably exhibited with low Rh between the HMX crystals and environment. Adiabatic heating, a case of shock, is an extreme to exhibit remarkable such ability. Thereby, we can well understand the twins-induced shock sensitivity enhancement of HMX and a small difference in DSC measurement values between p-HMX and t-HMX.

energy increase can be adopted to denote the heat input quantitatively. At the earlier stages, constant-temperature heating causes the fastest total energy increase, followed by programmed heating, and no variation is observed for adiabatic heating. By rough calculations (see section S7), we obtained the heat input rates under various heating conditions (Table 5). Rh decreases sharply from several thousands (constant-temperature heating) to several tens (programmed heating) to zero (adiabatic heating). The self-heating ability of twins in HMX is more distinct at slower Rh. Table 5. Rates of Heat Input (Rh) from Environment

■

constant-temperature heating p-HMX t-HMX

1500 K

1800 K

1797 1736

2119 2109

250 K/ ps

166.7 K/ ps

p-HMX t-HMX

43.5 44.3

29.2 29.7

p-HMX t-HMX

0 0

2000 K

2500 K

3000 K

2335 2930 3452 2333 2801 3343 programmed heating 125 K/ ps

100 K/ ps

21.9 17.4 22.2 17.8 adiabatic heating

3500 K

ASSOCIATED CONTENT

S Supporting Information *

4277 3823

80 K/ ps

25 K/ ps

5 K/ ps

14.0 14.4

4.6 4.7

0.9 0.9

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b04518. Additional text and nine figures showing experimental determination of peak temperatures of HMX decomposition, evolution of main intermediates and products during thermal decay of HMX under different conditions, fitting for calculating kinetic constants, evolution of total energy of HMX under programmed heating conditions, and rough calculations of heat input rates (PDF) G


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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; tel 86-816-2493506. ORCID

Chaoyang Zhang: 0000-0003-3634-7324 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful for financial support from the National Natural Science Foundation of China (U1530262) and Scientific Challenge Project.

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